{"id":9570,"date":"2024-01-02T11:39:54","date_gmt":"2024-01-02T06:09:54","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=9570"},"modified":"2024-01-03T10:08:13","modified_gmt":"2024-01-03T04:38:13","slug":"envision-math-common-core-grade-4-answer-key-topic-3","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-4-answer-key-topic-3\/","title":{"rendered":"enVision Math Common Core Grade 4 Answer Key Topic 3 Use Strategies and Properties to Multiply by 1-Digit Numbers"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 4 Answer Key<\/a>\u00a0Topic 3 Use Strategies and Properties to Multiply by 1-Digit Numbers<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

enVision Math Common Core 4th Grade Answers Key Topic 3 Use Strategies and Properties to Multiply by 1-Digit Numbers<\/h2>\n

Essential Questions:<\/strong>
\nHow can you multiply by multiples of 10, 100, and 1,000? How can you multiply whole numbers?
\n\"Envision<\/p>\n

enVision STEM Project: Maps and Math<\/strong>
\nDo Research Use the Internet or other sources to find information about three of Earth’s features on a topographic map, such as mountains or oceans. Write two facts about each of the features you researched.
\nJournal: Write a Report Include what you found. Also in your report:<\/p>\n

    \n
  • Write the height or depth of each feature you researched.<\/li>\n
  • Estimate to find 10 times the heights or depths of the features you researched.<\/li>\n<\/ul>\n

    Review What You Know<\/strong><\/p>\n

    Vocabulary<\/strong>
    \nChoose the best term from the box. Write it on the blank.<\/p>\n

      \n
    • breaking apart<\/li>\n
    • compensation<\/li>\n
    • inverse operations<\/li>\n
    • partial products<\/li>\n<\/ul>\n

      Question 1.
      \nMultiplication and division are _________.
      \nAnswer:
      \nMultiplication and division are ____inverse operations____.<\/p>\n

       <\/p>\n

      \"Use<\/p>\n

      Question 2.
      \nA mental math method used to rewrite a number as the sum of numbers to form an easier problem is called __________.
      \nAnswer:
      \nA mental math method used to rewrite a number as the sum of numbers to form an easier problem is called __breaking apart________.<\/p>\n

       <\/p>\n

      Question 3.
      \nChoosing numbers close to the numbers in a problem to make the computation easier, and then adjusting the answer is called ________.
      \nAnswer:
      \nChoosing numbers close to the numbers in a problem to make the computation easier, and then adjusting the answer is called ___partial products_____.<\/p>\n

       <\/p>\n

       <\/p>\n

      Multiplication<\/strong><\/p>\n

      Find each product.
      \nQuestion 4.
      \n6 \u00d7 2
      \nAnswer:
      \n6 \u00d7 2 = 12.<\/p>\n

      Explanation:
      \n6 \u00d7 2 = (3 \u00d7 2) + (3 \u00d7 2)
      \n6 \u00d7 2 = 6 + 6
      \n6 \u00d7 2 =12.<\/p>\n

       <\/p>\n

      Question 5.
      \n8 \u00d7 9
      \nAnswer:
      \n8 \u00d7 9 = 72.<\/p>\n

      Explanation:
      \n8 \u00d7 9 = (4 \u00d7 9) + (4\u00a0\u00d7 9)
      \n8 \u00d7 9 = 36 + 36
      \n8 \u00d7 9 = 72.<\/p>\n

      Question 6.
      \n6 \u00d7 5
      \nAnswer:
      \n6 \u00d7 5 = 30.<\/p>\n

      Explanation:
      \n6 \u00d7 5 = (2 \u00d7 5) + (4\u00a0\u00d7 5)
      \n6 \u00d7 5 = 10 + 20
      \n6 \u00d7 5 = 30.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 7.
      \n7 \u00d7 8
      \nAnswer:
      \n7 \u00d7 8 = 56.<\/p>\n

      Explanation:
      \n7 \u00d7 8 = (3 \u00d7 8) + (4\u00a0\u00d7 8)
      \n7 \u00d7 8 = 24 + 32
      \n7 \u00d7 8 = 56.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 8.
      \n4 \u00d7 8
      \nAnswer:
      \n4 \u00d7 8 = 32.<\/p>\n

      Explanation:
      \n4 \u00d7 8 = (1 \u00d7 8) + (3\u00a0\u00d7 8)
      \n4 \u00d7 8 = 8 + 24
      \n4 \u00d7 8 = 32.<\/p>\n

      \"Use<\/p>\n

       <\/p>\n

      Question 9.
      \n3 \u00d7 7
      \nAnswer:
      \n3 \u00d7 7 = 21.<\/p>\n

      Explanation:
      \n3 \u00d7 7 = (2 \u00d7 7) + (1\u00a0\u00d7 7)
      \n3 \u00d7 7 = 14 + 7
      \n3 \u00d7 7 = 21.<\/p>\n

       <\/p>\n

       <\/p>\n

      Rounding<\/strong><\/p>\n

      Round each number to the nearest ten.
      \nQuestion 10.
      \n16
      \nAnswer:
      \nNearest ten of 16 is 20.<\/p>\n

       <\/p>\n

      Question 11.
      \n82
      \nAnswer:
      \nNearest ten of 82 is 80.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 12.
      \n35
      \nAnswer:
      \nNearest ten of 35 is 40.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 13.
      \n53
      \nAnswer:
      \nNearest ten of 53 is 50.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 14.
      \n24
      \nAnswer:
      \nNearest ten of 24 is 20.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 15.
      \n49
      \nAnswer:
      \nNearest ten of 49 is 50.<\/p>\n

       <\/p>\n

       <\/p>\n

      Round each number to the nearest hundred.
      \nQuestion 16.
      \n868
      \nAnswer:
      \nNearest hundred of 868 is 900.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 17.
      \n499
      \nAnswer:
      \nNearest hundred of 499 is 500.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 18.
      \n625
      \nAnswer:
      \nNearest hundred of 625 is 600.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 19.
      \n167
      \nAnswer:
      \nNearest hundred of 167 is 200.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 20.
      \n341
      \nAnswer:
      \nNearest hundred of 341 is 300.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 21.
      \n772
      \nAnswer:
      \nNearest hundred of 772 is 800.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 22.
      \n919
      \nAnswer:
      \nNearest hundred of 919 is 900.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 23.
      \n552
      \nAnswer:
      \nNearest hundred of 552 is 600.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 24.
      \n321
      \nAnswer:
      \nNearest hundred of 321 is 300.<\/p>\n

       <\/p>\n

       <\/p>\n

      Problem Solving
      \n<\/strong>Question 25.
      \nCritique Reasoning<\/strong> Tyler says, 9 \u00d7 7 is greater than 7 \u00d7 9 because the greater number is first.” Explain Tyler’s error.
      \nAnswer:
      \nTyler’s is incorrect because 9 \u00d7 7 and 7 \u00d7 9 are same value numbers, just numbers are interchanged.<\/p>\n

      Explanation:
      \n9 \u00d7 7 = (5 \u00d7 7) + (4\u00a0\u00d7 7)
      \n9 \u00d7 7 = 35 + 28
      \n9 \u00d7 7 = 63.<\/p>\n

      7 \u00d7 9 = (3 \u00d7 9) + (4 \u00d7 9)
      \n7 \u00d7 9 = 27 + 36
      \n7 \u00d7 9 =\u00a0 63.<\/p>\n

       <\/p>\n

       <\/p>\n

      Pick a Project<\/strong><\/p>\n

      PROJECT \u0417\u0410
      \nHow zesty is Key lime pie?
      \nProject: Create Data for Key Lime Pie Ingredients
      \n\"Envision<\/p>\n

      Answer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Digit-Numbers-Pick<\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

      PROJECT \u0417\u0412
      \nWhat do a dozen Florida panthers weigh?
      \nProject: Draw a Captioned Picture
      \n\"Envision<\/p>\n

      Answer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Digit-Numbers-Pick<\/p>\n

       <\/p>\n

       <\/p>\n

      PROJECT 3C
      \nWhat’s the mass of a giraffe?
      \nProject: Create a Song
      \n\"Envision<\/p>\n

      Answer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Digit-Numbers-Pick<\/p>\n

       <\/p>\n

      3-ACT MATH PREVIEW
      \n<\/strong>Math Modeling
      \nCovered Up
      \n\"Envision
      \nI can…model with math to solve a problem that involves estimating and computing with area models.<\/p>\n

      Lesson 3.1 Multiply by Multiples of 10, 100, and 1,000<\/h3>\n

      Solve & Share<\/strong>
      \nFind the products for 3 \u00d7 4, 3 \u00d7 40, 3 \u00d7 400, and 3 \u00d7 4,000. Solve these problems using any strategy you choose.
      \nI can… find the products of multiples of 10, 100, and 1,000 using mental math and place-value strategies.
      \n\"Envision<\/p>\n

      Look Back! What pattern do you notice in the products?
      \nAnswer:
      \nThe patern noticed in the products is that for every product extra zero is added after the number.<\/p>\n

      Explanation:
      \n3 \u00d7 4 = (3 \u00d7 1) + ( 3 \u00d7 3) = 3 + 9 = 12.
      \n3 \u00d7 40 = (3 \u00d7 10) + (3 \u00d7 30) = 30 + 90 = 120.
      \n3 \u00d7 400 = (3 \u00d7 100) + ( 3 \u00d7 300) = 300 + 900 = 1200.
      \n3 \u00d7 4,000 = (3 \u00d7 1000) + ( 3 \u00d7 3000) = 3000 + 9000 = 12000.<\/p>\n

       <\/p>\n

       <\/p>\n

      Essential Question<\/strong>
      \nHow Can You Multiply by Multiples of 10, 100, and 1,000?
      \nAnswer:
      \nWe multiply the multiplicand by the non-zero digit of the multiplier. Then we add the same number of zero to the extreme right of the product as the multiplier has.<\/p>\n

      Explanation:
      \nWe use Multiply by Multiples of 10, 100, and 1,000 as follow:
      \nWe can understand this method as follows.
      \n1. First we count the zeros.
      \n2. We multiply the non \u2013 zero numbers.
      \n3. We place the same number of zero to the extreme right of the product<\/p>\n

       <\/p>\n

       <\/p>\n

      Visual Learning Bridge<\/strong>
      \nCalculate 3 \u00d7 50, 3 \u00d7 500, and 3 \u00d7 5,000 using basic multiplication facts and properties of operations.<\/p>\n

      The Associative Property of Multiplication states that you can change the grouping of the factors and the product stays the same.
      \n\"Envision<\/p>\n

      One Way
      \n<\/strong>Find 3 \u00d7 50, 3 \u00d7 500, and 3 \u00d7 5,000.
      \nUse basic facts and place value.
      \n3 \u00d7 50 = 3 \u00d7 5 tens
      \n= 15 tens
      \n= 150
      \n3 \u00d7 500 = 3 \u00d7 5 hundreds
      \n= 15 hundreds
      \n= 1,500
      \n3 \u00d7 5,000 = 3 \u00d7 5 thousands
      \n= 15 thousands
      \n= 15,000<\/p>\n

      Another Way<\/strong>
      \nFind 3 \u00d7 50, 3 \u00d7 500, and 3 \u00d7 5,000.
      \nBreak apart numbers. Use the Associative Property of Multiplication.
      \n3 \u00d7 50 = 3 \u00d7 (5 \u00d7 10)
      \n= (3 \u00d7 5) \u00d7 10
      \n= 15 \u00d7 10
      \n= 150
      \n3 \u00d7 500 = 3 \u00d7 (5 \u00d7 100)
      \n= (3 \u00d7 5) \u00d7 100
      \n= 15 \u00d7 100
      \n= 1,500
      \n3 \u00d7 5,000 = 3 \u00d7 (5 \u00d7 1,000)
      \n= (3 \u00d7 5) \u00d7 1,000
      \n= 15 \u00d7 1,000
      \n= 15,000<\/p>\n

      Convince Me! Reasoning What patterns do you see in the number of zeros in the products above?
      \nAnswer:
      \nThe pattern noticed in the zero’s in the products above is that for every number zero is added more from one to last number products.<\/p>\n

      Explanation:
      \nExtra zero is added for every product from one to last number.<\/p>\n

       <\/p>\n

      \"Use<\/p>\n

      Another Example!<\/strong>
      \nUse place value to calculate 5 \u00d7 400 and 6 \u00d7 5,000.
      \n5 \u00d7 400 = 5 \u00d7 4 hundreds
      \n= 20 hundreds
      \n= 2,000<\/p>\n

      6 \u00d7 5,000 = 6 \u00d7 5 thousands
      \n= 30 thousands
      \n= 30,000<\/p>\n

      If the product of the basic fact ends in zero, the product has one more zero than you see in the factors.<\/p>\n

       <\/p>\n

       <\/p>\n

      Guided Practice
      \n<\/strong>Do You Understand?<\/strong>
      \nQuestion 1.
      \nShow how you can use the basic fact 5 \u00d7 8 = 40 to determine the product of 5 \u00d7 800.
      \nAnswer:
      \n5 \u00d7 800 = (5 \u00d7 8 \u00d7 100) = 4000.<\/p>\n

      Explanation:
      \n5 \u00d7 8 = 40.
      \n5 \u00d7 800 = (5 \u00d7 8 \u00d7 100)
      \n5 \u00d7 800 = 40\u00a0 \u00d7 100
      \n5 \u00d7 800 = 4000.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 2.
      \nBob said 4 \u00d7 500 = 200. Explain his error using place value.
      \nAnswer:
      \nHis error is he missed zero to write in place value of the number.
      \n4 \u00d7 500 = 2000 not 4 \u00d7 500 = 200.<\/p>\n

      Explanation:
      \n4 \u00d7 500 = 200.
      \n4 \u00d7 500 = 4 \u00d7 5 \u00d7 100
      \n4 \u00d7 500 = 20 \u00d7 100
      \n4 \u00d7 500 = 2000.<\/p>\n

       <\/p>\n

       <\/p>\n

      Do You Know How?<\/strong>
      \nFor 3-5, use strategies you learned to help multiply.
      \nQuestion 3.
      \n8 \u00d7 7 = ________
      \n8 \u00d7 70 = ________
      \n8 \u00d7 700 = ________
      \n8 \u00d7 7,000 = ________
      \nAnswer:
      \n8 \u00d7 7 = __56______.
      \n8 \u00d7 70 = __560______.
      \n8 \u00d7 700 = __5600______.
      \n8 \u00d7 7,000 = ___56000_____.<\/p>\n

      Explanation:
      \n8 \u00d7 7 = 56.
      \n8 \u00d7 70 = 8 \u00d7 7 tens
      \n= 56 tens
      \n= 560.
      \n8 \u00d7 700 = 8 \u00d7 7 hundreds
      \n= 56 hundreds
      \n= 5600.
      \n8 \u00d7 7,000 = 8 \u00d7 7 thousands
      \n= 56 thousands
      \n= 56000.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 4.
      \n7 \u00d7 70
      \nAnswer:
      \n7 \u00d7 70 = 490.<\/p>\n

      Explanation:
      \n7 \u00d7 70 = 7 \u00d7 7 tens
      \n= 49 tens
      \n= 490.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 5.
      \n2 \u00d7 700
      \nAnswer:
      \n2 \u00d7 700 = 1400.<\/p>\n

      Explanation:
      \n2 \u00d7 700 = 2 \u00d7 7 hundreds
      \n= 14 hundreds
      \n= 1400.<\/p>\n

       <\/p>\n

       <\/p>\n

      Independent Practice
      \n<\/strong>Leveled Practice For 6-11, use basic facts, place value, and properties to help multiply.<\/p>\n

      You can use place-value strategies to calculate each product.
      \nQuestion 6.
      \n3 \u00d7 70 = ________
      \n3 \u00d7 700 = ________
      \n3 \u00d7 7,000 = ________
      \nAnswer:
      \n3 \u00d7 70 = __210______.
      \n3 \u00d7 700 = ___2100_____.
      \n3 \u00d7 7,000 = ___21000_____.<\/p>\n

      Explanation:
      \n3 \u00d7 70 = 3 \u00d7 7 tens
      \n= 21 tens
      \n= 210.
      \n3 \u00d7 700 = 3 \u00d7 7 hundreds
      \n= 21 hundreds
      \n= 2100.
      \n3 \u00d7 7,000 = 3 \u00d7 7 thousands
      \n= 21 thousands
      \n= 21000.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 7.
      \n________ = 6 \u00d7 40
      \n________ = 6 \u00d7 400
      \n________ = 6 \u00d7 4,000
      \nAnswer:
      \n___240_____ = 6 \u00d7 40.
      \n____2400____ = 6 \u00d7 400.
      \n__24000______ = 6 \u00d7 4,000.<\/p>\n

      Explanation:
      \n6 \u00d7 40 = 6 \u00d7 4 tens
      \n= 24 tens
      \n= 240.
      \n6 \u00d7 400 = 6 \u00d7 4 hundreds
      \n= 24 hundreds
      \n= 2400.
      \n6 \u00d7 4,000 = 6 \u00d7 4 thousands
      \n= 24 thousands
      \n= 24000.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 8.
      \n8 \u00d7 50 = ________
      \n8 \u00d7 500 = ________
      \n8 \u00d7 5,000 = ________
      \nAnswer:
      \n8 \u00d7 50 = ___400_____.
      \n8 \u00d7 500 = ___4000_____.
      \n8 \u00d7 5,000 = __40000______.<\/p>\n

      Explanation:
      \n8 \u00d7 50 = 8 \u00d7 5 tens
      \n= 4 hundreds
      \n= 400.
      \n8 \u00d7 500 = 8 \u00d7 5 hundreds
      \n= 4 thousands
      \n= 4000.
      \n8 \u00d7 5,000 = 8 \u00d7 5 thousands
      \n= .4 ten thousands
      \n= 40000.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 9.
      \n4 \u00d7 2,000
      \nAnswer:
      \n4 \u00d7 2,000 = 8000.<\/p>\n

      Explanation:
      \n4 \u00d7 2,000 = 4 \u00d7 2 thousands
      \n= 8 thousands
      \n= 8000.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 10.
      \n700 \u00d7 4
      \nAnswer:
      \n700 \u00d7 4 = 2800.<\/p>\n

      Explanation:
      \n700 \u00d7 4 = 7 hundreds \u00d7 4
      \n= 28 hundreds
      \n= 2800.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 11.
      \n6 \u00d7 60
      \nAnswer:
      \n6 \u00d7 60 = 360.<\/p>\n

      Explanation:
      \n6 \u00d7 60 = 6 \u00d7 6 tens
      \n= 36 tens
      \n= 360.<\/p>\n

       <\/p>\n

       <\/p>\n

      Problem Solving
      \n<\/strong>Question 12.
      \nenVision\u00ae STEM The Mississippi River is about 8 times the length of the Hudson River. If the Hudson River is about 300 miles long, about how many miles long is the Mississippi River? Write and solve an equation.
      \nAnswer:
      \nLength of Mississippi River = 2400 miles.<\/p>\n

      Explanation:
      \nLength of the Hudson River = 300 miles long.
      \nThe Mississippi River is about 8 times the length of the Hudson River.
      \n=> Length of Mississippi River = 8 \u00d7 Length of the Hudson River
      \n= 8 \u00d7 300
      \n= 8 \u00d7 3 hundreds
      \n= 24 hundreds
      \n= 2400 miles.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 13.
      \nTed, Jason, and Angelina are trying to raise $200 for a local shelter. Ted raised $30. Jason raised $90. How much money m does Angelina need to raise to reach their goal?
      \n\"Envision
      \nAnswer:
      \nAmount to be raised by m, Angelina = $80.<\/p>\n

      Explanation:
      \nAmount raised by Ted = $30.
      \nAmount raised by Jason = $90.
      \nTotal amount Ted, Jason, and Angelina are trying to raise = $200.
      \nAmount to be raised by m, Angelina = Total amount Ted, Jason, and Angelina are trying to raise\u00a0 – (Amount raised by Ted + Amount raised by Jason )
      \n= $200 – ($30 + $90)
      \n= $200 – $120
      \n= $80.
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Digit-Numbers-Lesson<\/p>\n

       <\/p>\n

       <\/p>\n

      For 14-15, use the table at the right.
      \n\"Envision
      \nQuestion 14.
      \nMake Sense and Persevere There are 9 girls and 4 adults in Aimee’s scout troop. How much did the troop pay for tickets to the amusement park?
      \nAnswer:
      \nTotal amount of fee to 9 girls and 4 adults troop paying for tickets to the amusement park = $430.<\/p>\n

      Explanation:
      \nNumber of girls to the amusement park = 9.
      \nAmount of fee to each girl to the amusement park = $30.
      \nNumber of adults to the amusement park = 4.
      \nAmount of fee to each adult to the amusement park = $40.
      \nTotal amount of fee to 9 girls and 4 adults troop paying for tickets to the amusement park = ( Number of girls to the amusement park \u00d7 Amount of fee to each girl to the amusement park =) + ( Number of adults to the amusement park \u00d7 Amount of fee to each adult to the amusement park )
      \n= (9 \u00d7 $30) + ( 4 \u00d7 $40)
      \n= $270 + $160
      \n= $430.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 15.
      \nHigher Order Thinking<\/strong> Tina visited Funland with her mom and a friend They bought tickets for Plan C. How much money did they save on the two children’s tickets for Plan C instead of buying separate tickets for Plan A and Plan B?
      \nAnswer:
      \nAmount of money they saved on the two children’s tickets for Plan C instead of buying separate tickets for Plan A and Plan B = $20.<\/p>\n

      Explanation:
      \nAmount of fee to each girl to the amusement park in Plan A = $20.
      \nAmount of fee to each girl to the amusement park in Plan B = $30.
      \nAmount of fee to each adult to the amusement park = $40.
      \nAmount of tickets for Plan C (combined A and B) for adult = $60.
      \nAmount of tickets for Plan C (combined A and B) for kids = $40.
      \nAmount for two children in Plan A = 2 \u00d7 $20 = $40.
      \nAmount for two children in Plan B = 2 \u00d7 $30 = $60.
      \nAmount for two children in Plan C (combined A and B) = 2 \u00d7 $40 = $80.
      \nDifference:
      \nAmount of money they saved on the two children’s tickets for Plan C instead of buying separate tickets for Plan A and Plan B = (Amount for two children in Plan A\u00a0 + Amount for two children in Plan B ) – Amount for two children in Plan C (combined A and B)
      \n= ($40 + $60) – $80.
      \n= $100 – $80
      \n= $20.<\/p>\n

       <\/p>\n

       <\/p>\n

      Assessment Practice
      \n<\/strong>Question 16.
      \nBrandon says 4 \u00d7 800 is greater than 8 \u00d7 4,000.
      \nRenee says 4 \u00d7 800 is less than 8 \u00d7 4,000.
      \nA. Without calculating the answer, explain ” how to use place-value strategies or the Associative Property to find which is greater.
      \nAnswer:
      \nBrandon says 4 \u00d7 800 is greater than 8 \u00d7 4,000 and Renee says 4 \u00d7 800 is less than 8 \u00d7 4,000 both are correct.<\/p>\n

      Explanation:
      \n4 \u00d7 800 is greater than 8 \u00d7 4,000.
      \n=> place value of 4000 is thousand greater than 800.
      \n4 \u00d7 800 is less than 8 \u00d7 4,000.
      \n=> place value of 800 is hundred less than thousands.<\/p>\n

       <\/p>\n

       <\/p>\n

      B. Without calculating the answer, explain how to use relationships or basic facts to find which is less.
      \nAnswer:
      \nWithout calculating the answer, we can use relationships or basic facts to find which is less by the place value of the numbers given.<\/p>\n

      Explanation:
      \nWe can use relationships or basic facts to find which is less by the place value of the numbers given without calculating the answer. Which is having less place value that is considered as less and vice versa.<\/p>\n

       <\/p>\n

       <\/p>\n

      Lesson 3.2 Estimate Products<\/h3>\n

      Solve & Share<\/strong>
      \nSarah earns $48 a week babysitting. She saves all of her earnings for 6 weeks. Estimate to determine about how much money Sarah saves. Solve this problem using any strategy you choose.
      \nI can …use rounding to estimate products and check if my answer is reasonable
      \n\"Envision<\/p>\n

