{"id":8899,"date":"2023-12-21T11:55:21","date_gmt":"2023-12-21T06:25:21","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=8899"},"modified":"2023-12-22T14:45:38","modified_gmt":"2023-12-22T09:15:38","slug":"envision-math-common-core-grade-4-answer-key-topic-7","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-4-answer-key-topic-7\/","title":{"rendered":"enVision Math Common Core Grade 4 Answer Key Topic 7 Factors and Multiples"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 4 Answer Key<\/a>\u00a0Topic 7 Factors and Multiples<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

enVision Math Common Core 4th Grade Answers Key Topic 7 Factors and Multiples<\/h2>\n

Essential Questions:<\/strong>
\nHow can you use arrays or multiplication to find the factors of a number? How can you identify prime and composite numbers? How can you find multiples of a number?
\n\"Envision<\/p>\n

enVision STEM Project: Analyzing the Animal Kingdom<\/strong>
\nDo Research As a defense against the cold, emperor penguins huddle together in large groups. Use the Internet or other sources to research how this helps them protect each other and their chicks.<\/p>\n

Journal: Write a Report Include what you found. Also in your report:<\/p>\n

    \n
  • Suppose 64 penguins form a huddle to keep warm. Use a grid to draw all the possible arrays for 64.<\/li>\n
  • If a huddle of 72 penguins breaks apart, how many different ways can the penguins form equal groups? Is 72 prime or composite? Write the factor pairs of 72 to show all the ways the penguins can form equal groups.<\/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
    • product<\/li>\n
    • dividend<\/li>\n
    • divisor<\/li>\n
    • quotient<\/li>\n<\/ul>\n

      Question 1.
      \nThe _________ is the answer to a division problem.
      \nAnswer:
      \nThe quotient is the answer to a division problem.<\/p>\n

      Question 2.
      \nThe number being divided is the ________.
      \nAnswer:
      \nThe number being divided is the dividend.<\/p>\n

      Question 3.
      \nThe _________ is the number that tells into how many groups something is being divided.
      \nAnswer:
      \nThe divisor is the number that tells into how many groups something is being divided.<\/p>\n

      \"Factors<\/p>\n

      Multiplication Find each product.<\/strong><\/p>\n

      Question 4.
      \n8 \u00d7 4
      \nAnswer:
      \n8 \u00d7 4 = 32
      \n32 is the product.<\/p>\n

      Question 5.
      \n17 \u00d7 6
      \nAnswer:
      \n17 \u00d7 6 = 102
      \n102 is the product.<\/p>\n

      Question 6.
      \n304 \u00d7 9
      \nAnswer:
      \n304 \u00d7 9 = 2,735
      \n2735 is the product.<\/p>\n

      Question 7.
      \n555 \u00d7 5
      \nAnswer:
      \n555 \u00d7 5 = 2775
      \n2775 is the product.<\/p>\n

      Question 8.
      \n22 \u00d7 26
      \nAnswer:
      \n22 \u00d7 26 = 572
      \n572 is the product.<\/p>\n

      Question 9.
      \n33 \u00d7 11
      \nAnswer:
      \n33 \u00d7 11 = 363
      \n363 is the product.<\/p>\n

      Question 10.
      \n56 \u00d7 70
      \nAnswer:
      \n56 \u00d7 70 = 3920
      \n3920 is the product.<\/p>\n

      Question 11.
      \n36 \u00d7 91
      \nAnswer:
      \n36 \u00d7 91 = 3,276
      \n3276 is the product.<\/p>\n

      Question 12.
      \n27 \u00d7 48
      \nAnswer:
      \n27 \u00d7 48 = 1296
      \n1296 is the product.<\/p>\n

      \"\"<\/p>\n

      Question 13.
      \n56 \u00d7 13
      \nAnswer:
      \n56 \u00d7 13 = 728
      \n728 is the product.<\/p>\n

      Question 14.
      \n12 \u00d7 19
      \nAnswer:
      \n12 \u00d7 19 = 228
      \n228 is the product.<\/p>\n

      Question 15.
      \n36 \u00d7 16
      \nAnswer:
      \n36 \u00d7 16 = 576
      \n576 is the product.
      \n
      \nDivision Find each quotient.
      \n<\/strong>Question 16.
      \n27 \u00f7 3
      \nAnswer:
      \n27 \u00f7 3 = 9
      \n9 is the quotient.<\/p>\n

      Question 17.
      \n56 \u00f7 8
      \nAnswer:
      \n56 \u00f7 8 = 7
      \n7 is the quotient.<\/p>\n

      Question 18.
      \n36 \u00f7 4
      \nAnswer:
      \n36 \u00f7 4 = 9
      \n9 is the quotient.<\/p>\n

      Question 19.
      \n72 \u00f7 9
      \nAnswer:
      \n72 \u00f7 9 = 8
      \n8 is the quotient.<\/p>\n

      Question 20.
      \n39 \u00f7 3
      \nAnswer:
      \n39 \u00f7 3 = 13
      \n13 is the quotient.<\/p>\n

      Question 21.
      \n64 \u00f7 4
      \nAnswer:
      \n64 \u00f7 4 = 16
      \n16 is the quotient.<\/p>\n

      \"Factors<\/p>\n

      Question 22.
      \n105 \u00f7 5
      \nAnswer:
      \n105 \u00f7 5 = 21
      \n21 is the quotient.<\/p>\n

      Question 23.
      \n824 \u00f7 4
      \nAnswer:
      \n824 \u00f7 4 = 206
      \n206 is the quotient.<\/p>\n

      Question 24.
      \n942 \u00f7 3
      \nAnswer:
      \n942 \u00f7 3 = 314.33
      \n314.33 is the quotient.<\/p>\n

      Question 5.
      \n9,156 \u00f7 3
      \nAnswer:
      \n9156 \u00f7 3 = 3052
      \n3052 is the quotient.<\/p>\n

      Question 26.
      \n2,156 \u00f7 4
      \nAnswer:
      \n2156 \u00f7 4 = 539
      \n539 is the quotient.<\/p>\n

      Question 27.
      \n4,136 \u00f7 8
      \nAnswer:
      \n4136 \u00f7 8 = 517
      \n517 is the quotient.
      \n
      \nProblem Solving
      \n<\/strong>Question 28.
      \nModel with Math Cecilia bought 2 sandwiches last week and 4 sandwiches this week. She spent a total of $42. If each sandwich costs the same amount, how much did Cecilia spend on each sandwich? Write and solve equations.
      \nAnswer:
      \nGiven that,
      \nTotal number of sandwich brought by Cecilia in last week = 2
      \nTotal number of sandwich brought by Cecilia in this week = 4
      \nTotal she spent money on sandwich = $42
      \nTotal number of sandwiches Cecilia brought in two weeks = 2 + 4 = 6
      \nMoney spent on one sandwich = $42\/6 = 7<\/p>\n

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

      PROJECT 7A
      \nWhere is Mammoth Cave National Park?
      \nProject: Model a Campground
      \n\"Envision<\/p>\n

      PROJECT 7B
      \nHow many people can fill a college basketball arena?
      \nProject: Create a Basketball Arena
      \n\"Envision<\/p>\n

      PROJECT 7C
      \nHow many arrays of potted plants do you see?
      \nProject: Design a Plant Array for a Store Display
      \n\"Envision<\/p>\n

      3-ACT MATH PREVIEW<\/strong><\/p>\n

      Math Modeling
      \nCan-Do Attitude
      \n\"Envision
      \nI can … model with math to solve a problem that involves estimating and using factors and multiples.<\/p>\n

      Lesson 7.1 Understand Factors<\/h3>\n

      Solve & Share<\/strong>
      \nFourth graders at Ames School have 24 carpet squares. What are all the different ways they can organize the carpet squares into a rectangular array? Solve this problem any way you choose.
      \nI can … find the factor pairs of a whole number
      \n\"Envision<\/p>\n

      Look Back! Look for Relationships What patterns do you see in the arrays?<\/p>\n

      Essential Question<\/strong>
      \nHow Can You Use Arrays to Find the Factor Pairs of a Number?<\/p>\n

      Visual Learning Bridge
      \nThe music director is trying to find the best way to arrange the chairs for a performance. The chairs must be arranged in a rectangular array. How many different ways can the chairs be arranged into a rectangular array? Use grids to show all the ways the chairs can be arranged.
      \n\"Envision<\/p>\n

      \"Envision<\/p>\n

      Convince Me! Critique Reasoning Blake says, “Greater numbers will always have more factors.” Do you agree? Explain.<\/p>\n

      Guided Practice<\/strong><\/p>\n

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nHow are the lengths of the sides of the arrays shown on the grids on the previous page related to the factors of 12?
      \nAnswer:
      \nGiven that,
      \nOn the previous page, the length of the sides of the arrays on the grids are shown by rows and columns.
      \nFor the factor of 12
      \nA factor divides exactly into a number , leaving no remainder is called a factors.
      \nRows and columns are arranged in
      \n1 row of 12 chairs and 12 rows of 1 chair.
      \nThe factors of 12 are 1 and 12.<\/p>\n

