{"id":9049,"date":"2023-12-26T17:35:12","date_gmt":"2023-12-26T12:05:12","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=9049"},"modified":"2023-12-27T11:52:23","modified_gmt":"2023-12-27T06:22:23","slug":"envision-math-common-core-grade-4-answer-key-topic-6","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-4-answer-key-topic-6\/","title":{"rendered":"enVision Math Common Core Grade 4 Answer Key Topic 6 Use Operations with Whole Numbers to Solve Problems"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 4 Answer Key<\/a>\u00a0Topic 6 Use Operations with Whole Numbers to Solve Problems<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

enVision Math Common Core 4th Grade Answers Key Topic 6 Use Operations with Whole Numbers to Solve Problems<\/h2>\n

Essential Questions:<\/strong>
\nHow is comparing with multiplication different from comparing with addition? How can you use equations to solve multi-step problems?
\nAnswer:
\nIn an additive comparison, we find the relation between two amounts by asking or telling how much more is one compared to the other. In multiplicative comparison, there are two different sets being compared. The first set contains a certain number of items. The second set contains multiple copies of the first set
\nExample:
\nAdditive Comparison:
\n2 + 2 + 5 + 3 + … n
\nMultiplicative Comparison:
\n3 \u00d7 4 \u00d7 5 \u00d7 … n
\n\"Envision<\/p>\n

enVision STEM Project: Energy and Multiplication<\/strong>
\nDo Research<\/strong>
\nUse the Internet or other sources to find and describe 3 examples of renewable energy?
\nAnswer:
\nThe examples of renewable energy are:
\na. Solar energy
\nb. Wind energy
\nc. Tidal energy
\nd. Geothermal energy<\/p>\n

Journal<\/strong>: Write a Report that Includes what you found. Also in your report:
\nA)
\nSolar panels are made up of smaller modules or sections called cells. Find a picture of a solar panel. How many cells are in 6 solar panels? How many cells are in 9 solar panels? How many more cells are in the 9 solar panels than the 6 solar panels?
\nAnswer:
\nIt is given that
\nSolar panels are made up of smaller modules or sections called cells
\nNow,
\nWe know that,
\nA solar power panel is made of photovoltaic cells arranged in a configuration that can contain 32, 36, 48, 60, 72, and 96 cells
\nNow,
\nLet a solar panel contains 32 cells
\nSo,
\nThe number of cells that present in 6 solar panels = (The number of solar panels) \u00d7 (The number of cells present in a solar panel)
\n= 6 \u00d7 32
\n= 6 \u00d7 (30 + 2)
\n= (6 \u00d7 30) + (6 \u00d7 2)
\n= 180 + 12
\n= 192 cells
\nSo,
\nThe number of cells that present in 9 solar panels = (The number of solar panels) \u00d7 (The number of cells present in a solar panel)
\n= 9 \u00d7 32
\n= 9 \u00d7 (30 + 2)
\n= (9 \u00d7 30) + (9 \u00d7 2)
\n= 270 + 18
\n= 288 cells
\nSo,
\nThe difference between the two solar panels = 288 – 192
\n= 96 cells
\nNow,
\nThe picture of a solar panel is:<\/p>\n

\"\"<\/p>\n

Hence, from the above,
\nWe can conclude that
\nThe difference of the cells between 9 solar panels and 6 solar panels is: 96 cells<\/p>\n

B)
\nFind examples of other items that use solar power?
\nAnswer:
\nSome of the items that use solar power are:
\nA) Solar charger.
\nB) Solar cell phone charger. Strawberry Tree.
\nC) Solar chimney.
\nD) Solar-powered waste compacting bin.
\nE) Solar cooker.
\nF) Solar dryer.
\nG) Solar-powered fan.
\nH) Solar furnace.<\/p>\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
  • Associative Property of Multiplication<\/li>\n
  • Commutative Property of Multiplication<\/li>\n
  • Compatible numbers<\/li>\n
  • Distributive Property<\/li>\n<\/ul>\n

    Question 1.
    \nThe __________ says that factors can be multiplied in any order and the product remains the same.
    \nAnswer:
    \nWe know that,
    \nThe “Commutative Property of Multiplication” says that factors can be multiplied in any order and the product remains the same.
    \nHence, from the above,
    \nWe can conclude that the best term that is suitable for the given definition is: Cumulative Property of Multiplication<\/p>\n

    \"Math<\/p>\n

    Question 2.
    \nBreaking apart a multiplication problem into the sum or difference of two simpler multiplication problems is an example of using the __________
    \nAnswer:
    \nWe know that,
    \nBreaking apart a multiplication problem into the sum or difference of two simpler multiplication problems is an example of using the “Distributive Property”
    \nHence, from the above,
    \nWe can conclude that the best term that is suitable for the given definition is: Distributive Property<\/p>\n

    Question 3.
    \nAccording to the ________, factors can be regrouped and the product remains the same.
    \nAnswer:
    \nWe know that,
    \nAccording to the “Associative property of Multiplication”, factors can be regrouped and the product remains the same.
    \nHence, from the above,
    \nWe can conclude that the best term that is suitable for the given definition is: Associative Property of Multiplication<\/p>\n

    Dividing by 1-Digit Numbers<\/strong><\/p>\n

    Estimate each quotient.
    \nQuestion 4.
    \n16 \u00f7 3
    \nAnswer:
    \nThe given expression is: 16 \u00f7 3
    \nNow,
    \nBy using the Long Division method,
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that the quotient value for the given expression is: 5<\/p>\n

    Question 5.
    \n25 \u00f7 4
    \nAnswer:
    \nThe given expression is: 25 \u00f7 4
    \nNow,
    \nBy using the Long Division method,
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that the quotient value for the given expression is: 6<\/p>\n

    Question 6.
    \n155 \u00f7 4
    \nAnswer:
    \nThe given expression is: 155 \u00f7 4
    \nNow,
    \nBy using the Long Division method,
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that the quotient value for the given expression is: 38<\/p>\n

    Question 7.
    \n304 \u00f7 3
    \nAnswer:
    \nThe given expression is: 304 \u00f7 3
    \nNow,
    \nBy using the Long Division method,
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that the quotient value for the given expression is: 101<\/p>\n

    Question 8.
    \n1,283 \u00f7 6
    \nAnswer:
    \nThe given expression is: 1,283 \u00f7 6
    \nNow,
    \nBy using the Long Division method,
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that the quotient value for the given expression is: 213<\/p>\n

    \"Math<\/p>\n

    Question 9.
    \n1,999 \u00f7 4
    \nAnswer:
    \nThe given expression is: 1,999 \u00f7 4
    \nNow,
    \nBy using the Long Division method,
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that the quotient value for the given expression is: 499<\/p>\n

    Multiplying by 1-Digit Numbers<\/strong><\/p>\n

    Find each product.
    \nQuestion 10.
    \n53 \u00d7 9
    \nAnswer:
    \nThe given expression is: 53 \u00d7 9
    \nNow,
    \nBy using the partial Products method,
    \n53 \u00d7 9
    \n= (50 + 3) \u00d7 9
    \n= (50 \u00d7 9) + (3 \u00d7 9)
    \n= 450 + 27
    \n= 477
    \nHence, from the above,
    \nWe can conclude that the product value for the given expression is: 477<\/p>\n

    Question 11.
    \n1,127 \u00d7 7
    \nAnswer:
    \nThe given expression is: 1,127 \u00d7 7
    \nNow,
    \nBy using the partial Products method,
    \n1,127 \u00d7 7
    \n= (1,000 + 100 + 27) \u00d7 7
    \n= (1,000 \u00d7 7) + (100 \u00d7 7) + (27 \u00d7 7)
    \n= 7,000 + 700 + 189
    \n= 7,889
    \nHence, from the above,
    \nWe can conclude that the product value for the given expression is: 7,889<\/p>\n

    Question 12.
    \n2,769 \u00d7 5
    \nAnswer:
    \nThe given expression is: 2,769 \u00d7 5
    \nNow,
    \nBy using the partial Products method,
    \n2,769 \u00d7 5
    \n= (2,000 + 700 + 60 + 9) \u00d7 5
    \n= (2,000 \u00d7 5) + (700 \u00d7 5) + (60 \u00d7 5) + (9 \u00d7 5)
    \n= 10,000 + 3,500 + 300 + 45
    \n= 13,845
    \nHence, from the above,
    \nWe can conclude that the product value for the given expression is: 13,845<\/p>\n

    Question 13.
    \n3 \u00d7 215
    \nAnswer:
    \nThe given expression is: 3 \u00d7 215
    \nNow,
    \nBy using the partial Products method,
    \n3 \u00d7 215
    \n= 3 \u00d7 (200 + 15)
    \n= (3 \u00d7 200) + (3 \u00d7 15)
    \n= 600 + 45
    \n= 645
    \nHence, from the above,
    \nWe can conclude that the product value for the given expression is: 645<\/p>\n

    Question 14.
    \n914 \u00d7 5
    \nAnswer:
    \nThe given expression is: 914 \u00d7 5
    \nNow,
    \nBy using the partial Products method,
    \n914 \u00d7 5
    \n= (900 + 14) \u00d7 5
    \n= (900 \u00d7 5) + (14 \u00d7 5)
    \n= 4,500 + 70
    \n= 4,570
    \nHence, from the above,
    \nWe can conclude that the product value for the given expression is: 4,570<\/p>\n

    Question 15.
    \n1,238 \u00d7 5
    \nAnswer:
    \nThe given expression is: 1,238 \u00d7 5
    \nNow,
    \nBy using the partial Products method,
    \n1,238 \u00d7 5
    \n= (1,000 + 200 + 30 + 8) \u00d7 5
    \n= (1,000 \u00d7 5) + (200 \u00d7 5) + (30 \u00d7 5) + (8 \u00d7 5)
    \n= 5,000 + 1,000 + 150 + 40
    \n= 6,190
    \nHence, from the above,
    \nWe can conclude that the product value for the given expression is: 6,190<\/p>\n

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

    Question 16.
    \nConstruct Arguments<\/strong> Explain why the array represents 3 \u00d7 21
    \n\"\"
    \nAnswer:
    \nThe given array is:
    \n\"\"
    \nNow,
    \nWe know that,
    \nAn “Array” is a collection of rows and columns
    \nNow,
    \nFrom the given figure,
    \nWe can observe that
    \nThe number of rows is: 21
    \nThe number of columns is: 3
    \nSo,
    \nTo find the number of cells in a given array,
    \nWe have to multiply the rows and columns
    \nHence, from the above,
    \nWe can conclude that the given array represents 21 \u00d7 3 since it represents the number of rows and number of columns<\/p>\n

    Question 17.
    \nJames multiplies 38 by 55. He finds three of the four partial products: 40, 150, and 400. Which partial product is James missing? What is the solution?
    \nAnswer:
    \nIt is given that
    \nJames multiplies 38 by 55. He finds three of the four partial products: 40, 150, and 400.
    \nNow,
    \nThe given expression is: 38 \u00d7 55
    \nNow,
    \nBy using the partial Products method,
    \n38 \u00d7 55
    \n= (30 + 8) \u00d7 (50 + 5)
    \n= (30 \u00d7 50) + (30 \u00d7 5) + (8 \u00d7 50) + (8 \u00d7 5)
    \n= 1,500 + 150 +400 + 40
    \n= 2,090
    \nHence, from the above,
    \nWe can conclude that
    \nThe Partial product James is missing is: 1,500
    \nThe solution for the given expression is: 2,090<\/p>\n

    \"Math<\/p>\n

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

    PROJECT 6A
    \nHow tall is tall?
    \nProject: Model the Height of a Redwood Tree
    \n\"Envision<\/p>\n

    PROJECT 6B
    \nWhat are some interesting number facts about a manatee?
    \nProject: Make a Presentation with Manatee Number Facts
    \n\"Envision<\/p>\n

    PROJECT 6C
    \nHow does temperature affect an alligator egg?
    \nProject: Create a Bar Diagram
    \n\"Envision<\/p>\n

    PROJECT 6D
    \nHow many eggs does the loggerhead turtle lay?
    \nProject: Model a Turtle’s Egg
    \n\"Envision<\/p>\n

    Lesson 6.1 Solve Comparison Problems<\/h3>\n

    \"Math<\/p>\n

    Solve & Share<\/strong>
    \nSarah is making a square pillow with edges that each measure 18 inches long. She needs a strip of fabric 4 times as long as one edge of the pillow to make a border around the pillow. How long does the strip of fabric need to be? Solve this problem any way you choose.
    \nI can … use multiplication or addition to compare one quantity to another.
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nSarah is making a square pillow with edges that each measure 18 inches long. She needs a strip of fabric 4 times as long as one edge of the pillow to make a border around the pillow
    \nNow,
    \nLet the length of the strip of fabric be x
    \nSo,
    \nAccording to the given data,
    \nThe length of the strip (x) = 4 \u00d7 (The length of the pillow at the edges)
    \n= 4 \u00d7 18
    \n= 72 inches
    \nHence, from the above,
    \nWe can conclude that
    \nThe length of the fabric needed is: 72 inches<\/p>\n