      Look Back! Is your estimate more or less than the amount Sarah actually earned? Explain.
      \nAnswer:
      \nMy estimation for Sarah earnings is around $290. My estimation saving is more than the actual savings of her.<\/p>\n

      Explanation:
      \nAmount of money Sarah earns for babysitting for a week = $48.
      \nNumber of weeks She saves all of her earnings = 6.
      \nAmount of money Sarah saves = Amount of money Sarah earns for babysitting for a week \u00d7 Number of weeks She saves all of her earnings
      \n= $48 \u00d7 6
      \n= $288.<\/p>\n

       <\/p>\n

       <\/p>\n

      Essential Question<\/strong>
      \nHow Can You Estimate When You Multiply?
      \nAnswer:
      \nWe can estimate when we multiply by using multiplication facts to get the solution and solve the problem.<\/p>\n

      Explanation:
      \nWe can estimate when we multiply by checking the numbers given and doing their multiplication or by using multiplication facts to get the solution and solve the problem.<\/p>\n

       <\/p>\n

       <\/p>\n

      Visual Learning Bridge<\/strong>
      \nMr. Hector’s class sold calendars and note pads for 3 weeks as a class fundraiser. About how much did Mr. Hector’s class make selling calendars? selling note pads?
      \n\"Envision<\/p>\n

      Use compatible numbers to estimate how many calendars C, were sold.
      \n28 + 73 + 63 = C
      \n164 = C
      \nEstimate $4 \u00d7 164.
      \n\"Envision
      \nEstimate by using compatible numbers. 164 is close to 150.
      \n4 \u00d7 150 = 600
      \nMr. Hector’s class made about $600 selling calendars.<\/p>\n

      Use rounding to estimate how many note pads n, were sold.
      \n272 + 475 + 232 = n
      \n979 = n
      \nEstimate $3 \u00d7 979.
      \n\"Envision
      \nTo the nearest thousand, 979 rounds to 1,000.
      \n3 \u00d7 1,000 = 3,000
      \nMr. Hector’s class made about $3,000 selling note pads.<\/p>\n

      Convince Me! Construct Arguments Could you solve the problem above by rounding to estimate the total number of calendars and the total number of note pads? Explain.
      \nAnswer:
      \nWe can estimate by rounding to estimate the total number of calendars and the total number of note pads and solve the problem.<\/p>\n

      Explanation:
      \nWe can estimate by rounding to estimate the total number of calendars and the total number of note pads and solve the problem. By rounding the total there cannot be any difference much its just rounding the number to the nearest tens, hundreds or thousands.<\/p>\n

       <\/p>\n

       <\/p>\n

      Another Example!<\/strong>
      \nMrs. Li’s class made $2,089 selling neon pencil packs. A student calculated that Mr. Hector’s class and Mrs. Li’s class together made $8,865 selling the school supplies. Is the student’s calculation reasonable?<\/p>\n

      You can estimate to check if an answer is reasonable.<\/p>\n

      Round Mrs. Li’s total to the nearest thousand: $2,000. Then, add the rounded amounts. $2,000 + $600 + $3,000 = $5,600<\/p>\n

      The student’s calculation is not reasonable because $8,865 is not close to $5,600.<\/p>\n

       <\/p>\n

       <\/p>\n

      Guided Practice
      \nDo You Understand?<\/strong>
      \nQuestion 1.
      \nMr. Harm’s class sold 1,275 items at $5 per item. One of his students calculates the class raised $2,375. Is the student’s calculation reasonable? Explain.
      \nAnswer:
      \nNo, student’s calculation is not reasonable because class raised $6375 not $2375.<\/p>\n

      Explanation:
      \nNumber of items Mr. Harm’s class sold\u00a0 = 1275.
      \nCost of each item Mr. Harm’s class sold = $5
      \nTotal cost of amount of items Mr. Harm’s class sold\u00a0 = Number of items Mr. Harm’s class sold \u00d7 Cost of each item Mr. Harm’s class sold
      \n= 1275 \u00d7 $5
      \n= $6375.
      \nOne of his students calculates the class raised $2,375.<\/p>\n

       <\/p>\n

       <\/p>\n

      Do You Know How?<\/strong>
      \nFor 2-5, estimate the product.
      \nQuestion 2.
      \n6 \u00d7 125
      \nAnswer:
      \n6 \u00d7 125 = 15000.<\/p>\n

      Explanation:
      \n6 \u00d7 125 = 6 \u00d7 (100 + 25)
      \n6 \u00d7 125 = 600 + 150
      \n6 \u00d7 125 = 750.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 3.
      \n4 \u00d7 2,610
      \nAnswer:
      \n4 \u00d7 2,610 = 10440.<\/p>\n

      Explanation:
      \n4 \u00d7 2,610 = 4 \u00d7 (2000 + 600 + 10)
      \n4 \u00d7 2,610 = 8000 + 2400 + 40
      \n4 \u00d7 2,610 = 10400 + 40
      \n4 \u00d7 2,610 = 10440.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 4.
      \n538 \u00d7 3
      \nAnswer:
      \n538 \u00d7 3 = 1614.<\/p>\n

      Explanation:
      \n538 \u00d7 3 = (500 + 30 + 8) \u00d7 3
      \n538 \u00d7 3 = 1500 + 90 +\u00a0 24
      \n538 \u00d7 3 = 1590 + 24
      \n538 \u00d7 3 = 1614.<\/p>\n

       <\/p>\n

      Question 5.
      \n314 \u00d7 7
      \nAnswer:
      \n314 \u00d7 7 = 2198.<\/p>\n

      Explanation:
      \n314 \u00d7 7 = (300 + 10 + 4) \u00d7 7
      \n314 \u00d7 7 = 2100 + 70 + 28
      \n314 \u00d7 7 = 2170 + 28
      \n314 \u00d7 7 = 2198.<\/p>\n

       <\/p>\n

       <\/p>\n

      Independent Practice
      \n<\/strong>Leveled Practice For 6-8, estimate the product.
      \nQuestion 6.
      \n\"Envision<\/p>\n

      Answer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

      Explanation:
      \n287 Rounded to 290.
      \n=> 3 \u00d7 290=270.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 7.
      \n\"Envision<\/p>\n

      Answer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

      Explanation:
      \n1310 Rounded to 1300.
      \n=> 6 \u00d7 1300 = 7800.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 8.
      \n\"Envision<\/p>\n

      Answer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

      Explanation:
      \n62 Rounded to 60.
      \n=> 9 \u00d7 60 = 540.<\/p>\n

       <\/p>\n

       <\/p>\n

      For 9-11, estimate to check if the answer is reasonable.
      \nQuestion 9.
      \n\"Envision<\/p>\n

      Answer:
      \nIts reasonable because 3430 is the rounded number of 3402 and there is not much difference.<\/p>\n

      Explanation:
      \n7 \u00d7 486 = 3402.
      \n486 is rounded to 490.
      \n=> 7 \u00d7 490 = 3430.<\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

      Question 10.
      \n\"Envision<\/p>\n

      Answer:
      \nIts not reasonable because 5 \u00d7 1240 = 6200 not 9200.<\/p>\n

      Explanation:
      \n5 \u00d7 1240 = 6200.
      \n1240 Rounded to 1240.
      \n=> 5 \u00d7 1240 = 6200<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 11.
      \n\"Envision<\/p>\n

      Answer:
      \nIts reasonable because 2610 is the rounded figure is 2583 and there is not much difference.<\/p>\n

      Explanation:
      \n9 \u00d7 287 = 2583.
      \n287 Rounded to 290.
      \n9 \u00d7 290 = 2610.<\/p>\n

       <\/p>\n

       <\/p>\n

      Problem Solving
      \n<\/strong>For 12-13, use the graph at the right.
      \n\"Envision
      \nQuestion 12.
      \nThe students voted on a school mascot. Which mascot had 4 times as many of votes as the flamingo?
      \nAnswer:
      \nMascot had 4 times as many of votes as the flamingo = Manatee = 158 votes.<\/p>\n

      Explanation:
      \nNumber of votes on Flamingo = 38.
      \nNumber of votes on Bobcat = 78.
      \nNumber of votes on Manatee = 158.
      \nNumber of votes on Alligator = 22.
      \nNumber of votes on Black Bear = 50.
      \nComparison:
      \nMascot had 4 times as many of votes as the flamingo = 4 \u00d7 Number of votes on Flamingo
      \n= 4 \u00d7 38
      \n= 152.
      \n=> Number of votes on Manatee = 158.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 13.
      \nConstruct Arguments<\/strong> Explain how you could estimate the number of students who voted on a school mascot. Then give your estimate.
      \nAnswer:
      \nWe can estimate by by adding the number of votes, they voted in school.
      \nTotal number of students = 346.<\/p>\n

      Explanation:
      \nNumber of votes on Flamingo = 38.
      \nNumber of votes on Bobcat = 78.
      \nNumber of votes on Manatee = 158.
      \nNumber of votes on Alligator = 22.
      \nNumber of votes on Black Bear = 50.
      \nTotal number of students = Number of votes on Flamingo + Number of votes on Bobcat + Number of votes on Manatee + Number of votes on Alligator + Number of votes on Black Bear
      \n= 38 + 78 + 158 + 22 + 50
      \n= 116 + 158 + 22 + 50
      \n= 274 + 22 + 50
      \n= 296 + 50
      \n= 346.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 14.
      \nNumber Sense<\/strong> Ellie says the product of 211 and 6 is 1,866. Is this calculation reasonable? Explain.
      \nAnswer:
      \nThis calculation is not reasonable because 211 \u00d7 6 = 1266 not 1866.<\/p>\n

      Explanation:
      \n211 \u00d7 6 = (200 + 11) \u00d7 6
      \n= 1200 + 66
      \n= 1266.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 15.
      \nHigher Order Thinking<\/strong> An adult sleeps about 480 minutes per day. An infant sleeps about 820 minutes per day. About how many more minutes does an infant sleep than an adult in one week? Solve the problem two different ways.
      \nAnswer:
      \n1Way:
      \nTime taken more by infant than an adult to sleep per one week = Time an infant sleeps per day – Time an adult sleeps per day
      \n= 820 – 480
      \n= 340 minutes.
      \n2Way:
      \nTime an adult sleeps per day\u00a0 = Time taken more by infant than an adult to sleep per one week + Time an infant sleeps per day
      \n=> 820 = ??? + 480
      \n=> 820 – 480 = ???
      \n= 340 minutes = ???<\/p>\n

      Explanation:
      \n1Way:
      \nTime an adult sleeps per day = 480 minutes.
      \nTime an infant sleeps per day = 820 minutes.
      \nTime taken more by infant than an adult to sleep per one week = Time an infant sleeps per day – Time an adult sleeps per day
      \n= 820 – 480
      \n= 340 minutes.
      \n2Way:
      \nTime an adult sleeps per day = 480 minutes.
      \nTime an infant sleeps per day = 820 minutes.
      \nTime an adult sleeps per day\u00a0 = Time taken more by infant than an adult to sleep per one week + Time an infant sleeps per day
      \n=> 820 = ??? + 480
      \n=> 820 – 480 = ???
      \n= 340 minutes = ???<\/p>\n

       <\/p>\n

       <\/p>\n

      Assessment Practice
      \n<\/strong>Question 16.
      \nGul can run 800 meters in 139 seconds. About how long would it take her to run 6 times as far if she runs at the same speed? Choose the best estimate.
      \nA. About 140 seconds
      \nB. About 600 seconds
      \nC. About 1,200 seconds
      \nD. About 6,000 seconds
      \nAnswer:
      \nTime taken by Gul to run 6 times as far if she runs at the same speed = 834 seconds.
      \nC. About 1,200 seconds<\/p>\n

      Explanation:
      \nTime taken by Gul to run 800 meters = 139 seconds.
      \nTime taken by Gul to run 6 times as far if she runs at the same speed = 6 \u00d7 Time taken by Gul to run 800 meters
      \n= 6 \u00d7 139
      \n= 834 seconds.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 17.
      \nA new two-seater car weighs 1,785 pounds. About how much would 8 of the two-seater cars weigh? Choose the best estimate.
      \nA. About 160 pounds
      \nB. About 1,600 pounds
      \nC. About 16,000 pounds
      \nD. About 60,000 pounds
      \nAnswer:
      \nWeight of 8 of the two-seater cars weigh = 14280 pounds.
      \nC. About 16,000 pounds<\/p>\n

      Explanation:
      \nWeight of new two-seater car = 1,785 pounds.
      \nWeight of 8 of the two-seater cars weigh = 8 \u00d7 Weight of new two-seater car
      \n= 8 \u00d7 1785
      \n= 14280 pounds.<\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

      Lesson 3.3 Use Arrays and Partial Products to Multiply<\/h3>\n

      Solve & Share<\/strong>
      \nA music room has chairs arranged in rows. There are 6 rows. Each row has 18 chairs. How many chairs are in the music room? Solve this problem any way you choose. Explain your answer.
      \nI can … use arrays and partial products to multiply.
      \n\"Envision<\/p>\n

      Look Back! Would the answer be different if there were 18 rows with 6 chairs in each row? Explain.
      \nAnswer:
      \nNo, there won’t be any change in the answer because 18 \u00d7 6 or 6 \u00d7 18 are both the same just numbers are interchanged, product = 108.<\/p>\n

      Explanation:
      \nNumber of rows chairs arranged = 18.
      \nNumber of chairs in each row = 6.
      \nTotal number of chairs used = Number of rows chairs arranged \u00d7 Number of chairs in each row
      \n= 18 \u00d7 6
      \n= 108.
      \nTotal number of chairs used = Number of chairs in each row \u00d7 Number of rows chairs arranged
      \n= 6 \u00d7 18
      \n= 108.<\/p>\n

       <\/p>\n

       <\/p>\n

      Essential Question<\/strong>
      \nHow Can You Use an Array and Partial Products to Multiply?
      \nAnswer:
      \nWe can use an array and Partial Products to Multiply by multiplying each digit of a number in turn with each digit of another where each digit maintains its place.<\/p>\n

      Explanation:
      \nThe partial product method involves multiplying each digit of a number in turn with each digit of another where each digit maintains its place.<\/p>\n

       <\/p>\n

       <\/p>\n

      Visual Learning Bridge<\/strong>
      \nThe windows of a building on International Drive are in an array. There are 5 rows with 13 windows in each row. How many windows are in this array?
      \n\"Envision<\/p>\n

      What You Show
      \n\"Envision<\/p>\n

      What You Think
      \nFind 5 \u00d7 13.
      \nEstimate: 5 \u00d7 13 is about 5 \u00d7 10 = 50.
      \n\"Envision
      \nThe numbers 15 and 50 are called partial products. 65 is the product.<\/p>\n

      What You Record
      \n\"Envision
      \nThere are 65 windows in the array.
      \nThe product, 65, is close to the estimate of 50. The answer is reasonable.
      \nYou can use place value to break factors apart and the Distributive Property to find partial products.<\/p>\n

      Convince Me! Use Structure How are the partial products represented with the place-value blocks?
      \nAnswer:
      \nThe partial product method\u00a0<\/strong>involves multiplying each digit of a number in turn with each digit of another where each digit maintains its place.<\/p>\n

      Explanation:
      \nThe partial product method\u00a0<\/strong>involves multiplying each digit of a number in turn with each digit of another where each digit maintains its place.
      \nFor Example:
      \n2 in 23 would actually be 20.
      \nFor instance, 23 x 42 would become (20 x 40) + (20 x 2) + (3 x 40) + (3 x 2).<\/p>\n

       <\/p>\n

       <\/p>\n

      Another Example!<\/strong>
      \nFind 2 \u00d7 126.
      \nEstimate: 2 \u00d7 126 is about 2 \u00d7 100 = 200.
      \n\"Envision<\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

      Guided Practice
      \n<\/strong>Do You Understand?<\/strong>
      \nQuestion 1.
      \nExplain how an array shows multiplication.
      \nAnswer:
      \nAn array is a way to represent multiplication and division using rows and columns.\u00a0 The word problem will determine which way to draw the array.<\/p>\n

      Explanation:
      \nRows represent the number of groups. Columns represent the number in each group or the size of each group. The word problem will determine which way to draw the array.<\/p>\n

       <\/p>\n

       <\/p>\n

      Do You Know How?<\/strong>
      \nFor 2-3, complete each calculation.
      \nQuestion 2.
      \n2 \u00d7 24
      \nAnswer:
      \n2 \u00d7 24 = 48.<\/p>\n

      Explanation:
      \n2 \u00d7 24 = ??
      \n=> 2 \u00d7 2 tens = 2 \u00d7 20 = 40.
      \n=> 2 \u00d7 4 ones = 2 \u00d7 4 = 8.
      \n2 \u00d7 24 = 40 + 8 = 48.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 3.
      \n3 \u00d7 218
      \nAnswer:
      \n3 \u00d7 218 = 654.<\/p>\n

      Explanation:
      \n3 \u00d7 218 = ??
      \n=> 3 \u00d7 2 hundreds = 3 \u00d7 200 = 600.
      \n=> 3 \u00d7 1 tens = 3 \u00d7 10 = 30.
      \n=> 3 \u00d7 8 ones = 3 \u00d7 8 = 24.
      \n3 \u00d7 218 = 600 + 30 + 24 = 654.<\/p>\n

       <\/p>\n

      Independent Practice
      \n<\/strong>Leveled Practice For 4-5, multiply. Complete each equation.
      \nQuestion 4.
      \nFind 3 \u00d7 13.
      \n\"Envision<\/p>\n

      Answer:
      \n3 \u00d7 13 = 39.
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

      Explanation:
      \n3 \u00d7 13 = ??
      \n3 rows, 1 ten in each.
      \n=> 3 \u00d7 10 = 30.
      \n3 rows, 3 ones in each.
      \n=> 3 \u00d7 3= 9.
      \n=> 30 + 9 = 39..<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 5.
      \nFind 2 \u00d7 105
      \n\"Envision<\/p>\n

      Answer:
      \n2 \u00d7 105 = 210.
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

      Explanation:
      \n2 \u00d7 105 = ??
      \n2 rows, 1 hundred in each.
      \n=> 2 \u00d7 100 = 200.
      \n2 rows, 5 ones in each.
      \n=> 2 \u00d7 5 = 10.
      \n=> 200 + 10 = 210.<\/p>\n

       <\/p>\n

       <\/p>\n

      Problem Solving
      \n<\/strong>Question 6.
      \nModel with Math<\/strong> What multiplication equation do the place-value blocks show? Find the product. Then write a problem that could be solved using this model.
      \n\"Envision
      \nAnswer:
      \n300 + 20 + 4 = 324 blocks 3 rows.
      \nMultiplication equation:
      \n3 \u00d7 324 = 972.<\/p>\n

      Explanation:
      \n3 rows, 3 hundred in each.
      \n=> 3 \u00d7 300 = 900.
      \n3 rows, 2 tens in each.
      \n=> 3 \u00d7 20 = 60.
      \n3 rows, 4 ones in each.
      \n=> 3 \u00d7 4 = 12.
      \n3 \u00d7 324 = 900 + 60+ 12 = 972.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 7.
      \nHow many marbles are in 3 large bags and 4 small bags?
      \n\"Envision
      \nAnswer:
      \nTotal number of marbles in 4 small bags = 60.
      \nTotal number of marbles in 3 large bags = 240.<\/p>\n

      Explanation:
      \nNumber of marbles in small bag = 15.
      \nTotal number of marbles in 4 small bags = 4 \u00d7 Number of marbles in small bag
      \n= 4 \u00d7 15
      \n= 60.
      \nNumber of marbles in large bag = 80.
      \nTotal number of marbles in 3 large bags = 3 \u00d7 Number of marbles in large bag
      \n= 3 \u00d7 80
      \n= 240.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 8.
      \nHigher Order Thinking<\/strong> How can the Distributive Property be used to find 4 \u00d7 875? Draw an array.
      \nAnswer:
      \n4 \u00d7 875 = 3500.
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

      Explanation:
      \n4 \u00d7 875 =???
      \n= 4 \u00d7 8hundreds = 4 \u00d7 800 = 3200.
      \n= 4 \u00d7 7tens = 4 \u00d7 70 = 280.
      \n= 4 \u00d7 5ones = 4 \u00d7 5 = 20.
      \n4 \u00d7 875 = 3200 + 280 + 5 = 3500.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 9.
      \nSelect all the expressions that have a value of 312.
      \n\u2610 (3 \u00d7 100) + (3 \u00d7 4)
      \n\u2610 3 \u00d7 12
      \n\u2610 3 \u00d7 112
      \n\u2610 (30 \u00d7 10) + (3 \u00d7 12)
      \n\u2610 3 \u00d7 104
      \nAnswer:
      \n(3 \u00d7 100) + (3 \u00d7 4) and 3 \u00d7 104 expressions have 312.<\/p>\n

      Explanation:
      \n312 = ???
      \n(3 \u00d7 100) + (3 \u00d7 4) = 300 + 12 = 312.
      \n3 \u00d7 12 = 36.
      \n3 \u00d7 112 = 336.
      \n(30 \u00d7 10) + (3 \u00d7 12) = 300 + 36 = 336.
      \n3 \u00d7 104 = 312.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 10.
      \nWhich are correct partial products for 54 \u00d7 9?
      \nA. 36, 45
      \nB. 36, 450
      \nC. 540, 36
      \nD. 32, 450
      \nAnswer:
      \n54 \u00d7 9 = 450 + 36 = 486.
      \nB. 36, 450 is the correct partial products for 54 \u00d7 9.<\/p>\n

      Explanation:
      \n54 \u00d7 9 = ??
      \n= 5tens \u00d7 9 = 9 \u00d7 50 = 450.
      \n= 4ones \u00d7 9 = 4 \u00d7 9 = 36.
      \n54 \u00d7 9 = 450 + 36 = 486.<\/p>\n

       <\/p>\n

       <\/p>\n

      Lesson 3.4 Use Area Models and Partial Products to Multiply<\/h3>\n

      Solve & Share<\/strong>
      \nUse only the numbers shown on the diagram and the operation symbols (+, -, \u00d7, +) to determine the area of the unshaded rectangle below. Solve this problem using any strategy you choose.
      \nI can use area models and partial products to multiply.
      \n\"Envision<\/p>\n

      Look Back! Use Structure Are these equations equal? Explain. 8 \u00d7 (10 \u2013 4) =\u00a0 (8 \u00d7 10) \u2013 (8 \u00d7 4)
      \nAnswer:
      \nYes, these equations are equal 8 \u00d7 (10 \u2013 4) =\u00a0 (8 \u00d7 10) \u2013 (8 \u00d7 4)\u00a0 = 48.<\/p>\n

      Explanation:
      \n8 \u00d7 (10 \u2013 4) = (8 \u00d7 10) \u2013 (8 \u00d7 4) = ??
      \n8 \u00d7 (10 \u2013 4) = 80 – 32 = 48.
      \n(8 \u00d7 10) \u2013 (8 \u00d7 4) = 80 – 32 = 48.<\/p>\n

       <\/p>\n

       <\/p>\n

      Essential Question<\/strong>
      \nHow Can You Use an Area Model and Partial Products to Multiply?
      \nAnswer:
      \nThe partial product method involves multiplying each digit of a number in turn with each digit of another where each digit maintains its place. Write each factor in expanded form. Then, draw your model. Next, multiply to find the area of each smaller rectangle. Finally, add those products to find the total area.<\/p>\n

      Explanation:
      \nFirst, write each factor in expanded form. Then, draw your\u00a0model. Next,\u00a0multiply\u00a0to find the\u00a0area\u00a0of each smaller rectangle. Finally, add those products to find the total\u00a0area.
      \nThe partial product method involves\u00a0multiplying each digit of a number in turn with each digit of another where each digit maintains its place.<\/p>\n

       <\/p>\n

       <\/p>\n

      Visual Learning Bridge<\/strong>
      \nA garden is in the shape of a rectangle. It is 8 feet wide and 25 feet long. What is the area of the garden?
      \nA numerical expression contains numbers and at least one operation. 8 \u00d7 25 is a numerical expression.<\/p>\n