      Question 2.
      \n<\/span>What are the lengths of the sides of the arrays that show how 5 chairs can be arranged?
      \nAnswer:
      \n5 chairs can be arranged in
      \n1 row of 5 chairs
      \n5 rows of 1chairs
      \n1 and 5 are the factors of 5.
      \n
      \nDo You Know How?<\/strong>
      \nFor 3-4, find all of the factor pairs for each number. You can use grids to help.
      \nQuestion 3.
      \n6
      \nAnswer:
      \nA factor divides exactly into a number , leaving no remainder is called a factors.
      \nThe factors of 6 are 1, 2, 3 and 6
      \nFactor pairs of 16 are
      \n1 and 6
      \n2 and 3
      \nWe can arrange the factor pairs on the grid paper be like
      \n1 and 6 = 1 row of 6
      \n2 and 3 = 2 rows of 3
      \nWe can also show in another away\u00a0 to arrange the factor pairs
      \n6 rows of 1 and 3 rows of 2.
      \n\"Envision-Math-Common-Core-4th-Grade-Answer-Key-Topic-7-Factors-and-Multiples-9
      \n
      \nQuestion 4.
      \n<\/span>16
      \nAnswer:
      \nA factor divides exactly into a number , leaving no remainder is called a factors.
      \nThe factors of 16 are 1, 2, 8 and 16
      \nFactor pairs of 16 are
      \n1 and 16
      \n2 and 8
      \nWe can arrange the factor pairs on the grid paper be like
      \n1 and 16 = 1 row of 16
      \n2 and 8 = 2 rows of 8
      \nWe can also show in another away\u00a0 to arrange the factor pairs
      \n16 rows of 1 and 8 rows of 2.
      \n\"Envision-Math-Common-Core-4th-Grade-Answer-Key-Topic-7-Factors-and-Multiples-9
      \nFor 5-6, find the factors of each number.<\/p>\n

      \"Factors<\/p>\n

      Question 5.
      \n45
      \nAnswer:
      \nA factor divides exactly into a number, leaving no remainder is called factors. Factors of 35 are the 1, 3, 5, 9, 15 and 45<\/p>\n

      Question 6.
      \n30
      \nAnswer:
      \nA factor divides exactly into a number, leaving no remainder is called factors.
      \nFactors of 30 are the 1, 2, 3, 5, 6, 10, 15 and 30
      \nIndependent Practice<\/strong><\/p>\n

      For 7-8, use the grids to find all the possible arrays for each number. Use the arrays to help write the factors.
      \nQuestion 7.
      \n\"Envision
      \nAnswer:<\/p>\n

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

      For 9-14, use grids to find the factor pair or pairs for each number.
      \nQuestion 9.
      \n5
      \nAnswer:
      \nA factor divides exactly into a number, leaving no remainder is called factors.
      \nThe factors of 5 are 1and 5
      \nFactor pairs of 5 are
      \n1 and 5
      \nWe can arrange the factor pairs on the grid paper be like
      \n1 and 5 = 1 row of 5
      \nWe can also show in another away to arrange the factor pairs.
      \n5 rows of 1
      \n\"Envision-Math-Common-Core-4th-Grade-Answer-Key-Topic-7-Factors-and-Multiples-9
      \n<\/span>
      \nQuestion 10.
      \n25
      \nAnswer:
      \nA factor divides exactly into a number, leaving no remainder is called factors.
      \nThe factors of 25 are 1, 5 and 25
      \nFactor pairs of 25 are
      \n1 and 25
      \n5 and 5
      \nWe can arrange the factor pairs on the grid paper be like
      \n1 and 25 = 1 row of 25
      \n5 and 5\u00a0 = 5 rows of 5
      \nWe can also show in another away\u00a0 to arrange the factor pairs
      \n25 rows of 1 and 5 rows of 5.<\/p>\n

      Question 11.
      \n8
      \nAnswer:
      \nA factor divides exactly into a number, leaving no remainder is called factors.
      \nThe factors of 8 are 1, 2, 4 and 8
      \nFactor pairs of 8 are
      \n1 and 8
      \n2 and 4
      \nWe can arrange the factor pairs on the grid paper be like
      \n1 and 8 = 1 row of 8
      \n2 and 4 = 2 rows of 4
      \nWe can also show in another away\u00a0 to arrange the factor pairs
      \n8 rows of 1 and 4 rows of 2.
      \n\"Envision-Math-Common-Core-4th-Grade-Answer-Key-Topic-7-Factors-and-Multiples-9<\/p>\n

      Question 12.
      \n36
      \nAnswer:
      \nA factor divides exactly into a number, leaving no remainder is called factors.
      \nThe factors of 36 are 1, 2, 3, 4, 9, 12, 18 and 36
      \nFactor pairs of 16 are
      \n1 and 36
      \n2 and 18
      \n2 and 12
      \n4 and 9
      \nWe can arrange the factor pairs on the grid paper be like
      \n1 and 36 = 1 row of 36
      \n2 and 18 = 2 rows of 18
      \n3 and 12 = 3 rows of 12
      \n4 and 9 = 4 rows of 9
      \nWe can also show in another away\u00a0 to arrange the factor pairs
      \n36 rows of 1, 18 rows of 2, 12 rows of 3, and 9 rows of 4.<\/p>\n

      Question 13.
      \n23
      \nAnswer:
      \nA factor divides exactly into a number, leaving no remainder is called factors.
      \nThe factors of 23 are 1 and 23
      \nFactor pairs of 23 are
      \n1 and 23
      \nWe can arrange the factor pairs on the grid paper be like
      \n1 and 16 = 1 row of 23
      \nWe can also show in another away\u00a0 to arrange the factor pairs
      \n23 rows of 1.<\/p>\n

      Question 14.
      \n27
      \nAnswer:
      \nA factor divides exactly into a number, leaving no remainder is called factors.
      \nThe factors of 27 are 1, 3, 9 and 27
      \nFactor pairs of 27 are
      \n1 and 27
      \n9 and 3
      \nWe can arrange the factor pairs on the grid paper be like
      \n1 and 27 = 1 row of 27
      \n9 and 3 = 9 rows of 3
      \nWe can also show in another way to arrange the factor pairs.
      \n27 rows of 1 and 3 rows of 9.
      \n
      \nProblem Solving
      \n<\/strong>Question 15.
      \nReasoning Use the grid to find two numbers that have 2 and 3 as factors.
      \n\"Envision
      \nAnswer:<\/p>\n

      Question 16.
      \nThe dwarf planet Pluto takes about 90,403 days to orbit the sun. Write this number in expanded form and using number names.
      \nAnswer:<\/p>\n

      Question 17.
      \nDavid makes 17 dollars in an hour and works 25 hours each week. Linda makes ! 25 dollars in an hour and works 17 hours ! each week. How much do David and Linda make together each week? What property of multiplication does this represent?
      \nAnswer:
      \nGiven that,
      \nTotal number of dollars that David makes in an hour = 17
      \nDavid works in a week = 25 hours
      \nTotal number of dollars that David makes in 25 hours = 25 \u00d7 17 =
      \nTotal number of dollars that Linda makes in an hour = 25
      \nLinda works in a week = 17
      \nTotal number of dollars that Linda makes in 17 hours = 17 \u00d7 25
      \nTotal number of dollars with David and Linda = (25 \u00d7 17) + (17 + 25) = 850
      \nThe equation represents the Associative property of multiplication<\/p>\n

      Question 18.
      \nWhat do you notice about the number of possible arrays and the number of factors of 22?
      \nAnswer:
      \nA factor divides exactly into a number, leaving no remainder is called factors.
      \nThe factors of 22 are 1, 11 and 22
      \nA number of factors of 22 are 3.<\/p>\n

      Question 19.
      \nHigher Order Thinking<\/strong> Jane says 5 is a factor of every whole number that has a 5 in the one’s place. Fred says 5 is a factor of every whole number that has a 0 in the one’s place. Who is correct? Explain.
      \nAnswer:
      \nBoth Jane and Fred said was correct
      \nIf you divide a number with a 5 in the one’s place by 5 they divide evenly.
      \nAnd if you do the same thing with any number with a 0 in the one’s place they divide evenly.
      \n
      \nAssessment Practice<\/strong><\/p>\n

      Question 20.
      \nWhich of the following are factors of both 18 and 42? Select all that apply.
      \n\u2610 1
      \n\u2610 3
      \n\u2610 4
      \n\u2610 6
      \n\u2610 14
      \nAnswer:
      \nA factor divides exactly into a number, leaving no remainder is called factors.
      \nThe factors of both 18 and 42 are 1, 3 and 6<\/p>\n

      Question 21.
      \nWhich of the numbers below have 2, 3, and 4 as factors? Select all that apply.
      \n\u2610 86
      \n\u2610 72
      \n\u2610 36
      \n\u2610 32
      \n\u2610 24
      \nAnswer:
      \nThe numbers 72, 36, 32, and 24 have a factor of 2, 3, and 4.<\/p>\n

      Lesson 7.2 Factors<\/h3>\n

      Solve & Share<\/strong>
      \nJared has 20 flowers. He wants to plant all of the flowers in equal rows in his garden. What are the different ways Jared can arrange the flowers in equal rows? Solve this problem any way you choose.
      \nI can … use multiplication to find the factor pairs for a whole number.
      \n\"Envision<\/p>\n

      Look Back! Make Sense and Persevere How can you check you have found all the different ways Jared can plant his flowers?<\/p>\n

      Essential Question<\/strong>
      \nHow Can You Use Multiplication to Find the Factors of a Number?<\/p>\n

      Visual Learning Bridge
      \nJean wants to arrange her action figures in equal-size groups. What are all the ways Jean can arrange her action figures?
      \nJean can think of all the factor pairs of 16. Factor pairs are two whole numbers that when multiplied give you
      \na certain product.
      \n\"Envision<\/p>\n