    Look Back!<\/strong>
    \nModel with Math<\/strong>
    \nHow could a bar diagram help you write and solve an equation for the problem?
    \nAnswer:
    \nIt is given that
    \nSarah is making a square pillow with edges that each measure 18 inches long. She needs a strip of fabric 4 times as long as one edge of the pillow to make a border around the pillow
    \nNow,
    \nThe representation of the given situation in the form of a bar diagram is:
    \n\"\"
    \nSo,
    \nFrom the above bar diagram,
    \nWe can observe that
    \nThe length of the string = 4 \u00d7 (The length of the edge of the pillow)
    \n= 4 \u00d7 18
    \n= 72 inches
    \nHence, from the above,
    \nWe can conclude that
    \nBy using the bar diagram, the length of the string is: 72 inches<\/p>\n

    \"Math<\/p>\n

    Essential Question<\/strong>
    \nHow Is Comparing with Multiplication Different from Comparing with Addition?
    \nAnswer:
    \nIn an additive comparison, we find the relation between two amounts by asking or telling how much more is one compared to the other. In multiplicative comparison, there are two different sets being compared. The first set contains a certain number of items. The second set contains multiple copies of the first set
    \nExample:
    \nAdditive Comparison:
    \n2 + 2 + 5 + 3 + … n
    \nMultiplicative Comparison:
    \n3 \u00d7 4 \u00d7 5 \u00d7 … n<\/p>\n

    Visual Learning Bridge
    \nMax said the Rangers scored 3 times as many runs as the Stars. Jody said the Rangers scored 8 more runs than the Stars. Could both Max and Jody be correct?
    \n\"Envision<\/p>\n

    Compare with Multiplication
    \nFind 3 times as many as 4 runs.
    \n\"Envision
    \nm = 3 \u00d7 4
    \nm = 12 runs
    \nAccording to Max, the Rangers scored 12 runs.<\/p>\n

    Compare with Addition
    \nFind 8 more than 4 runs.
    \n\"Envision
    \nj = 4 + 8
    \nj = 12 runs
    \nAccording to Jody, the Rangers scored 12 runs.
    \nMax and Jody are both correct.<\/p>\n

    Convince Me!
    \n<\/strong> Construct Arguments<\/strong> Describe when you would use multiplication and when you would use addition to make a comparison?
    \nAnswer:
    \nWhen distinguishing multiplicative comparison from additive comparison,
    \nWe should note that “Additive comparisons” focus on the difference between two quantities whereas “Multiplicative comparisons” focus on the difference between two qualities<\/p>\n

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

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nUse the information from the previous page. If the Rangers scored 5 times as many runs as the Stars, how many runs would the Rangers have scored?
    \na. Compare using multiplication. Write and solve an equation.
    \nAnswer:
    \nIt is given that
    \nRangers scored 5 times as many runs as the Stars
    \nNow,
    \nThe given figure is:
    \n\"Envision
    \nNow,
    \nThe representation of the given situation in the form of a bar diagram is:
    \n\"\"
    \nSo,
    \nThe total number of runs rangers scored = 5 \u00d7 (The number of runs Stars scored)
    \n= 5 \u00d7 4
    \n= 20 runs
    \nHence, from the above,
    \nWe can conclude that the number of runs scored by Rangers is: 20<\/p>\n

    b. How could you use addition to compare the runs for the two teams?
    \nAnswer:
    \nIt is given that
    \nRangers scored 5 times as many runs as the Stars
    \nNow,
    \nThe given figure is:
    \n\"Envision
    \nNow,
    \nThe representation of the given situation in the form of a bar diagram is:
    \n\"\"
    \nSo,
    \nThe total number of runs rangers scored = (The number of runs Stars scored) + (The number of runs Stars scored) + (The number of runs Stars scored) + (The number of runs Stars scored) + (The number of runs Stars scored)
    \n= 5 + 5 + 5 + 5 +5
    \n= 20 runs
    \nHence, from the above,
    \nWe can conclude that the number of runs scored by Rangers is: 20<\/p>\n

    \"Math<\/p>\n

    Do You Know How?<\/strong>
    \nFor 2-3, complete the comparison sentence. Find the value of the variable that makes the sentence true.
    \nQuestion 2.
    \nSam’s baseball team has 4 times as many helmets as Ed’s team. Ed’s team has 21 helmets. Let h = the number of helmets Sam’s team has.
    \nh is ___________ times as many as ________.
    \nh = _________
    \nAnswer:
    \nIt is given that
    \nSam’s baseball team has 4 times as many helmets as Ed’s team. Ed’s team has 21 helmets.
    \nSo,
    \nThe number of helmets Sam’s team has (h) = 4 \u00d7 (The number of helmets Ed’s team has)
    \n= 4 \u00d7 21
    \n= 4 \u00d7 (20 + 1)
    \n= (4 \u00d7 20) + (4 \u00d7 1)
    \n= 80 + 4
    \n= 84 helmets
    \nHence, from the above,
    \nWe can conclude that
    \nh is 4 times as many as the number of helmets Ed’s team has
    \nThe number of helmets Sam’s team has is: 84 helmets<\/p>\n

    Question 3.
    \nThere are 128 more trees in the park than at Ty’s house. There are 3 trees at Ty’s house. Let t = the number of trees in the park.
    \n_______ more than _____ is t.
    \nt = __________
    \nAnswer:
    \nIt is given that
    \nThere are 128 more trees in the park than at Ty’s house. There are 3 trees at Ty’s house.
    \nSo,
    \nThe number of trees in the park (t) = (The number of trees at Ty’s house) + (The number of more trees in the park)
    \n= 3 + 128
    \n= 131 trees
    \nHence, from the above,
    \nWe can conclude that
    \n128 trees more than 3 trees is t
    \nThe total number of trees in the park is: 131 trees<\/p>\n

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

    Use times as many as or more than to compare the amounts.
    \nFor 4-9, write a comparison sentence. For 4-7, find the value of the variable that makes the sentence true.
    \n\"Envision
    \nQuestion 4.
    \nKaty has 6 times as many nickels as Shaun. Shaun has 18 nickels. Let n = the number of nickels Katy has.
    \nn is _____________
    \nn = ___________.
    \nAnswer:
    \nIt is given that
    \nKaty has 6 times as many nickels as Shaun. Shaun has 18 nickels.
    \nSo,
    \nThe number of nickels Katy has (n) = 6 \u00d7 (The number of nickels Shaun has)
    \n= 6 \u00d7 18
    \n= 6 \u00d7 (10 + 8)
    \n= (6 \u00d7 10) + (6 \u00d7 8)
    \n= 60 + 48
    \n= 108 nickels
    \nHence, from the above,
    \nWe can conclude that
    \nn is 6 times as many as the number of nickels Shaun has
    \nThe number of nickels Katy has: 108 nickels<\/p>\n

    Question 5.
    \nKyle has watched 238 movies. Jason has watched 49 more movies than Kyle. Let m = the number of movies Jason has watched.
    \nm is _____________
    \nm = _____________
    \nAnswer:
    \nIt is given that
    \nKyle has watched 238 movies. Jason has watched 49 more movies than Kyle
    \nSo,
    \nThe number of movies Jason has watched (m) = The number of movies Kyle watched + 49
    \n= 238 + 49
    \n= 287 movies
    \nHence, from the above,
    \nWe can conclude that
    \nm is 49 mere than the number of movies Kyle has watched
    \nThe number of movies Jason has watched is: 287 movies<\/p>\n

    Question 6.
    \nAmber tied 89 knots to make a macrame wall hanging. Hunter tied 3 times as many knots as Amber. Let k= the number of knots Hunter tied. k is _____________
    \nk = _____________
    \nAnswer:
    \nIt is given that
    \nAmber tied 89 knots to make a macrame wall hanging. Hunter tied 3 times as many knots as Amber
    \nSo,
    \nThe number of knots Hunter tied (k) = 3 \u00d7 (The number of knots Amber tied)
    \n= 3 \u00d7 89
    \n= 3 \u00d7 (80 + 9)
    \n= (3 \u00d7 80) + (3 \u00d7 9)
    \n= 240 + 27
    \n= 267
    \nHence, from the above,
    \nWe can conclude that
    \nk is 3 times as many knots as Amber
    \nThe number of knots Hunter tied is: 267 knots<\/p>\n

    Question 7.
    \nTia sells 292 newspapers. Tess sells 117 more newspapers than Tia. Let n = the number of newspapers Tess sells.
    \nn is _____________
    \nn = _____________
    \nAnswer:
    \nIt is given that
    \nTia sells 292 newspapers. Tess sells 117 more newspapers than Tia
    \nSo,
    \nThe number of newspapers Tess sells (n) = 117 + (The number of newspapers tia sells)
    \n= 117 + 292
    \n= 409 newspapers
    \nHence, from the above,
    \nWe can conclude that
    \nn is 117 more than Tia’s newspapers
    \nThe number of newspapers Tess sells is: 409 newspapers<\/p>\n

    Question 8.
    \nTrent has 48 markers. Sharon has 8 markers.
    \nAnswer:<\/p>\n

    Question 9.
    \nLucy has 317 bottles. Craig has 82 bottles.
    \nAnswer:<\/p>\n

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

    Question 10.
    \nModel with Math<\/strong>
    \nRoger swam 19 laps in the pool. Anna Maria swam 4 times as many laps as Roger. How many laps did Anna Maria swim? Draw a bar diagram and write an equation to solve the problem.
    \nAnswer:
    \nIt is given that
    \nRoger swam 19 laps in the pool. Anna Maria swam 4 times as many laps as Roger
    \nSo,
    \nThe representation of the given situation in the form of a bar diagram is:
    \n\"\"
    \nSo,
    \nThe number of laps did Anna maria swam = 4 \u00d7 (The number of laps did Roger swam)
    \n= 4 \u00d7 19
    \n= 4 \u00d7 (10 + 9)
    \n= (4 \u00d7 10) + (4 \u00d7 9)
    \n= 40 + 36
    \n= 76 laps
    \nHence, from the above,
    \nWe can conclude that the number of laps did Anna swam is: 76 laps<\/p>\n

    \"Math<\/p>\n

    Question 11.
    \nCritique Reasoning<\/strong> Nina says the equation 600 = 12 \u00d7 50 means 600 is 12 times as many as 50. Julio says the equation means 600 is 50 times as many as 12. Who is correct? Explain.
    \nAnswer:
    \nIt is given that
    \nNina says the equation 600 = 12 \u00d7 50 means 600 is 12 times as many as 50. Julio says the equation means 600 is 50 times as many as 12
    \nNow,
    \nWe know that,
    \nAccording to Commutative Property of Multiplication,
    \na \u00d7 b = b \u00d7 a
    \nSo,
    \n12 \u00d7 50 is the same as 50 \u00d7 12
    \n“12 times as many as 50” is the same as “50 times as many as 12”
    \nHence, from the above,
    \nWe can conclude that
    \nBoth Nina and Julio are correct<\/p>\n

    Question 12.
    \nVocabulary<\/strong> The amount that is left after dividing a number into equal parts is called the _________.
    \n13 \u00f7 4 = ________
    \n\"Envision
    \nAnswer:
    \nWe know that,
    \nThe amount that is left after dividing a number into equal parts is called the “Remainder”
    \nNow,
    \nThe given expression is: 13 \u00f7 4
    \nNow,
    \nBy using the Long division method,
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that the remainder for the given expression is: 1<\/p>\n

    Question 13.
    \nHigher-Order Thinking<\/strong> A shirt is on sale for d dollars. The regular price is 4 times as much. Todd has enough money to buy 2 shirts at the regular price. How many shirts can Todd buy at the sale price? Explain.
    \nAnswer:
    \nIt is given that
    \nA shirt is on sale for d dollars. The regular price is 4 times as much. Todd has enough money to buy 2 shirts at the regular price
    \nSo,
    \nThe regular price of a shirt = 4 \u00d7 (The sale price of a shirt)
    \n= 4 \u00d7 d
    \n= 4d
    \nNow,
    \nAccording to the given information,
    \nThe sale price of the shirts that Todd can buy = (Regular price of a shirt) \u00d7 (The number of shirts Todd can buy)
    \n= 4d \u00d7 2
    \n= 8d
    \nSo,
    \nThe number of shirts Todd can buy = \\(\\frac{The sale price of the shirts Todd can buy}{The sale price of a shirt}\\)
    \n= \\(\\frac{8d}{d}\\)
    \n= 8
    \nHence, from the above,
    \nWe can conclude that Todd can buy 8 shirts at the sale price<\/p>\n

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

    Question 14.
    \nSelect all the sentences that involve a comparison using multiplication.
    \n\u2610 k is 26 times as many as 7.
    \n\u2610 u is 18 more than 314.
    \n\u2610 Tom ran 4 miles. Cindy ran 2 more miles than Tom. How many miles did Cindy run?
    \n\u2610 Yuan has 2 dogs and Jon has 3 times as many dogs. How many dogs does Jon have?
    \n\u2610 Kris has 4 times as many pairs of shoes as her brother. Her brother has 8 pairs of shoes.
    \nAnswer:
    \nThe sentences that involve a comparison using multiplication are:
    \n\"\"<\/p>\n