      What You Show
      \n\"Envision<\/p>\n

      What You Think
      \nEstimate: 8 \u00d7 25 is about 8 \u00d7 30 = 240. 20
      \n\"Envision<\/p>\n

      What You Record
      \n\"Envision
      \nThe area of the garden is 200 square feet.
      \nThe product, 200, is close to the estimate of 240. The answer is reasonable.<\/p>\n

      Convince Me! Use Structure Does 12 – (4 \u00d7 2) = (12 \u2013 4) (12 – 2)? Explain.
      \nAnswer:
      \nNo, this equation is not correct because 12 – (4 \u00d7 2) = 24 where as (12 \u2013 4) (12 – 2) =80.<\/p>\n

      Explanation:
      \n12 – (4 \u00d7 2) = (12 \u00d7 4) – (12 \u00d7 2) = 48 – 24 = 24.
      \n(12 \u2013 4) (12 – 2) = 8 \u00d7 10 = 80.<\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

      Another Example!<\/strong>
      \n\"Envision<\/p>\n

       <\/p>\n

      Guided Practice
      \n<\/strong>Do You Understand?<\/strong>
      \nQuestion 1.
      \nWhat numerical expression is shown by the area model below?
      \n\"Envision<\/p>\n

      Answer:
      \n265 \u00d7 7 = 1855.<\/p>\n

      Explanation:
      \n(200 + 60 + 5) 7 = 265 \u00d7 7
      \n=> 7 \u00d7 200 = 1400.
      \n=> 7 \u00d7 60 = 420.
      \n=> 7 \u00d7 5 = 35.
      \n1400 + 420 + 35 = 1855.<\/p>\n

       <\/p>\n

       <\/p>\n

      Do You Know How?<\/strong>
      \nQuestion 2.
      \nMultiply. Use the area model and partial products.
      \n\"Envision<\/p>\n

      Answer:
      \n560 \u00d7 7 = 3920.<\/p>\n

      Explanation:
      \n(500 + 60 ) 7 = 560 \u00d7 7
      \n=> 7 \u00d7 500 = 3500
      \n=> 7 \u00d7 60 = 420.
      \n3500 + 420 = 3920.<\/p>\n

       <\/p>\n

       <\/p>\n

      Independent Practice
      \n<\/strong>Leveled Practice For 3-6, multiply. Use the area model and partial products.
      \nQuestion 3.
      \n\"Envision
      \nAnswer:
      \n34 \u00d7 6 = 204.<\/p>\n

      Explanation:
      \n(30+ 4) 6 = 34 \u00d7 6
      \n=> 6 \u00d7 30 = 180.
      \n=> 6 \u00d7 4 = 24.
      \n180 + 24 = 204.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 4.
      \n\"Envision
      \nAnswer:
      \n99 \u00d7 2 = 198.<\/p>\n

      Explanation:
      \n(90 + 9) 2 = 99 \u00d7 2
      \n=> 2 \u00d7 90 = 180.
      \n=> 2 \u00d7 9 = 18.
      \n180 + 18 = 198.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 5.
      \n\"Envision
      \nAnswer:
      \n3 \u00d7 185 = 555.<\/p>\n

      Explanation:
      \n3 (100 + 80 + 5) = 3 \u00d7 185
      \n=> 3 \u00d7 100 = 300.
      \n=> 3 \u00d7 80 = 240.
      \n=> 3 \u00d7 5 = 15.
      \n300 + 240 + 15 = 555.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 6.
      \n\"Envision
      \nAnswer:
      \n8 \u00d7 440 = 3520.<\/p>\n

      Explanation:
      \n8 ( 400 + 40) = 8 \u00d7 440
      \n=> 8 \u00d7 400 = 3200.
      \n=> 8 \u00d7 40 = 320.
      \n3200 + 320 = 3520.<\/p>\n

       <\/p>\n

       <\/p>\n

      Problem Solving
      \n<\/strong>Question 7.
      \nModel with Math<\/strong> Last year, Anthony’s grandmother gave him 33 silver coins and 16 gold coins to start a coin collection. Now Anthony has six times as many coins in his collection. How many coins does Anthony have in his collection? Complete the bar diagram to show your work.
      \n\"Envision<\/p>\n

      Answer:
      \nNumber of coins Anthony have in his collection now = 294.<\/p>\n

      Explanation:
      \nNumber of silver coins Anthony’s grandmother gave him = 33.
      \nNumber of gold coins Anthony’s grandmother gave him = 16.
      \nNow Anthony has six times as many coins in his collection.
      \nNumber of coins Anthony have in his collection now = 6 \u00d7 (Number of silver coins Anthony’s grandmother gave him + Number of gold coins Anthony’s grandmother gave him)
      \n= 6 \u00d7 (33 + 16)
      \n= (6 \u00d7 33) + (6 \u00d7 16)
      \n= 198 + 96
      \n= 294.
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 8.
      \nWyatt said he used partial products to write 7 \u00d7 870 = 5,600 + 49. Explain Wyatt’s error and use math to justify your explanation.
      \nAnswer:
      \n7 \u00d7 870 = 5600 + 490 not 5,600 + 49\u00a0 because Wyatt’s error is that he took partial products value wrong and got the result wrong answer.<\/p>\n

      Explanation:
      \n7 \u00d7 870 = (7 \u00d7 800) + (7 \u00d7 70)
      \n7 \u00d7 870 = 5600 + 490
      \n7 \u00d7 870 = 6090.
      \n5,600 + 49 = 5649.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 9.
      \nHigher Order Thinking<\/strong> Tod Mountain is a mountain peak near Tyler, Texas. A ranger hiked 607 feet to and from the peak, each way. The ranger hiked 3 times in the past four weeks. How far did the ranger hike on Tod Mountain over the past four weeks?
      \nAnswer:
      \nLength of the ranger hiked on Tod Mountain over the past four weeks = 1821 feet.<\/p>\n

      Explanation:
      \nLength of the ranger hiked to and from the peak, each way of Tod Mountain = 607 feet.
      \nThe ranger hiked 3 times in the past four weeks.
      \nLength of the ranger hiked on Tod Mountain over the past four weeks = 3 \u00d7 Length of the ranger hiked to and from the peak, each way of Tod Mountain
      \n= 3 \u00d7 607
      \n= (3 \u00d7 600) + (3 \u00d7 7)
      \n= 1800 + 21
      \n= 1821 feet.<\/p>\n

       <\/p>\n

      Question 10.
      \nWendy plans to bring beverages for the school picnic. She has 5 gallons of iced tea. Also, she will bring 2 gallons of lemonade for every 10 people. How many total gallons of lemonade and iced tea does Wendy need to bring for 40 people? Complete the table.
      \n\"Envision
      \nAnswer:
      \nTotal gallons of lemonade and iced tea Wendy needs to bring for 40 people = 28.<\/p>\n

      Explanation:
      \nNumber of gallons of iced tea Wendy has for every 10 people = 5.
      \nNumber of gallons of lemonade Wendy has for every 10 people = 2.
      \nTotal gallons of lemonade and iced tea Wendy needs to bring for 40 people = 4 \u00d7 (Number of gallons of iced tea Wendy has for every 10 people + Number of gallons of lemonade Wendy has for every 10 people)
      \n= 4 \u00d7 (5 + 2)
      \n= (4 \u00d7 5) + (4 \u00d7 2)
      \n= 20 + 8
      \n= 28.<\/p>\n

       <\/p>\n

       <\/p>\n

      Assessment Practice
      \n<\/strong>Question 11.
      \nWhat is the missing factor?
      \n6 \u00d7 ? = 264
      \n\"Envision
      \nA. 50
      \nB. 44
      \nC. 40
      \nD. 30
      \nAnswer:
      \n6 \u00d7 44 = 264.
      \nB. 44<\/p>\n

      Explanation:
      \n6 \u00d7 ? = 264
      \n=> ? = 264 \u00f7 6
      \n=> ? = 44.
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

       <\/p>\n

      Question 12.
      \nWhich are the partial products for this area model?
      \n7 \u00d7 228
      \n\"Envision
      \nA. 1,400, 144, 56
      \nB. 14,000, 140, 56
      \nC. 56, 14, 1,400
      \nD. 56, 140, 1,400
      \nAnswer:
      \n7 \u00d7 228 = 1400 + 140 + 56 = 1596.
      \nD. 56, 140, 1,400<\/p>\n

      Explanation:
      \n7 \u00d7 228 = (7 \u00d7 200) + (7 \u00d7 20) + (7 \u00d7 8)
      \n7 \u00d7 228 = 1400 + 140 + 56
      \n7 \u00d7 228 =1540 + 56
      \n7 \u00d7 228 = 1596.<\/p>\n

       <\/p>\n

       <\/p>\n

      Lesson 3.5 More Use Area Models and Partial Products to Multiply<\/h3>\n

      Solve & Share<\/strong>
      \nThe horseshoe-pit model below has an area of 228 square feet. The length of one part of the pit was erased by mistake. What is the length of the missing section, x? Solve any way you choose. Explain how you found the answer.
      \nI can … use area models and partial products to multiply.
      \n\"Envision<\/p>\n

      Look Back! What multiplication equation can be used to represent the horseshoe-pit model above?
      \nAnswer:
      \nLength of the second section missing horseshoe-pit model = x = 8 feet.<\/p>\n

      Explanation:
      \nThe horseshoe-pit model below has an area of 228 square feet. The length of one part of the pit was erased by mistake. What is the length of the missing section, x? Solve any way you choose.
      \nArea of the horseshoe-pit model = 228 square feet.
      \nLength of the first section horseshoe-pit model = 30 feet.
      \nLength of the second section missing horseshoe-pit model = x feet.
      \nBreadth of the horseshoe-pit model\u00a0 = 6 feet.
      \nArea of the horseshoe-pit model = length \u00d7 Breadth
      \n=> 228 = (Length of the first section horseshoe-pit model + Length of the second section missing horseshoe-pit model) \u00d7 6
      \n=> 228 = (30 + x) \u00d7 6
      \n=> 228 \u00f7 6 = 30 + x
      \n=> 38 = 30 + x
      \n=> 38 – 30 = x
      \n=> 8 feet = x.<\/p>\n

       <\/p>\n

       <\/p>\n

      Essential Question<\/strong>
      \nHow Do You Multiply with Greater Numbers?
      \nAnswer:
      \nWe multiply greater number Multiplication by using the place values of each number given and multiply and get the result to that problem.<\/p>\n

      Explanation:
      \nWhen multiplying by larger numbers with two digits or more, use\u00a0one placeholding zero when multiplying by the tens digit, two placeholding zeros when multiplying by the hundreds digit, three zeros when multiplying by the thousands digit, and so forth.<\/p>\n

       <\/p>\n

      Visual Learning Bridge<\/strong>
      \nThe Rails-to-Trails Preservation opened a new section of a biking trail. The section is 6 yards wide. What is its area? Calculate 6 \u00d7 1,842.
      \nThe process for multiplying is the same regardless of the number of digits.
      \n\"Envision<\/p>\n

      Find 6 \u00d7 1,842 using an area model and partial products.
      \nEstimate: 6 \u00d7 1,842 is about 6 \u00d7 2,000 = 12,000.
      \n\"Envision<\/p>\n

      Remember you can find partial products in any order.
      \n\"Envision
      \nThe new section is 11,052 square yards.<\/p>\n

      Convince Me! Use Structure How is the process of using partial products to find the final product the same for each of these calculations? How is it different? Explain.
      \n\"Envision
      \nAnswer:
      \nThe process of using partial products to find the final product for each of these calculations is not same, its completely different because the numbers given for multiplication having different place values and result of their products also different.<\/p>\n

      Explanation:
      \n5 \u00d7 34 = (5 \u00d7 30) + (5 \u00d7 4)
      \n5 \u00d7 34 = 150 + 20
      \n5 \u00d7 34 = 170.<\/p>\n

      5 \u00d7 234 = (5 \u00d7 200) + (5 \u00d7 30) + (5 \u00d7 4)
      \n5 \u00d7 234 = 1000 + 150 + 20
      \n5 \u00d7 234 = 1150 + 20
      \n5 \u00d7 234 = 1170.<\/p>\n

      5 \u00d7 1234 = (5 \u00d7 1000) + (5 \u00d7 200) + (5 \u00d7 30) + (5 \u00d7 4)
      \n5 \u00d7 1234 = 5000 + 1000 + 150 + 20
      \n5 \u00d7 1234 = 6000 + 150 + 20
      \n5 \u00d7 1234 = 6150 + 20
      \n5 \u00d7 1234 = 6170.<\/p>\n

       <\/p>\n

      Guided Practice
      \n<\/strong>Do You Understand?<\/strong>
      \nQuestion 1.
      \nWhat multiplication expression is shown by the area model below?
      \n\"Envision
      \nAnswer:
      \n4 \u00d7 (1000 + 400 + 5) = 4 \u00d7 1405 = 5620.<\/p>\n

      Explanation:
      \n4 \u00d7 (1000 + 400 + 5) = ????
      \n4 \u00d7 (1000 + 400 + 5) = (4 \u00d7 1000) + (4 \u00d7 400) + ( 4 \u00d7 5)
      \n4 \u00d7 (1000 + 400 + 5) = 4000 + 1600 + 20
      \n4 \u00d7 (1000 + 400 + 5) = 5600 + 20
      \n4 \u00d7 (1000 + 400 + 5) = 5620.
      \n=> 4 \u00d7 1405 = 5620. (1000 + 400 + 5 = 1405)<\/p>\n

       <\/p>\n

       <\/p>\n

      Do You Know How?<\/strong>
      \nFor 2, multiply. Use the area model and partial products.
      \nQuestion 2.
      \n5 \u00d7 1,117
      \n\"Envision
      \nAnswer:
      \n5 \u00d7 1,117 = 5585.<\/p>\n

      Explanation:
      \nLength of the given rectangle figure = 1000 + 100 + 10 + 7 = 1117.
      \nBreadth of the given rectangle figure = 5.
      \nArea of the given rectangle figure = Length of the given rectangle figure \u00d7 Breadth of the given rectangle figure
      \n= 1117 \u00d7 5
      \n= (1000 \u00d7 5) + (100 \u00d7 5) + (10 \u00d7 5) + (7 \u00d7 5)
      \n= 5000 + 500 + 50 + 35
      \n= 5500 + 50 + 35
      \n= 5550 + 35
      \n= 5585.<\/p>\n

       <\/p>\n

       <\/p>\n

      Independent Practice
      \n<\/strong>For 3-8, multiply. Use the area model and partial products.
      \n\"Envision<\/p>\n

      Question 3.
      \n\"Envision
      \nAnswer:
      \n1092 \u00d7 8 = (1000 \u00d7 8) + (90 \u00d7 8) + (2 \u00d7 8) = 8736.<\/p>\n

      Explanation:
      \nLength of the given rectangle figure = 1000 + 90+ 2 = 1092.
      \nBreadth of the given rectangle figure = 8.
      \nArea of the given rectangle figure = Length of the given rectangle figure \u00d7 Breadth of the given rectangle figure
      \n= 1092\u00d7 8
      \n= (1000 \u00d7 8) + (90 \u00d7 8) + (2 \u00d7 8)
      \n= 8000 + 720 + 16
      \n= 8720 + 16
      \n= 8736.<\/p>\n

       <\/p>\n

      Question 4.
      \n\"Envision<\/p>\n

      Answer:
      \n4261 \u00d7 3 = (4000 \u00d7 3) + (200\u00d7 3) + (60 \u00d7 3) + (1 \u00d7 3) = 12783.<\/p>\n

      Explanation:
      \nLength of the given rectangle figure = 4000 + 200 + 60 + 1= 4261.
      \nBreadth of the given rectangle figure = 3.
      \nArea of the given rectangle figure = Length of the given rectangle figure \u00d7 Breadth of the given rectangle figure
      \n= 4261 \u00d7 3
      \n= (4000 \u00d7 3) + (200\u00d7 3) + (60 \u00d7 3) + (1 \u00d7 3)
      \n= 12000 + 600 + 180 + 3
      \n= 12600 + 180 + 3
      \n= 12780 + 3
      \n= 12783.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 5.
      \n\"Envision
      \nAnswer:
      \n1990\u00d7 2 = (1000 \u00d7 2) + (900\u00d7 2) + (90 \u00d7 2) = 3980.<\/p>\n

      Explanation:
      \nLength of the given rectangle figure = 1000 + 900 + 90 = 1990
      \nBreadth of the given rectangle figure = 2.
      \nArea of the given rectangle figure = Length of the given rectangle figure \u00d7 Breadth of the given rectangle figure
      \n= 1990\u00d7 2
      \n= (1000 \u00d7 2) + (900\u00d7 2) + (90 \u00d7 2)
      \n= 2000 + 1800 + 180
      \n= 3800 + 180
      \n= 3980.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 6.
      \n\"Envision<\/p>\n

      Answer:
      \n2347 \u00d7 6 = (2000 \u00d7 6) + (300\u00d7 6) + (40 \u00d7 6) + (7 \u00d7 6) = 14082.<\/p>\n

      Explanation:
      \nLength of the given rectangle figure = 2000 + 300 + 40 + 7 = 2347
      \nBreadth of the given rectangle figure = 6.
      \nArea of the given rectangle figure = Length of the given rectangle figure \u00d7 Breadth of the given rectangle figure
      \n= 2347 \u00d7 6
      \n= (2000 \u00d7 6) + (300\u00d7 6) + (40 \u00d7 6) + (7 \u00d7 6)
      \n= 12000 + 1800 + 240 + 42
      \n= 13800 + 240 + 42
      \n= 14040 + 42
      \n= 14082.<\/p>\n

       <\/p>\n

      Question 7.
      \n\"Envision<\/p>\n

      Answer:
      \n3022 \u00d7 5 = (3000 \u00d7 5) + (20 \u00d7 5) + (2 \u00d7 5)\u00a0 = 15110.<\/p>\n

      Explanation:
      \nLength of the given rectangle figure = 3000 + 20 + 2 = 3022.
      \nBreadth of the given rectangle figure = 5.
      \nArea of the given rectangle figure = Length of the given rectangle figure \u00d7 Breadth of the given rectangle figure
      \n= 3022 \u00d7 5
      \n= (3000 \u00d7 5) + (20 \u00d7 5) + (2 \u00d7 5)
      \n= 15000 + 100 + 10
      \n= 15100 + 10
      \n= 15110.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 8.
      \n\"Envision
      \nAnswer:
      \n1999 \u00d7 7 = (1000 \u00d7 7) + (900 \u00d7 7) + (90 \u00d7 7) + (9 \u00d7 7) = 13993.<\/p>\n

      Explanation:
      \nLength of the given rectangle figure = 1000 + 900 + 90 + 9 = 1999.
      \nBreadth of the given rectangle figure = 7.
      \nArea of the given rectangle figure = Length of the given rectangle figure \u00d7 Breadth of the given rectangle figure
      \n= 1999 \u00d7 7
      \n= (1000 \u00d7 7) + (900 \u00d7 7) + (90 \u00d7 7) + (9 \u00d7 7)
      \n= 7000 + 6300 + 630 + 63
      \n= 13300 + 630 + 63
      \n= 13930 + 63
      \n= 13993.<\/p>\n

       <\/p>\n

       <\/p>\n

      Problem Solving
      \n<\/strong>Question 9.
      \nBe Precise<\/strong> There are usually 365 days in each year. Every fourth year is called a leap year and has one extra day in February. How many days are there in 8 years if 2 of the years are leap years?
      \nAnswer:
      \nNumber of days in 8 years = 2922.<\/p>\n

      Explanation:
      \nNumber of days in each year = 365.
      \nEvery fourth year is called a leap year and has one extra day in February.
      \n=> Number of days in leap year = 366.
      \nNumber of days in 8 years = 6 ( Number of days in each year) + 2 (Number of days in leap year)
      \n= (6 \u00d7 365) + (2 \u00d7 366)
      \n= 2190 + 732
      \n= 2922.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 10.
      \nThere are 1,250 seeds in each package. There are 5 packages. How many seeds are there in all?
      \nAnswer:
      \n1250 \u00d7 5 = (1000 \u00d7 5) + (200 \u00d7 5) + ( 50 \u00d7 5) = 6250.<\/p>\n

      Explanation:
      \nNumber of seeds in each package = 1250.
      \nNumber of packages = 5.
      \nTotal number of seeds in all = Number of seeds in each package \u00d7 Number of packages
      \n= 1250 \u00d7 5
      \n= (1000 \u00d7 5) + (200 \u00d7 5) + ( 50 \u00d7 5)
      \n= 5000 + 1000 + 250
      \n= 6000 + 250
      \n= 6250.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 11.
      \nA cat breeder has 6 Sphynx kittens and 7 Persian kittens for sale. If all 13 kittens sell, how much money will the breeder earn? Write and solve equations. Tell what your variables represent.
      \n\"Envision<\/p>\n

      Answer:
      \nTotal money the breeder earns = $9613.<\/p>\n

      Explanation:
      \nNumber of Sphynx kittens a cat breeder has for sale = 6.
      \nNumber of Persian kittens a cat breeder has for sale = 7.
      \nCost of each Sphynx kitten = $698.
      \nCost of each Persian kitten = $775.
      \nTotal money the breeder earns = ( Number of Sphynx kittens a cat breeder has for sale \u00d7 Cost of each Sphynx kitten) + (Number of Persian kittens a cat breeder has for sale \u00d7 Cost of each Persian kitten )
      \n= (6 \u00d7 $698) + (7 \u00d7 $775)
      \n= $4188 + $5425
      \n= $9613.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 12.
      \nHigher Order Thinking<\/strong> Patricia creates a design using 1,025 tiles. She doubles the number of tiles to make a second design. Her third design uses 3 times as many tiles as the second design. How many tiles does Patricia use in her third design? Explain.
      \nAnswer:
      \nNumber of tiles Patricia uses for creating third design =\u00a06150.<\/p>\n

      Explanation:
      \nNumber of tiles Patricia uses for creating first design = 1025.
      \nShe doubles the number of tiles to make a second design.
      \n=> Number of tiles Patricia uses for creating second design = 2\u00d71025 = 2050.
      \nHer third design uses 3 times as many tiles as the second design.
      \n=> Number of tiles Patricia uses for creating third design = 3 \u00d7 Number of tiles Patricia uses for creating second design
      \n=> 3 \u00d7 2050
      \n=> 6150.<\/p>\n

       <\/p>\n

       <\/p>\n

      Assessment Practice
      \n<\/strong>Question 13.
      \nWhich are the correct partial products of 3 \u00d7 3,672?
      \nA. 6; 21; 1,800; 9,000
      \nB. 9,000; 1,800; 210; 6
      \nC. 210; 1,800; 9,000
      \nD. 6; 210; 180; 9,000
      \nAnswer:
      \nThe correct partial products of 3 \u00d7 3,672:
      \nB. 9,000; 1,800; 210; 6<\/p>\n

      Explanation:
      \n3 \u00d7 3,672 = (3 \u00d7 3000) + (3 \u00d7 600) + (3 \u00d7 70) + (3 \u00d7 2)
      \n3 \u00d7 3,672 = 9000 + 1800 + 210 + 6
      \n3 \u00d7 3,672 = 10800 + 210 + 6
      \n3 \u00d7 3,672 = 11010 + 6
      \n3 \u00d7 3,672 = 11016.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 14.
      \nSelect all the expressions that have 1,600 as a partial product.
      \n\u2610 4 \u00d7 4,381
      \n\u2610 8 \u00d7 3,240
      \n\u2610 4 \u00d7 1,408
      \n\u2610 2 \u00d7 7,881
      \n\u2610 8 \u00d7 2,021
      \nAnswer:
      \nExpressions that have 1,600 as a partial product:
      \n8 \u00d7 3,240
      \n4 \u00d7 1,408
      \n2 \u00d7 7,881.<\/p>\n

      Explanation:
      \n4 \u00d7 4,381 = (4 \u00d7 4000) + (4 \u00d7300) + (4 \u00d7 80) + (4 \u00d7 1)
      \n4 \u00d7 4,381 = 16000 + 1200 + 320 + 4
      \n4 \u00d7 4,381 = 17200 + 320 + 4
      \n4 \u00d7 4,381 = 17520 + 4
      \n4 \u00d7 4,381 = 17524.<\/p>\n