      \"Envision
      \nJean can arrange 1 group of 16 figures or 16 groups of 1 figure.
      \n1 \u00d7 16 = 16
      \n16 \u00d7 1 = 16
      \nSo, 1 and 16 are factors of 16.<\/p>\n

      \"Envision
      \nJean can arrange 8 groups of 2 figures or 2 groups of 8 figures.
      \n2 \u00d7 8 = 16
      \n8 \u00d7 2 = 16
      \nSo, 2 and 8 are factors of 16.<\/p>\n

      \"Envision
      \nJean can arrange 4 groups of 4 figures. 4 is a factor of 16.
      \n4 \u00d7 4 = 16
      \nThe factor pairs for 16 are 1 and 16, 2 and 8, and 4 and 4.<\/p>\n

      Convince Me! Construct Arguments How do you know there are no other factors for 16 other than 1, 2, 4, 8, and 16? Explain.<\/p>\n

      Guided Practice<\/strong><\/p>\n

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nJean bought 7 more action figures. What are the different equal-sized groups she can make now?
      \nAnswer:
      \nTotal number of action figures\u00a0 = 16
      \nTotal number of action figures that Jean brought = 7
      \nTotal number of figure at Jean\u00a0 = 16 + 7 = 23
      \nJean can arrange in two ways that are
      \n1 group of 23 and 23 groups of 1<\/p>\n

      Question 2.
      \nWhat factor besides 1 does every even number have?
      \nAnswer:<\/p>\n

      Any even number one factor is always 2 wheather one or many all the others be odd prime number.<\/p>\n

      Do You Know How?<\/strong>
      \nFor 3-6, write the factors of each number. Use counters to help.
      \nQuestion 3.
      \n2
      \nAnswer:
      \nA factor divides exactly into a number leaving no remainder is called the factors.
      \nFactors of 2 are the 1, 2<\/p>\n

      Question 4.
      \n20
      \nAnswer:
      \nA factor divides exactly into a number leaving no remainder is called the factors.
      \nFactors of 20 are 1, 2, 4, 5, 10 and 20<\/p>\n

      Question 5.
      \n28
      \nAnswer:
      \nA factor divides exactly into a number leaving no remainder is called the factors.
      \nFactors of 28 are 1, 2, 4, 7, 14 and 28<\/p>\n

      Question 6.
      \n54
      \nAnswer:
      \nA factor divides exactly into a number leaving no remainder is called the factors.
      \nFactors of 54 are 1, 2, 3, 6, 9, 18, 27 and 50
      \n
      \nIndependent Practice
      \n<\/strong>Leveled Practice For 7-12, write the factor pairs for each number.
      \nRemember, the factors of a number always include 1 and the number.<\/p>\n

      Question 7.
      \n34
      \n______ and 34
      \n2 and ______
      \nAnswer:
      \nFactor pairs are the set of two factors that, when they are multiplied together to give a particular product is called factor pairs.
      \nPair factors of 34 are
      \n1 and 34
      \n<\/span>2 and 17<\/p>\n

      Question 8.
      \n39
      \n1 and ______
      \n______ and 13
      \nAnswer:
      \nFactor pairs are the set of two factors that, when they are multiplied together to give a particular product is called factor pairs.
      \nThe factors of 39 are
      \n1 and 39
      \n3 and 13<\/p>\n

      Question 9.
      \n61
      \n1 and ______
      \nAnswer:
      \nFactor pairs are the set of two factors that, when they are multiplied together to give a particular product is called factor pairs.
      \nThe factors of 61 are
      \n1 and 61<\/p>\n

      Question 10.
      \n14
      \n______ and ______
      \n______ and ______
      \nAnswer:
      \nFactor pairs are the set of two factors that, when they are multiplied together to give a particular product is called factor pairs.
      \nThe factors of 14 are
      \n1 and 14
      \n2 and 17<\/p>\n

      Question 11.
      \n22
      \n______ and ______
      \n______ and ______
      \nAnswer:
      \nFactor pairs are the set of two factors that, when they are multiplied together to give a particular product is called factor pairs.
      \nFactors of 22 are
      \n1 and 14
      \n2 and 7
      \nQuestion 12.
      \n<\/span>51
      \n______ and ______
      \n______ and ______
      \nAnswer:
      \nFactor pairs are the set of two factors that, when they are multiplied together to give a particular product is called factor pairs.
      \nThe factors of 51 are
      \n1 and 51
      \n3 and 17<\/p>\n

      For 13-21, write the factors of each number. Use counters to help as needed.
      \nQuestion 13.
      \n6
      \nAnswer:
      \nA factor divides exactly into a number leaving no remainder is called the factors.
      \nThe factors of 6 are 1, 2, 3 and 6<\/p>\n

      Question 14.
      \n32
      \nAnswer:
      \nA factor divides exactly into a number leaving no remainder is called the factors.
      \nThe factors of 32 are 1, 2, 3, 4, 8, 16 and 32<\/p>\n

      Question 15.
      \n83
      \nAnswer:
      \nA factor divides exactly into a number leaving no remainder is called the factors.
      \nThe factors of 83 are 1 and 83<\/p>\n

      Question 16.
      \n11
      \nAnswer:
      \nA factor divides exactly into a number leaving no remainder is called the factors.
      \nThe factors of 11 are 1 and 11<\/p>\n

      Question 17.
      \n49
      \nAnswer:
      \nA factor divides exactly into a number leaving no remainder is called the factors.
      \nThe factors of 49 are 1, 7 and 49<\/p>\n

      Question 18.
      \n25
      \nAnswer:
      \nA factor divides exactly into a number leaving no remainder is called the factors.
      \nThe factors of 25 are 1, 5 and 25<\/p>\n

      Question 19.
      \n30
      \nAnswer:
      \nA factor divides exactly into a number leaving no remainder is called the factors.
      \nThe factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30<\/p>\n

      Question 20.
      \n63
      \nAnswer:
      \nA factor divides exactly into a number leaving no remainder is called the factors.
      \nThe factors of 63 are 1, 3, 7, 9, 21 and 63<\/p>\n

      Question 21.
      \n19
      \nAnswer:
      \nA factor divides exactly into a number leaving no remainder is called the factors.
      \nThe factors of 19 are 1 and 19
      \n
      \nProblem Solving
      \n<\/strong>Question 22.
      \nIrene wants to list the factors for 88. She writes 2, 4, 8, 11, 22, 44, and 88. Is Irene correct? Explain.
      \nAnswer:
      \nGiven that,
      \nThe Irene write the list of factors for are
      \n2, 4, 8, 11, 22, 44, and 88 all these are the factors of 88.
      \nYes, Irena is correct.
      \nBut we have one another factor that is 1.<\/p>\n

      Question 23.
      \n<\/span>enVision\u00ae STEM The roots of a plant are often the largest part of the plant. Winter rye can grow combined root tissue well over 984,000 feet in length. Write this number in expanded form.
      \nAnswer:<\/p>\n

      Question 24.
      \nModel with Math A restaurant receives a shipment of 5,000 ketchup packets. In one week, they use 1,824 packets. The next week, they use 2,352 packets. Write and solve equations to find how many ketchup packets the restaurant has left.
      \nAnswer:
      \nGiven that,
      \nThe restaurant receives a shipment of ketchup packets = 5000
      \nTotal number of ketchup packets that the restaurant used in one week = 1824
      \nTotal number of ketchup packets that the restaurant used in next week = 2352
      \n<\/span>Total number of packets that the restaurant used in one week and next week = 1824 + 2352 = 4176<\/p>\n

      Question 25.
      \nAny number that has 9 as a factor also has 3 as a factor. Why is this?
      \nAnswer:<\/p>\n

      Question 26.
      \nHigher Order Thinking<\/strong> A mother manatee, pictured to the right, is three times as long as her baby manatee.
      \n\"Envision
      \na. How long is her baby manatee? Write and solve an equation.
      \nAnswer:<\/p>\n

      b. If a blue whale is 9 times as long as the manatee shown, how much longer is a blue whale than the manatee? Write and solve equations:
      \nAnswer:
      \nGiven that,
      \nThe given manatee show length = 12 feets
      \nThe blue whale length = 9 times longer than the manatee.
      \nTotal length of the blue whale = 12 \u00d7 9 = 108 feets
      \nAssessment Practice<\/strong><\/p>\n

      Question 27.
      \nWhich number has 3 and 29 as one of its factor pairs?
      \nA. 3
      \nB. 17
      \nC. 67
      \nD. 87
      \nAnswer:
      \nD is correct.
      \n87 has the factor pair of 3 and 29.
      \nFactor pair is a set of two factors which, when multiplied together give a particular product is called factor pairs.
      \nQuestion 28.
      \nA store manager wants to display 45 cans of soup in an array. Which of the following shows 3 ways the cans could be displayed?
      \nA. 1 \u00d7 9, 9 \u00d7 5, 3 \u00d7 15
      \nB. 15 \u00d7 3, 9 \u00d7 1, 5 \u00d7 9
      \nC. 5 \u00d7 9, 3 \u00d7 15, 9 \u00d7 5
      \nD. 45 \u00d7 1, 15 \u00d7 1, 9 \u00d7 1
      \nAnswer:
      \nGiven that,
      \nThe store manager wants to display 45 cans of soup in an array.
      \nWe want to arrange in 3 ways from the following
      \n5 \u00d7 9, 3 \u00d7 15, 9 \u00d7 5
      \nOption C is the correct<\/p>\n