    Question 15.
    \nSelect all the statements that can be represented by the equation 5 \u00d7 9 = w.
    \n\u2610 w is 9 more than 5.
    \n\u2610 w is 5 times as much as 9.
    \n\u2610 Henry sang 9 songs during practice. He sang 5 times as many as Joe, who sang w songs.
    \n\u2610 Greg carried 9 buckets of water to his sister’s baby pool. His mother carried w buckets, which were 5 times as many.
    \n\u2610 Tom has 9 pens. Joan has w pens, which is 5 fewer.
    \nAnswer:
    \nThe sentences that can be represented by the equation 5 \u00d7 9 = w are:
    \n\"\"<\/p>\n

    Lesson 6.2 Continue to solve Comparison Problems<\/h3>\n

    Solve & Share<\/strong>
    \nThe students in Ms. Chang’s fourth-grade class plant a tree every year. One tree they planted is now 288 inches tall. This height is 6 times as great as when the tree was first planted. How tall was the tree when it was first planted? Solve this problem any way you choose. Show your work.
    \nI can … use multiplication or division to compare one quantity to another.
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nThe students in Ms. Chang’s fourth-grade class plant a tree every year. One tree they planted is now 288 inches tall. This height is 6 times as great as when the tree was first planted
    \nNow,
    \nLet the height of the tree when first planted be x
    \nNow,
    \nAccording to the given information,
    \n6 \u00d7 x = 288
    \nx = \\(\\frac{288}{6}\\)
    \nx = 48 inches
    \nHence, from the above,
    \nWe can conclude that
    \nThe height of the tree when it was first planted is: 48 inches<\/p>\n

    Look Back!<\/strong> Compare the heights of the 2 trees using addition.
    \nAnswer:
    \nFrom part (a),
    \nWe can observe that
    \nThe height of the tree when it was first planted is: 48 inches
    \nThe current height of the tree is: 288 inches
    \nSo,
    \nThe difference between the heights of the two trees = (The current height of the tree) – (The height of the tree when it was first planted)
    \n= 288 – 48
    \n= 240 inches
    \nHence, from the above,
    \nWe can conclude that the current height of the tree is 240 inches more than the height of the tree when it was first planted<\/p>\n

    Essential Question<\/strong>
    \nHow Can You Solve a Problem Involving Multiplication as Comparison?
    \nAnswer:
    \nInterpret a multiplication equation as a comparison
    \nExample:
    \nInterpret 35 = 5 \u00d7 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5.<\/p>\n

    Visual Learning Bridge
    \nCarla and Calvin are twins that attend different colleges. Carla’s college is four times as far from home as Calvin’s college. How far does Calvin travel to college?
    \n\"Envision<\/p>\n

    The number of miles Carla travels, or 192 miles, is 4 times as far as Calvin travels.<\/p>\n

    Write a multiplication equation to find the number of miles Calvin travels to college.
    \n192 = 4 \u00d7 m
    \nm = 48 miles
    \nWhat number times 4 equals 192?<\/p>\n

    If 192 = 4 \u00d7 m, them m = 192 \u00f7 4.
    \n\"Envision
    \nCalvin travels 48 miles to college.<\/p>\n

    Convince Me!<\/strong><\/p>\n

    Use Structure<\/strong> When do you use division to make a comparison?
    \nAnswer:
    \nA ratio\u00a0is a comparison of two numbers by division. The value of a ratio is the quotient that results from dividing the two numbers.
    \nExample:
    \nThe value of the ratio 35: 7 is 5, which you find by computing 35 \u00f7 7 = 5.<\/p>\n

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

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nCarla travels 3 times as far to college as her friend Mandy travels to college. Write and solve a related multiplication and division equation to find how far Mandy travels to college.
    \nAnswer:
    \nIt is given that
    \nCarla travels 3 times as far to college as her friend Mandy travels to college
    \nNow,
    \nFrom the example on the previous page,
    \nWe can observe that
    \nCarla travels 192 miles to college
    \nNow,
    \nLet x be\u00a0 how far Mandy travels to college
    \nSo,
    \nFrom the given information,
    \n192 = 3 \u00d7 x
    \nx = \\(\\frac{192}{3}\\)
    \nx = 64 miles
    \nHence, from the above,
    \nWe can conclude that Mandy travels 64 miles to the college<\/p>\n

    Do You Know How?<\/strong>
    \nQuestion 2.
    \nComplete the comparison sentence. Find the value of the variable that makes the sentence true.
    \nIf 3 \u00d7 m = 48, then m = 48 \u00f7 3.
    \n3 times as many as m is 48.
    \nm = 16
    \nAnswer:
    \nThe given expression is:
    \n3 \u00d7 m = 48
    \nm = \\(\\frac{48}{3}\\)
    \nm = 16
    \nHence, from the above,
    \nWe can conclude that
    \n3 times as many as m is 48
    \nThe value of m is: 16<\/p>\n

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

    For 3-8, write a comparison sentence and an equation. Find the value of the variable that makes the sentence true.
    \nQuestion 3.
    \nConnor has 77 magazines. That is 7 times as many magazines Kristen has. How many magazines, n, does Kristen have?
    \nAnswer:
    \nIt is given that
    \nConnor has 77 magazines. That is 7 times as many magazines Kristen has
    \nNow,
    \nLet n be the number of magazines Kristen has
    \nSo,
    \nAccording to the given information,
    \n7 \u00d7 n = 77
    \nn = \\(\\frac{77}{7}\\)
    \nn = 11
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of magazines that Kristen has: 11<\/p>\n

    Question 4.
    \nEric completed 75 math problems. That is 5 times as many math problems as Katie completed. How many math problems, m, did Katie complete?
    \nAnswer:
    \nIt is given that
    \nEric completed 75 math problems. That is 5 times as many math problems as Katie completed
    \nNow,
    \nLet m be the math problems Katie completed
    \nSo,
    \nAccording to the given information,
    \n5 \u00d7 m = 75
    \nm = \\(\\frac{75}{5}\\)
    \nm = 15
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of math problems Katie completed is: 15<\/p>\n

    Question 5.
    \nClare counted 117 different colors at the paint store. That is 9 times as many as the number James counted. How many different colors, c, did James count?
    \nAnswer:
    \nIt is given that
    \nClare counted 117 different colors at the paint store. That is 9 times as many as the number James counted.
    \nNow,
    \nLet c be the number of colors James counted
    \nSo,
    \nAccording to the given information,
    \n9 \u00d7 c = 117
    \nc = \\(\\frac{117}{9}\\)
    \nc = 13
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of different colors James counted is: 13<\/p>\n

    Question 6.
    \nAlisa has 153 dominoes. That is 3 times as many dominoes as Stan has. How many dominoes, d, does Stan have?
    \nAnswer:
    \nIt is given that
    \nAlisa has 153 dominoes. That is 3 times as many dominoes as Stan has
    \nNow,
    \nLet d be the number of dominoes does Stan have
    \nSo,
    \nAccording to the given information,
    \n3 \u00d7 d = 153
    \nd = \\(\\frac{153}{3}\\)
    \nd = 51
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of dominoes does Stan have is: 51<\/p>\n

    Question 7.
    \nJustin practiced piano for h hours. His sister practiced for 12 hours, which was 3 times as many hours as Justin practiced. Write and solve an equation to find how many hours Justin practiced piano.
    \nAnswer:
    \nIt is given that
    \nJustin practiced piano for h hours. His sister practiced for 12 hours, which was 3 times as many hours as Justin practiced
    \nNow,
    \nLet h be the number of hours Justin practiced piano
    \nSo,
    \nAccording to the given information,
    \nh \u00d7 3 = 12
    \nh = \\(\\frac{12}{3}\\)
    \nh = 4
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of hours that Justin practiced piano is: 4 hours<\/p>\n

    Question 8.
    \nMary practiced violin for 2 hours and her brother practiced trombone t times as long or 8 hours. Write and solve an equation to find how many times as long Mary’s brother practiced trombone.
    \nAnswer:
    \nIt is given that
    \nMary practiced violin for 2 hours and her brother practiced trombone t times as long or 8 hours
    \nNow,
    \nLet t be the number of hours Mary’s brother practiced trombone
    \nSo,
    \nAccording to the given information,
    \n2 \u00d7 t = 8
    \nt = \\(\\frac{8}{2}\\)
    \nt = 4
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of hours mary’s brother practiced trombone is: 4 hours<\/p>\n

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

    Question 9.
    \nModel with Math<\/strong>
    \nDave is making soup that includes 12 cups of water and 3 cups of broth. How many times as much water as the broth will be in the soup? Draw a bar diagram and write and solve an equation.
    \nAnswer:
    \nIt is given that
    \nDave is making soup that includes 12 cups of water and 3 cups of broth.
    \nNow,
    \nLet x be the number of cups of water present in the broth
    \nSo,
    \nAccording to the given information,
    \n3 \u00d7 x = 12
    \nx = \\(\\frac{12}{3}\\)
    \nx = 4
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of cups of water present in the broth is: 4<\/p>\n

    Question 10.
    \nTrevor wants to buy three light fixtures that cost $168 each. He has $500. Does he have enough money to buy the three light fixtures? Use a comparison sentence to explain your reasoning.
    \nAnswer:
    \nIt is given that
    \nTrevor wants to buy three light fixtures that cost $168 each. He has $500.
    \nSo,
    \nThe cost of three light fixtures that Trevor wants to buy = 3 \u00d7 (The cost of each light fixture)
    \n= 3 \u00d7 168
    \n= 3 \u00d7 (100 + 68)
    \n= (3 \u00d7 100) + (3 \u00d7 68)
    \n= 300 + 204
    \n= $504
    \nSo,
    \nFrom the given information,
    \n$500 < $504
    \nHence, from the above,
    \nWe can conclude that
    \nThe cost of the three light fixtures that Trevor wants to buy is $4 more than the amount of money Trevor has
    \nHe does not have enough money to buy the three light fixtures<\/p>\n

    Question 11.
    \nMiranda has 4 times as many leaves in her collection as Joy Joy has 13 more leaves than Armani. Armani has 10 leaves in his collection. How many leaves does Miranda have in her collection? Explain.
    \nAnswer:
    \nIt is given that
    \nMiranda has 4 times as many leaves in her collection as Joy Joy has 13 more leaves than Armani. Armani has 10 leaves in his collection
    \nNow,
    \nLet the number of leaves Miranda has in her collection be x
    \nLet the number of leaves Joy has be j
    \nLet the number of leaves Armani has be a
    \nSo,
    \nAccording to the given information,
    \na = 10
    \nj = a + 13
    \n4 \u00d7 j = x
    \nNow,
    \nj = 10 + 13
    \nj = 23
    \nSo,
    \n4 \u00d7 23 = x
    \nx = 4 \u00d7 (20 + 3)
    \nx = (4 \u00d7 20) + (4 \u00d7 3)
    \nx = 80 + 12
    \nx = 92 leaves
    \nHence, from the above,
    \nWe can conclude that the number of leaves Miranda has in her collection is: 92<\/p>\n

    Question 12.
    \nHigher-Order Thinking<\/strong> Jordan needs $9,240 for her first year of college tuition. Each of her two grandfathers said they would match what she saves. She has 8 years before she goes to college. How much does Jordan need to save on her own each year to have enough for her first year with the help from her two grandfathers?
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nJordan needs $9,240 for her first year of college tuition. Each of her two grandfathers said they would match what she saves. She has 8 years before she goes to college
    \nSo,
    \nThe amount of money that will be saved by Jordan and her 2 grandfathers = \\(\\frac{$9,240}{3}\\)
    \n= $3,080
    \nSo,
    \nThe amount of money Jordan has to save each year so that she would have enough money for her first year = \\(\\frac{$3,080}{8}\\)
    \n= $385
    \nHence, from the above,
    \nWe can conclude that
    \nJordan needs to save on her own each year to have enough for her first year with the help from her two grandfathers will be: $385<\/p>\n

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

    Question 13.
    \nTina walked 20 miles for a fundraiser. Lia walked m miles. Tina walked 4 times as far as Lia. Which equation can be used to find m, the number of miles Lia walked?
    \nA. m = 4 \u00d7 20
    \nB. 20 = 4 \u00d7 m
    \nC. 20 = m \u00f7 4
    \nD. m = 20 + 4
    \nAnswer:
    \nIt is given that
    \nTina walked 20 miles for a fundraiser. Lia walked m miles. Tina walked 4 times as far as Lia
    \nSo,
    \nAccording to the given information,
    \n4 \u00d7 m = 20
    \nHence, from the above,
    \nWe can conclude that the number of miles Lia walked is:
    \n\"\"<\/p>\n