      8 \u00d7 3,240 = (8 \u00d7 3000) + (8 \u00d7200) + (8 \u00d7 40) + (8 \u00d7 1)
      \n8 \u00d7 3,240 = 24000 + 1600 + 320 + 8
      \n8 \u00d7 3,240 = 25600 + 320 + 8
      \n8 \u00d7 3,240 = 25920 + 8
      \n8 \u00d7 3,240 = 25928.<\/p>\n

      4 \u00d7 1,408 = (4 \u00d7 1000) + (4 \u00d7400) + (4 \u00d7 8)
      \n4 \u00d7 1,408 = 4000 + 1600 + 32
      \n4 \u00d7 1,408 = 5600 + 32
      \n4 \u00d7 1,408 = 5632.<\/p>\n

      2 \u00d7 7,881 = (2 \u00d7 7000) + (2 \u00d7800) + (2 \u00d7 80) + (2 \u00d7 1)
      \n2 \u00d7 7,881 = 14000 + 1600 + 160 + 2
      \n2 \u00d7 7,881 = 15600 + 160 + 2
      \n2 \u00d7 7,881 = 15760 + 2
      \n2 \u00d7 7,881 = 15762.<\/p>\n

      8 \u00d7 2,021 = (8 \u00d7 2000) + (8 \u00d7 20) + (8 \u00d7 1)
      \n8 \u00d7 2,021 = 16000 + 160 + 8
      \n8 \u00d7 2,021 = 16160 + 8
      \n8 \u00d7 2,021 = 16168.<\/p>\n

       <\/p>\n

       <\/p>\n

      Lesson 3.6 Mental Math Strategies for Multiplication<\/h3>\n

      Solve & Share<\/strong>
      \nDetermine the products for the expressions given below. Use mental math to solve. Explain your thinking. Solve these problems using any strategy you choose.
      \nI can … use mental math strategies based on place value and properties of operations to multiply.
      \n\"Envision<\/p>\n

      Look Back! Describe two different ways to find 4 \u00d7 97.
      \nAnswer:
      \nWay:1:
      \n4 \u00d7 97 = (4 \u00d7 100) – (4 \u00d7 3) = 400 – 12 = 388.
      \nWay:2:
      \n4 \u00d7 97 = 4 \u00d7 (90 + 7) = (4 \u00d7 90) + (4 \u00d7 7) = 360 + 28 = 388.<\/p>\n

      Explanation:
      \nWay:1:
      \n4 \u00d7 97 = 4 \u00d7 (100 – 3)
      \n4 \u00d7 97 = (4 \u00d7 100) – (4 \u00d7 3)
      \n4 \u00d7 97 = 400 – 12
      \n4 \u00d7 97 = 388.
      \nWay:2:
      \n4 \u00d7 97 = 4 \u00d7 (90 + 7)
      \n4 \u00d7 97 = (4 \u00d7 90) + (4 \u00d7 7)
      \n4 \u00d7 97 = 360 + 28
      \n4 \u00d7 97 = 388.<\/p>\n

       <\/p>\n

       <\/p>\n

      Essential Question<\/strong>
      \nHow Can You Multiply Mentally?
      \nAnswer:
      \nWe can Multiply Mentally by rounding the numbers to nearest place and doing the required operation necessary to solve the problem.<\/p>\n

      Explanation:
      \nFor example: Any time you square a two-digit number that ends in 5, the last digits of the answer will be 25 and the digits before that are given by multiplying the first digit of the number\u00a0by the number that’s one greater.<\/p>\n

       <\/p>\n

      Visual Learning Bridge<\/strong>
      \nThree cyclists rode their bikes the distances shown in the table. Use mental math to calculate the total distance Pam and Anna each rode.
      \n\"Envision<\/p>\n

      Multiply 4 \u00d7 325 to find the distance Pam rode.
      \nTo multiply mentally, you can break apart numbers using place value and the Distributive Property.
      \nThink:
      \n4 \u00d7 325 = 4 \u00d7 300 + 4 \u00d7 25
      \n= 1,200 + 100
      \n= 1,300
      \nPam rode 1,300 miles.<\/p>\n

      Multiply 8 \u00d7 25 to find the distance Anna rode.
      \nTo multiply mentally, you can break apart and rearrange numbers using the Commutative and Associative Properties.
      \nThink: 8 \u00d7 25 = (4 \u00d7 2) \u00d7 25
      \n= 2 \u00d7 (4 \u00d7 25)
      \n= 2 \u00d7 100
      \n= 200
      \nAnna rode 200 miles.<\/p>\n

      Convince Me! Use Structure in the work for 4 \u00d7 325 above, why was 25 not broken into 20 and 5? Explain.
      \nAnswer:
      \n25 was not broken into 20 and 5 because 325 already was broken into two parts 300 and 25 , so its not broken again.<\/p>\n

      Explanation:
      \nTo multiply mentally, you can break apart numbers using place value and the Distributive Property.
      \n4 \u00d7 325 = 4 \u00d7 300 + 4 \u00d7 25
      \n4 \u00d7 325 = 1,200 + 100
      \n4 \u00d7 325 = 1,300.
      \nPam rode 1,300 miles.<\/p>\n

       <\/p>\n

       <\/p>\n

      Another Example!<\/strong>
      \nDetermine the distance George rode.
      \nFind 3 \u00d7 398. 400 is close to 398.
      \nFind 3 \u00d7 400 and adjust the answer.
      \n3 \u00d7 400 = 1,200
      \n398 + 2 = 400 3 \u00d7 2 = 6
      \nAdjust the answer by subtracting 6. 1,200 \u2013 6 = 1,194
      \nGeorge rode 1,194 miles in 3 months.
      \n\"Envision<\/p>\n

      Guided Practice
      \n<\/strong>Do You Understand?<\/strong>
      \nQuestion 1.
      \nWhy was 6 subtracted from 1,200 in the problem above?
      \nAnswer:
      \n6 was subtracted from 1,200 in the problem above, because 398 was rounded nearest to hundreds number 400 and it was rearranged to get its actual figure.<\/p>\n

      Explanation:
      \nGeorge rode ???? miles in 3 months.
      \n3 \u00d7 398. 400 is close to 398.
      \n3 \u00d7 400 = 1,200
      \n398 + 2 = 400.
      \n3 \u00d7 2 = 6.
      \nAdjust the answer by subtracting 6.
      \n1,200 \u2013 6 = 1,194.
      \nGeorge rode 1,194 miles in 3 months.<\/p>\n

       <\/p>\n

      Do You Know How?<\/strong>
      \nFor 2, multiply mentally to find the product. Explain which strategy you used.
      \nQuestion 2.
      \n8 \u00d7 903?
      \nAnswer:
      \n8 \u00d7 903 = 7224.<\/p>\n

      Explanation:
      \n8 \u00d7 903 = (8 \u00d7 900) + (8 \u00d7 3)
      \n8 \u00d7 903 = 7200 + 24
      \n8 \u00d7 903 = 7224.<\/p>\n

       <\/p>\n

       <\/p>\n

      Independent Practice
      \n<\/strong>Leveled Practice For 3-10, multiply mentally to find each product. Explain which strategy you used.
      \nQuestion 3.
      \n6 \u00d7 250 = (3 + _____) \u00d7 250
      \nAnswer:
      \n6 \u00d7 250 = (3 + __3___) \u00d7 250 = 1500.<\/p>\n

      Explanation:
      \n6 \u00d7 250 = (3 + 3) \u00d7 250
      \n6 \u00d7 250 = (3 \u00d7 250) + (3 \u00d7 250)
      \n6 \u00d7 250 = 750 + 750
      \n6 \u00d7 250 = 1500.<\/p>\n

       <\/p>\n

      Question 4.
      \n4 \u00d7 506 = 4 \u00d7 (_____+ _____)
      \nAnswer:
      \n4 \u00d7 506 = 4 \u00d7 (__500___+ ___6__) = 2024.<\/p>\n

      Explanation:
      \n4 \u00d7 506 = 4 \u00d7 (__500___+ ___6__)
      \n4 \u00d7 506 = (4 \u00d7 500) + (4 \u00d7 6)
      \n4 \u00d7 506 = 2000 + 24
      \n4 \u00d7 506 = 2024.<\/p>\n

       <\/p>\n

      Question 5.
      \n4 \u00d7 1,995
      \nAnswer:
      \n4 \u00d7 1,995 = 4 (2000 – 5) = 7980.<\/p>\n

      Explanation:
      \n4 \u00d7 1,995 = 4 (2000 – 5)
      \n4 \u00d7 1,995 = (4 \u00d7 2000) – (4 \u00d7 5)
      \n4 \u00d7 1,995 = 8000 – 20
      \n4 \u00d7 1,995 = 7980.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 6.
      \n22 \u00d7 5
      \nAnswer:
      \n22 \u00d7 5 = (20 + 2) 5 = 100 + 10 = 110.<\/p>\n

      Explanation:
      \n22 \u00d7 5 = (20 + 2) 5
      \n22 \u00d7 5 = (20 \u00d7 5) + (2 \u00d7 5)
      \n22 \u00d7 5 = 100 + 10
      \n22 \u00d7 5 = 110.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 7.
      \n404 \u00d7 6
      \nAnswer:
      \n404 \u00d7 6 = (400 + 4) 6 = (400 \u00d7 6) + ( 4 \u00d7 6) = 2424.<\/p>\n

      Explanation:
      \n404 \u00d7 6 = (400 + 4) 6
      \n404 \u00d7 6 = (400 \u00d7 6) + ( 4 \u00d7 6)
      \n404 \u00d7 6 = 2400 + 24
      \n404 \u00d7 6 = 2424.<\/p>\n

       <\/p>\n

      Question 8.
      \n7 \u00d7 250
      \nAnswer:
      \n7 \u00d7 250 = 7 ( 200 + 50) = 1400 + 350 = 1750.<\/p>\n

      Explanation:
      \n7 \u00d7 250 = 7 ( 200 + 50)
      \n7 \u00d7 250 = (7 \u00d7 200) + (7 \u00d7 50)
      \n7 \u00d7 250 = 1400 + 350
      \n7 \u00d7 250 = 1750.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 9.
      \n2 \u00d7 395
      \nAnswer:
      \n2 \u00d7 395 = 2 (400 – 5) = 800 – 10 = 790.<\/p>\n

      Explanation:
      \n2 \u00d7 395 = 2 (400 – 5)
      \n2 \u00d7 395 = (2 \u00d7 400) – (2 \u00d7 5)
      \n2 \u00d7 395 = 800 – 10
      \n2 \u00d7 395 = 790.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 10.
      \n9 \u00d7 56
      \nAnswer:
      \n9 \u00d7 56 = 9 (50 + 6) = (9 \u00d7 50) + ( 9 \u00d7 6) = 450 + 54 = 504.<\/p>\n

      Explanation:
      \n9 \u00d7 56 = 9 (50 + 6)
      \n9 \u00d7 56 = (9 \u00d7 50) + ( 9 \u00d7 6)
      \n9 \u00d7 56 = 450 + 54
      \n9 \u00d7 56 = 504.<\/p>\n

       <\/p>\n

       <\/p>\n

      Problem Solving
      \n<\/strong>Question 11.
      \nEach elephant at a zoo eats 100 pounds of hay and 5 pounds of fruits and vegetables every day. How many pounds of food does the zoo need to feed one elephant for one week? Use mental math to solve.
      \n\"Envision
      \nAnswer:
      \nNumber of pounds of food the zoo needs to feed one elephant for one week = 735.<\/p>\n

      Explanation:
      \nNumber of pounds of hay every day each elephant at a zoo eats = 100.
      \nNumber of pounds of fruits and vegetables every day each elephant at a zoo eats = 5.
      \n1 Week = 7 days.
      \nNumber of pounds of food the zoo needs to feed one elephant for one week = 7 (Number of pounds of hay every day each elephant at a zoo eats + Number of pounds of fruits and vegetables every day each elephant at a zoo eats)
      \n= 7 (100 + 5)
      \n= (7 \u00d7 100) + (7 \u00d7 5)
      \n= 700 + 35
      \n= 735.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 12.
      \nAshley and 3 friends are planning a trip. The cost of the trip is $599 per person. How much will the trip cost Ashley and her friends? Explain the mental math strategy you used to find the answer.
      \nAnswer:
      \nTotal trip cost\u00a0 of Ashley and her friends = $2396.
      \nThe mental math strategy you used to find the answer is break apart numbers using place value and the Distributive Property.<\/p>\n

      Explanation:
      \nNumber of people planning for a trip =(Ashley and 3 friends) = 1 + 3 = 4.
      \nCost of the trip per person = $599.
      \nTotal trip cost\u00a0 of Ashley and her friends = Number of people planning for a trip \u00d7 Cost of the trip per person
      \n= 4 \u00d7 $599
      \n= (4 \u00d7 500) + (4 \u00d7 99)
      \n= 2000 + 396
      \n= $2396.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 13.
      \nKyle has a rock collection. On Monday, he found 16 new rocks. On Tuesday, he gave 9 rocks to his friends. After giving away the rocks, Kyle had 122 rocks left in his collection. How many rocks did Kyle have to start with?
      \nAnswer:
      \nNumber of rocks Kyle have to start with = 129.<\/p>\n

      Explanation:
      \nNumber of new rocks on Monday, Kyle found = 16.
      \nNumber of rocks on Tuesday, Kyle gave to his friends = 9.
      \nNumber of rocks left in his collection after giving = 122.
      \nNumber of rocks Kyle have to start with = Number of new rocks on Monday, Kyle found – Number of rocks on Tuesday, Kyle gave to his friends + Number of rocks left in his collection after giving
      \n= 16 – 9 + 122
      \n= 7 + 122
      \n= 129.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 14.
      \nCritique Reasoning<\/strong> Quinn used compensation to find the product of 4 \u00d7 307. First, she found 4 \u00d7 300 = 1,200. Then she adjusted the product by subtracting 4 groups of 7 to get her final answer of 1,172. Explain Quinn’s mistake and find the correct answer.
      \nAnswer:
      \n4 \u00d7 307 = 1228 not 1172. Quinn’s mistake is that 4 \u00d7 300 = 1200 is correct yet subtracting\u00a0 did\u00a0 4 groups of 7\u00a0 is wrong, they needed to be added to get the correct answer.<\/p>\n

      Explanation:
      \n4 \u00d7 307 = 4 (300 + 7)
      \n4 \u00d7 307 = (4 \u00d7 300) + (4 \u00d7 7)
      \n4 \u00d7 307 = 1200 + 28
      \n4 \u00d7 307 = 1228.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 15.
      \nHigher Order Thinking<\/strong> Do you think it would be better to use breaking apart and the Distributive Property or compensation to find the product of 5 \u00d7 328? Explain why and show how to find the product.
      \nAnswer:
      \nIt would be better to use breaking apart and the Distributive Property or compensation to find the product of 5 \u00d7 328 because its a big number to do multiplication at once, so breaking them into parts and doing the process helps to get correct answer without any mistakes.<\/p>\n

      Explanation:
      \n5 \u00d7 328 = 5 (300 + 28)
      \n5 \u00d7 328 = (5 \u00d7 300) + (5 \u00d7 28)
      \n5 \u00d7 328 = 1500 + 140
      \n5 \u00d7 328 =1640.<\/p>\n

       <\/p>\n

       <\/p>\n

      Assessment Practice
      \n<\/strong>Question 16.
      \nSelect all of the expressions that show how to use mental math to find the product of 4 \u00d7 27.
      \n\"Envision
      \n\u2610 (4 \u00d7 20) + (4 \u00d7 7)
      \n\u2610 4 \u00d7 (20 \u00d7 7)
      \n\u2610 (4 \u00d7 30) \u2013 (4 \u00d7 3)
      \n\u2610 (4 \u00d7 25) + (4 \u00d7 2)
      \n\u2610 4 \u00d7 2 \u00d7 7
      \nAnswer:
      \nThe expressions that show how to use mental math to find the product of 4 \u00d7 27:
      \n(4 \u00d7 20) + (4 \u00d7 7)
      \n4 \u00d7 (20 \u00d7 7)
      \n(4 \u00d7 30) \u2013 (4 \u00d7 3)
      \n(4 \u00d7 25) + (4 \u00d7 2)<\/p>\n

      Explanation:
      \n4 \u00d7 27 = 4 (20 + 7)
      \n4 \u00d7 27 = (4 \u00d7 20) + (4 \u00d7 7)
      \n4 \u00d7 27 = 80 + 28
      \n4 \u00d7 27 = 108.<\/p>\n

      4 \u00d7 27 = 4 (30 – 3)
      \n4 \u00d7 27 = (4 \u00d7 30) – (4 \u00d7 3)
      \n4 \u00d7 27 = 120 – 12
      \n4 \u00d7 27 = 108.<\/p>\n

      4 \u00d7 27 = 4 (25 + 2)
      \n4 \u00d7 27 = (4 \u00d7 25) + (4 \u00d7 2)
      \n4 \u00d7 27 = 100 + 8
      \n4 \u00d7 27 = 108.<\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

      Lesson 3.7 Choose a Strategy to Multiply<\/h3>\n

      Solve & Share<\/strong>
      \nA cineplex has 4 movie theaters. Each theater has 342 floor seats and 85 mezzanine seats. How many people can the cineplex seat? Solve this problem using any strategy you choose. Explain your solution.
      \nI can… choose an appropriate strategy to multiply.
      \n\"Envision
      \nLook Back! What strategy or strategies did you use to solve this problem? Explain why.
      \nAnswer:
      \nManipulation tools strategy the use of blocks, fruits, balls, or other manipulation tools help students learn the basics of place value, addition, subtraction, and other areas of basic math. It\u00a0is used to solve this problem.
      \nNumber of people in the cineplex seat = 1708.<\/p>\n

      Explanation:
      \nA cineplex has 4 movie theaters. Each theater has 342 floor seats and 85 mezzanine seats. How many people can the cineplex seat.
      \nNumber of floor seats each theater has = 342.
      \nNumber of mezzanine seats each theater has = 85.
      \nNumber of movie theaters a cineplex has = 4.
      \nNumber of people in the cineplex seat = 4 (342 + 85)
      \n= (4 \u00d7 342) + (4 \u00d7 85)
      \n= 1368 + 340
      \n= 1708.<\/p>\n

       <\/p>\n

       <\/p>\n

      Essential Question<\/strong>
      \nWhat Strategy Will You Use to Multiply?
      \nAnswer:
      \nThe Strategy Used to do Multiply\u00a0 is using the place value of the numbers given and do the required operation to solve the problem.<\/p>\n

      Explanation:
      \nThe place value of the numbers given and do the required operation to solve the problem can be followed to multiply.<\/p>\n

       <\/p>\n

       <\/p>\n

      Visual Learning Bridge<\/strong>
      \nPaying for pothole damage to cars can be costly. The table shows the cost of some car repairs. What is the total cost of the repairs?
      \n\"Envision<\/p>\n

      Find the cost for the tires, c.
      \n4 \u00d7 $125 = 0
      \nEstimate: 4 \u00d7 125 is about 4 \u00d7 120 = 480.
      \nBreak apart 125 using place value and the Distributive Property.
      \n4 \u00d7 125 = 4 \u00d7 (100 + 25)
      \n= 4 \u00d7 100 + 4 \u00d7 25
      \n= 400 + 100
      \n= 500
      \nc = 500
      \nThe tire repairs cost $500.<\/p>\n

      Find the cost of the paint, y.
      \n2 \u00d7 $1,450 = y
      \nEstimate: 2 \u00d7 1,450 is about 2 x\u00d7 1,500 = 3,000.
      \nUse an area model and partial products.
      \n\"Envision
      \nTo paint the car costs $2,900.<\/p>\n

      Find the total cost of the repairs, z.
      \n$500 + $2,900 = 2
      \nEstimate: 500 + 2,900 is about 500 + 3,000 = 3,500.
      \nUse compensation to add.
      \n500 + 3,000 = 3,500
      \n3,000 is 100 more than 2,900.
      \nSubtract 100.
      \n3,500 \u2013 100 = 3,400
      \nz = 3,400
      \nThe total cost of the repairs was $3,400.<\/p>\n

      Convince Me! Reasoning Explain why the answers to each part of the problem above are reasonable.
      \nAnswer:
      \nThe total cost of the repairs was $3,400. The answers to each part of the problem above are reasonable because they are correctly solved using all required strategies.<\/p>\n

      Explanation:
      \nThe cost for the tires, c.
      \n4 \u00d7 $125 = c.
      \n4 \u00d7 125 = 4 \u00d7 (100 + 25)
      \n4 \u00d7 125 = 4 \u00d7 100 + 4 \u00d7 25
      \n4 \u00d7 125 = 400 + 100
      \n4 \u00d7 125 = 500.
      \nc = 500
      \nThe tire repairs cost $500.<\/p>\n

      The cost of the paint, y.
      \n2 \u00d7 $1,450 = y
      \n2 \u00d7 1,450 = 2 (1000 + 450)
      \n2 \u00d7 1,450 = (2 \u00d7 1000) + (2 \u00d7 450)
      \n2 \u00d7 1,450 = 2000 + 900
      \n2 \u00d7 1,450 = $2900.<\/p>\n

      The total cost of the repairs, z.
      \nx + y = z.
      \n=> $500 + $2,900
      \n=> $3400.<\/p>\n

       <\/p>\n

      Guided Practice
      \n<\/strong>Do You Understand?<\/strong>
      \nQuestion 1.
      \nA tire shop sells 3 tires that cost $175 each, which includes a fourth tire for free. Is this more or less expensive than buying 4 tires that cost $135 each?
      \nAnswer:
      \nCost of all tires a tire shop sells = $700\u00a0 is more than Cost of all tires = $540.<\/p>\n

      Explanation:
      \nNumber of tires a tire shop sells = 3.
      \nCost of each tire a tire shop sells = $175.
      \nNumber of tires includes a fourth tire for free a tire shop sells = 1.
      \nCost of all tires a tire shop sells = (Number of tires a tire shop sells + Number of tires includes a fourth tire for free a tire shop sells) \u00d7 Cost of each tire a tire shop sells
      \n= (3 + 1) 175
      \n= (3 \u00d7 175) + (1 \u00d7 175)
      \n= 525 + 175
      \n= $700.<\/p>\n

      Number of tires = 4.
      \nCost of each tire = $135.
      \nCost of all tires = Number of tires \u00d7 Cost of each tire
      \n= 4 \u00d7 135
      \n= 4 (100 + 35)
      \n= (4 \u00d7 100) + (4 \u00d7 35)
      \n= 400 + 140
      \n= $540.<\/p>\n

       <\/p>\n

       <\/p>\n

      Do You Know How?<\/strong>
      \nFor 2-5, find each product by choosing an appropriate strategy.
      \nQuestion 2.
      \n\"Envision
      \nAnswer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

      Explanation:
      \n74 \u00d7 6 = (70 \u00d7 6) + (4 \u00d7 6)
      \n74 \u00d7 6 = 420 + 24
      \n74 \u00d7 6 = 444.<\/p>\n

       <\/p>\n

      Question 3.
      \n\"Envision
      \nAnswer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

      Explanation:
      \n819 \u00d7 5 = (800 \u00d7 5) + (19 \u00d7 5)
      \n819 \u00d7 5 = 4000 + 95
      \n819 \u00d7 5 = 4095.<\/p>\n

       <\/p>\n

      Question 4.
      \n4 \u00d7 309
      \nAnswer:
      \n4 \u00d7 309 = 1236.<\/p>\n

      Explanation:
      \n4 \u00d7 309 = (4 \u00d7 300) + (4 \u00d7 9)
      \n4 \u00d7 309 = 1200 + 36
      \n4 \u00d7 309 = 1236.<\/p>\n

       <\/p>\n

      Question 5.
      \n3 \u00d7 354
      \nAnswer:
      \n3 \u00d7 354 = 1062.<\/p>\n

      Explanation:
      \n3 \u00d7 354 = (3 \u00d7 300) + (3 \u00d7 50) + (3 \u00d7 4)
      \n3 \u00d7 354 = 900 + 150 + 12
      \n3 \u00d7 354 = 1050 + 12
      \n3 \u00d7 354 = 1062.<\/p>\n