      Lesson 7.3 Problem Solving<\/h3>\n

      Repeated Reasoning<\/strong>
      \nSolve & Share<\/strong>
      \nA closet company sells wooden storage cubicles. Jane bought 24 cubicles. She wants to arrange them in a rectangular array. What are all of the different ways Jane can arrange them, using all of her cubicles? Explain how you know you found them all.
      \nI can … use repeated reasoning to generalize how to solve similar problems.
      \n\"Envision<\/p>\n

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

        \n
      • Are any calculations repeated?<\/li>\n
      • Can I generalize from examples?<\/li>\n
      • What shortcuts do I notice?
        \n\"Envision<\/li>\n<\/ul>\n

        Look Back! Generalize Do you need to try all numbers from 1 to 24 to be sure you have all the factor pairs for 24? Explain.<\/p>\n

        Essential Question<\/strong>
        \nHow Can You Use Repeated Reasoning to Find All the Factors for a Number?<\/p>\n

        Visual Learning Bridge
        \nA new city park is opening. The gardener needs to select 15 trees from a nursery and plant the trees in a rectangular array. What are all the different ways the gardener can plant the trees?
        \n\"Envision
        \nCan you look for a general method to solve this problem?
        \nI can find all the possible factors of 15 that can be arranged in a rectangular array.<\/p>\n

        How can I make a generalization from repeated reasoning?
        \nI can<\/p>\n

          \n
        • look for things that repeat in a problem.<\/li>\n
        • look for shortcuts.<\/li>\n
        • generalize from the example.<\/li>\n<\/ul>\n

          To find all of the factors of 15, I divide 15 by divisors starting with 1. Then I use the Commutative Property to write two multiplication equations.
          \n1 \u00d7 15 = 15 and 15 \u00d7 1= 15
          \n2 is not a factor<\/p>\n

          3 \u00d7 5 = 15 and 5 \u00d7 3 = 15
          \n4 is not a factor<\/p>\n

          5 \u00d7 3 = 15 and 3 \u00d7 5 = 15
          \nWhen factor pairs start repeating, you can make a general statement, or generalize, that all the factors of a number
          \nare found.<\/p>\n

          I already found the factor paired with 5, 3 \u00d7 5 and 5 \u00d7 3.
          \nThe gardener has 4 different ways to plant the trees: 1 \u00d7 15, 15 \u00d7 1, 5 \u00d7 3, and 3 \u00d7 5 arrays.<\/p>\n

          Convince Me! Construct Arguments The diagram shows all the factor pairs of 24. Use the diagram to justify the conclusion that when factor pairs start repeating, you know you have found all the factors of a number.
          \n\"Envision<\/p>\n

          Guided Practice<\/strong><\/p>\n

          Generalize<\/strong> Ms. Maribel wants to arrange the 20 desks in her classroom into rows with the same number of desks in each row. She wants at least 2, but not more than 8 rows.
          \n\"Envision
          \nQuestion 1.
          \nWhat are the factor pairs for 20? Explain how you know you have found them all.
          \nAnswer:
          \nThe factor pairs of 20 are
          \n1 and 20
          \n2 and 10
          \n4 and 5
          \nFactors are often given as pairs of numbers that multiply together to give the original numbers these are called factor pairs.<\/p>\n

          Question 2.
          \nFind the ways Ms. Maribel can arrange the desks.
          \nAnswer:
          \nGiven that,
          \nTotal number of desks = 20
          \nMs. Maribel can arrange the desks in 3 ways that are
          \n1 row of 20 desks
          \n2 row of 10 desks
          \nIndependent Practice<\/strong><\/p>\n

          Generalize<\/strong> Kevin invited 15 friends to his birthday party. They played a game where everyone had to separate into groups. Each group had the same number of children. The game could not be played with all 16 children in one group and each group had to have more than 1 child.<\/p>\n

          Question 3.
          \nList the factor pairs of 16 and then find the different ways Kevin and his friends could divide into groups.
          \nAnswer:
          \nFactors are often given as pairs of numbers that multiply together to give the original numbers these are called factor pairs.
          \nThe factor pairs of 16 are 1 and 16, 2 and 8 .
          \nKevin and his friends could divide the children’s groups into two ways that are
          \n16 children in 1 group
          \n8 Children in\u00a0 2 groups<\/p>\n

          Question 4.
          \nWhy does 16 have an odd number of factors?
          \nAnswer:
          \nA factor divides exactly into a number leaving no remainder is called the factors.
          \nThe factors of 16 are 1, 2, 8 and 16
          \nThe total number of factors of 16 is 4
          \nThen it is not an odd number of factors.<\/p>\n

          Question 5.
          \nCan you stop checking for factor pairs when you find a pair that repeats? Explain.
          \nAnswer:
          \nYes, we can stop the factor pairs when we find the repeated factors.
          \nWe can write one factor only one time.
          \nProblem Solving<\/strong><\/p>\n

          Performance Task<\/strong>
          \nStore Displays A pet store needs 3 displays with the products shown. The boxes of kitty litter need to be stacked with the same number of boxes in each row. There needs to be at least 3 rows with at least 3 boxes in each row. What are all the ways the boxes of kitty litter could be stacked?
          \n\"Envision<\/p>\n

          Question 6.
          \nMake Sense and Persevere What quantities are given in the problem and what do the numbers mean?
          \n\"Envision
          \nAnswer:<\/p>\n

          Question 7.
          \nReasoning<\/strong> What are the factor pairs for 48?
          \nAnswer:
          \nThe factor pairs mean the pair of numbers that multiply together to give the original number is called factor pairs.
          \nFactor pairs of 48 are
          \n1 and 48
          \n2 and 24
          \n3 and 16
          \n4 and 12
          \n6 and 8
          \nBy multiplying these numbers we get 48.<\/p>\n

          Question 8.
          \nBe Precise What are all the ways the boxes of kitty litter can be stacked with at least 3 rows with at least 3 boxes in each row?
          \nAnswer:
          \nHere we can arrange the boxes of Kitty litter in different ways with atleast 3 rows with at least 3 boxes.
          \nTotal number of Kitty litter boxes = 48
          \nFirst, we can arrange 48 boxes in 3 rows of 16 boxes.
          \nSecond, we can arrange in 4 rows of 12 boxes.
          \nThird, we can arrange in 6 rows of 8 boxes.
          \nLesson 7.4 Prime and Composite Numbers<\/p>\n

          Solve & Share<\/strong>
          \nMax has 2 red tiles, 3 blue tiles, 4 yellow tiles, and 8 green tiles. How many different rectangular arrays of each color can Max make? Explain how you know you found all the arrays. Solve this problem any way you choose.
          \nI can … use factors to determine if a whole number is prime or composite.
          \n\"Envision<\/p>\n

          Look Back! What do you notice about the factors of each number of color tiles and the number of arrays?<\/p>\n

          Essential Question<\/strong>
          \nHow Can You Identify Prime and Composite Numbers?<\/p>\n

          Visual Learning Bridge
          \nThe data table lists the factors for 2, 3, 4, 5, and 6. What do you notice about the factors for 5? What do you notice about the factors for 6?
          \n\"Envision<\/p>\n

          Prime Numbers
          \n5 is a prime number.
          \nIt has only 2 factors, 1 and itself.
          \n\"Envision<\/p>\n

          Composite Numbers
          \n6 is a composite number.
          \nThe factors for 6 are 1, 2, 3, and 6.
          \n\"Envision<\/p>\n

          Convince Me! Generalize Can a number be both prime and composite? Explain.<\/p>\n

          Guided Practice<\/strong><\/p>\n

          Do You Understand?<\/strong>
          \nQuestion 1.
          \nWhat is the only even prime number?
          \nAnswer:
          \n2 is the only even prime number.
          \n2 has only two factors that are 1 and 2
          \nThe factors that are less than two factors are called prime numbers.<\/p>\n

          Question 2.
          \nWrite an odd number that is not prime. What makes it a composite number?
          \nAnswer:
          \n49 is the odd number and it is not prime because it has more than 2 factors.
          \nFactors of 49 are 1, 7 and 49
          \nSo, it is a composite number.<\/p>\n

          Question 3.
          \nRoger has 47 cars. Can he group the cars in more than 2 ways?
          \nAnswer:
          \nGiven that,
          \nTotal number of cars at Roger = 47
          \nWe can arrange in two groups
          \n17 cars in 1 group
          \n1 group of 17 cars
          \nDo You Know How?<\/strong>
          \nFor 4-9, tell whether each number is prime or composite.<\/p>\n

          Question 4.
          \n32
          \nAnswer:
          \nA factor divides exactly into a number leaving no remainder is called the factors.
          \nThe factors of 32 are 1, 2, 4, 8, 16 and 32
          \n32 is not a prime number because it has more than 2 factors.
          \nThe number that having more than two factors are called composite numbers.
          \nSo 32 is a composite number.<\/p>\n

          Question 5.
          \n51
          \nAnswer:
          \nA factor divides exactly into a number leaving no remainder is called the factors.
          \nThe factors of 51 are 1, 3, 17 and 51
          \n51 is not a prime number because it has more than 2 factors.
          \nThe number that having more than two factors are called composite numbers.
          \nSo, 51 is a composite number.<\/p>\n

          Question 6.
          \n73
          \nAnswer:
          \nA factor divides exactly into a number leaving no remainder is called the factors.
          \nThe factors of 73 are 1 and 17 and
          \n51 is a prime number because it has\u00a0 2 factors.
          \nThe number that having more than two factors are called composite numbers.
          \nSo, 73 is not a composite number.<\/p>\n