    Question 14.
    \nJason and Raul kept a reading log for the year. Jason read 7 books and Raul read 105. How many times as many books as Jason did Raul read?
    \nA. 13 times
    \nB. 14 times
    \nC. 15 times
    \nD. 16 times
    \nAnswer:
    \nIt is given that
    \nJason and Raul kept a reading log for the year. Jason read 7 books and Raul read 105
    \nNow,
    \nLet the number of times Jason read as many as Raul did be x
    \nSo,
    \n(The number of books Jason read) \u00d7 (The number of times Jason read as many as Raul did) = The number of books Raul did
    \n7 \u00d7 x = 105
    \nx = \\(\\frac{105}{7}\\)
    \nx = 15
    \nHence,from the above,
    \nWe can conclude that the number of times Raul read as many books as Jason is:
    \n\"\"<\/p>\n

    Lesson 6.3 Model Multi-Step Problems<\/h3>\n

    Solve & Share<\/strong>
    \nLast year, 18 people went on a family camping trip. This year, three times as many people went. How many more people went this year than last year? Complete the bar diagram and show how you solve it?
    \nI can … find hidden questions and use bar diagrams and equations to model and solve multi-step problems.
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nLast year, 18 people went on a family camping trip. This year, three times as many people went
    \nSo,
    \nThe number of people that went on a family camping trip this year = 3 \u00d7 (The number of people that went on a family camping trip last year)
    \n= 3 \u00d7 18
    \n= 3 \u00d7 (10 + 8)
    \n= (3 \u00d7 10) + (3 \u00d7 8)
    \n= 30 + 24
    \n= 54 people
    \nSo,
    \nThe representation of the number of people that went on a camping trip in the form of a bar diagram is:
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that the number of people that went on a camping trip this year is: 54<\/p>\n

    Look Back!<\/strong>
    \nHow can you use estimation to decide if your answer is reasonable?
    \nAnswer:
    \nFrom the above problem,
    \nWe can observe that
    \nThe expression we used to find the number of people that went on a camping trip this year is:
    \n3 \u00d7 18
    \nNow,
    \nEstimate:
    \n3 \u00d7 18
    \n= 3 \u00d7 20
    \n= 3 \u00d7 2 \u00d710
    \n= (3 \u00d7 2) \u00d7 10
    \n= 6 \u00d7 10
    \n= 60
    \nSo,
    \nThe difference between the number of people we obtained in the previous problem and in this problem is not large
    \nHence, from the above,
    \nWe can conclude that your estimation for the answer is reasonable<\/p>\n

    Essential Question<\/strong>
    \nHow Can You Use Diagrams and Equations to Solve Multi-Step Problems?
    \nAnswer:
    \nThe process we can use to solve Multi-step problems is:
    \nStep 1:
    \nCircle and underline. Circle only the necessary information and underline what ultimately needs to be figured out.
    \nStep 2:
    \nFigure out the first step\/problem in the paragraph and solve it.
    \nStep 3:
    \nFind the answer by using the information from Steps 1 and 2<\/p>\n

    Visual Learning Bridge
    \nA school uses 8 buses to transport the fourth-grade students and 6 vans to transport the third-grade students on a field trip. How many fewer third-grade students than fourth-grade students are on the field trip?
    \n\"Envision<\/p>\n

    Step 1<\/strong>
    \nFind and answer the hidden questions.
    \nHidden Question: How many fourth-grade students are on the field trip?
    \n\"Envision
    \nF = 8 \u00d7 24
    \n= 192 fourth-grade students
    \nHidden Question: How many third-grade students are on the field trip?
    \n\"Envision
    \nT= 6 \u00d7 15
    \n= 90 third-grade students<\/p>\n

    Step 2<\/strong>
    \nUse the answers to the hidden questions to answer the original question.
    \nOriginal Question: How many fewer third-grade students than fourth-grade students are on the field trip?
    \nS = the number fewer third-grade students than fourth-grade students
    \n\"Envision
    \nS = 192 – 90
    \n= 102
    \n102 fewer third-grade students than fourth-grade students are on the field trip.<\/p>\n

    Convince Me!<\/strong>
    \nConstruct Arguments<\/strong> Amanda says she can solve the problem using the equation below. Do you agree? Explain.
    \nS = (8 \u00d7 24) – (6 \u00d7 15)
    \nAnswer:
    \nIt is given that
    \nAmanda says she can solve the problem using the equation below.
    \nS = (8 \u00d7 24) – (6 \u00d7 15)
    \nNow,
    \nFrom the example on the previous page,
    \nWe have to find out the number of fewer third-grade students than the fourth-grade students
    \nSo,
    \nWe can find the difference between the third-grade and the fourth-grade students by finding the total number of third-grade and the fourth-grade students
    \nSo,
    \nThe total number of fourth-grade students = (The number of buses) \u00d7 (The number of students in each bus)
    \n= 8 \u00d7 24
    \nThe total number of third-grade students = (The number of vans) \u00d7 (The number of students in each van)
    \n= 6 \u00d7 15
    \nSo,
    \nThe difference between the fourth-grade and the third-grade students = (8 \u00d7 24) – (6 \u00d7 15)
    \nHence, from the above,
    \nWe can conclude that we can agree with Amanda<\/p>\n

    Another Example!<\/strong>
    \nThe Lopez family gets 2 pizzas and 4 hot dogs at Eat-It-Up. What is the total cost?
    \n\"Envision<\/p>\n

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

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nDoug says he can use the equation T = 18 + 18 + 6 + 6 + 6 + 6 to solve the problem above. Is Doug correct? Explain.
    \nAnswer:
    \nIt is given that
    \nDoug says he can use the equation T = 18 + 18 + 6 + 6 + 6 + 6 to solve the problem above.
    \nNow,
    \nFrom the example on the previous page,
    \nWe can observe that
    \nThe cost of each pizza is $18 and there are 2 pizzas
    \nThe cost of each hot-dog is $6 and there are 4 hot-dogs
    \nSo,
    \nThe total cost = (The total cost of pizzas) + (The total cost of hot-dogs)
    \n= [(The cost of each pizza) \u00d7 (The total number of pizzas)] + [(The cost of each hot-dog) \u00d7 (The total number of hot-dogs)]
    \n= [18 \u00d7 2] + [6 \u00d7 4]
    \n= [18 + 18] + [6 + 6 + 6 + 6]
    \nHence, from the above,
    \nWe can conclude that Doug is correct<\/p>\n

    Question 2.
    \nWrite one or more equations you could use to find the total cost C, of 2 turkey wraps, 2 hamburgers, and 4 drinks.
    \n\"\"
    \nAnswer:
    \nIt is given that
    \nThere are 2 turkey wraps, 2 hamburgers, and 4 drinks
    \nNow,
    \nThe given table is:
    \n\"\"
    \nSo,
    \nThe total cost of the three items (C) = [(The cost of each turkey wrap) \u00d7 (The number of turkey wraps)] + [(The cost of each hamburger) \u00d7 (The number of hamburgers)] + [(The cost of each drink) \u00d7 (The number of drinks)]
    \n= (2 \u00d7 $4) + (2 \u00d7 $8) + (4 \u00d7 $2) ———-> 1 way of writing the equation to find the total cost
    \n= ($4 + $4) + ($8 + $8) + ($2 + $2 + $2 + $2) —– > Other way of writing the equation to find the total cost
    \n= $8 + $16 + $8
    \n= $32
    \nHence, from the above,
    \nWe can conclude that
    \nThe total cost of all the given items is: $32<\/p>\n

    Do You Know How?<\/strong>
    \nQuestion 3.
    \nIn the problem on the previous page, suppose the school fills 11 buses and lets the remaining students ride in vans. How many students ride in vans? Use one or more bar diagrams and equations to show how you solve.
    \nAnswer:
    \nIt is given that
    \nIn the problem on the previous page, the school fills 11 buses and the remaining students ride in vans.
    \nNow,
    \nFrom the example on the previous page,
    \nThe total number of students = (The number of fourth-grade students that travel in buses) + (The number of third-grade students that travel in vans)
    \n= 192 + 90
    \n= 282 students
    \nNow,
    \nWe know that,
    \nThe number of students each bus carries is: 24
    \nSo,
    \nThe total number of students present in 11 buses = (The number of students present in each bus) \u00d7 (The number of buses)
    \n= 24 \u00d7 11
    \n= 24 \u00d7 (10 + 1)
    \n= (24 \u00d7 10) + (24 \u00d7 1)
    \n= 240 + 24
    \n= 264 students
    \nSo,
    \nThe number of remaining students who travel in vans = (The total number of students) – (The number of students who travel in 11 buses)
    \n= 282 – 264
    \n= 18 students
    \nNow,
    \nThe representation of the given problem in the form of bar diagrams is:
    \n\"\"
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that the number of students that ride in vans is: 18<\/p>\n

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

    Draw a bar diagram, and write an equation to solve the problem. Use a variable to represent an unknown quantity and tell what the variable represents.
    \nQuestion 4.
    \nFour boys and five girls went to the movies together. Between them, they had $120 to spend. Tickets cost $8 each. How much money did they have to buy refreshments?
    \nAnswer:
    \nIt is given that
    \nFour boys and five girls went to the movies together. Between them, they had $120 to spend. Tickets cost $8 each
    \nSo,
    \nThe total number of people that went to the movies = 4 + 5
    \n= 9
    \nNow,
    \nWe know that,
    \nThe total money spent by 9 people = (The amount of money spent on Tickets) + (The amount of money spent to buy refreshments)
    \n$120 = [(The total number of people) \u00d7 (The cost of each ticket)] + (The amount of money spent to buy refreshments)
    \n$120 = (9 \u00d7 $8) + (The amount of money spent to buy refreshments)
    \nThe amount of money spent to buy refreshments = $120 – $72
    \n= $48
    \nNow,
    \nThe representation of the given information in the form of a bar diagram is:
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that the amount of money spent on refreshments is: $48<\/p>\n

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

    Question 5.
    \nModel with Math<\/strong>
    \nA power plant has 4 tons of coal. A ton of coal produces 2,460 kilowatt-hours of electricity. The plant reserves enough electricity to power 9 light bulbs for a year. How many additional kilowatt-hours of electricity is produced? Draw the bar diagrams and write one or more equations to show how you solve them. Tell what your variables represent.
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nA power plant has 4 tons of coal. A ton of coal produces 2,460 kilowatt-hours of electricity. The plant reserves enough electricity to power 9 light bulbs for a year
    \nNow,
    \nThe energy produced by 4 tons of coal = (The energy produced by a ton of coal) \u00d7 (The number of tons of coal)
    \n= 2,460 \u00d7 4
    \n(2,000 + 400 + 60) \u00d7 4
    \n= (2,000 \u00d7 4) + (400 \u00d7 4) + (60 \u00d7 4)
    \n= 8,000 + 1,600 + 240
    \n= 9,280 Kilowatt-hours
    \nNow,
    \nThe energy produced by 9 light bulbs for a year = (The energy produced by a light bulb for a year) \u00d7 (The number of light bulbs)
    \n= 876 \u00d7 9
    \n= (800 + 70 + 6) \u00d7 9
    \n= (800 \u00d7 9) + (70 \u00d7 9) + (6 \u00d7 9)
    \n= 7,200 + 630 + 54
    \n= 7,884 Kilowatt-hours
    \nSo,
    \nThe number of additional Kilowatt-hours produced = (The energy produced by 4 tons of coal) – (The energy produced by 9 light bulbs for a year)
    \n= 9,280 – 7,884
    \n= 1,396 Kilowatt-hours
    \nNow,
    \nThe representation of the given information in the form of a bar diagram is:
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that the amount of additional Kilowatt-hours produced is: 1,39 Kilowatt-hours<\/p>\n

    Question 6.
    \nHigher-Order Thinking<\/strong> You have $360 to buy 26 tickets for a baseball game. You need to buy some of each kind of seat. You want to spend most of the money. How many of each type of ticket can you buy? Find two different solutions to the problem. Use an equation to show each solution.
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nYou have $360 to buy 26 tickets for a baseball game. You need to buy some of each kind of seat. You want to spend most of the money.
    \nNow,
    \nThe given cost for each type of seat is:
    \n\"Envision
    \nNow,
    \nLet the number of tickets for Box seats be b
    \nLet the number of tickets for Upper deck be u
    \nSo,
    \nIn terms of total number of tickets,
    \nb + u = 26 —- (1)
    \nSo,
    \nIn terms of cost of the tickets,
    \nTotal cost =[ (The cost of each ticket of box seat) \u00d7 (The number of tickets of box seats)] + [(The cost of each ticket of Upper deck) \u00d7 (The number of tickets of Upper deck)]
    \n18b + 12u = 360 —- (2)
    \nSo,
    \nb = 26 – u —- (3)
    \nNow,
    \nBy using the method of substitution,
    \n18 (26 – u) + 12u = 350
    \n(18 \u00d7 26) – 18u + 12u = 350
    \n[18 \u00d7 (20 + 6)] – 6u = 350
    \n[(18 \u00d7 20) + (18 \u00d7 6)] – 6u = 350
    \n[360 + 108] – 6u = 350
    \n468 – 6u = 350
    \n6u = 468 – 360
    \n6u = 108
    \nu = \\(\\frac{108}{6}\\)
    \nu = 18 tickets
    \nSo,
    \nb = 26\u00a0 -u
    \n= 26\u00a0 -18
    \n= 8 tickets
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of tickets of box seat is: 8
    \nThe number of tickets of Upper desk is: 18<\/p>\n