       <\/p>\n

      Independent Practice
      \n<\/strong>For 6-21, find each product by choosing an appropriate strategy.
      \nQuestion 6.
      \n\"Envision<\/p>\n

      Answer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

      Explanation:
      \n25 \u00d7 6 = (20 \u00d7 6 ) + ( 5 \u00d7 6)
      \n25 \u00d7 6 = 120 + 30
      \n25 \u00d7 6 = 150.<\/p>\n

       <\/p>\n

      Question 7.
      \n\"Envision<\/p>\n

      Answer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

      Explanation:
      \n83 \u00d7 5 = (80 \u00d7 5) + ( 3 \u00d7 5)
      \n83 \u00d7 5 = 400 + 15
      \n83 \u00d7 5 = 415.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 8.
      \n\"Envision<\/p>\n

      Answer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

      Explanation:
      \n62 \u00d7 4 = (60 \u00d7 4) + (2 \u00d7 4)
      \n62 \u00d7 4 = 240 + 8
      \n62 \u00d7 4 = 248.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 9.
      \n\"Envision<\/p>\n

      Answer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

      Explanation:
      \n89 \u00d7 7 = (100 \u00d7 7) – (11 \u00d7 7)
      \n89 \u00d7 7 = 700 – 77
      \n89 \u00d7 7 = 623.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 10.
      \n\"Envision<\/p>\n

      Answer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

      Explanation:
      \n245 \u00d7 3 = (250 \u00d7 3) – (5 \u00d7 3)
      \n245 \u00d7 3 = 750 – 15
      \n245 \u00d7 3 = 735.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 11.
      \n\"Envision<\/p>\n

      Answer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

      Explanation:
      \n318 \u00d7 9 = (300 \u00d7 9) + (18 \u00d7 9)
      \n318 \u00d7 9 = 2700 + 162
      \n318 \u00d7 9 = 2862.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 12.
      \n\"Envision<\/p>\n

      Answer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

      Explanation:
      \n103 \u00d7 5 = (100 \u00d7 5) + (3 \u00d7 5)
      \n103 \u00d7 5 = 500 + 15
      \n103 \u00d7 5 = 515.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 13.
      \n\"Envision<\/p>\n

      Answer:
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

      Explanation:
      \n314 \u00d7 8 = (300 \u00d7 8) + (14 \u00d7 8)
      \n314 \u00d7 8 = 2400 + 112
      \n314 \u00d7 8 = 2512.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 14.
      \n4 \u00d7 4,347
      \nAnswer:
      \n4 \u00d7 4,347 = 17388.<\/p>\n

      Explanation:
      \n4 \u00d7 4,347 = (4 \u00d7 4000) + (4 \u00d7 300) + (4 \u00d7 40) + (4 \u00d7 7)
      \n4 \u00d7 4,347 = 16000 + 1200 + 160\u00a0 + 28
      \n4 \u00d7 4,347 = 17200 + 160\u00a0 + 28
      \n4 \u00d7 4,347 = 17360 + 28
      \n4 \u00d7 4,347 =17388.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 15.
      \n6 \u00d7 2,716
      \nAnswer:
      \n6 \u00d7 2,716 = 16296.<\/p>\n

      Explanation:
      \n6 \u00d7 2,716 = (6 \u00d7 2000) + ( 6 \u00d7 700) + ( 6 \u00d7 10) + (6 \u00d7 6)
      \n6 \u00d7 2,716 = 12000 + 4200 + 60 + 36
      \n6 \u00d7 2,716 = 16200 + 60 + 36
      \n6 \u00d7 2,716 = 16260 + 36
      \n6 \u00d7 2,716 = 16296.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 16.
      \n7 \u00d7 1,287
      \nAnswer:
      \n7 \u00d7 1,287 = 9009.<\/p>\n

      Explanation:
      \n7 \u00d7 1,287 = (7 \u00d7 1000) + (7 \u00d7 200) + (7 \u00d7 80) + (7 \u00d7 7)
      \n7 \u00d7 1,287 = 7000 + 1400 + 560 + 49
      \n7 \u00d7 1,287 = 8400 + 560 + 49
      \n7 \u00d7 1,287 = 8960 + 49
      \n7 \u00d7 1,287 = 9009.<\/p>\n

       <\/p>\n

      Question 17.
      \n3 \u00d7 1,942
      \nAnswer:
      \n3 \u00d7 1,942 = 5826.<\/p>\n

      Explanation:
      \n3 \u00d7 1,942 = (3 \u00d7 1000) + ( 3 \u00d7 900) + (3 \u00d7 40) + (3 \u00d7 2)
      \n3 \u00d7 1,942 = 3000 + 2700 + 120 + 6
      \n3 \u00d7 1,942 = 5700 + 120 + 6
      \n3 \u00d7 1,942 = 5820 + 6
      \n3 \u00d7 1,942 = 5826.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 18.
      \n2,319 \u00d7 5
      \nAnswer:
      \n2,319 \u00d7 5 = 11595.<\/p>\n

      Explanation:
      \n2,319 \u00d7 5 = (2000 \u00d7 5) + (300 \u00d7 5) + (10 \u00d7 5) + (9 \u00d7 5)
      \n2,319 \u00d7 5 = 10000 + 1500 + 50 + 45
      \n2,319 \u00d7 5 =\u00a0 11500 + 50 + 45
      \n2,319 \u00d7 5 = 11550 + 45
      \n2,319 \u00d7 5 = 11595.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 19.
      \n1,467 \u00d7 5
      \nAnswer:
      \n1,467 \u00d7 5 = 7335.<\/p>\n

      Explanation:
      \n1,467 \u00d7 5 = (1000 \u00d7 5) + (400 \u00d7 5) + (60 \u00d7 5) + (7 \u00d7 5)
      \n1,467 \u00d7 5 = 5000 + 2000 + 300 + 35
      \n1,467 \u00d7 5 = 7000 + 300 + 35
      \n1,467 \u00d7 5 = 7300 + 35
      \n1,467 \u00d7 5 = 7335.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 20.
      \n6,006 \u00d7 9
      \nAnswer:
      \n6,006 \u00d7 9 = 54054.<\/p>\n

      Explanation:
      \n6,006 \u00d7 9 = (6000 \u00d7 9) + (6 \u00d7 9)
      \n6,006 \u00d7 9 = 54000 + 54
      \n6,006 \u00d7 9 = 54054.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 21.
      \n9,749 \u00d7 5
      \nAnswer:
      \n9,749 \u00d7 5 = 48745.<\/p>\n

      Explanation:
      \n9,749 \u00d7 5 = (9000 \u00d7 5) + (700 \u00d7 5) + (40 \u00d7 5) + (9 \u00d7 5)
      \n9,749 \u00d7 5 = 45000 + 3500 + 200 + 45
      \n9,749 \u00d7 5 = 48500 + 200 + 45
      \n9,749 \u00d7 5 = 48700 + 45
      \n9,749 \u00d7 5 = 48745.<\/p>\n

       <\/p>\n

       <\/p>\n

      Problem Solving
      \n<\/strong>Question 22.
      \nMake Sense and Persevere<\/strong> Maura’s dance team wants to buy costumes that cost $56 each. They have $523 saved in a fund. How much money will they have left in the fund after they buy 9 costumes?
      \n\"Envision<\/p>\n

      Answer:
      \nAmount of money left in the fund after they buy 9 costumes = $19.<\/p>\n

      Explanation:
      \nCost of each costumes Maura’s dance team wants to buy = $56.
      \nTotal amount saved in fund by Maura’s dance team = $523.
      \nCost of 9 costumes Maura’s dance team wants to buy = 9 \u00d7 Cost of each costumes Maura’s dance team wants to buy
      \n= 9 \u00d7 $56
      \n= (9 \u00d7 50) + (9 \u00d7 6)
      \n= 450 + 54
      \n= $504.
      \nAmount of money left in the fund after they buy 9 costumes = Total amount saved in fund by Maura’s dance team – Cost of 9 costumes Maura’s dance team wants to buy
      \n= $523 – $504
      \n= $19.<\/p>\n

       <\/p>\n

      Question 23.
      \nElaine rents a car for 5 days. It costs $44 each day to rent the car and $7 each day for insurance. At the end of the trip she spends $35 to fill the car with gas. What is the total cost for Elaine to use the car?
      \nAnswer:
      \nTotal cost for Elaine to use the car = $86.<\/p>\n

      Explanation:
      \nNumber of days Elaine rents a car = 5.
      \nCost of renting car each day = $44.
      \nCost of each day for insurance = $7.
      \nCost for filling car with gas = $35.
      \nTotal cost for Elaine to use the car = Cost of renting car each day + Cost of each day for insurance + Cost for filling car with gas
      \n= $44 + $7 + $35
      \n= $51 + $35
      \n= $86.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 24.
      \nAt the Math Club ceremony, there were 17 tables with 8 people seated at each table. Each guest received 2 certificates. How many certificates were distributed at the ceremony?
      \nAnswer:
      \nTotal number of certificates were distributed at the ceremony = 272.<\/p>\n

      Explanation:
      \nNumber of tables at the Math Club ceremony = 17.
      \nNumber of people seated at each table = 8.
      \nNumber of certificates each guest received = 2.
      \nTotal number of people at the Math Club ceremony = Number of tables at the Math Club ceremony \u00d7 Number of people seated at each table
      \n= 17 \u00d7 8
      \n= 136.
      \nTotal number of certificates were distributed at the ceremony = Total number of people at the Math Club ceremony \u00d7 Number of certificates each guest received
      \n= 136 \u00d7 2
      \n= (100 \u00d7 2) + (36 \u00d7 2)
      \n= 200 + 72
      \n= 272.<\/p>\n

       <\/p>\n

       <\/p>\n

      Question 25.
      \nWater erupting from geysers can reach a temperature of 244\u00b0F. The average temperature in Yellowstone National Park is 35\u00b0F. Calculate the difference between these two temperatures.
      \nAnswer:
      \nDifference between these two temperatures = 87\u00b0F.<\/p>\n

      Explanation:
      \nTemperature of Water erupting from geysers = 244\u00b0F
      \nAverage temperature in Yellowstone National Park = 35\u00b0F
      \nAverage temperature of Water erupting from geysers = 244\u00b0F \u00f7 2
      \n= 122\u00b0F
      \nDifference between these two temperatures = Average temperature of Water erupting from geysers \u00a0– Average temperature in Yellowstone National Park
      \n= 122\u00b0F – 35\u00b0F
      \n= 87\u00b0F.<\/p>\n

       <\/p>\n

      Question 26.
      \nHigher Order Thinking<\/strong> On Monday, Paolo sold 21 tickets to the dance. On Tuesday, he sold three times as many tickets as he sold on Monday. On Wednesday, he sold twice as many tickets as he sold on Tuesday. How many total tickets did Paolo sell in the three days?
      \nAnswer:
      \nTotal number of tickets Paolo sells in the three days = 210.<\/p>\n

      Explanation:
      \nNumber of tickets to the dance Paolo sold on Monday = 21.
      \nOn Tuesday, he sold three times as many tickets as he sold on Monday.
      \n=> Number of tickets to the dance Paolo sold on Tuesday = 3 \u00d7 Number of tickets to the dance Paolo sold on Monday
      \n= 3 \u00d7 21
      \n= 63.
      \nOn Wednesday, he sold twice as many tickets as he sold on Tuesday.
      \n=> Number of tickets to the dance Paolo sold on Wednesday = 3 \u00d7 Number of tickets to the dance Paolo sold on Tuesday
      \n=> 2 \u00d7 63
      \n=> 126.
      \nTotal number of tickets Paolo sells in the three days = Number of tickets to the dance Paolo sold on Monday + Number of tickets to the dance Paolo sold on Tuesday + Number of tickets to the dance Paolo sold on Wednesday
      \n= 21 + 63 + 126
      \n= 84 + 126
      \n= 210.<\/p>\n

       <\/p>\n

       <\/p>\n

      Assessment Practice
      \n<\/strong>Question 27.
      \nMr. Tran would like to buy a new sofa that costs $934. He can pay the total all at once, or he can make a $125 payment each month for 8 months. How much less does it cost to pay all at once? Write equations to show how you solve. Tell what your variables represent.
      \n\"Envision
      \nAnswer:
      \n$66 less it costs to pay all at once for Mr. Tran.<\/p>\n

      Explanation:
      \nCost of new sofa Mr. Tran wants to buy = $934.
      \nCost of each month payment = $125.
      \nNumber of months for each month payment = 8.
      \nTotal amount for each month payment = Cost of each month payment \u00d7 Number of months for each month payment
      \n= $125 \u00d7 8
      \n= $1000.
      \nDifference:
      \nTotal amount for each month payment\u00a0 – Cost of new sofa Mr. Tran wants to buy
      \n= $1000 – $934
      \n= $66.<\/p>\n

       <\/p>\n

       <\/p>\n

      Lesson 3.8 Problem Solving<\/h3>\n

      Model with Math<\/strong>
      \nSolve & Share<\/strong>
      \nKevin took 120 color photos and 128 black and white photos on a field trip. Marco took 2 times as many photos as Kevin. How many photos did Marco take? Solve this problem using any strategy you choose. Use the bar diagram to help.
      \nI can … apply the math I know to solve problems.
      \n\"Envision<\/p>\n

      Answer:
      \nNumber of photos Marco took = 496.<\/p>\n

      Explanation:
      \nNumber of color photos Kevin took on a field trip = 120.
      \nNumber of white photos\u00a0 Kevin took on a field trip = 128.
      \nMarco took 2 times as many photos as Kevin.
      \n=> Number of photos Marco took = 2 (Number of color photos Kevin took on a field trip + Number of white photos\u00a0 Kevin took on a field trip)
      \n=> 2\u00a0 (120 + 128)
      \n=> 2 \u00d7 248
      \n=> 496.
      \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

       <\/p>\n

       <\/p>\n

       <\/p>\n

      Thinking Habits<\/strong>
      \nBe a good thinker! These questions can help you.<\/p>\n

        \n
      • How can I use math I know to solve this problem?<\/li>\n
      • How can I use pictures, objects, or an equation to represent the problem?<\/li>\n
      • How can I use numbers, words, and symbols to solve the problem?<\/li>\n<\/ul>\n

        Look Back! Model with Math What representation did you use to solve the problem and show relationships?
        \nAnswer:
        \nNumber of photos Marco took = 2 (Number of color photos Kevin took on a field trip + Number of white photos\u00a0 Kevin took on a field trip)
        \n=> 2\u00a0 (120 + 128)
        \n=> 2 \u00d7 248
        \n=> 496.<\/p>\n

        Explanation:
        \nNumber of color photos Kevin took on a field trip = 120.
        \nNumber of white photos\u00a0 Kevin took on a field trip = 128.
        \nMarco took 2 times as many photos as Kevin.
        \n=> Number of photos Marco took = 2 (Number of color photos Kevin took on a field trip + Number of white photos\u00a0 Kevin took on a field trip)
        \n=> 2\u00a0 (120 + 128)
        \n=> 2 \u00d7 248
        \n=> 496.<\/p>\n

         <\/p>\n

        Essential Question<\/strong>
        \nHow Can You Represent a Situation with a Math Model?
        \nAnswer:
        \nWe can represent a Situation with a Math Model using the given data, knowing what is asked and then solving the problem to find the solution asked for.<\/p>\n

        Explanation:
        \nA mathematical model is a description of a\u00a0system using mathematical\u00a0 concepts and language . The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences and engineering\u00a0 disciplines, as well as in non-physical systems such as the social sciences.<\/p>\n

         <\/p>\n

         <\/p>\n

        Visual Learning Bridge<\/strong>
        \nAn art show uses 9 teams of art judges. If each team judges the work of 13 painters and 14 sculptors, how many artists attend the show?
        \n\"Envision
        \nWhat do you need to find?
        \nI need to find how many artists each team judges.
        \nI need to find the total number of artists.<\/p>\n

        How can I model with math?
        \nI can
        \nuse bar diagrams and equations to represent and solve this problem.
        \ndecide if my results make sense.<\/p>\n

        Here’s my thinking.
        \nFind 9 \u00d7 27.
        \nUse a bar diagram. Write and solve an equation.
        \n\"Envision
        \na = 9 \u00d7 27
        \na = 243
        \nThere are 243 artists at the show.<\/p>\n

        Convince Me! Model with Math How could you decide if your answer makes sense?
        \nAnswer:
        \nNumber of artists attended the show = 243.<\/p>\n

        Explanation:
        \nAn art show uses 9 teams of art judges. If each team judges the work of 13 painters and 14 sculptors, how many artists attend the show?
        \nNumber of teams of art judges an art show uses = 9.
        \nNumber of painters each team judges the work = 13.
        \nNumber of sculptors each team judges the work = 14.
        \nNumber of artists attended the show = Number of teams of art judges an art show uses (Number of painters each team judges the work + Number of sculptors each team judges the work)
        \n= 9 (13 + 14)
        \n= 9 \u00d7 27
        \n= (9 \u00d7 20) + (9 \u00d7 7)
        \n= 180 + 63
        \n= 243.<\/p>\n

         <\/p>\n

         <\/p>\n

        Guided Practice
        \n<\/strong>Model with Math<\/strong>
        \nWhen you model with Sharon’s Stationery Store contains 1,219 boxes of cards. May’s Market contains 3 times as many boxes of cards. How many boxes, b, does May’s Market contain?
        \n\"Envision
        \nQuestion 1.
        \nExplain how to use a picture to represent the problem and show relationships.
        \nAnswer:
        \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

        Explanation:
        \nNumber of boxes of cards Sharon’s Stationery Store contains = 1,219.
        \nMay’s Market contains 3 times as many boxes of cards.
        \nNumber of boxes May’s Market contains = ???<\/p>\n

         <\/p>\n

        Question 2.
        \nWhat equation can you write to represent the problem?
        \nAnswer:
        \nNumber of boxes May’s Market contains = 3 \u00d7 Number of boxes of cards Sharon’s Stationery Store contains
        \n=> 3 \u00d7 1219 = ???<\/p>\n

        Explanation:
        \nNumber of boxes of cards Sharon’s Stationery Store contains = 1,219.
        \nMay’s Market contains 3 times as many boxes of cards.
        \n=> Number of boxes May’s Market contains = 3 \u00d7 Number of boxes of cards Sharon’s Stationery Store contains
        \n=> 3 \u00d7 1219<\/p>\n

         <\/p>\n

        Question 3.
        \nWhat is the solution to the problem?
        \nAnswer:
        \nNumber of boxes May’s Market contains = 3 \u00d7 1219 = 3657.<\/p>\n

        Explanation:
        \nNumber of boxes of cards Sharon’s Stationery Store contains = 1,219.
        \nMay’s Market contains 3 times as many boxes of cards.
        \n=> Number of boxes May’s Market contains = 3 \u00d7 Number of boxes of cards Sharon’s Stationery Store contains
        \n=> 3 \u00d7 1219
        \n=> (3 \u00d7 1000) + (3 \u00d7 200) + (3 \u00d7 10) + (3 \u00d7 9)
        \n=> 3000 + 600 + 30 + 27
        \n=> 3600 + 30 + 27
        \n=> 3630 + 27
        \n=> 3657.<\/p>\n

         <\/p>\n

         <\/p>\n

        Independent Practice
        \n<\/strong>Model with Math<\/strong> Annie has 6 albums of stamps in her stamp collection. Each album contains 440 stamps. How many stamps, does Annie have in her collection? Use Exercises 4-6 to answer the question.
        \nQuestion 4.
        \nDraw a picture and write an equation to represent the problem.
        \nAnswer:
        \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

        Explanation:
        \nNumber of albums of stamps in her stamp collection Annie has = 6.
        \nNumber of stamps each album contains = 440.
        \nTotal number of stamps Annie have in her collection = ???<\/p>\n

         <\/p>\n

         <\/p>\n

        Question 5.
        \nWhat previously learned math can you use to solve the problem?
        \nAnswer:
        \nNumber of albums of stamps in her stamp collection Annie has = 6.
        \nNumber of stamps each album contains = 440.
        \nTotal number of stamps Annie have in her collection = Number of albums of stamps in her stamp collection Annie has \u00d7 Number of stamps each album contains
        \n= 6 \u00d7 440<\/p>\n

        Explanation:
        \nNumber of albums of stamps in her stamp collection Annie has = 6.
        \nNumber of stamps each album contains = 440.
        \nTotal number of stamps Annie have in her collection = Number of albums of stamps in her stamp collection Annie has \u00d7 Number of stamps each album contains
        \n= 6 \u00d7 440<\/p>\n

         <\/p>\n

         <\/p>\n

        Question 6.
        \nWhat is the solution to the problem? Explain why your solution makes sense.
        \nAnswer:
        \nTotal number of stamps Annie have in her collection = 2640.<\/p>\n

        Explanation:
        \nNumber of albums of stamps in her stamp collection Annie has = 6.
        \nNumber of stamps each album contains = 440.
        \nTotal number of stamps Annie have in her collection = Number of albums of stamps in her stamp collection Annie has \u00d7 Number of stamps each album contains
        \n= 6 \u00d7 440
        \n= (6 \u00d7 400) + (6 \u00d7 40)
        \n= 2400 + 240
        \n= 2640.<\/p>\n

         <\/p>\n

         <\/p>\n

        Problem Solving
        \n<\/strong>Performance Task<\/strong>
        \nHauling Fuel A truck like the one shown delivers a load of gasoline to a gas station 3 times a week. The storage tank at the gas station holds 9 loads of fuel. How much more gas does the storage tank hold than the truck?
        \n\"Envision
        \nQuestion 7.
        \nMake Sense and Persevere What do you know and what do you need to determine?
        \nAnswer:
        \nNumber of times a truck delivers a load of gasoline to a gas station a week = 3.
        \nQuantity of loads of fuel a storage tank at the gas station holds = 9.
        \nQuantity of loads of fuel a storage tank holds = 2700 gallons.
        \nQuantity of gas the storage tank holds = ???
        \nQuantity of gas the truck holds = ???<\/p>\n

        Explanation:
        \nKnown information:
        \nNumber of times a truck delivers a load of gasoline to a gas station a week = 3.
        \nQuantity of loads of fuel a storage tank at the gas station holds = 9.
        \nQuantity of loads of fuel a storage tank holds = 2700 gallons.
        \nTo determine:
        \nQuantity of gas the storage tank holds = ???
        \nQuantity of gas the truck holds = ???<\/p>\n

         <\/p>\n

        Question 8.
        \nMake Sense and Persevere What do you need to know to determine how much more the tank holds than the truck?
        \n\"Envision<\/p>\n

        Answer:
        \n16200 gallons more gas the storage tank hold than the truck.<\/p>\n

        Explanation:
        \nNumber of times a truck delivers a load of gasoline to a gas station a week = 3.
        \nQuantity of loads of fuel a storage tank at the gas station holds = 9.
        \nQuantity of loads of fuel a storage tank holds = 2700 gallons.
        \nQuantity of gas the storage tank holds = ???
        \nQuantity of gas the truck holds = ???
        \nQuantity of gas the storage tank holds = Quantity of loads of fuel a storage tank at the gas station holds\u00a0 \u00d7 Quantity of loads of fuel a storage tank holds
        \n= 9 \u00d7 2700
        \n= 9 ( 2000 + 700)
        \n= (9 \u00d7 2000) + (9 \u00d7 700)
        \n= 18000 + 6300
        \n= 24300 gallons.
        \nQuantity of gas the truck holds = Number of times a truck delivers a load of gasoline to a gas station a week\u00a0 \u00d7 Quantity of loads of fuel a storage tank holds
        \n= 3 \u00d7 2700
        \n= 3 ( 2000 + 700)
        \n= (3 \u00d7 2000) + (3 \u00d7 700)
        \n= 6000 + 2100
        \n= 8100 gallons.
        \nDifference:
        \n= Quantity of gas the storage tank holds – Quantity of gas the truck holds
        \n= 24300 – 8100
        \n= 16200 gallons.<\/p>\n

        Question 9.
        \nModel with Math Explain how to use bar diagrams and equations to represent the problem and solve.
        \nAnswer:
        \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