          Question 7.
          \n21
          \nAnswer:
          \nA factor divides exactly into a number leaving no remainder is called the factors.
          \nThe factors of 21 are 1, 3, 7 and 21
          \n21 is not a prime number because it has more than 2 factors.
          \nThe number that having more than two factors are called composite numbers.
          \nSo, 21 is a composite number.<\/p>\n

          Question 8.
          \n95
          \nAnswer:
          \nA factor divides exactly into a number leaving no remainder is called the factors.
          \nThe factors of 95 are 1, 5, 19 and 95
          \n95 is not a prime number because it has more than 2 factors.
          \nThe number that having more than two factors are called composite numbers.
          \nSo, 95 is a composite number.<\/p>\n

          Question 9.
          \n29
          \nAnswer:
          \nA factor divides exactly into a number leaving no remainder is called the factors.
          \nThe factors of 29 are 1 and 29
          \n29 is a prime number because it has\u00a0 2 factors.
          \n<\/span>The number that having more than two factors are called composite numbers.
          \nSo,29 is not a composite number.
          \nA number is composite if it has more than 2 factors.
          \nIndependent Practice<\/strong><\/p>\n

          Leveled Practice For 10-19, tell whether each number is prime or composite.
          \nQuestion 10.
          \n\"Envision
          \nAnswer:
          \nA factor divides exactly into a number leaving no remainder is called the factors.
          \nThe factors of 7 are 1 and 7
          \n7 is a prime number because it has\u00a0 2 factors.
          \nThe number that having more than two factors are called composite numbers.
          \nSo, 7 is not a composite number.
          \nQu<\/span>estion 11.<\/span><\/p>\n

          \"Envision
          \nAnswer:
          \nA factor divides exactly into a number leaving no remainder is called the factors.
          \nThe factors of 10 are 1, 2, 5 and 10
          \n7 is a composite number because it has more than\u00a0 2 factors.<\/p>\n

          Question 12.
          \n12
          \nAnswer:
          \nA factor divides exactly into a number leaving no remainder is called the factors.
          \nThe factors of 12 are 1, 2, 3, 4, 6 and 12
          \nThe number 12 is a composite number because it has more than\u00a0 2 factors.<\/p>\n

          Question 13.
          \n97
          \nAnswer:
          \nA factor divides exactly into a number leaving no remainder is called the factors.
          \nThe factors of 97 are 1 and 97
          \nThe number 97 is a prime number because it has\u00a0 2 factors.
          \nThe number that having more than two factors are called composite numbers.
          \nSo, 97 is not a composite number.<\/p>\n

          Question 14.
          \n90
          \nAnswer:
          \nA factor divides exactly into a number leaving no remainder is called the factors.
          \nThe factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90
          \nThe number 90 is a composite number because it has more than\u00a0 2 factors.<\/p>\n

          Question 15.
          \n31
          \nAnswer:
          \nA factor divides exactly into a number leaving no remainder is called the factors.
          \nThe factors of 30 are 1 and 30
          \nThe number 30 is a prime number because it has\u00a0 2 factors.
          \nThe number that having more than two factors are called composite numbers.
          \nSo, 30 is not a composite number.<\/p>\n

          Question 16.
          \n11
          \nAnswer:
          \nA factor divides exactly into a number leaving no remainder is called the factors.
          \nThe factors of 11 are 1 and 11
          \nThe number 11 is a prime number because it has\u00a0 2 factors.
          \nThe number that having more than two factors are called composite numbers.
          \nSo, 11 is not a composite number.<\/p>\n

          Question 17.
          \n44
          \nAnswer:
          \nA factor divides exactly into a number leaving no remainder is called the factors.
          \nThe factors of 44 are 1, 2, 4, 11, 22 and 44
          \nThe number 44 is a composite number because it has more than\u00a0 2 factors.<\/p>\n

          Question 18.
          \n3
          \nAnswer:
          \nA factor divides exactly into a number leaving no remainder is called the factors.
          \nThe factors of 3 are 1 and 3
          \n3 is a prime number because it has\u00a0 2 factors.
          \nThe number that having more than two factors are called composite numbers.
          \nSo, 3 is not a composite number.<\/p>\n

          Question 19.
          \n59
          \nAnswer:
          \nA factor divides exactly into a number leaving no remainder is called the factors.
          \nThe factors of 59 are 1 and 59
          \nThe number 59 is a prime number because it has\u00a0 2 factors.
          \nThe number that having more than two factors are called composite numbers.
          \nSo, 59 is not a composite number.<\/p>\n

          Problem Solving<\/strong><\/p>\n

          For 20-21, use the graph at the right.
          \n\"Envision<\/p>\n

          Question 20.
          \nWhich type of flower received a prime number of votes?
          \nAnswer:
          \nTotal number of Daffodils flowers = 5
          \nThe factors of 5 are 1 and 5
          \nThe number 5 is a prime number because it has only two factors.
          \nThe Daffodils flowers received the prime number of votes.<\/p>\n

          Question 21.
          \nHow many votes are represented by the picture graph?
          \nAnswer:
          \nGiven that,
          \nTotal number of Daffodils flowers = 2 and half
          \nTotal number of Daisies flowers = 3
          \nTotal number of Tulips flowers = 5
          \nEach flower icon = 2 votes
          \nTotal number of flowers = 2 and half + 3 + 5 = 10 and half
          \n10 and half flowers \u00d7 2 = 21
          \nTotal number of votes = 21<\/p>\n

          Question 22.
          \nCritique Reasoning<\/strong> Maria says every number in the nineties is composite. Jackie says 1 number in the nineties is prime. Who is correct? Explain your answer.
          \nAnswer:
          \nGiven that,
          \nMaria says every number in the nineties is composite.
          \nJackie says 1 number in the nineties is prime.
          \nJackie said was correct 1 number in the nineties is prime that is 97.
          \nThe number 97 has 2 factors so it is a prime number.<\/p>\n

          Question 23.
          \nCritique Reasoning<\/strong> Greta says the product of two prime numbers must also be prime. Joan disagreed. Who is correct?
          \nAnswer:
          \nThe product of two prime numbers is a composite numbers
          \nFor example, 3 and 7 are the two prime numbers.
          \nThe product of 3 and 7 is 21
          \nThe factors of 21 are 1, 3, 7 and 21
          \n21 is not a prime number it is a composite number.<\/p>\n

          Question 24.
          \nJanelle has 342 pennies, 62 nickels, and 12 dimes. If Janelle exchanges her coins for dollars, how many dollars will she have? How many cents will remain?
          \nAnswer:<\/p><\/blockquote>\n

          Question 25.
          \nHigher Order Thinking<\/strong> Why is 1 neither a prime number nor a composite number?
          \nAnswer:
          \nA prime number is a whole number that only has two factors which are itself and one.
          \nA composite number has a factor in addition to one and itself the number is neither prime nor composite.
          \n
          \nAssessment Practice
          \n<\/strong>Question 26.
          \nSelect all the groups of numbers that are prime.
          \n\u2610 17, 19, 53
          \n\u2610 37, 43, 79
          \n\u2610 52, 67, 99
          \n\u2610 63, 72, 83
          \n\u2610 59, 89, 97
          \nAnswer:
          \n17, 19, 53
          \n37, 43, 79
          \n59, 89, 97 these set of groups having the prime numbers.<\/p>\n

          Question 27.
          \nSelect all the expressions with sums that are composite.
          \n\u2610 17 + 25
          \n\u2610 33 + 51
          \n\u2610 16 + 83
          \n\u2610 29 + 32
          \n\u2610 47 + 29
          \nAnswer:
          \n17 + 25 = 42
          \n33 + 51 = 84
          \n16 + 83 = 99
          \n47 + 29 = 76
          \nThe factors of 42 are 1, 2, 3,6, 7, 14, 21 and 42
          \nThe factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28 and 84
          \nThe factors of 99 are 1, 3, 9, 11, 33 and 99
          \nThe factors of 76 are 1, 2, 4, 19, 38 and 76
          \n42, 84, 99, 76 are the composite number because the factors of all these numbers are<\/p>\n

          Lesson 7.5 Multiples<\/h3>\n

          Solve & Share<\/strong>
          \nThere are 9 players on the golf practice range. If each player practices with the same number of golf balls, how many balls might be in play at the same time? Solve this problem any way you choose.
          \nI can … use multiplication to find multiples of a number
          \n\"Envision<\/p>\n

          Look Back! Can you show all of the answers to the problem? Explain.<\/p>\n

          Essential Question<\/strong>
          \nHow Can You Find Multiples of a Number?<\/p>\n

          Visual Learning Bridge
          \nIt takes 8 minutes for Car A to make one full turn on the Ferris wheel. If the Ferris wheel continues to turn at the same speed for the next hour, at what times during the hour will Car A return to the starting point?
          \n\"Envision<\/p>\n

          Step 1
          \nOne full turn takes 8 minutes.
          \n1 \u00d7 8 = 8
          \n8 is a multiple of 1 and 8 because 1 \u00d7 8 = 8.
          \nCar A is back at the starting point after another 8 minutes.<\/p>\n

          Step 2
          \nTwo full turns take 16 minutes.
          \n2 \u00d7 8 = 16
          \nCar A is back at the starting point after 8 minutes.
          \n2 and 8 are factors of 16. 16 is a multiple of 2 and 8.<\/p>\n