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

    Question 7.
    \nThe gym teacher has $250 to spend on volleyball equipment. She buys 4 volleyball nets for $28 each volleyball costs $7 each. How many volleyballs can she buy? Explain how you solve. Use one or more equations and bar diagrams in your explanation. Tell what your variables represent.
    \nAnswer:
    \nIt is given that
    \nThe gym teacher has $250 to spend on volleyball equipment. She buys 4 volleyball nets for $28 each volleyball costs $7 each.
    \nNow,
    \nLet the number of volleyballs be x
    \nSo,
    \nThe total cost of volleyball equipment = (The total cost of volleyball nets) + (The total cost of volleyballs)
    \n$250 = [(The cost of each volleyball net) \u00d7 (The number of volleyballs)] + [(The number of volleyballs) \u00d7 (The cost of each volleyball)]
    \n$250 = (4 \u00d7 $28) + (x \u00d7 $7)
    \n$250 = 4 \u00d7 (20 + 8) + x \u00d7 7
    \n$250 = (4 \u00d7 20) + (4 \u00d7 8) + x\u00d7 7
    \n$250 = 80 + 32 + 7x
    \n$250 = 112 + 7x
    \n7x = 250 – 112
    \n7x = 138
    \nx = \\(\\frac{138}{7}\\)
    \nx = 19.7
    \nx \u2248 20
    \nNow,
    \nThe representation of the given information in the form of a bar diagram is:
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that the number of volleyballs is: 20<\/p>\n

    Lesson 6.4 More Model MultiStep Problems<\/h3>\n

    Solve & Share<\/strong>
    \nThree eight-year-old children, one adult, and one senior had $125 saved to go to the Happy Days amusement park. After buying tickets, how much money did they have left to buy refreshments? Complete the bar diagram, and use it to write one or more equations to solve the problem. Tell what your variables represent.
    \nI can … Solve multi-step problems by drawing bar diagrams and writing expressions and equations.
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nThree eight-year-old children, one adult, and one senior had $125 saved to go to the Happy Days amusement park
    \nNow,
    \nThe given table is:
    \n\"\"
    \nNow,
    \nFrom the given table,
    \nThe ticket cost of 1 8-year old child is: $12
    \nThe ticket cost of 1 adult is: $25
    \nThe ticket cost of 1 senior is: $18
    \nSo,
    \nThe total amount of money saved by the given people = (The total ticket cost of the people) + (The total cost of buying refreshments for the people)
    \n= $125 = [(3 \u00d7 The ticket cost of each 8-year old child) + (The ticket cost of 1 adult) + (The ticket cost of 1 senior)] + (The total cost of buying refreshments for the people)
    \n$125 = [(3 \u00d7 $12) + $25 + $18] + (The total cost of buying refreshments for the people)
    \n$125 = ($36 + $25 + $18) + (The total cost of buying refreshments for the people)
    \nThe total cost of buying refreshments for the people = $125 – $79
    \nThe total cost of buying refreshments for the people = $46
    \nNow,
    \nThe representation of the given information in the form of a bar diagram is:
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that
    \nThe total cost spent on refreshments by the given people is: $46<\/p>\n

    Look Back!<\/strong> What expressions and equations did you use to solve this problem? What hidden questions did you need to answer?
    \nAnswer:
    \nThe equation used to solve the above problem is:
    \nThe total amount of money saved by the given people = (The total ticket cost of the people) + (The total cost of buying refreshments for the people)
    \nNow,
    \nThe hidden question we have to answer for the above problem is:
    \nWhat is the total cost of the tickets for 3 8-year old children, 1 adult, and 1 senior?<\/p>\n

    Essential Question<\/strong>
    \nHow Can You Model and Solve Multi-Step Problems?
    \nAnswer:
    \nThe steps to solve Multi-steps Problems are:
    \nStep 1:
    \nCircle and underline. Circle only the necessary information and underline what ultimately needs to be figured out.
    \nStep 2:
    \nFigure out the first step\/problem in the paragraph and solve it.
    \nStep 3:
    \nFind the answer by using the information from Steps 1 and 2<\/p>\n

    Visual Learning Bridge
    \nChef Angela needs 8 cartons of eggs to make the cakes that are ordered. She has 2 cartons of eggs and 4 single eggs in the refrigerator. How many more eggs does she need to make all of the cakes?
    \n\"Envision<\/p>\n

    One Way<\/strong>
    \nHow many eggs does the chef have?
    \n(2 \u00d7 12) + 4 = 24 + 4
    \n= 28 eggs
    \nHow many more eggs does the chef need?
    \nN = number of additional eggs needed
    \nN = (8 \u00d7 12) \u2013 28
    \n= 96 – 28 = 68
    \nThe expression 8 \u00d7 12 is how many eggs the chef needs in all.
    \nThe chef needs 68 more eggs.
    \nSince 68 is close to 72, the answer is reasonable.<\/p>\n

    Another Way<\/strong>
    \nHow many full cartons should the chef buy?
    \n8 \u2013 2 = 6 full cartons
    \nHow many more eggs does the chef need?
    \nN = number of additional eggs needed
    \nN =(6 \u00d7 12) \u2013 4
    \n= 72 – 4 = 68
    \nThe expression 6 \u00d7 12 is the number of eggs in 6 cartons.
    \nThe chef needs 68 more eggs.
    \nSince 68 is close to 72, the answer is reasonable.<\/p>\n

    Convince Me!<\/strong>
    \nA model with Math<\/strong>
    \nDraw the bar diagrams to represent a solution to the problem above.
    \nAnswer:
    \nThe representations of the bar diagrams for the above problem are:
    \n\"\"\"\"<\/p>\n

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

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nExplain the meaning of the expression (2 \u00d7 12) + 4 in the problem on the previous page.
    \nAnswer:
    \nIn the problem on the previous page,
    \nThe meaning of the expression (2 \u00d7 12) + 4 is:
    \n2 \u00d7 12:
    \nThe number of single eggs present in the 2 cartons
    \n4:
    \nThe number of single eggs that are present separately
    \nHence, from the above,
    \nWe can conclude that
    \n(2 \u00d7 12) + 4:
    \nThe total number of single eggs present for chef Angela to make a cake<\/p>\n

    Question 2.
    \nIn the problem on the previous page, how many eggs will the chef have leftover? Explain.
    \nAnswer:
    \nIn the problem on the previous page,
    \nIt is given that
    \nThe total number of cartons the chef needed is: 8 cartons
    \nThe number of cartons the chef have: 2 cartons
    \nSo,
    \nThe remaining number of cartons the chef needed = (The total number of cartons the chef needed) – (The number of cartons the chef have)
    \n= 8 – 2
    \n= 6 cartons
    \nNow,
    \nWe know that,
    \nA single carton has 12 eggs
    \nSo,
    \nThe number of eggs present in 6 cartons = 12 \u00d7 6
    \n= 72 eggs
    \nBut,
    \nIt is given that the 4 single eggs are present
    \nSo,
    \nFrom 72 eggs, only 8 single eggs are needed along with 2 cartons
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of eggs will the chef have leftover is: 4 eggs<\/p>\n

    Do You Know How?<\/strong>
    \nQuestion 3.
    \nCarrie’s stamp book has 20 pages and each page can hold 15 stamps. She has 45 international stamps. She has 4 times as many U.S. stamps. Can all her stamps fit in her book? Use the bar diagram below to help solve this problem. Draw other bar diagrams as needed. Show the equations used to solve this problem.
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nCarrie’s stamp book has 20 pages and each page can hold 15 stamps. She has 45 international stamps. She has 4 times as many U.S. stamps
    \nSo,
    \nThe total number of stamps present in Carrie’s stamp book = (The number of pages present in Carrie’s stamp book) \u00d7 (The number of stamps that each stamp can hold)
    \n= 20 \u00d7 15
    \n= 20 \u00d7 (10 + 5)
    \n= (20 \u00d7 10) + (20 \u00d7 5)
    \n= 200 + 100
    \n= 300 stamps
    \nNow,
    \nAccording to the given information,
    \nThe number of U.S stamps Carrie have = 4 \u00d7 (The number of International stamps)
    \n= 4 \u00d7 45
    \n= 4 \u00d7 (40 + 5)
    \n= (4 \u00d7 40) + (4 \u00d7 5)
    \n= 160 +20
    \n= 180 U.S stamps
    \nSo,
    \n300 > 180
    \nNow,
    \nThe representation of the given information in the form of a bar diagram is:
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that all of Carrie’s stamps fit in her book since the number of stamps Carrie’s book can accommodate is greater than the number of stamps Carrie have<\/p>\n

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

    For 4-5, draw the bar diagrams, and write equations to solve each problem. Use variables to represent unknown quantities and tell what each variable represents.
    \nQuestion 4.
    \nFive toymakers each carved 28 blocks and 17 airplanes. Three other toymakers each carved the same number of airplanes and twice as many blocks. How many toys did the eight carve in all?
    \nAnswer:
    \nIt is given that
    \nFive toymakers each carved 28 blocks and 17 airplanes. Three other toymakers each carved the same number of airplanes and twice as many blocks.
    \nSo,
    \nThe total number of toys the eight people carved = (The number of toys 5 toymakers carved) + (The number of toys the remaining 3 toymakers carved)
    \n= ([The number of blocks] + [The number of airplanes]) + ([The number of airplanes as the same as 5 toymakers made] + [The number of blocks as the same as 5 toymakers made] \u00d7 2)
    \n= (28 + 17) + (17 + [28 \u00d7 2])
    \n= 45 + (17 + 56)
    \n= 45 + 73
    \n= 118 toys
    \nNow,
    \nThe representation of the given information in the form of a bar diagram is:
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that
    \nThe total number of toys that the eight toymakers carved are: 118 toys<\/p>\n

    Question 5.
    \nKendra is using 27 blue patches and some white patches to make a quilt. The quilt has a total area of 540 square inches. Each patch has an area of 9 square inches. How much of the area of the quilt is white?
    \nAnswer:
    \nIt is given that
    \nKendra is using 27 blue patches and some white patches to make a quilt. The quilt has a total area of 540 square inches. Each patch has an area of 9 square inches.
    \nNow,
    \nLet the area of the white patch be x
    \nNow,
    \nThe total number of patches = (The number of blue patches) + (The number of white patches)
    \n= (27 + x)
    \nNow,
    \nThe total area of the patches (or) The total area of the quilt = (The total number of patches) \u00d7 (The area of each patch)
    \n= (27 + x) \u00d7 9 square inches
    \nNow,
    \nAccording to the given information,
    \n(27 + x) \u00d7 9 = 540
    \n27 + x = \\(\\frac{540}{9}\\)
    \n27 + x = 60
    \nx = 60 – 27
    \nx = 33 square inches
    \nNow,
    \nThe representation of the given information in the form of a bar diagram is:
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that
    \nThe area of the white patch is: 33 square inches<\/p>\n

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

    Question 6.
    \nMake Sense and Persevere<\/strong> A ticket to a movie for a student is $7. The cost for an adult is $2 more than for a student. How much would it cost 5 adults and 29 students for tickets to the movie?
    \nAnswer:
    \nIt is given that
    \nA ticket to a movie for a student is $7. The cost for an adult is $2 more than for a student
    \nNow,
    \nThe cost of a ticket for an adult = $2 + (The cost of a ticket for a student)
    \n= $2 + $7
    \n= $9
    \nSo,
    \nThe cost of the tickets for 5 adults = 5 \u00d7 (The cost of a ticket for an adult)
    \n= 5 \u00d7 $9
    \n= $45
    \nSo,
    \nThe cost of the tickets for 29 students = 29 \u00d7 (The cost of a ticket for a student)
    \n= 29 \u00d7 $7
    \n= (20 + 9) \u00d7 $7
    \n= (20 \u00d7 $7) + (9 \u00d7 $7)
    \n= 140 + 63
    \n= $203
    \nSo,
    \nThe total cost of the tickets for 5 adults and 29 students = $45 + $203
    \n= $248
    \nHence, from the above,
    \nWe can conclude that the total cost of the tickets for 5 adults and 29 students to a movie is: $248<\/p>\n

    Question 7.
    \nVocabulary<\/strong> Give an example of an expression. Then give an example of an equation.
    \nAnswer:
    \nAn example of an expression is:
    \n25 \u00d7 3
    \nAn example of an equation is:
    \n20 \u00d7 3 + a \u00d7 3 = 250
    \nWhere,
    \n‘a’ is an unknown variable<\/p>\n

    Question 8.
    \nHigher-Order Thinking<\/strong> Cody and Max both solve the problem below correctly. Explain how each solves.
    \nEmma has $79 to spend at the toy store. She wants to buy a building set, a board game, and 2 action figures from her favorite movie. What else can she buy?
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nEmma has $79 to spend at the toy store. She wants to buy a building set, a board game, and 2 action figures from her favorite movie
    \nNow,
    \nThe given table is:
    \n\"\"<\/p>\n