        Explanation:
        \nQuantity of gas the storage tank holds = Quantity of loads of fuel a storage tank at the gas station holds\u00a0 \u00d7 Quantity of loads of fuel a storage tank holds
        \n= 9 \u00d7 2700
        \n= 9 ( 2000 + 700)
        \n= (9 \u00d7 2000) + (9 \u00d7 700)
        \n= 18000 + 6300
        \n= 24300 gallons.
        \nQuantity of gas the truck holds = Number of times a truck delivers a load of gasoline to a gas station a week\u00a0 \u00d7 Quantity of loads of fuel a storage tank holds
        \n= 3 \u00d7 2700
        \n= 3 ( 2000 + 700)
        \n= (3 \u00d7 2000) + (3 \u00d7 700)
        \n= 6000 + 2100
        \n= 8100 gallons.
        \nDifference:
        \n= Quantity of gas the storage tank holds – Quantity of gas the truck holds
        \n= 24300 – 8100
        \n= 16200 gallons.
        \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

         <\/p>\n

         <\/p>\n

        Topic 3 Fluency Practice Activity<\/h3>\n

        Follow the Path<\/strong>
        \nShade a path from START to FINISH. Follow the differences that are correct. You can only move up, down, right, or left.
        \nI can … subtract multi-digit whole numbers.
        \n\"Envision
        \nAnswer:
        \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Topic<\/p>\n

        Explanation:
        \n812 \u2013 44 = 768. (Correct)
        \n621 \u2013 85 = 536. (Correct)
        \n543 \u2013 97 = 446. (Correct)
        \n111 \u2013 87 = 76. (Incorrect)
        \n684 \u2013 485 = 299. (Incorrect)
        \n929 \u2013 879 = 150. (Incorrect)
        \n341 \u2013 299 =\u00a0 142. (Incorrect)
        \n836 \u2013 788 = 48. (Correct)
        \n876 \u2013 55 = 72. (Incorrect)
        \n922 \u2013 87 = 865. (Incorrect)
        \n511 \u2013 423 = 112. (Incorrect)
        \n486 \u2013 230 =256. (Correct)
        \n178 \u2013 98 =80. (Correct)
        \n912 \u2013 842 = 170. (Incorrect)
        \n312 \u2013 219 = 193. (Incorrect)
        \n767 \u2013 31 = 636. (Incorrect)
        \n825 \u2013 789 = 36. (Correct)
        \n123 \u2013 53 = 30. (Incorrect)
        \n282 \u2013 32 = 150. (Incorrect)
        \n986 \u2013 887 = 199. (Incorrect)
        \n698 \u2013 12 = 586. (Incorrect)
        \n333 \u2013 111 = 222. (Correct)
        \n342 \u2013 88 = 254. (Correct)
        \n293 \u2013 95 = 198. (Correct)
        \n876 \u2013 543 = 333. (Correct)<\/p>\n

         <\/p>\n

        Topic 3 Vocabulary Review<\/h3>\n

        Understand Vocabulary
        \nWord List<\/p>\n

          \n
        • \u00a0array<\/li>\n
        • Associative Property of Multiplication<\/li>\n
        • Commutative Property of Multiplication<\/li>\n
        • compensation<\/li>\n
        • Distributive Property<\/li>\n
        • estimate<\/li>\n
        • numerical expression<\/li>\n
        • partial product<\/li>\n<\/ul>\n

          Question 1.
          \nCircle the property shown by 4 \u00d7 (6 + 2) = (4 \u00d7 6) + (4 \u00d7 2).
          \nAssociative
          \nCommutative
          \nDistributive
          \nAnswer:
          \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

          Explanation:
          \nThe property shown by 4 \u00d7 (6 + 2) = (4 \u00d7 6) + (4 \u00d7 2):
          \nAssociative<\/p>\n

           <\/p>\n

          Question 2.
          \nCircle the property shown by 2 \u00d7 134 = 134 \u00d7 2.
          \nAssociative
          \nCommutative
          \nDistributive
          \nAnswer:
          \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

          Explanation:
          \nThe property shown by 2 \u00d7 134 = 134 \u00d7 2:
          \nCommutative<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 3.
          \nCircle the property shown by (1 \u00d7 3) \u00d7 7 = 1 \u00d7 (3 \u00d7 7).
          \nAssociative
          \nCommutative
          \nDistributive
          \nAnswer:
          \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

          Explanation:
          \nThe property shown by (1 \u00d7 3) \u00d7 7 = 1 \u00d7 (3 \u00d7 7):
          \nDistributive<\/p>\n

           <\/p>\n

          Question 4.
          \nDraw a line from each vocabulary word to its example.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

          Explanation:
          \nEach vocabulary word is matched to the examples:
          \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

           <\/p>\n

           <\/p>\n

          Use Vocabulary in Writing<\/strong>
          \nQuestion 5.
          \nFind 4 \u00d7 114. Use at least three terms from the Word List to describe how to find the product.
          \nAnswer:
          \n4 \u00d7 114 = 456.<\/p>\n

          Explanation:
          \n4 \u00d7 114 = ??? { Estimate}
          \n4 \u00d7 114 = (4 \u00d7 100) + (4 \u00d7 10) + (4 \u00d7 4) { numerical expression}
          \n4 \u00d7 114 = 400 + 40+ 16
          \n4 \u00d7 114 = 440 + 16 {partial products}
          \n4 \u00d7 114 = 456.<\/p>\n

           <\/p>\n

           <\/p>\n

          Topic 3 Reteaching<\/h3>\n

          Set A pages 81-84<\/strong><\/p>\n

          Use basic facts, place value, and multiplication properties to multiply by multiples of 10 and 100.
          \nFind 4 \u00d7 60.
          \n4 \u00d7 60 = 4 \u00d7 6 tens
          \n4 \u00d7 60 = (4 \u00d7 6) tens
          \n4 \u00d7 60 = 24 \u00d7 10
          \n4 \u00d7 60 = 240<\/p>\n

          Find 4 \u00d7 600.
          \n4 \u00d7 600 = 4 \u00d7 6 hundreds
          \n4 \u00d7 600 = (4 \u00d7 6) hundreds
          \n4 \u00d7 600 = 24 \u00d7 100
          \n4 \u00d7 600 = 2,400<\/p>\n

          Find 4 \u00d7 6,000.
          \n4 \u00d7 6,000 = 4 \u00d7 6 thousands
          \n4 \u00d7 6,000 = (4 \u00d7 6) thousands
          \n4 \u00d7 6,000 = 24 \u00d7 1,000
          \n4 \u00d7 6,000 = 24,000<\/p>\n

          Remember<\/strong> when the product of a basic fact ends in zero, the answer will have an extra zero.<\/p>\n

          Question 1.
          \n8 \u00d7 60
          \nAnswer:
          \n8 \u00d7 60 = 480.<\/p>\n

          Explanation:
          \n8 \u00d7 60 = (8 \u00d7 6) tens
          \n8 \u00d7 60 = 48 tens
          \n8 \u00d7 60 = 48 \u00d7 10
          \n8 \u00d7 60 = 480.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 2.
          \n3 \u00d7 10
          \nAnswer:
          \n3 \u00d7 10 = 30.<\/p>\n

          Explanation:
          \n3 \u00d7 10 = (3 \u00d7 1) tens
          \n3 \u00d7 10 = 3 tens
          \n3 \u00d7 10 = 3 \u00d7 10
          \n3 \u00d7 10 = 30.<\/p>\n

           <\/p>\n

          Question 3.
          \n6 \u00d7 50
          \nAnswer:
          \n6 \u00d7 50 = 300.<\/p>\n

          Explanation:
          \n6 \u00d7 50 = (6 \u00d7 5) tens
          \n6 \u00d7 50 = 30 tens
          \n6 \u00d7 50 = 30 \u00d7 10
          \n6 \u00d7 50 = 300.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 4.
          \n5 \u00d7 300
          \nAnswer:
          \n5 \u00d7 300 = 1500.<\/p>\n

          Explanation:
          \n5 \u00d7 300 = (5 \u00d7 3) hundreds
          \n5 \u00d7 300 = 15 \u00d7 hundreds
          \n5 \u00d7 300 = 15 \u00d7 100
          \n5 \u00d7 300 = 1500.<\/p>\n

           <\/p>\n

          Question 5.
          \n7,000 \u00d7 4
          \nAnswer:
          \n7,000 \u00d7 4 = 28000.<\/p>\n

          Explanation:
          \n7,000 \u00d7 4 = thousands (7 \u00d7 4)
          \n7,000 \u00d7 4 = thousands\u00a0 \u00d7 28
          \n7,000 \u00d7 4 = 1000 \u00d7 28
          \n7,000 \u00d7 4 = 28000.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 6.
          \n2 \u00d7 900
          \nAnswer:
          \n2 \u00d7 900 = 1800.<\/p>\n

          Explanation:
          \n2 \u00d7 900 = (2 \u00d7 9) hundreds
          \n2 \u00d7 900 = 18 \u00d7 hundreds
          \n2 \u00d7 900 = 18 \u00d7 100
          \n2 \u00d7 900 = 1800.<\/p>\n

           <\/p>\n

          Question 7.
          \n80 \u00d7 8
          \nAnswer:
          \n80 \u00d7 8 = 640.<\/p>\n

          Explanation:
          \n80 \u00d7 8 = tens (8 \u00d7 8)
          \n80 \u00d7 8 = tens \u00d7 64
          \n80 \u00d7 8 = 10 \u00d7 64
          \n80 \u00d7 8 = 640.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 8.
          \n400 \u00d7 5
          \nAnswer:
          \n400 \u00d7 5 = 2000.<\/p>\n

          Explanation:
          \n400 \u00d7 5 = hundreds (4 \u00d7 5)
          \n400 \u00d7 5 = hundreds \u00d7 20
          \n400 \u00d7 5 = 100 \u00d7 20
          \n400 \u00d7 5 = 2000.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 9.
          \n30 \u00d7 9
          \nAnswer:
          \n30 \u00d7 9 = 270.<\/p>\n

          Explanation:
          \n30 \u00d7 9 = tens ( 3 \u00d7 9)
          \n30 \u00d7 9 = tens \u00d7 27
          \n30 \u00d7 9 = 10 \u00d7 27
          \n30 \u00d7 9 = 270.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 10.
          \n5 \u00d7 8,000
          \nAnswer:
          \n5 \u00d7 8,000 = 40000.<\/p>\n

          Explanation:
          \n5 \u00d7 8,000 = (5 \u00d7 8) thousands
          \n5 \u00d7 8,000 = 40 \u00d7\u00a0thousands
          \n5 \u00d7 8,000 = 40 \u00d7 1000
          \n5 \u00d7 8,000 = 40000.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 11.
          \n700 \u00d7 8
          \nAnswer:
          \n700 \u00d7 8 = 5600.<\/p>\n

          Explanation:
          \n700 \u00d7 8 = hundreds (7 \u00d7 8)
          \n700 \u00d7 8 = hundreds \u00d7 56
          \n700 \u00d7 8 = 100 \u00d7 56
          \n700 \u00d7 8 = 5600.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 12.
          \n9,000 \u00d7 6
          \nAnswer:
          \n9,000 \u00d7 6 = 54000.<\/p>\n

          Explanation:
          \n9,000 \u00d7 6 = thousands (9 \u00d7 6)
          \n9,000 \u00d7 6 = thousands \u00d7 54
          \n9,000 \u00d7 6 = 1000 \u00d7 54
          \n9,000 \u00d7 6 = 54000.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 13.
          \n7 \u00d7 9,000
          \nAnswer:
          \n7 \u00d7 9,000 = 63000.<\/p>\n

          Explanation:
          \n7 \u00d7 9,000 = (7 \u00d7 9) thousands
          \n7 \u00d7 9,000 = 63 \u00d7 thousands
          \n7 \u00d7 9,000 = 63 \u00d7 1000
          \n7 \u00d7 9,000 = 63000.<\/p>\n

           <\/p>\n

          Question 14.
          \n5 \u00d7 100
          \nAnswer:
          \n5 \u00d7 100 = 500.<\/p>\n

          Explanation:
          \n5 \u00d7 100 = (5 \u00d7 1) hundreds
          \n5 \u00d7 100 = 5 \u00d7 hundreds
          \n5 \u00d7 100 = 5 \u00d7 100
          \n5 \u00d7 100 = 500.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 15.
          \n20 \u00d7 5
          \nAnswer:
          \n20 \u00d7 5 = 100.<\/p>\n

          Explanation:
          \n20 \u00d7 5 = tens (2 \u00d7 5)
          \n20 \u00d7 5 = tens \u00d7 10
          \n20 \u00d7 5 = 10 \u00d7 10
          \n20 \u00d7 5 = 100.<\/p>\n

           <\/p>\n

          Question 16.
          \n5 \u00d7 4,000
          \nAnswer:
          \n5 \u00d7 4,000 = 20000.<\/p>\n

          Explanation:
          \n5 \u00d7 4,000 = (5 \u00d7 4) thousands
          \n5 \u00d7 4,000 = 20 \u00d7 thousands
          \n5 \u00d7 4,000 = 20 \u00d7 1000
          \n5 \u00d7 4,000 = 20000.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 17.
          \n5 \u00d7 500
          \nAnswer:
          \n5 \u00d7 500 = 2500.<\/p>\n

          Explanation:
          \n5 \u00d7 500 = (5 \u00d7 5) hundreds
          \n5 \u00d7 500 = 25 \u00d7 hundreds
          \n5 \u00d7 500 = 25 \u00d7 100
          \n5 \u00d7 500 = 2500.<\/p>\n

           <\/p>\n

          Question 18.
          \n3 \u00d7 2,000
          \nAnswer:
          \n3 \u00d7 2,000 = 6000.<\/p>\n

          Explanation:
          \n3 \u00d7 2,000 = (3 \u00d7 2) thousands
          \n3 \u00d7 2,000 = 6 \u00d7 thousands
          \n3 \u00d7 2,000 = 6 \u00d7 1000
          \n3 \u00d7 2,000 = 6000.<\/p>\n

           <\/p>\n

           <\/p>\n

          Set B pages 85-88
          \n<\/strong>Use rounding to estimate 9 \u00d7 1,993.
          \nRound 1,993 to 2,000.
          \n\"Envision
          \nSo, 9 \u00d7 1,993 is about 18,000.<\/p>\n

          Remember<\/strong> to round a three-digit number to the nearest hundred and a four-digit number to the nearest thousand.<\/p>\n

          Estimate each product.
          \nQuestion 1.
          \n8 \u00d7 7,632
          \nAnswer:
          \n8 \u00d7 7,632 is about 64000.<\/p>\n

          Explanation:
          \n8 \u00d7 7,632 = ?????
          \nRounding 7632 to nearest thousand.
          \n=> 8 \u00d7 7,632 = 8 \u00d7 8000
          \n=> 8 \u00d7 7,632 =\u00a0 64000.<\/p>\n

           <\/p>\n

          Question 2.
          \n493 \u00d7 3
          \nAnswer:
          \n493 \u00d7 3 is about 1500.<\/p>\n

          Explanation:
          \n493 \u00d7 3 = ????
          \nRounding 493 to nearest hundred.
          \n=> 493 \u00d7 3 = 500 \u00d7 3
          \n=> 493 \u00d7 3 = 1500.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 3.
          \n9,379 \u00d7 5
          \nAnswer:
          \n9,379 \u00d7 5 is about 45000.<\/p>\n

          Explanation:
          \n9,379 \u00d7 5 = ?????
          \nRounding 9379 to nearest thousand.
          \n=> 9,379 \u00d7 5 = 9000 \u00d7 5
          \n=> 9,379 \u00d7 5 = 45000.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 4.
          \n678 \u00d7 6
          \nAnswer:
          \n678 \u00d7 6 is about 4200.<\/p>\n

          Explanation:
          \n678 \u00d7 6 = ????
          \nRounding 678 to nearest hundred.
          \n=> 678 \u00d7 6 = 700 \u00d7 6
          \n=> 678 \u00d7 6 = 4200.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 5.
          \n707 \u00d7 4
          \nAnswer:
          \n707 \u00d7 4 is about 2800.<\/p>\n

          Explanation:
          \n707 \u00d7 4 = ????
          \nRounding 707 to nearest hundred.
          \n=> 707 \u00d7 4 = 700 \u00d7 4
          \n=> 707 \u00d7 4 = 2800.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 6.
          \n5,703 \u00d7 3
          \nAnswer:
          \n5,703 \u00d7 3 is about 18000.<\/p>\n

          Explanation:
          \n5,703 \u00d7 3 = ?????
          \nRounding 5703 to nearest thousand.
          \n=> 5,703 \u00d7 3 = 6000 \u00d7 3
          \n=> 5,703 \u00d7 3 = 18000.<\/p>\n

           <\/p>\n

          Question 7.
          \n483 \u00d7 6
          \nAnswer:
          \n483 \u00d7 6 is about 3000.<\/p>\n

          Explanation:
          \n483 \u00d7 6 = ????
          \nRounding 483 to nearest hundred.
          \n=> 483 \u00d7 6 = 500 \u00d7 6
          \n=> 483 \u00d7 6 = 3000.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 8.
          \n6 \u00d7 8,166
          \nAnswer:
          \n6 \u00d7 8,166 is about 48000.<\/p>\n

          Explanation:
          \n6 \u00d7 8,166 = ?????
          \nRounding 9379 to nearest thousand.
          \n=> 6 \u00d7 8,166 = 6 \u00d7 8000
          \n=> 6 \u00d7 8,166 = 48000.<\/p>\n

           <\/p>\n

           <\/p>\n

          Set C pages 89-92
          \n<\/strong>Use an array and partial products to find 3 \u00d7 121.
          \n\"Envision<\/p>\n

          Remember<\/strong> to line up the partial products carefully.<\/p>\n

          Question 1.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

          Explanation:
          \n75 \u00d7 5 = (70 \u00d7 5) + ( 5 \u00d7 5)
          \n75 \u00d7 5 = 350 + 25
          \n75 \u00d7 5 = 375.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 2.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

          Explanation:
          \n253 \u00d7 4 = (200 \u00d7 4) + ( 50 \u00d7 4) + (3 \u00d7 4)
          \n253 \u00d7 4 = 800 + 200 + 12
          \n253 \u00d7 4 = 1000 + 12
          \n253 \u00d7 4 = 1012.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 3.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

          Explanation:
          \n214 \u00d7 7 = (200 \u00d7 7) + (10 \u00d7 7) + (4 \u00d7 7)
          \n214 \u00d7 7 = 1400 + 70 + 28
          \n214 \u00d7 7 = 1470 + 28
          \n214 \u00d7 7 = 1498.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 4.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

          Explanation:
          \n1341 \u00d7 7 = (1000 \u00d7 7) + (300 \u00d7 7) + (40 \u00d7 7) + (1 \u00d7 7)
          \n1341 \u00d7 7 = 7000 + 2100 + 280 + 7
          \n1341 \u00d7 7 = 9100 + 280 + 7
          \n1341 \u00d7 7 = 9380 + 7
          \n1341 \u00d7 7 = 9387.<\/p>\n

           <\/p>\n

           <\/p>\n

           <\/p>\n

          Set D pages 93-96
          \n<\/strong>Use the Distributive Property to find 5 \u00d7 45.
          \nUse place value to break apart 45 as 40 + 5.
          \n\"Envision
          \nUse the Distributive Property:
          \n5 \u00d7 45 = 5 \u00d7 (40 + 5)
          \n= (5 \u00d7 40) + (5 \u00d7 5)
          \n= 200 + 25
          \n= 225
          \nSo, 5 \u00d7 45 = 225.<\/p>\n

          Remember<\/strong> that you can use the Distributive Property to help multiply larger numbers.<\/p>\n

          Question 1.
          \n7 \u00d7 45
          \nAnswer:
          \n7 \u00d7 45 = 315.<\/p>\n

          Explanation:
          \n7 \u00d7 45 = 7 \u00d7 (40 + 5)
          \n= (7 \u00d7 40) + (7 \u00d7 5)
          \n= 280+ 35
          \n= 315.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 2.
          \n326 \u00d7 9
          \nAnswer:
          \n326 \u00d7 9 = 2934.<\/p>\n

          Explanation:
          \n326 \u00d7 9 = (300 + 26)\u00a0 9
          \n= (300 \u00d7 9) + (26 \u00d7 9)
          \n= 2700 + 234
          \n= 2934.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 3.
          \n720 \u00d7 6
          \nAnswer:
          \n720 \u00d7 6 = 4320.<\/p>\n

          Explanation:
          \n720 \u00d7 6 = (700 + 20) 6
          \n= (700 \u00d7 6) + (20 \u00d7 6)
          \n= 4200 + 120
          \n= 4320.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 4.
          \n3 \u00d7 46
          \nAnswer:
          \n3 \u00d7 46 = 138.<\/p>\n

          Explanation:
          \n3 \u00d7 46 = 3 ( 40 + 6)
          \n= (3 \u00d7 40) + (3 \u00d7 6)
          \n= 120 + 18
          \n= 138.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 5.
          \n371 \u00d7 8
          \nAnswer:
          \n371 \u00d7 8 = 2968.<\/p>\n

          Explanation:
          \n371 \u00d7 8 = (300 + 71) 8
          \n= (300 \u00d7 8) + (71 \u00d7 8)
          \n= 2400 + 568
          \n= 2968.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 6.
          \n5 \u00d7 95
          \nAnswer:
          \n5 \u00d7 95 = 475.<\/p>\n

          Explanation:
          \n5 \u00d7 95 = 5 ( 90 + 5)
          \n= (5 \u00d7 90) + (5 \u00d7 5)
          \n= 450 + 25
          \n= 475.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 7.
          \n88 \u00d7 3
          \nAnswer:
          \n88 \u00d7 3 = 264.<\/p>\n

          Explanation:
          \n88 \u00d7 3 = (80 + 8) 3
          \n= (80 \u00d7 3) + ( 8 \u00d7 3)
          \n= 240 + 24
          \n= 264.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 8.
          \n4 \u00d7 1,865
          \nAnswer:
          \n4 \u00d7 1,865 = 7460.<\/p>\n

          Explanation:
          \n4 \u00d7 1,865 = 4 ( 1000 + 800 + 60 + 5)
          \n= (4 \u00d7 1000) + ( 4 \u00d7 800) + (4 \u00d7 60) + (4 \u00d7 5)
          \n= 4000 + 3200 + 240 + 20
          \n= 7200 + 240 + 20
          \n= 7440 + 20
          \n= 7460.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 9.
          \n57 \u00d7 3
          \nAnswer:
          \n57 \u00d7 3 = 171.<\/p>\n

          Explanation:
          \n57 \u00d7 3 = (50 + 7) 3
          \n= (50 \u00d7 3) + ( 7 \u00d7 3)
          \n= 150 + 21
          \n= 171.<\/p>\n

           <\/p>\n

          Question 10.
          \n209 \u00d7 7
          \nAnswer:
          \n209 \u00d7 7 = 1463.<\/p>\n

          Explanation:
          \n209 \u00d7 7 = (200 + 9) 7
          \n= (200 \u00d7 7) + (9 \u00d7 7)
          \n= 1400 + 63
          \n= 1463.<\/p>\n

           <\/p>\n

           <\/p>\n

          Set E pages 97-100
          \n<\/strong>All your strategies may be used to find larger products.
          \nUse the Distributive Property to find 3 \u00d7 1,275.
          \nUse expanded notation and place value to construct an area model. 1,000
          \n\"Envision<\/p>\n

          Remember<\/strong> to estimate to check that your answer is reasonable.<\/p>\n

          Question 1.
          \n1,468 \u00d7 4
          \nAnswer:
          \n1,468 \u00d7 4 = 5872.<\/p>\n

          Explanation:
          \n1,468 \u00d7 4 = (1000 + 400 + 60 + 8) 4
          \n1,468 \u00d7 4 = (1000 \u00d7 4) + (400 \u00d7 4) + ( 60 \u00d7 4) + (8 \u00d7 4)
          \n1,468 \u00d7 4 = 4000 + 1600 + 240 + 32
          \n1,468 \u00d7 4 = 5600 + 240 + 32
          \n1,468 \u00d7 4 = 5840 + 32
          \n1,468 \u00d7 4 = 5872.
          \nCheck:
          \n??? \u00d7 4 = 5872
          \n= ??? = 5872 \u00f7 4
          \n= ??? = 1468. (Answer is reasonable)<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 2.
          \n361 \u00d7 3
          \nAnswer:
          \n361 \u00d7 3 = 1083.<\/p>\n