          Step 3
          \nCar A is at the starting point every 8 minutes after that:
          \n3 \u00d7 8 = 24
          \n4 \u00d7 8 = 32
          \n5 \u00d7 8 = 40
          \n6 \u00d7 8 = 48
          \n7 \u00d7 8 = 56
          \nDuring the hour, Car A returns to the starting point after 8, 16, 24, 32, 40, 48, and 56 minutes.<\/p>\n

          Convince Me! Reasoning What is the next multiple after 56? Explain why it is NOT used.<\/p>\n

          Another Example!<\/strong>
          \nFactors are numbers that when multiplied together give a product. A whole number is a multiple of each of its factors.
          \nFactors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
          \n24 is a multiple of 1, 2, 3, 4, 6, 8, 12, and 24.<\/p>\n

          Guided Practice<\/strong><\/p>\n

          Do You Understand?<\/strong>
          \nQuestion 1.
          \nIf the Ferris wheel in the example on the previous page turns at the same speed, will Car A return to the starting point at 75 minutes? Explain.
          \nAnswer:<\/p>\n

          Question 2.
          \nSuppose the Ferris wheel speeds up so it makes one full turn every 6 minutes. When will Car A return to the starting point if the Ferris wheel continues to turn for one half hour?
          \nAnswer:<\/p>\n

          Do You Know How?<\/strong>
          \nFor 3-4, write five multiples of each number
          \nQuestion 3.
          \n2
          \nAnswer:
          \nFive multiples of 2 are
          \n2 \u00d7 1 = 2
          \n2 \u00d7 2 = 4
          \n2 \u00d7 3 = 6
          \n2 \u00d7 4 = 8
          \n2 \u00d7 5 = 10<\/p>\n

          Question 4.
          \n9
          \nAnswer:
          \nFive multiples of 9 are
          \n9 \u00d7 1 = 9
          \n9 \u00d7 2 = 18
          \n9 \u00d7 3 = 27
          \n9 \u00d7 4 = 36
          \n9 \u00d7 5 = 45<\/p>\n

          For 5-6, tell whether the first number is a multiple of the second number.
          \nQuestion 5.
          \n14, 2
          \nAnswer:
          \nMultiple of a number is exactly divisible by the number.
          \n14 is exactly divisible by 2.
          \nSo, 14 is not a multiple of 2.<\/p>\n

          Question 6.
          \n3, 18
          \nAnswer:
          \nMultiple of a number is exactly divisible by the number
          \n3 is not exactly divisible by 18.
          \nSo, 3 is not a multiple of 6<\/p>\n

          Independent Practice\u00a0<\/strong><\/p>\n

          For 7-14, write five multiples of each number.
          \nYou can skip count to find multiples of numbers. Be Precise.
          \nQuestion 7.
          \n7
          \nAnswer:
          \nFive multiples of 7 are
          \n7 \u00d7 1 = 7
          \n7 \u00d7 2 = 14
          \n7 \u00d7 3 = 21
          \n7 \u00d7 4 = 28
          \n7 \u00d7 5 = 35
          \nThe five numbers 7, 14, 21, 28 and 35 are multiples of 7<\/p>\n

          Question 8.
          \n4
          \nAnswer:
          \nFive multiples of 4
          \n4 \u00d7 1 = 4
          \n4 \u00d7 2 = 8
          \n4 \u00d7 3 = 12
          \n4 \u00d7 4 = 16
          \n4 \u00d7 5 = 20
          \nThe five numbers 4, 8, 12, 16, and 20 are the multiples of 4.<\/p>\n

          Question 9.
          \n6
          \nAnswer:
          \n6 \u00d7 1 = 6
          \n6 \u00d7 2 = 12
          \n6 \u00d7 3 = 18
          \n6 \u00d7 4 = 24
          \n6 \u00d7 5 = 30
          \nThe five numbers 6, 12, 18, 24, and 30 are the multiples of 30<\/p>\n

          Question 10.
          \n5.
          \nAnswer:
          \nFive multiples of 5 are
          \n5 \u00d7 1 = 5
          \n5 \u00d7 2 = 10
          \n5 \u00d7 3 = 15
          \n5 \u00d7 4 = 20
          \n5 \u00d7 5 = 25
          \nThe five numbers 5, 10, 15, 20 and 25 are the multiples of 5<\/p>\n

          Question 11.
          \n11
          \nAnswer:
          \nFive multiples of 11 are
          \n11 \u00d7 1 = 11
          \n11\u00d7 2 = 22
          \n11 \u00d7 3 = 33
          \n11 \u00d7 4 = 44
          \n11 \u00d7 5 = 55
          \nThe first five numbers 11, 22, 33, 44 and 55 are the multiples of 11<\/p>\n

          Question 12.
          \n1
          \nAnswer:
          \nFive multiples of 1 are
          \n1 \u00d7 1 = 1
          \n1 \u00d7 2 = 2
          \n1 \u00d7 3 = 3
          \n1 \u00d7 4 = 4
          \n1 \u00d7 5 = 5
          \nThe first five numbers 1, 2, 3, 4 and are the multiples of 1
          \n
          \nQuestion 13.
          \n<\/span>20
          \nAnswer:
          \nFive multiples of 20 are
          \n20 \u00d7 1 = 20
          \n20 \u00d7 2 = 40
          \n20 \u00d7 3 = 60
          \n20 \u00d7 4 = 80
          \n20 \u00d7 5 = 100
          \nThe five numbers 20, 40, 60, 80 and 100 are the multiples of 20
          \n
          \nQuestion 14.
          \n<\/span>15
          \nAnswer:
          \n15 \u00d7 1 = 15
          \n15 \u00d7 2 = 30
          \n15 \u00d7 3 = 45
          \n15 \u00d7 4 = 60
          \n15 \u00d7 5 = 75
          \nThe five numbers 15, 30, 45, 60, and 75 are the multiples of 15<\/p>\n

          For 15-18, tell whether the first number is a multiple of the second number.
          \nQuestion 15.
          \n44, 6
          \nAnswer:
          \nMultiple of a number is exactly divisible by the number.
          \n44 is not exactly divisible by 6.
          \nSo, 44 is not a multiple of 6.<\/p>\n

          Question 16.
          \n25, 5
          \nAnswer:
          \nMultiple of a number is exactly divisible by the number.
          \n25 is exactly divisible by 5.
          \nSo, 25 is a multiple of 5.<\/p>\n

          Question 17.
          \n30, 6
          \nAnswer:
          \nMultiple of a number is exactly divisible by the number.
          \n30 is exactly divisible by 6.
          \n<\/span>So, 30 is a multiple of 6.<\/p>\n

          Problem Solving<\/strong><\/p>\n

          Question 19.
          \nName all the numbers of which 45 is multiple.
          \nAnswer:<\/p>\n

          The numbers 45, 90, 135, 180 and 225 are the multiples of 45<\/p>\n

          Question 20.
          \nCritique Reasoning Lindsay says all numbers that are multiples of 4 have 2 as a factor. Is Lindsay correct? Explain.
          \nAnswer:<\/p>\n

          Question 21.
          \nTrisha bought bags of tennis balls. There are eight tennis balls in each bag. Could Trisha have 75 tennis balls? Explain.
          \nAnswer:<\/p>\n

          Given that,
          \nNumber of tennis ball in each bags at Trisha = 8
          \nExpected tennis balls at Trisha = 75
          \nHow many Balls at Trisha = 75 \u00f7 8<\/p>\n

          Question 22.<\/span><\/p>\n

          Higher Order Thinking<\/strong> Gerri says that if a number is a multiple of 9 it is also a multiple of 3. Do you agree? Explain.
          \nAnswer:<\/p>\n

          Multiple of 9 is also a multiple of 3
          \nFor example 27 \u00f7 9 = 3
          \nSo, 27 is a multiple of 3 and 9.<\/p>\n

          Question 23.
          \nDescribe how 20,000 and 2,000 are related.
          \nAnswer:<\/p>\n

          Question 24.
          \nIsabel wrote this mystery problem: The quotient is a multiple of 6. The dividend is a multiple of 9. The divisor is a factor of 12. Write one possible equation to Isabel’s mystery problem.
          \nAnswer:<\/p>\n

          Assessment Practice<\/strong><\/p>\n

          Question 25.
          \nLatifa and John played a game of multiples. Each player picks a number card and says a multiple of that number. Latifa picked a 9. Write all the multiples of 9 from the box.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-Grade-4-Answer-Key-Topic-7-Factors-and-Multiples-32\"<\/p>\n

          Multiples of 9 from the given numbers are 9, 12, and 33.<\/p>\n

          Question 26.
          \nA roller-coaster ride completes a full loop every 3 minutes. Seth listed multiples of 1 3 to determine when the ride would be back at its starting point. Write all the multiples of 3 from the box.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-Grade-4-Answer-Key-Topic-7-Factors-and-Multiples-33\"<\/p>\n

          Multiples of 3 from the given numbers are 9, 45, and 36.<\/p>\n

          Topic 12 Fluency Practice Activity<\/h3>\n

          Follow the Path<\/strong>
          \nShade a path from START to FINISH. Follow the sums and differences that are correct. You can only move up, down, right, or left.
          \nI can … add and subtract multi-digit whole numbers.
          \n\"Envision<\/p>\n

          Topic 7 Vocabulary Review<\/strong><\/p>\n

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

            \n
          • array<\/li>\n
          • composite number<\/li>\n
          • factor<\/li>\n
          • factor pairs<\/li>\n
          • generalization<\/li>\n
          • multiple<\/li>\n
          • prime number<\/li>\n
          • whole number<\/li>\n<\/ul>\n