    Now,
    \nAccording to Max:
    \nLet the money Emma has after she bought the mentioned items be x
    \nSo,
    \nThe amount of money Emma has left = (The total amount of money Emma has) – (The total amount of money spent on buying the items)
    \n= $79 – ($32 + $19 + 2 ($8))
    \n= $79 – ($32 + $19 + $16)
    \n= $79 – 67
    \n= $12
    \nSo,
    \nFrom the given table,
    \nWe can observe that
    \nFor $12, we can buy a doll or an action figure
    \nNow,
    \nAccording to Cody:
    \nThe amount of money Emma have after she bought a building set = (The total amount of money Emma have) – (The amount of money spent by Emma on buying a building set)
    \n= $79 – $32
    \n= $47
    \nThe amount of money Emma have after she bought a board game = (The remaining amount of money Emma have after she bought a building set) – (The amount of money spent by Emma on buying a board game)
    \n= $47 – $19
    \n= $28
    \nThe amount of money Emma have after she bought 2 action figures = (The remaining amount of money Emma have after she bought a board game) – (The amount of money spent by Emma on buying 2 action figures)
    \n= $28 – 2 ($8)
    \n= $28 – $16
    \n= $12
    \nHence, from the above,
    \nWe can conclude that Emma can buy a doll or an action figure<\/p>\n

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

    Question 9.
    \nA company has 2 geothermal plants which can power a total of 2,034 homes. After they build 3 additional, more powerful, geothermal plants, they can power a total of 5,799 homes. How many homes does each of the new plants’ power? Explain how you solve. Use one or more equations and bar diagrams in your explanation. Tell what your variables represent.
    \nAnswer:
    \nIt is given that
    \nA company has 2 geothermal plants which can power a total of 2,034 homes. After they build 3 additional, more powerful, geothermal plants, they can power a total of 5,799 homes
    \nSo,
    \nThe total number of geothermal plants = 2 + 3
    \n= 5 geothermal plants
    \nThe number of homes that can be powered by all the geothermal plants =(The number of homes powered by 2 geothermal plants) + (The number of homes powered by 3 geothermal plants)
    \n= 2,034 + 5,799
    \n= 7,833 homes
    \nSo,
    \nThe number of homes powered by each geothermal plant = \\(\\frac{The number of homes powered by all the geothermal plants}{5}\\)
    \n= \\(\\frac{7,833}{5}\\)
    \n= 1,766.5
    \n\u2245 1,777 homes
    \nNow,
    \nThe representation of the given information in the form of a bar diagram is:
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that the number of homes provided by each geothermal plant is: 1,777 homes<\/p>\n

    Lesson 6.5 Solve Multi-Step Problems<\/h3>\n

    Solve & Share<\/strong>
    \nA farmer needs $3,500 to buy a previously owned truck. If she sells 45 maple trees and 27 pine trees, will she earn enough to buy the truck? If not, how much more money does she need? Solve this problem any way you choose.
    \nI can … solve multi-step problems by finding and solving hidden questions and by writing expressions and equations.
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nA farmer needs $3,500 to buy a previously owned truck and she sells 45 maple trees and 27 pine trees
    \nNow,
    \nThe given table is:
    \n\"\"
    \nNow,
    \nThe amount earned by selling 45 maple trees = (The number of maple trees) \u00d7 (The cost of each maple tree)
    \n= 45 \u00d7 $56
    \n= (40 + 5) \u00d7 (50 + 6)
    \n= (40 \u00d7 50) + (40 \u00d7 6) + (5 \u00d7 50) + (5 \u00d7 6)
    \n= 2,000 + 240 + 250 + 30
    \n= $2,520
    \nNow,
    \nThe amount earned by selling 27 pine trees = (The number of pine trees) \u00d7 (The cost of each pine tree)
    \n= 27 \u00d7 $33
    \n= (20 + 7) \u00d7 (30 + 3)
    \n= (20 \u00d7 30) + (20 \u00d7 3) + (7 \u00d7 30) + (7 \u00d7 3)
    \n= 600 + 60 + 210 + 21
    \n= $891
    \nSo,
    \nThe total amount of money earned by selling 45 maple trees and 27 pine trees = $2,520 + $891
    \n= $3,411
    \nBut,
    \nA farmer needs $3,500
    \nHence, from the above,
    \nWe can conclude that she will not earn enough money to buy the truck<\/p>\n

    Look Back!<\/strong> In the question above, how many more of each tree could the farmer sell to get enough money to buy the truck? Explain.
    \nAnswer:
    \nFrom the above problem,
    \nWe can observe that
    \nThe total amount of money earned by selling 45 maple trees and 27 pine trees is: $3,411
    \nShe will need $3,500
    \nNow,
    \nThe extra money she have = $3,500 – $3,411
    \n= $189
    \nHence, from the above,
    \nWe can conclude that
    \nWith the remaining money,
    \nShe can buy
    \nThe number of maple trees she can buy are: 2
    \nThe number of pine trees she can buy are: 2<\/p>\n

    Essential Question<\/strong>
    \nHow Can You Use Equations to Solve Multi-Step Problems?
    \nAnswer:
    \nThe steps to solve Multi-Step problems using equations are:
    \na. Multiply to clear any fractions or decimals.
    \nb. Simplify each side by clearing parentheses and combining like terms.
    \nc. Add or subtract to isolate the variable term\u2014you may have to move a term with the variable.
    \nd. Multiply or divide to isolate the variable.
    \ne. Check the solution.<\/p>\n

    Visual Learning Bridge
    \nThe students in the fourth and fifth grades are going to a concert. There are 178 students. How many rows are needed for the fourth graders?
    \n\"Envision<\/p>\n

    Step 1<\/strong>
    \nFind and solve the first hidden question.
    \nHidden Question: How many fifth graders are there?
    \n12 \u00d7 8 = s
    \nS = 96
    \nThere are 96 fifth graders.<\/p>\n

    Step 2<\/strong>
    \nFind and solve the second hidden question.
    \nHidden Question: How many fourth graders are there?
    \n178 \u2013 96 = f
    \nf = 82
    \nThere are 82 fourth graders.<\/p>\n

    Step 3<\/strong>
    \nAnswer the original question.
    \nOriginal Question: How many rows are needed for the fourth graders?
    \n82 \u00f7 8 = r
    \nr = 10 R2
    \nTen rows will be filled with 2 fourth graders left over. So, 11 rows will be needed.<\/p>\n

    Convince Me!<\/strong>
    \nConstruct Arguments<\/strong> Does the answer of 11 rows makes sense for the problem above? Explain.
    \nAnswer:
    \nFrom the above problem,
    \nWe can observe that
    \nThe number of rows needed for the fourth graders is: 10 R 2
    \nNow,
    \nThe meaning of 10 R 2 in the given situation is:
    \n10 rows with the remainder 2 seats and we have to arrange that remainder in the next row
    \nSo,
    \nThe total number of rows is: 11
    \nHence, from the above,
    \nWe can conclude that the answer of 11 rows makes sense for the above problem<\/p>\n

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

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nOn the previous page, suppose there were only 11 rows of fifth-graders, but the same total number of students. Do you need to solve the whole problem again to find how many rows are needed for the fourth graders? Explain.
    \nAnswer:
    \nIt is given that
    \nOn the previous page, there were only 11 rows of fifth-graders, but the same total number of students
    \nNow,
    \nIn the example on the previous page,
    \nIt is given that
    \nThere are 8 students in each row and the total number of students are 178
    \nSo,
    \nThe number of rows needed for the fourth-grade students = [(The total number of students) – (The number of rows needed for the fifth-graders) \u00d7 (The number of students in each row)] \u00f7 8
    \nHence, from the above,
    \nWe can conclude that
    \nWe need to solve the whole problem again to find the number of rows needed for the fourth-graders<\/p>\n

    Do You Know How?<\/strong>
    \nQuestion 2.
    \nShow another way to solve the problem on the previous page.
    \nAnswer:
    \nThe given figure is:
    \n\"\"
    \nNow,
    \nIn the previous example on the previous page,
    \nIt is given that
    \nThere are a total of 178 students
    \nNow,
    \nThe number of students in the fifth-grade = (The number of rows filled by the fifth-graders) \u00d7 (The number of students in each row)
    \n= 12 \u00d7 8
    \n= (10 + 2) \u00d7 8
    \n= (10 \u00d7 8) + (2 \u00d7 8)
    \n= 80 + 16
    \n= 96 students
    \nSo,
    \nThe number of students in the fourth-grade = (The total number of students) – (The number of students in the fifth grade)
    \n= 178 – 96
    \n= 82 students
    \nSo,
    \nThe number of rows filled by the fourth-graders = \\(\\frac{The number of students in the fourth-grade}{8}\\)
    \n= \\(\\frac{82}{8}\\)
    \n= 10 R 2
    \nHence,from the above,
    \nWe can conclude that the number of rows filled by the fourth-grade students is: 11<\/p>\n

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

    For 3-4, solve each multi-step problem. Write equations to show how you solve. Draw the bar diagrams to help if needed. Use estimation to decide if your answer is reasonable.
    \n\"Envision
    \nQuestion 3.
    \nVanya bought 5 medium packages of buttons and 3 small packages of buttons. What was the total number of buttons Vanya bought?
    \nAnswer:
    \nThe given data is:
    \n\"\"
    \nSo,
    \nThe total number of buttons Vanya bought = (The number of buttons present in 5 medium packages of buttons) + (The number of buttons present in 3 small packages of buttons)
    \n= (5 \u00d7 The number of buttons present in a medium package of buttons) + (3 \u00d7 The number of buttons present in a\u00a0 small package of buttons)
    \n= (5 \u00d7 38) + (3 \u00d7 18)
    \n= 5 \u00d7 (30 + 8) + 3 \u00d7 (10 + 8)
    \n= (5 \u00d7 30) + (5 \u00d7 8) + (3 \u00d7 10) + (3 \u00d7 8)
    \n= 150 + 40 + 30 + 24
    \n= 244 buttons
    \nHence, from the above,
    \nWe can conclude that
    \nThe total number of buttons Vanya bought is: 244 buttons<\/p>\n

    Question 4.
    \nVance bought 2 packages of large beads, 1 package of medium beads, 2 packages of large buttons, and 2 packages of medium buttons. How many more beads than buttons did Vance buy?
    \nAnswer:
    \nThe given data is:
    \n\"\"
    \nSo,
    \nThe total number of beads Vance bought = (The total number of beads present in 2 packages of large beads) + (The total number of beads present in 1 package of medium beads)
    \n= (2 \u00d7 96) + (1 \u00d7 64)
    \n= 2 \u00d7 (90 + 6) + 64
    \n= (2 \u00d7 90) + (2 \u00d7 6) + 64
    \n= 180 + 12 + 64
    \n= 256 beads
    \nSo,
    \nThe total number of buttons Vance bought = (The total number of buttons present in 2 packages of large buttons) + (The total numbr of buttons present in 2 packages of medium buttons)
    \n= (2 \u00d7 56) + (2 \u00d7 38)
    \n= 2 \u00d7 (50 + 6) + 2 \u00d7 (30 + 8)
    \n= (2 \u00d7 50) + (2 \u00d7 6) + (2 \u00d7 30) + (2 \u00d7 8)
    \n= 100 + 12 + 600 + 16
    \n= 728 buttons
    \nSo,
    \nThe difference between the number of buttons and beads = 728 – 256
    \n= 472 beads
    \nHence, from the above,
    \nWe can conclude that there are 472 more buttons than beads that Vance bought<\/p>\n

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

    Question 5.
    \nen Vision\u00ae STEM How much more does it cost to generate 9 megawatt-hours of electricity with conventional coal than with wind energy? Write one or more equations to show how you solve. Tell what your variables represent.
    \n\"Envision
    \nAnswer:
    \nThe given figure is:
    \n\"Envision
    \nNow,
    \nThe cost to generate 9 megawatt hours of electricity with wind energy = 9 \u00d7 (The cost to generate 1 megawatt hours of electricity with wind energy)
    \n= 9 \u00d7 $87
    \n= 9 \u00d7 (80 + 7)
    \n= (9 \u00d7 80) + (9 \u00d7 7)
    \n= 720 + 63
    \n= $783
    \nNow,
    \nThe cost to generate 9 megawatt hours of electricity with conventional coal = 9 \u00d7 (The cost to generate 1 megawatt hours of electricity with conventional coal)
    \n= 9 \u00d7 $105
    \n= 9 \u00d7 (100 + 5)
    \n= (9 \u00d7 100) + (9 \u00d7 5)
    \n= 900 + 45
    \n= $945
    \nSo,
    \nThe difference between the energy produced with conventional coal and the wind energy = $945 – $783
    \n= $162
    \nHence, from the above,
    \nWe can conclude that
    \nIt takes $162 more to generate 9 megawatt-hours of electricity with conventional coal than the wind energy<\/p>\n