          Explanation:
          \n361 \u00d7 3 = (300 + 60 + 1) 3
          \n361 \u00d7 3 = (300 \u00d7 3) + (60 \u00d7 3) + (1 \u00d7 3)
          \n361 \u00d7 3 = 900 + 180 + 3
          \n361 \u00d7 3 = 1080 + 3
          \n361 \u00d7 3 = 1083.
          \nCheck:
          \n??? \u00d7 3 = 1083.
          \n??? = 1083 \u00f7 3
          \n??? = 361. (Answer is reasonable)<\/span><\/p>\n

           <\/p>\n

           <\/p>\n

           <\/p>\n

          Question 3.
          \n25 \u00d7 7
          \nAnswer:
          \n25 \u00d7 7 = 175.<\/p>\n

          Explanation:
          \n25 \u00d7 7 = (20 + 5) 7
          \n25 \u00d7 7 = (20 \u00d7 7) + (5 \u00d7 7)
          \n25 \u00d7 7 = 140 + 35
          \n25 \u00d7 7 = 175.
          \nCheck:
          \n?? \u00d7 7 = 175.
          \n=> ??= 175 \u00f7 7
          \n=> ?? = 25. (Answer is reasonable)<\/span><\/p>\n

           <\/p>\n

           <\/p>\n

          Question 4.
          \n2,189 \u00d7 7
          \nAnswer:
          \n2,189 \u00d7 7 = 15323.<\/p>\n

          Explanation:
          \n2,189 \u00d7 7 = (2000 + 100 + 80 + 9) 7
          \n2,189 \u00d7 7 = (2000 \u00d7 7) + ( 100\u00d7 7) + (80 \u00d7 7) + ( 9 \u00d7 7)
          \n2,189 \u00d7 7 = 14000 + 700 + 560 + 63
          \n2,189 \u00d7 7 = 14700 + 560 + 63
          \n2,189 \u00d7 7 =\u00a0 15260 + 63
          \n2,189 \u00d7 7 = 15323.
          \nCheck:
          \n???? \u00d7 7 = 15323.
          \n???? = 15323 \u00f7 7
          \n???? = 2189. (Answer is reasonable)<\/span><\/p>\n

           <\/p>\n

           <\/p>\n

          Question 5.
          \n6 \u00d7 987
          \nAnswer:
          \n6 \u00d7 987 = 5922.<\/p>\n

          Explanation:
          \n6 \u00d7 987 = 6 ( 900 + 80 + 7)
          \n6 \u00d7 987 = (6 \u00d7 900) + (6 \u00d7 80) + (6 \u00d7 7)
          \n6 \u00d7 987 = 5400 + 480 + 42
          \n6 \u00d7 987 = 5880 + 42
          \n6 \u00d7 987 = 5922.
          \nCheck:
          \n6 \u00d7 ??? = 5922.
          \n??? = 5922 \u00f7 6
          \n??? = 987.(Answer is reasonable)<\/span><\/p>\n

           <\/p>\n

           <\/p>\n

          Question 6.
          \n8 \u00d7 22
          \nAnswer:
          \n8 \u00d7 22 = 176.<\/p>\n

          Explanation:
          \n8 \u00d7 22 =\u00a0 8 (20 + 2)
          \n8 \u00d7 22 = (8 \u00d7 20) + (8 \u00d7 2)
          \n8 \u00d7 22 = 160 + 16
          \n8 \u00d7 22 = 176.\u00a0(Answer is reasonable)<\/span><\/p>\n

           <\/p>\n

           <\/p>\n

          Question 7.
          \n763 \u00d7 5
          \nAnswer:
          \n763 \u00d7 5 = 3815.<\/p>\n

          Explanation:
          \n763 \u00d7 5 = (700 + 60 + 3) 5
          \n763 \u00d7 5 = (700 \u00d7 5) + (60 \u00d7 5) + (3 \u00d7 5)
          \n763 \u00d7 5 = 3500 + 300 + 15
          \n763 \u00d7 5 = 3800 + 15
          \n763 \u00d7 5 = 3815.\u00a0(Answer is reasonable)<\/span><\/p>\n

           <\/p>\n

           <\/p>\n

          Question 8.
          \n14 \u00d7 9
          \nAnswer:
          \n14 \u00d7 9 = 126.<\/p>\n

          Explanation:
          \n14 \u00d7 9 = (10 + 4) 9
          \n14 \u00d7 9 = (10 \u00d7 9) + (4 \u00d7 9)
          \n14 \u00d7 9 = 90 + 36
          \n14 \u00d7 9 = 126.\u00a0(Answer is reasonable)<\/span><\/p>\n

           <\/p>\n

           <\/p>\n

          Question 9.
          \n171 \u00d7 8
          \nAnswer:
          \n171 \u00d7 8 = 1368.<\/p>\n

          Explanation:
          \n171 \u00d7 8 = (100 + 70 + 1) 8
          \n171 \u00d7 8 = (100 \u00d7 8) + (70 \u00d7 8) + (1 \u00d7 8)
          \n171 \u00d7 8 = 800 + 560 + 8
          \n171 \u00d7 8 = 1360 + 8
          \n171 \u00d7 8 = 1368.\u00a0(Answer is reasonable)<\/span><\/p>\n

           <\/p>\n

           <\/p>\n

          Question 10.
          \n22 \u00d7 9
          \nAnswer:
          \n22 \u00d7 9 = 198.<\/p>\n

          Explanation:
          \n22 \u00d7 9 = (20 + 2) 9
          \n22 \u00d7 9 = (20 \u00d7 9) + (2 \u00d7 9)
          \n22 \u00d7 9 = 180 + 18
          \n22 \u00d7 9 = 198.\u00a0(Answer is reasonable)<\/span><\/p>\n

           <\/p>\n

           <\/p>\n

          Question 11.
          \n1,409 \u00d7 5
          \nAnswer:
          \n1,409 \u00d7 5 = 7045.<\/p>\n

          Explanation:
          \n1,409 \u00d7 5 = (1000 + 400 + 9) 5
          \n1,409 \u00d7 5 = (1000 \u00d7 5) + (400 \u00d7 5) + (9 \u00d7 5)
          \n1,409 \u00d7 5 = 5000 + 2000 + 45
          \n1,409 \u00d7 5 = 7000 + 45
          \n1,409 \u00d7 5 =\u00a0 7045.\u00a0(Answer is reasonable)<\/span><\/p>\n

           <\/p>\n

           <\/p>\n

          Question 12.
          \n17 \u00d7 6
          \nAnswer:
          \n17 \u00d7 6 = 102.<\/p>\n

          Explanation:
          \n17 \u00d7 6 = (10 + 7) 6
          \n17 \u00d7 6 = (10 \u00d7 6) + (7 \u00d7 6)
          \n17 \u00d7 6 = 60 + 42
          \n17 \u00d7 6 = 102.\u00a0(Answer is reasonable)<\/span><\/p>\n

           <\/p>\n

           <\/p>\n

           <\/p>\n

           <\/p>\n

          Set F pages 101-104
          \n<\/strong>You can use properties of operations or compensation to multiply mentally.
          \nUse the Commutative and Associative Properties to find 8 \u00d7 50.
          \n8 \u00d7 50 = (2 \u00d7 4) 50
          \n= (4 \u00d7 2) \u00d7 50
          \n= 4 \u00d7 (2 \u00d7 50)
          \n= 4 \u00d7 100
          \n= 400
          \nUse compensation to find 9 \u00d7 67.
          \nThink: 67 = 70 – 3
          \nMultiply mentally 9 \u00d7 70.
          \n9 \u00d7 70 = 630
          \nAdjust by subtracting
          \n9 \u00d7 3, or 27.
          \nSubtract: 630 \u2013 27 = 603
          \nSo, 9 \u00d7 67 = 603.<\/p>\n

          Remember<\/strong> that you can use diagrams or properties of operations to help multiply mentally<\/p>\n

          Question 1.
          \n18 \u00d7 2
          \nAnswer:
          \n18 \u00d7 2 = 36.<\/p>\n

          Explanation:
          \n18 \u00d7 2 = (10 + 8) 2
          \n18 \u00d7 2 = (10 \u00d7 2) + (8 \u00d7 2)
          \n18 \u00d7 2 = 20 + 16
          \n18 \u00d7 2 = 36.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 2.
          \n48 \u00d7 5
          \nAnswer:
          \n48 \u00d7 5 = 240.<\/p>\n

          Explanation:
          \n48 \u00d7 5 = (50 – 2) 5
          \n48 \u00d7 5 = (50 \u00d7 5) – (2 \u00d7 5)
          \n48 \u00d7 5 = 250 – 10
          \n48 \u00d7 5 = 240.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 3.
          \n52 \u00d7 7
          \nAnswer:
          \n52 \u00d7 7 = 364.<\/p>\n

          Explanation:
          \n52 \u00d7 7 = (50 + 2) 7
          \n52 \u00d7 7 = (50 \u00d7 7) + (2 \u00d7 7)
          \n52 \u00d7 7 = 350 + 14
          \n52 \u00d7 7 = 364.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 4.
          \n33 \u00d7 6
          \nAnswer:
          \n33 \u00d7 6 = 198.<\/p>\n

          Explanation:
          \n33 \u00d7 6 = (30 + 3) 6
          \n33 \u00d7 6 = (30 \u00d7 6) + (3 \u00d7 6)
          \n33 \u00d7 6 = 180 + 18
          \n33 \u00d7 6 = 198.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 5.
          \n97 \u00d7 7
          \nAnswer:
          \n97 \u00d7 7 = 679.<\/p>\n

          Explanation:
          \n97 \u00d7 7 = (100 – 3) 7
          \n97 \u00d7 7 = (100 \u00d7 7) – (3 \u00d7 7)
          \n97 \u00d7 7 = 700 – 21
          \n97 \u00d7 7 = 679.<\/p>\n

           <\/p>\n

           <\/p>\n

           <\/p>\n

          Question 6.
          \n88 \u00d7 4
          \nAnswer:
          \n88 \u00d7 4 = 352.<\/p>\n

          Explanation:
          \n88 \u00d7 4 = (90 – 2) 4
          \n88 \u00d7 4 = (90 \u00d7 4) – (2 \u00d7 4)
          \n88 \u00d7 4 = 360 -8
          \n88 \u00d7 4 = 352.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 7.
          \n239 \u00d7 4
          \nAnswer:
          \n239 \u00d7 4 = 956.<\/p>\n

          Explanation:
          \n239 \u00d7 4 = (200 + 30 + 9) 4
          \n239 \u00d7 4 = (200 \u00d7 4) + (30 \u00d7 4) + (9 \u00d7 4)
          \n239 \u00d7 4 = 800 + 120 + 36
          \n239 \u00d7 4 = 920 + 36
          \n239 \u00d7 4 = 956.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 8.
          \n148 \u00d7 5
          \nAnswer:
          \n148 \u00d7 5 = 740.<\/p>\n

          Explanation:
          \n148 \u00d7 5 = (100 + 40 + 8) 5
          \n148 \u00d7 5 = (100 \u00d7 5) + (40 \u00d7 5) + (8 \u00d7 5)
          \n148 \u00d7 5 = 500 + 200 + 40
          \n148 \u00d7 5 = 700 + 40
          \n148 \u00d7 5 = 740.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 9.
          \n233 \u00d7 6
          \nAnswer:
          \n233 \u00d7 6 = 1398.<\/p>\n

          Explanation:
          \n233 \u00d7 6 = (200 + 30 + 3) 6
          \n233 \u00d7 6 = (200 \u00d7 6) + (30 \u00d7 6) + (3 \u00d7 6)
          \n233 \u00d7 6 = 1200 + 180 + 18
          \n233 \u00d7 6 = 1380 + 18
          \n233 \u00d7 6 = 1398.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 10.
          \n937 \u00d7 7
          \nAnswer:
          \n937 \u00d7 7 = 6559.<\/p>\n

          Explanation:
          \n937 \u00d7 7 = (900 + 30 + 7) 7
          \n937 \u00d7 7 = (900 \u00d7 7) + (30 \u00d7 7) + (7 \u00d7 7)
          \n937 \u00d7 7 = 6300 + 210 + 49
          \n937 \u00d7 7 = 6510 + 49
          \n937 \u00d7 7 = 6559.<\/p>\n

           <\/p>\n

           <\/p>\n

           <\/p>\n

          Set G pages 105-108
          \n<\/strong>You can use the strategy that fits the problem best. You know place-value strategies, the Distributive Property, area models, and compensation.
          \nPlace value: 8 \u00d7 359 = 8 \u00d7 3 hundreds + 8 \u00d7 5 tens + 8 \u00d7 9 ones<\/p>\n

          The Distributive Property: 7 \u00d7 4,056 = 7 \u00d7 (4,000 + 50 + 6)
          \n= (7 \u00d7 4,000) + (7 \u00d7 50) + (7 \u00d7 6)<\/p>\n

          Compensation: 6 \u00d7 495
          \n(6 \u00d7 500) \u2013 (6 \u00d7 5)<\/p>\n

          Remember<\/strong> to use an estimate to check if your answer is reasonable.<\/p>\n

          Question 1.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

          Explanation:
          \n43 \u00d7 8 = (40 + 3) 8
          \n43 \u00d7 8 = (40 \u00d7 8) + (3 \u00d7 8)
          \n43 \u00d7 8 = 320 + 24
          \n43 \u00d7 8 = 344.
          \nCheck:
          \n?? \u00d7 8 = 344.
          \n=> ?? = 344 \u00f7 8
          \n=> ?? = 43.<\/p>\n

           <\/p>\n

          Question 2.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

          Explanation:
          \n57 \u00d7 9 = (60 – 3) 9
          \n57 \u00d7 9 = (60 \u00d7 9) – (3 \u00d7 9)
          \n57 \u00d7 9 = 540 – 27
          \n57 \u00d7 9 = 513.
          \nCheck:
          \n?? \u00d7 9 = 513.
          \n=> ?? = 513 \u00f7 9
          \n=> ??\u00a0 = 57.<\/p>\n

           <\/p>\n

           <\/p>\n

           <\/p>\n

          Question 3.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

          Explanation:
          \n215 \u00d7 7 = (200 + 10 + 5) 7
          \n215 \u00d7 7 = (200 \u00d7 7) + (10 \u00d7 7) + (5 \u00d7 7)
          \n215 \u00d7 7 = 1400 + 70 + 35
          \n215 \u00d7 7 = 1470 + 35
          \n215 \u00d7 7 = 1505.
          \nCheck:
          \n?? \u00d7 7 = 1505.
          \n=> ?? = 1505 \u00f7 7
          \n=> ??\u00a0 = 215.<\/p>\n

           <\/p>\n

          Question 4.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

          Explanation:
          \n869 \u00d7 2 = (800 + 60 + 9)\u00a0 2
          \n869 \u00d7 2 = (800 \u00d7 2) + (60 \u00d7 2) + (9 \u00d7 2)
          \n869 \u00d7 2 = 1600 + 120 + 18
          \n869 \u00d7 2 = 1720 + 18
          \n869 \u00d7 2 = 1738.
          \nCheck:
          \n??? \u00d7 2 = 1738.
          \n=> ??? = 1738 \u00f7 2
          \n=> ??? = 869.<\/p>\n

           <\/p>\n

           <\/p>\n

          Question 5.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

          Explanation:
          \n4233 \u00d7 7 = (4000 + 200 + 30 + 3) 7
          \n4233 \u00d7 7 = (4000 \u00d7 7) + (200 \u00d7 7) + (30 \u00d7 7) + (3 \u00d7 7)
          \n4233 \u00d7 7 = 28000 + 1400 + 210 + 21
          \n4233 \u00d7 7 = 29400 + 210 + 21
          \n4233 \u00d7 7 = 29610 + 21
          \n4233 \u00d7 7 = 29631.
          \nCheck:
          \n??? \u00d7 7 = 29631.
          \n=> ??? = 29631 \u00f7 7
          \n=>??? \u00a0= 4233.<\/p>\n

          Question 6.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

          Explanation:
          \n3261 \u00d7 4 = (3000 + 200 + 60 + 1) 4
          \n3261 \u00d7 4 = (3000 \u00d7 4) + ( 200 \u00d7 4) + (60 \u00d7 4) + (1 \u00d7 4)
          \n3261 \u00d7 4 = 12000 + 800 + 240 + 4
          \n3261 \u00d7 4 = 12800 + 240 + 4
          \n3261 \u00d7 4 = 13040 + 4
          \n3261 \u00d7 4 =\u00a0 13044.
          \nCheck:
          \n??? \u00d7 4 =\u00a0 13044.
          \n=> ??? =\u00a0 13044 \u00f7 4
          \n=> ??? =\u00a0 3261.<\/p>\n

           <\/p>\n

           <\/p>\n

           <\/p>\n

          Question 7.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

          Explanation:
          \n1250 \u00d7 8 = (1000 + 200 + 50) 8
          \n1250 \u00d7 8 = (1000 \u00d7 8) + (200 \u00d7 8) + (50 \u00d7 8)
          \n1250 \u00d7 8 = 8000 + 1600 + 400
          \n1250 \u00d7 8 = 9600 + 400
          \n1250 \u00d7 8 = 10000.
          \nCheck:
          \n??? \u00d7 8 = 10000.
          \n=> ??? = 10000 \u00f7 8
          \n=> ??? = 1250.<\/p>\n

           <\/p>\n

           <\/p>\n

           <\/p>\n

          Question 8.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

          Explanation:
          \n2239 \u00d7 5 = (2000 + 200 + 30 + 9) 5
          \n2239 \u00d7 5 = (2000 \u00d7 5) + (200 \u00d7 5) + (30 \u00d7 5) + (9 \u00d7 5)
          \n2239 \u00d7 5 = 10000 + 1000 + 150 + 45
          \n2239 \u00d7 5 = 11000 + 150 + 45
          \n2239 \u00d7 5 = 11150 + 45
          \n2239 \u00d7 5 = 11195.
          \nCheck:
          \n??? \u00d7 5 = 11195.
          \n=> ??? = 11195 \u00f7 5
          \n=> ???\u00a0 = 2239.<\/p>\n

           <\/p>\n

           <\/p>\n

           <\/p>\n

          Set H pages 109-112
          \n<\/strong>Think about these questions to help you model with math.
          \nThinking Habits<\/p>\n

            \n
          • How can I use math I know to help solve this problem?<\/li>\n
          • How can I use pictures, objects, or an equation to represent the problem?<\/li>\n
          • How can I use numbers, words, and symbols to solve the problem?
            \n\"Envision<\/li>\n<\/ul>\n

            Remember<\/strong> that a bar diagram can help you write an equation.<\/p>\n

            Mia has a collection of 34 dolls. A toy store’s warehouse has 5 times as many dolls.
            \nQuestion 1.
            \nUse pictures, a bar diagram, or an equation to find the number of dolls in the warehouse.
            \nAnswer:
            \nNumber of dolls in the warehouse = 5 \u00d7 Number of dolls collection Mia has
            \n= 5 \u00d7 34
            \n= 170.<\/p>\n

            Explanation:
            \nNumber of dolls collection Mia has = 34.
            \nA toy store’s warehouse has 5 times as many dolls.
            \n=> Number of dolls in the warehouse = 5 \u00d7 Number of dolls collection Mia has
            \n= 5 \u00d7 34
            \n= 170.<\/p>\n

             <\/p>\n

            Question 2.
            \nHow can you decide if your answer is reasonable?
            \nAnswer:
            \nTo be reasonable means to be\u00a0as much as is appropriate or fair.<\/p>\n

            Explanation:
            \nIn math, reasonableness can be defined as checking to verify that the result of the solution or the calculation of the problem is correct or not, be either estimating or by plugging in your result to check it.<\/p>\n

             <\/p>\n

            Topic 3 Assessment Practice<\/h3>\n

            Question 1.
            \nUse numbers from the box to show how to multiply 126 by 3.
            \n\"Envision
            \nAnswer:
            \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

            Explanation:
            \n126 \u00d7 3 = (100 + 20 + 6) 3
            \n126 \u00d7 3 = (100 \u00d7 3) + ( 20 \u00d7 3) + (6 \u00d7 3)
            \n126 \u00d7 3 = 300 + 60 + 18
            \n126 \u00d7 3 = 360 + 18
            \n126 \u00d7 3 = 378.<\/p>\n

             <\/p>\n

            Question 2.
            \nAlberto rode the train 198 miles round trip 4 times last month. Explain how to use mental math to find the total distance Alberto traveled.
            \nAnswer:
            \nTotal distance Alberto traveled = 792.<\/p>\n

            Explanation:
            \nNumber of miles Alberto rode the train = 198.
            \nNumber of trips he did last month = 4.
            \nTotal distance Alberto traveled = Number of miles Alberto rode the train \u00d7 Number of trips he did last month
            \n= 198 \u00d7 4
            \n= (100 + 90 + 8) 4
            \n= (100 \u00d7 4) + (90 \u00d7 4) + (8 \u00d7 4)
            \n= 400 + 360 + 32
            \n= 760 + 32
            \n= 792.<\/p>\n

             <\/p>\n

            Question 3.
            \nMr. Ortiz sells tortillas in bags of 25 and in bags of 50. If he sells 4 bags of 50 and 6 bags of 25, how many tortillas did Mr. Ortiz sell?
            \nA. 10 tortillas
            \nB. 350 tortillas
            \nC. 170 tortillas
            \nD. 3,500 tortillas
            \nAnswer:
            \nTotal number of tortillas\u00a0 Mr. Ortiz sells = 350.
            \nB. 350 tortillas<\/p>\n

            Explanation:
            \nNumber of tortillas in bags of 25 Mr. Ortiz sells = 6.
            \nNumber of tortillas in bags of 50 Mr. Ortiz sells = 4.
            \nTotal number of tortillas\u00a0 Mr. Ortiz sells = (25 \u00d7 Number of tortillas in bags of 25 Mr. Ortiz sells) + 50 \u00d7Number of tortillas in bags of 50 Mr. Ortiz sells)
            \n= (25 \u00d7 6) + (50 \u00d7 4)
            \n= 150 + 100
            \n= 350.<\/p>\n

             <\/p>\n

             <\/p>\n

            Question 4.
            \nA. What are the partial products when finding 1,874 \u00d7 3? Select all that apply.
            \n\u2610 5,400
            \n\u2610 2,000
            \n\u2610 3,000
            \n\u2610 210
            \n\u2610 2,400
            \n\u2610 12
            \nAnswer:
            \nThe partial products when finding 1,874 \u00d7 3 are:
            \n\u2610 5,400
            \n\u2610 3,000
            \n\u2610 210
            \n\u2610 2,400
            \n\u2610 12<\/p>\n

            Explanation:
            \n1,874 \u00d7 3 = (1000 + 800 + 70 + 4) 3
            \n1,874 \u00d7 3 = (1000 \u00d7 3) + (800 \u00d7 3) + (70 \u00d7 3) + (4 \u00d7 3)
            \n1,874 \u00d7 3 = 3000 + 2400 + 210 + 12
            \n1,874 \u00d7 3 = 5400 + 210 + 12
            \n1,874 \u00d7 3 = 5610 + 12
            \n1,874 \u00d7 3 = 5622.<\/p>\n

             <\/p>\n

            B. Find the product of 1,874 and 3.
            \nAnswer:
            \n1,874 \u00d7 3 = 5622.<\/p>\n

            Explanation:
            \n1,874 \u00d7 3 = (1000 + 800 + 70 + 4) 3
            \n1,874 \u00d7 3 = (1000 \u00d7 3) + (800 \u00d7 3) + (70 \u00d7 3) + (4 \u00d7 3)
            \n1,874 \u00d7 3 = 3000 + 2400 + 210 + 12
            \n1,874 \u00d7 3 = 5400 + 210 + 12
            \n1,874 \u00d7 3 = 5610 + 12
            \n1,874 \u00d7 3 = 5622.<\/p>\n