            Question 1.
            \nCross out the numbers that are NOT factors of 16.
            \n1
            \n2
            \n3
            \n4
            \n8
            \nAnswer:<\/p>\n

            Question 2.
            \nCross out the numbers that are NOT multiples of 3.
            \n3
            \n6
            \n9
            \n13
            \n23
            \nAnswer:<\/p>\n

            The numbers 13 and 23 are not the multiples of 3.<\/p>\n

            Question 3.
            \nCross out the numbers that are NOT whole numbers.
            \n\\(\\frac{1}{4}\\)
            \n\\(\\frac{1}{2}\\)
            \n7
            \n17\\(\\frac{1}{5}\\)
            \n6,219
            \nAnswer:<\/p>\n

            Question 4.
            \nCross out the numbers that are NOT factor pairs for 24.
            \n1 and 24
            \n2 and 12
            \n3 and 6
            \n4 and 8
            \n4 and 6
            \nAnswer:<\/p>\n

            Label each example with a term from the Word List.
            \nQuestion 5.
            \n13 __________
            \nAnswer:<\/p>\n

            Question 6.
            \n12 _____________
            \nAnswer:<\/p>\n

            Question 7.
            \n\"Envision ____________
            \nAnswer:<\/p>\n

            Question 8.
            \nWhen factor pairs begin repeating, I have found all the pairs for a number.
            \nAnswer:<\/p>\n

            Use Vocabulary in Writing<\/strong>
            \nQuestion 9.
            \nMarisol says 23 is both a prime and a composite number because 2 and 3 are both prime. Use at least 3 terms from the Word List to explain the error in Marisol’s reasoning.
            \nAnswer:
            \n23 is only a prime number it is not a composite number
            \nThe factors of 23 are 1 and 23
            \nThe factors that are more than two are composite numbers.
            \nHere there are only 2 factors so it is called a prime number.
            \n23 is a whole number.<\/p>\n

            Topic 7 Reteaching<\/h3>\n

            Set A pages 261-264<\/strong><\/p>\n

            Draw arrays to find all the factor pairs for 8.
            \n\"Envision
            \nThe factor pairs for 8 are 1 and 8, 2 and 4.<\/p>\n

            Remember<\/strong> that 1 is a factor of every number.<\/p>\n

            Use grid paper to find the factor pairs for each number.
            \nQuestion 1.
            \n26
            \nAnswer:<\/p>\n

            Factor pairs are the set of two factors that, when they are multiplied together to give a particular product is called factor pairs.
            \nFactors pairs of 26 are
            \n1 and 26
            \n2 and 13<\/p>\n

            Question 2.
            \n9
            \nAnswer:<\/p>\n

            Factor pairs are the set of two factors that, when they are multiplied together to give a particular product is called factor pairs.
            \nFactor pairs of 9 are
            \n1 and 9
            \n3 and 3<\/p>\n

            Question 3.
            \n37
            \nAnswer:<\/p>\n

            Factor pairs are the set of two factors that, when they are multiplied together to give a particular product is called factor pairs.
            \nFactor pairs of 37 are
            \n37 and 1
            \n1 and 37<\/p>\n

            Question 5.
            \n19
            \nAnswer:
            \nFactor pairs are the set of two factors that, when they are multiplied together to give a particular product is called factor pairs.
            \nFactor pairs of 19 are
            \n1 and 19<\/p>\n

            Set B pages 265-268<\/strong><\/p>\n

            Find the factor pairs for 12.
            \n1 and 12
            \n2 and 6
            \n3 and 4
            \nThe factors of 12 are 1, 2, 3, 4, 6, and 12.<\/p>\n

            Remember<\/strong> you can use counters or grids to make arrays and find the factors of a number.<\/p>\n

            Find the factors of each number.
            \nQuestion 1.
            \n45
            \nAnswer:
            \nA factor divides exactly into a number leaving no remainder is called the factors.
            \nThe factors of\u00a0 45 are 1, 3, 5, 15 and 45<\/p>\n

            Question 2.
            \n40
            \nAnswer:
            \nA factor divides exactly into a number leaving no remainder is called the factors.
            \nThe factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40<\/p>\n

            Question 3.
            \n56
            \nAnswer:
            \nA factor divides exactly into a number leaving no remainder is called the factors.
            \nThe factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56<\/p>\n

            Question 4.
            \n63
            \nAnswer:
            \nA factor divides exactly into a number leaving no remainder is called the factors.
            \nThe factors of 63 are 1, 3, 7, 9, 21 and 63<\/p>\n

            Set C pages 269-272<\/strong><\/p>\n

            Think about these questions to help you use repeated reasoning.
            \nThinking Habits<\/p>\n

              \n
            • Are any calculations repeated?<\/li>\n
            • Can I generalize from examples?<\/li>\n
            • What shortcuts do I notice?
              \n\"Envision<\/li>\n<\/ul>\n

              Remember<\/strong> to look for repeating factors when dividing to find the factor pairs of a number.<\/p>\n

              A valet has 34 cars to park in a rectangular array.
              \nQuestion 1.
              \nWhat are the different ways the valet could park the cars?
              \nAnswer:
              \nGiven that,
              \nTotal number of cars = 34
              \nFactors of 34 are 1, 2, 17, and 34
              \nThe different ways the valet could park the cars are
              \n1 and 34
              \n34 and 1
              \n2 and 17
              \n17 and 2<\/p>\n

              Question 2.
              \nHow do you know when you can stop looking for factors of a number?
              \nAnswer:<\/p>\n

              Set D pages 273-276<\/strong><\/p>\n

              Is 49 prime or composite?
              \nTo determine if 49 is prime or composite, find whether 49 has factors other than 1 and 49.
              \n49 is composite because it is divisible by 7.
              \n49 = 7 \u00d7 7
              \n\"Envision<\/p>\n

              Remember<\/strong> you can use an array to determine if a number is prime or composite.<\/p>\n

              Tell whether each number is prime or composite.
              \nQuestion 1.
              \n13
              \nAnswer:
              \nA factor divides exactly into a number leaving no remainder is called the factors.
              \nThe factors of 13 are 1 and 13
              \nThe number that has only two factors is called a prime number.
              \nSo, The number 12 is a prime number.
              \nSo it is not a composite number.<\/p>\n

              Question 2.
              \n25
              \nAnswer:
              \nA factor divides exactly into a number leaving no remainder is called the factors.
              \nThe factors of 25 are 1,5 and 25
              \nThe number that has more than two factors are called composite numbers.
              \nSo, The number 25 is composite number.<\/p>\n

              Question 3.
              \n55
              \nAnswer:
              \nA factor divides exactly into a number leaving no remainder is called the factors.
              \nThe factors of 55 are 1,5, 11 and 55
              \nThe number that has more than two factors are called composite numbers.
              \nSo, The number 55 is a composite number.<\/p>\n

              Question 4.
              \n2
              \nAnswer:
              \nA factor divides exactly into a number leaving no remainder is called the factors.
              \nThe factors of 2 are 1 and 2
              \nThe number that has only two factors is called a prime number.
              \nSo, The number 2 is a prime number.<\/p>\n

              Question 5.
              \n29
              \nAnswer:
              \nA factor divides exactly into a number leaving no remainder is called the factors.
              \nThe factors of 25 are 1 and 29
              \nThe number that has only two factors is called a prime number.
              \nSo, The number 25 is a prime number.<\/p>\n

              Question 6.
              \n23
              \nAnswer:
              \nA factor divides exactly into a number leaving no remainder is called the factors.
              \nThe factors of 23 are 1 and 23
              \nThe number that has only two factors is called a prime number.
              \nSo, The number 23 is a prime number.<\/p>\n

              Question 7.
              \n64
              \nAnswer:
              \nA factor divides exactly into a number leaving no remainder is called the factors.
              \nThe factors of 64 are 1, 2, 4, 8, 16 32and 64
              \nThe number that has more than two factors are called composite numbers.
              \nSo, The number 64 is a composite number.<\/p>\n

              Question 8.
              \n99
              \nAnswer:
              \nA factor divides exactly into a number leaving no remainder is called the factors.
              \nThe factors of 99 are 1, 3, 9, 11, 33 and 99
              \nThe number that has more than two factors are called composite numbers.
              \nSo, The number 99 is a composite number.<\/p>\n

              Question 9.
              \n5
              \nAnswer:
              \nA factor divides exactly into a number leaving no remainder is called the factors.
              \nThe factors of 5 are 1 and 5
              \nThe number that has only two factors is called a prime number.
              \n<\/span>So, The number 5 is a prime number.<\/p>\n

              Question 10.
              \n21
              \nAnswer:
              \nA factor divides exactly into a number leaving no remainder is called the factors.
              \nThe factors of 21 are 1, 3, 7 and 21
              \nThe number that has more than two factors are called composite numbers.
              \nSo, The number 21 is a composite number.<\/p>\n

              Set E pages 277-280<\/strong><\/p>\n

              Find five multiples of 7.
              \nUse multiplication.
              \n7 \u00d7 1 = 7
              \n7 \u00d7 2 = 14
              \n7 \u00d7 3 = 21
              \n7 \u00d7 4 = 28
              \n7 \u00d7 5 = 35
              \n\"Envision<\/p>\n

              Remember<\/strong> that to find multiples of a number, multiply the number by any whole number.<\/p>\n