    Question 6.
    \nA model with Math<\/strong> Anna earns $8 an hour babysitting and $6 an hour working in the garden. Last month, she worked 15 hours babysitting and 8 hours in the garden. How much more money does she need to buy a robot which costs $199? Explain how you solve. Use one or more equations in your explanation. Tell what your variables represent.
    \nAnswer:
    \nIt is given that
    \nAnna earns $8 an hour babysitting and $6 an hour working in the garden. Last month, she worked 15 hours babysitting and 8 hours in the garden.
    \nSo,
    \nThe amount of money earned by Anna for babysitting = (The number of hours Anna did babysitting) \u00d7 (The amount of money earned by Anna for 1 hour of babysitting)
    \n= 15 \u00d7 $8
    \n= (10 + 5) \u00d7 $8
    \n= (10 \u00d7 8) + (5 \u00d7 8)
    \n= 80 + 40
    \n= $120
    \nSo,
    \nThe amount of money earned by Anna for working in the garden = (The number of hours Anna did work in the garden) \u00d7 (The amount of money earned by Anna for 1 hour working in the garden)
    \n= 8 \u00d7 $6
    \n= $48
    \nSo,
    \nThe total amount of money earned by Anna = $120 + $48
    \n= $168
    \nBut,
    \nShe needed to buy a robot which costs $199
    \nSo,
    \nThe amount of more money she needed to buy a robot = $199 – $168
    \n= $31
    \nHence, from the above,
    \nWe can conclude that
    \nShe needs $31 more to buy a robot which costs $199<\/p>\n

    Question 7.
    \nHigher-Order Thinking<\/strong> Show two different ways to find the answer to the problem below.
    \nDog and cat food are sold in 20-pound bags. There are 14 bags of dog food and 12 bags of cat food on the store shelves. How many pounds of dog and cat food is on the shelves?
    \nAnswer:
    \nIt is given that
    \nDog and cat food are sold in 20-pound bags. There are 14 bags of dog food and 12 bags of cat food on the store shelves
    \nSo,
    \nThe number of pounds of dog food = (The number of bags of dog food) \u00d7 (The number of pounds each bag contains)
    \n= 14 \u00d7 20
    \n= (10 + 4) \u00d7 20
    \n= (10 \u00d7 20) + (4 \u00d7 20)
    \n= 200 + 80
    \n= 280 pounds
    \nThe number of pounds of cat food = (The number of bags of cat food) \u00d7 (The number of pounds each bag consists)
    \n= 12 \u00d7 20
    \n= (10 + 2) \u00d7 20
    \n= (10 \u00d7 20) + (2 \u00d7 20)
    \n= 200 + 40
    \n= 240 pounds
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of pounds of dog food present on the shelves is: 280 pounds
    \nThe number of pounds of cat food present on the shelves is: 240 pounds<\/p>\n

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

    Question 8.
    \nChris needs $858 to buy a computer. She has already saved $575. She gets $15 an hour for babysitting and will babysit 12 hours in the next month. She can save $8 a week from her allowance. How many weeks of allowance will it take Chris to save enough to buy the computer? Explain how you solve. Use one or more equations in your explanation. Tell what your variables represent.
    \nAnswer:
    \nIt is given that
    \nChris needs $858 to buy a computer. She has already saved $575. She gets $15 an hour for babysitting and will babysit 12 hours in the next month. She can save $8 a week from her allowance
    \nSo,
    \nThe amount of money she required to buy a computer = (The amount of money Chris needs to buy a computer) – (The amount of money she already saved)
    \n= $858 – $575
    \n= $283
    \nNow,
    \nThe amount of money she will earn for babysitting = (The number of hours she did babysitting) \u00d7 (The amount of money she gets for babysitting for an hour)
    \n= 12 \u00d7 $15
    \n= (10 + 2) \u00d7 $15
    \n= (10 \u00d7 15) + (2 \u00d7 15)
    \n= 150 + 30
    \n= $180
    \nSo,
    \nThe remaining money she will need to buy a computer = $283 – $180
    \n= $103
    \nNow,
    \nThe amount of money she earned from allowance = (The number of weeks) \u00d7 (The amount of money she will earn for a week as an allowance)
    \n$103 = x \u00d7 $8
    \nx = \\(\\frac{103}{8}\\)
    \nx = 12.8
    \nx \u2248 13 weeks
    \nHence, from the above,
    \nWe can conclude that
    \nAbout 13 weeks of allowance will it take Chris to save enough to buy the computer<\/p>\n

    Lesson 6.6 Problem Solving<\/h3>\n

    Make Sense and Persevere<\/strong>
    \nSolve & Share<\/strong>
    \nMs. Valenzuela had her students design a snake house for the zoo. In the design shown, the anaconda has 538 more square feet than the python. The python has twice as many square feet as the rattlesnake. How much of the house’s area does each snake have? Solve this problem any way you choose.
    \nI can … make sense of problems and keep working if I get stuck.
    \n\"Envision<\/p>\n

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

      \n
    • What do I need to find?<\/li>\n
    • What do I know?<\/li>\n
    • What’s my plan for solving the problem?<\/li>\n
    • What else can I try if I get stuck?<\/li>\n
    • How can I check that my solution makes sense?<\/li>\n<\/ul>\n

      Answer:
      \nIt is given that
      \nMs. Valenzuela had her students design a snake house for the zoo. In the design shown, the anaconda has 538 more square feet than the python. The python has twice as many square feet as the rattlesnake
      \nNow,
      \nThe given figure is:
      \n\"Envision
      \nNow,
      \nLet the area of the rattlesnake be r square feet
      \nLet the area of the python be p square feet
      \nSo,
      \nThe area of the python = 2 \u00d7 (The area of the rattlesnake)
      \n= 2r square feet
      \nNow,
      \nAccording to the given information,
      \n(The area of the anaconda) – (The area of the python) = 538
      \nSo,
      \n1,928 – p = 538
      \np = 1,928 – 538
      \np = 1,390 square feet
      \nSo,
      \nThe area of the rattlesnake = \\(\\frac{The area of the python (p)}{2}\\)
      \n= \\(\\frac{1,390}{2}\\)
      \n= 695 square feet
      \nHence, from the above,
      \nWe can conclude that
      \nThe area of an anaconda is: 1,928 square feet
      \nThe area of python is: 1,390 square feet
      \nThe area of the rattlesnake is: 695 square feet<\/p>\n

      Look Back!<\/strong>
      \nMake Sense and Persevere<\/strong> How can you check that your solution makes sense?
      \nAnswer:
      \nTo check whether the given solution makes sense or not,
      \nEstimate the solution
      \nNow,
      \nBy the process of Estimation,
      \nThe area of the anaconda is: 1,900 square feet
      \nSo,
      \n(The area of the anaconda) – (The area of python) = 540
      \nThe area of python = 1,900 – 540
      \n= 1,360 square feet
      \nSo,
      \nThe area of rattlesnake = \\(\\frac{The area of python}{2}\\)
      \n= \\(\\frac{1,360}{2}\\)
      \n= 685 square feet
      \nSo,
      \nThe area of the anaconda is: 1,900 square feet
      \nThe area of python is: 1,360 square feet
      \nThe area of the rattlesnake is: 685 square feet
      \nNow,
      \nBy observing the answers in the above problem and the answers for this problem,
      \nWe can say that your answer is reasonable
      \nHence, from the above,
      \nWe can conclude that your solution makes sense<\/p>\n

      Essential Question<\/strong>
      \nHow Do You Make Sense of a Multi-Step Problem and Persevere in Solving It?
      \nAnswer:
      \nThe steps to make sense of a Multi-Step Problem and Persevere in Solving it are:
      \na. Identify the Problem. Begin by determining the scenario the problem wants you to solve.
      \nb. Gather Information.
      \nc. Create an Equation.
      \nd. Solve the Problem.
      \ne. Verify the Answer.<\/p>\n

      Visual Learning Bridge
      \nBryan and Alex have to buy their own instruments for the band. Alex made $1,025 from a fundraiser. He has a part-time job that pays $8 an hour. How many hours does Alex need to work to have enough money to buy his instrument?
      \n\"Envision
      \nWhat do you need to do to solve this problem?
      \nI need to determine how much Alex’s tuba costs and how much Alex needs to earn to buy the tuba.<\/p>\n

      How can I make sense of and solve this problem?
      \nI can<\/p>\n

        \n
      • identify the quantities given.<\/li>\n
      • understand how the quantities are related.<\/li>\n
      • choose and implement an appropriate strategy.<\/li>\n
      • check to be sure my work and answer make sense.<\/li>\n<\/ul>\n

        Here’s my thinking
        \nUse the cost of the trumpet to find the cost of the tuba.
        \n$159 x 9 = $1,431 Alex’s tuba costs $1,431.
        \nFind how much more money Alex needs to earn.
        \n$1,431 \u2013 $1,025 = $406 Alex needs to earn $406.
        \nFind how many hours Alex needs to work.
        \n$406 \u00f7 8 = 50 R6
        \nAlex will not have enough money by working 50 hours, so he needs to work 51 hours.<\/p>\n

        Convince Me!<\/strong>
        \nMake Sense and Persevere<\/strong> How can you check to make sure the work and answer given above make sense?
        \nAnswer:
        \nTo check whether the given answer is reasonable or not,
        \nEstimate the answer by using Estimation methods
        \nNow,
        \nThe given figure is:
        \n\"Envision
        \nNow,
        \nFrom the given figure,
        \nWe can observe that
        \nThe cost of Bryan’s trumpet is about $160
        \nSo,
        \nThe cost of Alex’s tuba = 9 \u00d7 (The cost of Bryan’s trumpet)
        \n= 9 \u00d7 $160
        \n= 9 \u00d7 (100 + 60)
        \n= (9 \u00d7 100) + (9 \u00d7 60)
        \n= 900 + 540
        \n= $1,440
        \nNow,
        \nThe more money Alex must have to buy his instrument = (The cost of Alex’s tuba) – (The money raised by fundraiser)
        \n= $1,440 – $1,025
        \n= $415
        \nNow,
        \nThe number of hours needed for Alex to earn more money = \\(\\frac{The more money Alex must have to buy his instrument}{8}\\)
        \n= \\(\\frac{$415}{8}\\)
        \n= 51 R 7
        \nHence, from the above,
        \nWe can conclude that Alex needs about 7 hours for Alex to earn more money
        \nYour solution is reasonable since the difference between the number of hours in the above example and this problem is not large<\/p>\n

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

        Make Sense and Persevere<\/strong> In the problem on the previous page, suppose Alex wanted to know how many weeks it would take him to work
        \nThink about 51 hours. Alex works 3 hours a day and 4 days a week. this question to help you
        \n\"Envision
        \nQuestion 1.
        \nWhat are you asked to find and what is the hidden question What’s a good plan for solving question?
        \nAnswer:
        \nThe hidden question to answer is:
        \nHow many weeks it would take him to work?
        \nNow,
        \nA good plan for solving the given question is:
        \na. The number of hours in a day that Alex works
        \nb. The number of days in a week that Alex works
        \nc. The number of weeks Alex will take to complete the work<\/p>\n

        Question 2.
        \nWrite and solve equations to solve the problem. Be sure to tell what each variable represents.
        \nAnswer:
        \nIt is given that
        \nAlex works 3 hours a day and 4 days a week
        \nSo,
        \nThe number of hours in a week that Alex will work = (The number of hours a day) \u00d7 (The number of days in a week that Alex will work)
        \n= 3 \u00d7 4
        \n= 12 hours a week
        \nSo,
        \nThe number of weeks Alex will need to complete the work = \\(\\frac{The total number of hore Alex completed the week}{The number of hours in a week that Alex will work}\\)
        \n= \\(\\frac{51}{12}\\)
        \n= 4 R 3
        \nHence, from the above,
        \nWe can conclude that Alex will need about 4 weeks to complete the work<\/p>\n

        Question 3.
        \nDoes your answer make sense? Explain.
        \nAnswer:
        \nTo make whether your answer makes sense or not,
        \nEstimate the solution using the Estimation methods
        \nNow,
        \nThe number of hours in a week that Alex will work = (The number of hours a day) \u00d7 (The number of days in a week that Alex will work)
        \n= 3 \u00d7 4
        \n= 12 hours a week
        \nSo,
        \nThe number of hours in a week that Alex will work is about 10 hours
        \nSo,
        \nThe number of weeks Alex will need to complete the work = \\(\\frac{The total number of hore Alex completed the week}{The number of hours in a week that Alex will work}\\)
        \n= \\(\\frac{51}{10}\\)
        \n= 5 R 1
        \nSo,
        \nWe can conclude that Alex will need about 5 weeks to complete the work
        \nHence, from the above,
        \nWe can conclude that your answer is reasonable since the difference between the actual answer and the estimated answer is not large<\/p>\n