             <\/p>\n

            Question 5.
            \nA science class is growing some fruit and vegetable plants on a plot of land behind their school. Each section is laid out in rows.
            \n\"Envision
            \nA. There are 9 strawberry plants planted in each row. Write and solve an equation to find how many strawberry plants were planted.
            \nAnswer:
            \nTotal number of strawberry plants were planted = 585.<\/p>\n

            Explanation:
            \nNumber of strawberry plants planted in each row = 9.
            \nNumber of rows strawberry plants planted = 65.
            \nTotal number of strawberry plants were planted = Number of rows strawberry plants planted\u00a0 \u00d7 Number of strawberry plants planted in each row
            \n= 65 \u00d7 9
            \n= (60 + 5) 9
            \n= (60 \u00d7 9) + (5 \u00d7 9)
            \n= 540 + 45
            \n= 585.<\/p>\n

             <\/p>\n

            B. There are 9 pepper plants planted in each row. Draw an area model and show the partial products to find how many pepper plants are planted behind the school.
            \nAnswer:
            \nNumber of pepper plants are planted behind the school = 162.<\/p>\n

            Explanation:
            \nNumber of pepper plants planted in each row = 9.
            \nNumber of rows pepper plants planted = 18.
            \nNumber of pepper plants are planted behind the school = Number of pepper plants planted in each row \u00d7 Number of rows pepper plants planted
            \n= 9 \u00d7 18
            \n= 9 (10 + 8)
            \n= (9 \u00d7 10) + (9 \u00d7 8)
            \n= 90 + 72
            \n= 162.
            \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

             <\/p>\n

             <\/p>\n

             <\/p>\n

            Question 6.
            \nSelect all the expressions that could be used to find 1,235 \u00d7 9.
            \n\u2610 9 \u00d7 (1,000 + 200 + 20 + 5)
            \n\u2610 9 \u00d7 (1,000 + 200 + 30 + 5)
            \n\u2610 (9 \u00d7 1,000) + (9 \u00d7 200) + (9 \u00d7 30) + (9 \u00d7 5)
            \n\u2610 9 \u00d7 1,235
            \n\u2610 1,235 + 9
            \nAnswer:
            \n1,235 \u00d7 9 = 11115.
            \nThe expressions that are used to find 1,235 \u00d7 9:
            \n9 \u00d7 (1,000 + 200 + 30 + 5)
            \n(9 \u00d7 1,000) + (9 \u00d7 200) + (9 \u00d7 30) + (9 \u00d7 5)
            \n9 \u00d7 1,235<\/p>\n

            Explanation:
            \n1,235 \u00d7 9 = (1000 + 200 + 30 + 5) 9
            \n1,235 \u00d7 9 = (1000 \u00d7 9) + (200 \u00d7 9) + (30 \u00d7 9) + (5 \u00d7 9)
            \n1,235 \u00d7 9 = 9000 + 1800 + 270 + 45
            \n1,235 \u00d7 9 = 10800 + 270 + 45
            \n1,235 \u00d7 9 = 11070 + 45
            \n1,235 \u00d7 9 = 11115.<\/p>\n

             <\/p>\n

            Question 7.
            \nDraw a model to find 365 \u00d7 3.
            \n365 \u00d7 3 = _________
            \nAnswer:
            \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson
            \n365 \u00d7 3 = __1095____.<\/p>\n

            Explanation:
            \n365 \u00d7 3 = (300 + 60 + 5) 3
            \n365 \u00d7 3 = (300 \u00d7 3) + (60 \u00d7 3) + (5 \u00d7 3)
            \n365 \u00d7 3 = 900 + 180 + 15
            \n365 \u00d7 3 = 1080 + 15
            \n365 \u00d7 3 = 1095.<\/p>\n

             <\/p>\n

             <\/p>\n

            Question 8.
            \nSelect all of the expressions that have a product of 640.
            \n\u2610 (6 \u00d7 100) + (4 \u00d7 10)
            \n\u2610 9 \u00d7 54
            \n\u2610 60 \u00d7 4 \u00d7 1
            \n\u2610 160 \u00d7 4
            \n\u2610 (6 \u00d7 100) \u00d7 (4 \u00d7 10)
            \nAnswer:
            \nThe expressions that have a product of 640:
            \n\u2610 160 \u00d7 4<\/p>\n

            Explanation:
            \n640 = (600 + 40)
            \n640 = 160 \u00d7 4<\/p>\n

             <\/p>\n

             <\/p>\n

            Question 9.
            \nThe table shows the number of hot drinks sold in a busy coffee shop in 1 week.
            \n\"Envision<\/p>\n

            A. If the same number of cups of coffee were sold for 6 weeks in a row, how many cups would be sold in all?
            \nAnswer:
            \nNumber of cups of coffee were sold in all = 5010.<\/p>\n

            Explanation:
            \nNumber of cups of coffee were sold in a week = 835.
            \nNumber of cups of coffee were sold in all = 6 \u00d7 Number of cups of coffee were sold in a week
            \n= 6 \u00d7 835
            \n= 6 (800 + 30 + 5)
            \n= (6 \u00d7 800) + ( 6 \u00d7 30) + ( 5 \u00d7 6)
            \n= 4800 + 180 + 30
            \n= 4980 + 30
            \n= 5010.<\/p>\n

             <\/p>\n

            B. The special drink of the month was an iced mocha. The shop sold 5 times as many iced mochas in one week as hot mochas. How many more iced mochas were sold than hot mochas in 4 weeks? Explain.
            \nAnswer:
            \n1468 more iced mochas were sold than hot mochas in 4 weeks.<\/p>\n

            Explanation:
            \nThe shop sold 5 times as many iced mochas in one week as hot mochas.
            \nNumber of iced mochas were sold in a week = 567.
            \nNumber of hot mochas were sold in a week = 200.
            \nNumber of more iced mochas were sold than hot mochas in 4 weeks = (4 \u00d7 Number of iced mochas were sold in a week) – (4 \u00d7 Number of hot mochas were sold in a week )
            \n= (4 \u00d7 567) – (4 \u00d7 200)
            \n= 2268 – 800
            \n= 1468.<\/p>\n

             <\/p>\n

             <\/p>\n

            Question 10.
            \nTickets for a resort cost $1,182 each for adults and $459 each for children. Find the cost for 3 adult tickets and 3 child tickets. Explain how you know your answer is reasonable.
            \nAnswer:
            \nCost for 3 adult tickets and 3 child tickets = $4923.
            \nAnswer is reasonable because the solution is correct for given problem.<\/p>\n

            Explanation:
            \nCost of Tickets for each adult = $1182.
            \nCost of Tickets for each children = $459.
            \nCost for 3 adult tickets and 3 child tickets = (3 \u00d7 Cost of Tickets for each adult ) +\u00a0 (3 \u00d7 Cost of Tickets for each children)
            \n= (3 \u00d7 $1182) + (3 \u00d7 $459)
            \n= $3546 + $1377
            \n= $4923.<\/p>\n

             <\/p>\n

             <\/p>\n

            Question 11.
            \nWhich expression has the same value as 5 \u00d7 617?
            \nA. (5 \u00d7 6) + (5 \u00d71) + (5 \u00d7 7)
            \nB. (5 \u00d7 60) + (5 \u00d7 10) + (5 \u00d7 70)
            \nC. (5 \u00d7 600) + (5 \u00d7 1) + (5 \u00d7 7)
            \nD. (5 \u00d7 600) + (5 \u00d7 10) + (5 \u00d7 7)
            \nAnswer:
            \nExpression has the same value as 5 \u00d7 617 is:
            \nD. (5 \u00d7 600) + (5 \u00d7 10) + (5 \u00d7 7)<\/p>\n

            Explanation:
            \n5 \u00d7 617 = 5 (600\u00a0 10 + 7)
            \n5 \u00d7 617 = (5 \u00d7 600) + (5 \u00d7 10) + (5 \u00d7 7)
            \n5 \u00d7 617 = 3000 + 50 + 35
            \n5 \u00d7 617 = 3050 + 35
            \n5 \u00d7 617 = 3085.
            \nA. (5 \u00d7 6) + (5 \u00d71) + (5 \u00d7 7) = 30 + 5 + 35 = 35 + 335 = 70.
            \nB. (5 \u00d7 60) + (5 \u00d7 10) + (5 \u00d7 70) = 300 + 50 + 350 = 350 + 350 = 700.
            \nC. (5 \u00d7 600) + (5 \u00d7 1) + (5 \u00d7 7) = 3000 + 5 + 35 = 3005 + 35 = 3040.
            \nD. (5 \u00d7 600) + (5 \u00d7 10) + (5 \u00d7 7) = 3000 + 50 + 35 = 3050 + 35 = 3085.<\/p>\n

             <\/p>\n

             <\/p>\n

             <\/p>\n

             <\/p>\n

             <\/p>\n

            Question 12.
            \nWhich of the following is equivalent to (400 \u00d7 3) + (36 \u00d7 3)?
            \nA. 436 \u00f7 3
            \nB. 400 \u00d7 10
            \nC. 436 \u00d7 3
            \nD. 400 \u00d7 3 + 36
            \nAnswer:
            \nEquivalent to (400 \u00d7 3) + (36 \u00d7 3) is:
            \nC. 436 \u00d7 3 = 1308.<\/p>\n

            Explanation:
            \n(400 \u00d7 3) + (36 \u00d7 3) = 1200 + 108
            \n(400 \u00d7 3) + (36 \u00d7 3) = 1308.
            \nA. 436 \u00f7 3 = 145.33
            \nB. 400 \u00d7 10 = 4000.
            \nC. 436 \u00d7 3 = 1308.
            \nD. 400 \u00d7 3 + 36 = 1200 + 36 = 1236.<\/p>\n

             <\/p>\n

             <\/p>\n

             <\/p>\n

            Question 13.
            \nFind 3 \u00d7 312. Draw a bar diagram to solve.
            \nAnswer:
            \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

            Explanation:
            \n3 \u00d7 312 = 3 (300 + 10 + 2)
            \n3 \u00d7 312 = (3 \u00d7 300) + (3 \u00d7 10) + (3 \u00d7 2)
            \n3 \u00d7 312 = 900 + 30 + 6
            \n3 \u00d7 312 = 930 + 6
            \n3 \u00d7 312 = 936.<\/p>\n

             <\/p>\n

             <\/p>\n

             <\/p>\n

            Question 14.
            \nBea’s Bakery bakes 215 cookies and 45 muffins every hour. How many baked goods are baked in 4 hours?
            \nAnswer:
            \nNumber of baked goods are baked in 4 hours = 1040.<\/p>\n

            Explanation:
            \nNumber of cookies Bea’s Bakery bakes every hour = 215.
            \nNumber of muffins Bea’s Bakery bakes every hour = 45.
            \nNumber of baked goods are baked in 4 hours = (4 \u00d7 Number of cookies Bea’s Bakery bakes every hour) + (4 \u00d7 Number of muffins Bea’s Bakery bakes every hour)
            \n= (4 \u00d7 215)+ (4 \u00d7 45)
            \n= 860 + 180
            \n= 1040.<\/p>\n

             <\/p>\n

             <\/p>\n

            Question 15.
            \nWrite and solve an equation that represents the given bar diagram.
            \n\"Envision
            \nAnswer:
            \nTotal number of biscuits made in 4 hours = b = 192.<\/p>\n

            Explanation:
            \nNumber of hours used to make them = 1.
            \nNumber of biscuits made every hour = 48.
            \nTotal number of biscuits made in 4 hours = b = 4 \u00d7\u00a0Number of biscuits made every hour
            \n= 4 \u00d7 48
            \n= 4 (40 + 8)
            \n= (4 \u00d7 40) + (4 \u00d7 8)
            \n= 160 + 32
            \n= 192.<\/p>\n

             <\/p>\n

             <\/p>\n

            Question 16.
            \nWhich of the following is equivalent to 8 \u00d7 493? Select all that apply.
            \n\u2610 (8 \u00d7 400) + (8 \u00d7 90) + (8 \u00d7 3)
            \n\u2610 (8 \u00d7 400) + 93
            \n\u2610 493 \u00d7 8
            \n\u2610 (8 \u00d7 500) \u2013 (8 \u00d7 93)
            \n\u2610 (8 \u00d7 500) \u2013 (8 \u00d7 7)
            \nAnswer:
            \n8 \u00d7 493 = 3944.
            \nEquivalent to 8 \u00d7 493 is:
            \n(8 \u00d7 400) + (8 \u00d7 90) + (8 \u00d7 3)
            \n493 \u00d7 8
            \n(8 \u00d7 500) \u2013 (8 \u00d7 7)<\/p>\n

            Explanation:
            \n8 \u00d7 493 = 8 (400 + 90 + 3)
            \n8 \u00d7 493 = (8 \u00d7 400) + (8 \u00d7 90) + (8 \u00d7 3)
            \n8 \u00d7 493 = 3200 + 720 + 24
            \n8 \u00d7 493 = 3920 + 24
            \n8 \u00d7 493 = 3944.
            \nExpression given:
            \n(8 \u00d7 400) + (8 \u00d7 90) + (8 \u00d7 3) = 3200 + 720 + 24 = 3920 + 24 = 3944.
            \n(8 \u00d7 400) + 93 = 3200 + 93 = 3293.
            \n493 \u00d7 8 = (400 \u00d7 8) + (90 \u00d7 8) + (3 \u00d7 8) = 3200 + 720 + 24 = 3920 + 24 = 3944.
            \n(8 \u00d7 500) \u2013 (8 \u00d7 93) = 4000 – 744 = 3256.
            \n(8 \u00d7 500) \u2013 (8 \u00d7 7) = 4000 – 56 = 3944.<\/p>\n

             <\/p>\n

             <\/p>\n

             <\/p>\n

            Question 17.
            \nMr. Luca would like to purchase a digital keyboard for each of his 3 nieces and 1 nephew. The keyboard costs $105.
            \nA. Mr. Luca thinks the total cost should be about $200. Is this amount reasonable? Explain.
            \nAnswer:
            \nNo, the amount is not reasonable because total cost of the keyboard Mr. Luca\u00a0 wants to buy for each of his 3 nieces and 1 nephew is $420 not $200. His estimation is wrong.<\/p>\n

            Explanation:
            \nCost of the keyboard = $105.
            \nNumber of nieces Mr. Luca has = 3.
            \nNumber of nephew Mr. Luca has = 1.
            \nTotal cost of the keyboard Mr. Luca\u00a0 wants to buy for each of his 3 nieces and 1 nephew = (3 \u00d7 $105) + (1 \u00d7 $105)
            \n= $315 + $105
            \n= $420.<\/p>\n

             <\/p>\n

             <\/p>\n

            B. Write and solve an equation to find the total cost of the keyboards. Explain why your answer is reasonable.
            \nAnswer:
            \nTotal cost of the keyboard Mr. Luca\u00a0 wants to buy for each of his 3 nieces and 1 nephew = (3 \u00d7 $105) + (1 \u00d7 $105)
            \n= $315 + $105
            \n= $420.
            \nMy answer is reasonable because its calculation is correct with correct solution for the problem.<\/p>\n

            Explanation:
            \nCost of the keyboard = $105.
            \nTotal cost of the keyboard Mr. Luca\u00a0 wants to buy for each of his 3 nieces and 1 nephew = (3 \u00d7 $105) + (1 \u00d7 $105)
            \n= $315 + $105
            \n= $420.<\/p>\n

             <\/p>\n

             <\/p>\n

            Question 18.
            \nWhat is the product of 5 \u00d7 1,903?
            \nA. 9,515
            \nB. 9,505
            \nC. 9,155
            \nD. 965
            \nAnswer:
            \n5 \u00d7 1,903 = 9515.
            \nA. 9,515
            \nC. 9,155<\/p>\n

            Explanation:
            \n5 \u00d7 1,903 = 5 (1000 + 900 + 3)
            \n5 \u00d7 1,903 = (5 \u00d7 1000) + (5 \u00d7 900) + (5 \u00d7 3)
            \n5 \u00d7 1,903 = 5000 + 4500 + 15
            \n5 \u00d7 1,903 = 9500 + 15
            \n5 \u00d7 1,903 = 9515.<\/p>\n

             <\/p>\n

             <\/p>\n

            Question 19.
            \nHow can you use mental math to find the product of 6 \u00d7 295?
            \nAnswer:
            \nWe can use mental math to find the product of 6 \u00d7 295 by using partial products or by distributive property.<\/p>\n

            Explanation:
            \n6 \u00d7 295 = 6 (200 + 95)
            \n6 \u00d7 295 = (6 \u00d7 200 ) + (6 \u00d7 95)
            \n6 \u00d7 295 = 1200 + 570
            \n6 \u00d7 295 = 1770.<\/p>\n

             <\/p>\n

             <\/p>\n

            Question 20.
            \nA. Select all the partial products for 8 \u00d7 321.
            \n\u2610 8
            \n\u2610 80
            \n\u2610 160
            \n\u2610 1,600
            \n\u2610 2,400
            \nAnswer:
            \nPartial products for 8 \u00d7 321 :
            \n\u2610 8
            \n\u2610 160
            \n\u2610 2,400<\/p>\n

            Explanation:
            \n8 \u00d7 321 = 8 ( 300 + 20 + 1)
            \n8 \u00d7 321 = (8 \u00d7 300) + (8 \u00d7 20) + (8 \u00d7 1)
            \n8 \u00d7 321 = 2400 + 160 + 8
            \n8 \u00d7 321 = 2560 + 8
            \n8 \u00d7 321 = 2568.<\/p>\n

             <\/p>\n

             <\/p>\n

            B. Find the product for Part A using the partial products.
            \nAnswer:
            \n8 \u00d7 321 = 2568.<\/p>\n

            Explanation:
            \n8 \u00d7 321 = 8 ( 300 + 20 + 1)
            \n8 \u00d7 321 = (8 \u00d7 300) + (8 \u00d7 20) + (8 \u00d7 1)
            \n8 \u00d7 321 = 2400 + 160 + 8
            \n8 \u00d7 321 = 2560 + 8
            \n8 \u00d7 321 = 2568.<\/p>\n

             <\/p>\n

             <\/p>\n

            Topic 3 Performance Task<\/h3>\n

            Buying Classroom Computers Jorge’s school can purchase computers and printers for the prices shown. Information about the fourth-grade classes are given in the table.
            \n\"Envision<\/p>\n

            Question 1.
            \nJorge’s teacher is Ms. Sanchez. His class wants to buy 8 desktop computers and 3 printers.
            \n\"Envision
            \nPart A
            \nWhat is the total cost of 8 desktop computers? Use place-value strategies and properties of operations.
            \nAnswer:
            \nCost of 8 desktop computers = $8400.<\/p>\n

            Explanation:
            \nCost of desktop computers = $1050.
            \nCost of 8 desktop computers = 8 \u00d7 $1050
            \n= 8 (1000 + 50)
            \n= (8 \u00d7 1000) + (8 \u00d7 50)
            \n= 8000 + 400
            \n= $8400.<\/p>\n

             <\/p>\n

             <\/p>\n

            Part B
            \nWhat is the total cost of 3 printers? Draw an array and show the partial products to find the cost.
            \nAnswer:
            \nTotal cost of 3 printers = $1024.
            \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

            Explanation:
            \nCost of printers= $128.
            \nTotal cost of 3 printers = 8 \u00d7 $128
            \n= 8(100 + 20 + 8)
            \n= (8 \u00d7 100) + (8 \u00d7 20) + (8 \u00d7 8)
            \n= 800 + 160 + 64
            \n= 960 + 64
            \n= $1024.<\/p>\n

             <\/p>\n

             <\/p>\n

            Part C
            \nDid Jorge’s class raise enough money to buy 8 computers and 3 printers? Explain.
            \nAnswer:
            \nNo, Jorge’s class did not raise enough money to buy 8 computers and 3 printers because cost of them is $9424 and their raise amount $9000 is less to buy them.<\/p>\n

            Explanation:
            \nTotal cost of 3 printers = $1024.
            \nCost of 8 desktop computers = $8400.
            \nMoney raised by Jorge’s class = $9000.
            \nTotal amount of money to buy 8 computers and 3 printers = Total cost of 3 printers + Cost of 8 desktop computers
            \n= $1024 + $8400
            \n= $9424.
            \nDifference:
            \n= Total amount of money to buy 8 computers and 3 printers – Money raised by Jorge’s class
            \n= $9424 – $9000
            \n= $424.<\/p>\n

            Question 2.
            \nRachel’s teacher is Mr. Jones. Her class wants to buy 7 computers and 2 printers.
            \nPart A
            \nHow much more do 7 desktop computers cost than 7 laptop computers? Use bar diagrams and equations to represent and solve the problem.
            \nAnswer:
            \n$1904 Cost of 7 desktop computers is more cost than 7 laptop computers.
            \n\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson\"Envision-Math-Common-Core-4th-Grade-Answers-Key-Topic-3-Use-Strategies-and-Properties-to-Multiply-by-1-Lesson<\/p>\n

            Explanation:
            \nCost of desktop computers = $1050.
            \nTotal cost of 7 desktop computers = 7 \u00d7 Cost of desktop computers
            \n= 7 \u00d7 $1050
            \n= 7 ( 1000 + 50)
            \n= (7 \u00d7 1000) + (7 \u00d7 50)
            \n= 7000 + 350
            \n= $7350.
            \nCost of laptop computers = $798.
            \nTotal cost of 7 laptop computers = 7 \u00d7 Cost of laptop computers
            \n= 7 \u00d7 $798
            \n= 7 \u00d7( 700+ 90 + 8)
            \n= (7 \u00d7 700) + (7 \u00d7 90) + (7 \u00d7 8)
            \n= 4900 + 490 + 56
            \n= 5390 + 56
            \n= $5446.
            \nCost of 7 desktop computers more cost than 7 laptop computers = Total cost of 7 desktop computers – Total cost of 7 laptop computers
            \n= $7350 – $5446
            \n= $1904.<\/p>\n

             <\/p>\n

             <\/p>\n

            Part B
            \nWhat is another way to find the difference in the cost of 7 desktop computers and 7 laptop computers? Explain.
            \nAnswer:
            \nDifference between 7 desktop computers and 7 laptop computers is $1904.<\/p>\n

            Explanation:
            \nAnother way:
            \nCost of 7 desktop computers = $7350.
            \nCost of 7 laptop computers = $5446.
            \nDifference:
            \n= Total cost of 7 desktop computers – Total cost of 7 laptop computers
            \n= $7350 – $5446
            \n= $1904.<\/p>\n

             <\/p>\n

             <\/p>\n

             <\/p>\n

            Question 3.
            \nMiranda’s teacher is Ms. Katz. Her class wants to buy 9 laptop computers and 4 printers. Miranda said the total cost should be $7,494. Is this amount reasonable? Explain. Does the class have enough money?
            \nAnswer:
            \nNo, the amount is not reasonable because there is a difference $200 less than the actual amount to that of expected amount.<\/p>\n

            Explanation:
            \nCost of laptop computer = $798.
            \nCost of printer = $128.
            \nTotal cost expected to be by\u00a0 Miranda = $7,494
            \nCost of 9 laptop computers and 4 printers = (9 \u00d7 Cost of laptop computer) + ( 4 \u00d7 Cost of printer)
            \n= (9 \u00d7 $798) + (4 \u00d7 $128)
            \n= $7182 + $512
            \n= $7694.
            \nDifference:
            \n= Cost of 9 laptop computers and 4 printers – Total cost expected to be by\u00a0 Miranda
            \n= $7694 – $7494
            \n= $200.<\/p>\n","protected":false},"excerpt":{"rendered":"

            Go through the\u00a0enVision Math Common Core Grade 4 Answer Key\u00a0Topic 3 Use Strategies and Properties to Multiply by 1-Digit Numbers\u00a0regularly and improve your accuracy in solving questions. enVision Math Common Core 4th Grade Answers Key Topic 3 Use Strategies and Properties to Multiply by 1-Digit Numbers Essential Questions: How can you multiply by multiples of …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/9570"}],"collection":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/comments?post=9570"}],"version-history":[{"count":4,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/9570\/revisions"}],"predecessor-version":[{"id":28235,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/9570\/revisions\/28235"}],"wp:attachment":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media?parent=9570"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/categories?post=9570"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/tags?post=9570"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}