              Find five multiples of each number.
              \nQuestion 1.
              \n3
              \nAnswer:
              \nFive multiples of 3 are
              \n3 \u00d7 1 = 3
              \n3 \u00d7 2 = 6
              \n3 \u00d7 3 = 9
              \n3 \u00d7 4 = 12
              \n3 \u00d7 5 = 15<\/p>\n

              Question 2.
              \n6
              \nAnswer:
              \nFive multiples of 6 are
              \n6 \u00d7 1 = 6
              \n6 \u00d7 2 = 12
              \n6 \u00d7 3 = 18
              \n6 \u00d7 4 = 24
              \n6 \u00d7 5 = 25<\/p>\n

              Question 3.
              \n4
              \nAnswer:
              \nFive multiples of 4
              \n4 \u00d7 1 = 4
              \n4 \u00d7 2 = 8
              \n4 \u00d7 3 = 12
              \n4 \u00d7 4 = 16
              \n4 \u00d7 5 = 20<\/p>\n

              Question 4.
              \n9
              \nAnswer:
              \nFive multiples of 9 are
              \n9 \u00d7 1 = 9
              \n9 \u00d7 2 = 18
              \n9 \u00d7 3 = 27
              \n9 \u00d7 4 = 36
              \n9 \u00d7 5 = 45
              \nFive multiples of 9 are\u00a0 9, 18, 27, 36 and 45
              \nTell whether the first number is a multiple of the second number.<\/p>\n

              Question 5.
              \n22, 2
              \nAnswer:
              \nMultiple of number is exactly divisible by the number.
              \nHere 22 is exactly divisible by 2
              \nSo, 22 is a multiple of 2.<\/p>\n

              Question 6.
              \n29, 3
              \nAnswer:
              \nMultiple of number is exactly divisible by the number.
              \nHere 29 is not exactly divisible by 3.
              \nSo, 29 is not a multiple of 3.<\/p>\n

              Question 7.
              \n25, 5
              \nAnswer:
              \nMultiple of number is exactly divisible by the number.
              \nHere 25 is exactly divisible by 5.
              \nSo, 25 is a multiple of 5.<\/p>\n

              Question 8.
              \n40, 8
              \nAnswer:
              \nMultiple of number is exactly divisible by the number.
              \nHere 40 is exactly divisible by 8.
              \nSo, 40 is a multiple of 8.<\/p>\n

              Topic 7 Assessment Practice<\/h3>\n

              Question 1.
              \nCourtney has 36 photos to arrange on a gallery wall.
              \nA. How many arrays can Courtney make with the 36 photos? List all the possible arrays.
              \nAnswer:
              \nGiven that the total number of\u00a0 photos = 36
              \nFactors of 36 are 1, 2, 3, 4, 9, 12, 18 and 36
              \nThe number of possible arrays are
              \n1 and 36, 36 and 1
              \n3 and 12, 12 and 3
              \n2 and 18, 18 and 2
              \n4 and 9, 9 and 4
              \nThe number of possible arrays is 8<\/p>\n

              B. How many factors are there for 36? Write them. What do you notice about the number of factors of 36 and the number of arrays Courtney can make with the photos?
              \nAnswer:
              \nGiven that the total number of\u00a0 photos = 36
              \nFactors of 36 are 1, 2, 3, 4, 9, 12, 18 and 36
              \nA number of factors of 36 are 8.
              \nThe number of possible arrays are
              \n1 and 36, 36 and 1
              \n3 and 12, 12 and 3
              \n2 and 18, 18 and 2
              \n4 and 9, 9 and 4
              \nThe number of possible arrays is 8.
              \n
              \nC. Write all the factor pairs for 36. Is 36 prime or composite? Explain.
              \n<\/span>Answer:
              \nThe factor pairs of 36 are
              \n1 and 36
              \n2 and 18
              \n3 and 12
              \n4 and 9
              \nThe factors of 36 are 1, 2, 3, 4, 18, 12, 9 and 36
              \nThe number 36 is not a prime number it is a composite number because the factors of 36 are more than 2 so it is a composite number.<\/p>\n

              Question 2.
              \nDetermine whether the numbers in each list are factors or multiples of 16.
              \n\"Envision
              \nAnswer:<\/p>\n

              Question 3.
              \nWhich statement is true?
              \nA. The only factors of 3 are 3 and 1; therefore, 3 is prime.
              \nB. The only factors of 4 are 4 and 1; therefore, 4 is prime.
              \nC. The only factors of 5 are 5 and 1; therefore, 5 is composite.
              \nD. The only factors of 8 are 8 and 1; therefore, 8 is composite.
              \nAnswer:<\/p>\n

              Question 4.
              \nDetermine if each number is prime or composite. Then write all the factors for each number. 19, 33
              \nAnswer:
              \nThe factors of 19 are 1 and 19
              \nThe number 19 is a prime number because it has only two factors.
              \nThe factors of 33 are 1, 11 and 33
              \nThe number 33 is a composite number because it has more than two factors .
              \n
              \nQuestion 5.
              \n<\/span>Select all equations that have a dividend that is a multiple of 4 and a quotient that is a factor of 18.
              \n\u2610 8 \u00f7 4 = 2
              \n\u2610 48 \u00f7 8 = 6
              \n\u2610 18 \u00f7 6 = 3
              \n\u2610 16 \u00f7 4 = 4
              \n\u2610 36 \u00f7 3 = 12
              \nAnswer:
              \nQuestion 6.
              \nWrite 3 multiples and 3 factors for 24.
              \nAnswer:
              \n3 factors of 24 are 1, 2, 3
              \n3 multiple of 24 are
              \n24 \u00d7 1 = 24
              \n24 \u00d7 2 = 48
              \n24 \u00d7 3 = 72
              \nThe numbers 24, 48, 72 are the multiples of 24<\/p>\n

              Question 7.
              \nWrite two multiples of 3 that have a factor of 7. Use equations to explain.
              \nAnswer:<\/p>\n

              Question 8.
              \nSelect all the true statements.
              \n\u2610 33 has more than two factors.
              \n\u2610 All of the factors of 34 are even numbers.
              \n\u2610 35 has exactly two factors.
              \n\u2610 3 is a factor of 36.
              \n\u2610 37 is a prime number.
              \n\u2610 38 is a composite number.
              \nAnswer:<\/p>\n

              Question 9.
              \nMartika says factors and multiples are related. Use the equation 6 \u00d7 7 = 42 to describe the relationship between factors and multiples.
              \nAnswer:<\/p>\n

              Question 10.
              \nWhich lists all the factors of 25 that are also prime?
              \nA. 1, 25
              \nB. 5
              \nC. 1, 10, 25
              \nD. 5, 25
              \nAnswer:<\/p>\n

              Question 11.
              \n<\/span>Carter lives on a street where all the house numbers are multiples of 6. Name two possible house numbers between 70 and 80. Explain.
              \n<\/span>Answer:<\/p>\n

              Question 12.
              \nWrite the factors of 30 that are also prime numbers.
              \nAnswer:
              \nA factor divides exactly into a number leaving no remainder is called the factors.
              \nFactors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30
              \n30 is not a prime number it is a composite number.
              \nIt has more than two factors .<\/p>\n

              Question 13.
              \nJavier says all odd numbers greater than 2 and less than 20 are prime. Find an odd number greater than 2 and less than 20 that is NOT prime. Explain why the number is not prime.
              \nAnswer:<\/p>\n

              Topic 7 Performance Task<\/p>\n

              Arranging Cars to Sell Ms. Ortiz owns a car dealership. The dealership has the inventory of cars listed in the Ortiz Car Dealership table.
              \n\"Envision<\/p>\n

              Question 1.
              \nMs. Ortiz wants to arrange all of the trucks in the front lot. She would like to have same number of trucks in each row.
              \nPart A
              \nHow many different ways can the trucks be arranged in the front lot if the same number of trucks are parked in each row?
              \nAnswer:<\/p>\n

              Part B
              \nWhat are all the ways the trucks can be arranged? Draw and label the different arrays.
              \nAnswer:
              \nThe trucks can be arranged in four different ways that are
              \nTotal number of trucks = 15
              \nThe factors of 15 are 1, 3, 5 and 15
              \nFactor pairs of 15 are 1 and 15, 3 and 5
              \nThe trucks can be arranged in
              \n<\/span>1 row of 15 cars
              \n<\/span>3 rows of 5 cars
              \n15 cars in 1 row
              \n5 cars in 3 rows
              \nPart C<\/span><\/p>\n

              Ms. Ortiz would like the arrangement to have more than 2 rows of trucks but less than 6 rows. What are the ways the trucks can be arranged? Explain.
              \nAnswer:
              \nThe trucks can be arranged in four different ways that are
              \nTotal number of trucks = 15
              \nThe factors of 15 are 1, 3, 5 and 15
              \nFactor pairs of 15 are 1 and 15, 3 and 5
              \nThe trucks can be arranged in more than two rows and less than six rows
              \n3 rows of 5 cars
              \n5 cars in 3 rows<\/p>\n

              Question 2.
              \nAs Ms. Ortiz sells sedans, those sedans remaining are parked in different arrangements.<\/p>\n

              Complete the Arranging Sedans table to find the number of ways Ms. Ortiz can arrange each number of sedans in the front lot so there are at least 2 rows with the same number of sedans in each row and more than one sedan in each row.
              \n\"Envision
              \nAnswer:<\/p>\n","protected":false},"excerpt":{"rendered":"

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