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

        Make Sense and Persevere<\/strong> The high school tennis team is selling tennis balls to raise $500 for new equipment. They sell the balls for $2 each. Will they make enough money if they sell 4 cases?
        \n\"Envision
        \nQuestion 4.
        \nWhat are the hidden questions? Write equations to solve each.
        \nAnswer:
        \nIt is given that
        \nThe high school tennis team is selling tennis balls to raise $500 for new equipment. They sell the balls for $2 each
        \nSo,
        \nThe hidden question for the given problem is:
        \nWhat is the cost of each case?
        \nNow,
        \nThe cost of each case = (The number of packages in each case) \u00d7 (The number of tennis balls in each package) \u00d7 (The cost of each tennis ball)
        \n= 24 \u00d7 3 \u00d7 $2
        \n= 24 \u00d7 $6
        \n= (20 + 4) \u00d7 6
        \n= (20 \u00d7 6) + (6 \u00d7 4)
        \n= 120 + 24
        \n= $144
        \nSo,
        \nThe cost of 4 cases = 4 \u00d7 (The cost of each case)
        \n= 4 \u00d7 $144
        \n= 4 \u00d7 (100 + 40 + 4)
        \n= (4 \u00d7 100) + (4 \u00d7 40) + (4 \u00d7 4)
        \n= 400 + 160 + 16
        \n= $576
        \nBut,
        \nIt is given that the high school tennis team is selling tennis balls to raise $500 for new equipment
        \nHence, from the above,
        \nWe can conclude that they will not make enough money if they sell 4 cases<\/p>\n

        Question 5.
        \nWill the team makes enough money? Explain.
        \nAnswer:
        \nFrom the above problem,
        \nWe can observe that
        \nThe high school tennis team is selling tennis balls to raise $500 for new equipment
        \nThe cost of tennis balls present in 4 cases is: $576
        \nSo,
        \n$500 < $576
        \nHence, from the above,
        \nWe can conclude that the team will not make enough money<\/p>\n

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

        Performance Task<\/strong>
        \nDesigning a Flag<\/strong> Rainey’s group designed the flag shown for a class project. They used 234 square inches of green fabric. After making one flag, Rainey’s group has 35 square inches of yellow fabric left. How can Rainey’s group determine the total area of the flag?
        \n\"Envision
        \nQuestion 6.
        \nMake Sense and Persevere<\/strong> What hidden question(s) do you need to answer first?
        \nAnswer:
        \nIt is given that
        \nRainey’s group designed the flag shown for a class project. They used 234 square inches of green fabric. After making one flag, Rainey’s group has 35 square inches of yellow fabric left
        \nNow,
        \nThe hidden questions you need to answer first are:
        \na. Find the remaining colors present in the flag?
        \nb. What is the area of the remaining colors in the flag?
        \nc. What is the total area of the flag?<\/p>\n

        Question 7.
        \nAppropriate Tools<\/strong> Draw diagrams and write equations to represent the hidden question(s). Be sure to tell what each variable represents.
        \n\"Envision
        \nAnswer:
        \nThe given figure is:
        \n\"Envision
        \nNow,
        \nIt is given that
        \nThey used 234 square inches of green fabric
        \nSo,
        \nThe area of the orange fabric = 2 \u00d7 (The area of the green fabric)
        \n= 2 \u00d7 234
        \n= 2 \u00d7 (200 + 30 + 4)
        \n= (2 \u00d7 200) + (2 \u00d7 30) + (2 \u00d7 4)
        \n= 400 + 60 + 8
        \n= 468 square inches
        \nSo,
        \nThe area of the yellow fabric = 3 \u00d7 (The arae of the green fabric)
        \n= 3 \u00d7 234
        \n= (2 \u00d7 234) + (1 \u00d7 234)
        \n= 468 + 234
        \n= 702 square inches
        \nBut,
        \nIt is given that Rainey’s group has 35 square inches of yellow fabric left
        \nSo,
        \nThe area of the yellow fabric = 702 – 35
        \n= 667 square inches
        \nSo,
        \nThe total area of the flag = (The area of the green flag) + (The area of the orange flag) + (The area of the yellow flag)
        \n= 234 + 702 + 667
        \n= 1,603 square inches
        \nHence, from the above,
        \nWe can conclude that
        \nThe total area of the flag is: 1,603 square inches<\/p>\n

        Question 8.
        \nBe Precise<\/strong> Use your drawings and equations to find the total area of the flag. Explain carefully, using the correct units.
        \nAnswer:
        \nFrom the above problem,
        \nWe can observe that
        \nThe total area of the flag can be found out by adding the areas of the three colors
        \nSo,
        \nThe total area of the flag = (The area of the green flag) + (The area of the orange flag) + (The area of the yellow flag)
        \n= 234 + 702 + 667
        \n= 1,603 square inches
        \nHence, from the above,
        \nWe can conclude that
        \nThe total area of the flag is: 1,603 square inches<\/p>\n

        Question 9.
        \nMake Sense and Persevere<\/strong> What information was not needed to solve the problem?
        \nAnswer:
        \nThere is not any unnecessary information present that is not used to solve the given problem<\/p>\n

        Topic 6 Fluency Practice Activity<\/h3>\n

        Find a Match<\/strong>
        \nWork with a partner. Point to a clue. Read the clue. Look below the clues to find a match. Write the clue letter in the box next to the match. Find a match for every clue.
        \nI can … subtract multi-digit whole numbers.<\/p>\n

        Clues
        \nA. The difference is exactly 528.
        \nB. The difference is between 550 and 560.
        \nC. The difference is between 800 and 900.
        \nD. The difference is exactly 614.
        \nE. The difference is between 100 and 105.
        \nF. The difference is between 470 and 480.
        \nG. The difference is exactly 392.
        \nH. The difference is between 70 and 80.
        \n\"Envision
        \nAnswer:
        \n\"\"<\/p>\n

        Topic 6 Vocabulary Review<\/h3>\n

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

          \n
        • addition comparison<\/li>\n
        • Associative Property of Multiplication<\/li>\n
        • Commutative Property of Multiplication<\/li>\n
        • Distributive Property of Multiplication<\/li>\n
        • equation<\/li>\n
        • multiplication comparison<\/li>\n
        • product<\/li>\n
        • variable<\/li>\n<\/ul>\n

          Write T for true and F for false.
          \nQuestion 1.
          \n__________ Addition comparison is used when you can multiply to find how one quantity is related to another.
          \nAnswer:
          \nWe know that,
          \nAdditive comparisons focus on the difference between two quantities
          \nHence, from the above,
          \nWe can conclude that the given statement is: False<\/p>\n

          Question 2.
          \n___________ Multiplication comparison is used when one quantity is x times more than another quantity.
          \nAnswer:
          \nWe know that,
          \nIn multiplicative comparison, there are two different sets being compared. The first set contains a certain number of items. The second set contains multiple copies of the first set.
          \nHence, from the above,
          \nWe can conclude that the given statement is: False<\/p>\n

          Question 3.
          \n__________ A number sentence that uses an equal sign to show that two expressions have the same value is called an equation.
          \nAnswer:
          \nWe know that,
          \nA number sentence that uses an equal sign to show that two expressions have the same value is called an “Equation”
          \nHence, from the above,
          \nWe can conclude that the given statement is: True<\/p>\n

          Question 4.
          \n___________ The answer to a subtraction problem is called the product.
          \nAnswer:
          \nWe know that,
          \nThe answer to a multiplication problem is called the “Product”
          \nHence, from the above,
          \nWe can conclude that the given statement is: True<\/p>\n

          Question 5.
          \n_________ A symbol or letter that stands for a number is called a variable.
          \nAnswer:
          \nWe know that,
          \nA “Variable” is a symbol that works as a placeholder for expression or quantities that may vary or change
          \nHence, from the above,
          \nWe can conclude that the given statement is: True<\/p>\n

          Label each example with a term from the Word List.
          \nQuestion 6.
          \n(3 \u00d7 4) \u00d7 5 = 3 (4 \u00d7 5) _______________
          \nAnswer:
          \nWe know that,
          \nAccording to Associative Property of Multiplication,
          \na \u00d7 (b \u00d7 c) = (a \u00d7 b) \u00d7 c
          \nSo,
          \nwe can observe that
          \nThe given expression is also in the same form
          \nHence, from the above,
          \nWe can conclude that the term that is suitable for the given problem is: Associative Property of Multiplication<\/p>\n

          Question 7.
          \n3 \u00d7 (4 + 5) = (3 \u00d7 4) + (3 \u00d7 5) _______________
          \nAnswer:
          \nWe know that,
          \nAccording to the Distributive Property of Multiplication,
          \na \u00d7 (b + c) = (a \u00d7 b) + (a \u00d7 c)
          \nSo,
          \nwe can observe that
          \nThe given expression is also in the same form
          \nHence, from the above,
          \nWe can conclude that the term that is suitable for the given problem is: Distributive Property of Multiplication<\/p>\n

          Question 8.
          \n3 \u00d7 4 \u00d7 5 = 4 \u00d7 3 \u00d7 5 _______________
          \nAnswer:
          \nWe know that,
          \nAccording to the Commutative Property of Multiplication,
          \na \u00d7 b = b \u00d7 a
          \nSo,
          \nWe can observe that
          \nThe given expression is also in the same form
          \nHence, from the above,
          \nWe can conclude that the term that is suitable for the given problem is: Commutative Property of Multiplication<\/p>\n

          Use Vocabulary in Writing<\/strong>
          \nQuestion 9.
          \nSeth wrote and solved the following comparison:
          \nFind 6 times as many as 5.
          \n6 \u00d7 5 = n
          \nn = 30
          \nUse at least 3 terms from the Word List to describe Seth’s comparison.
          \nAnswer:
          \nIt is given that
          \nFind 6 times as many as 5 ———-> Multiplication comparison
          \nSo,
          \nThe given sentence can be written as:
          \n6 \u00d7 5 = n ——-> Equation
          \nn = 30 ——-> Product
          \nWhere,
          \nn ——> variable<\/p>\n

          Topic 6 Reteaching<\/h3>\n

          Set A pages 225-232<\/strong><\/p>\n

          Write an equation for each comparison. Find the value of the variable that makes the equation true.
          \nk is 9 times as many as 3.
          \nk = 9 \u00d7 3
          \nk = 27
          \nm is 6 more than 21.
          \nm = 6 + 21
          \nm = 27
          \nThere are 30 apples and 6 bananas in a basket. How many times as many apples as bananas are in the basket?
          \nLet t = the number of times as many apples as bananas.
          \nt times as many as 6 is 30.
          \nt \u00d7 6 = 30
          \nSince 5 \u00d7 6 = 30, there are 5 times as many apples as bananas in the basket.<\/p>\n

          Remember<\/strong> to use addition or subtraction when you know how much more, and multiplication or division when you know how many times as many.<\/p>\n

          Write and solve an equation to match each comparison.
          \nQuestion 1.
          \nx is 21 more than 21.
          \nAnswer:
          \nIt is given that
          \nx is 21 more than 21
          \nSo,
          \nAccording to the Property of Addition comparison,
          \nx = 21 + 21
          \nx = 42
          \nHence, from the above,
          \nWe can conclude that the value of x is: 42<\/p>\n

          Question 2.
          \nMacon has 32 rocks in his collection. He has 4 times as many rocks as his brother. How many rocks, r, does Macon’s brother have?
          \nAnswer:
          \nIt is given that
          \nMacon has 32 rocks in his collection. He has 4 times as many rocks as his brother
          \nNow,
          \nLet the number of rocks Macon’s brother has to be: r
          \nSo,
          \nAccording to the given information,
          \nr \u00d7 4 = 32
          \nr = \\(\\frac{32}{4}\\)
          \nr = 8 rocks
          \nHence from the above,
          \nWe can conclude that Macon’s brother has 8 rocks<\/p>\n

          Question 3.
          \nPam has 24 pencils and 6 erasers. How many times, t, as many pencils as erasers does Pam have?
          \nAnswer:
          \nIt is given that
          \nPam has 24 pencils and 6 erasers
          \nNow,
          \nLet the number of erasers be: x
          \nSo,
          \nAccording to the given information,
          \nx \u00d7 6 = 24
          \nx = \\(\\frac{24}{6}\\)
          \nx = 4 erasers
          \nHence, from the above,
          \nWe can conclude that
          \nPam has the number of pencils 4 times as many as erasers<\/p>\n

          Set B pages 233-240<\/strong><\/p>\n

          At a restaurant, a children’s meal costs $5, and an adult meal costs $9. Four children and 2 adults order meals. The family has a $25 gift certificate to use. How much will their total be before tax?
          \n\"Envision<\/p>\n

          Remember<\/strong> to first find and answer any hidden questions.<\/p>\n

          Question 1.
          \nThere are 64 singers in the choir. The tenors and sopranos are in separate rows. There are 8 singers in each row. There are 4 rows of tenors. How many rows of sopranos are there?
          \nAnswer:
          \nIt is given that
          \nThere are 64 singers in the choir. The tenors and sopranos are in separate rows. There are 8 singers in each row. There are 4 rows of tenors.
          \nNow,
          \nLet the number of rows of sopranos be x
          \nSo,
          \nThe total number of rows = (The number of rows of sopranos) + (The number of rows of tenors)
          \n= (x + 4)
          \nNow,
          \nAccording to the given information,
          \nThe total number of rows = \\(\\frac{The total number of singers}{The number of singers in each row}\\)
          \n= \\(\\frac{64}{8}\\)
          \n= 8
          \nSo,
          \nx + 4 = 8
          \nx = 8 – 4
          \nx = 4 rows
          \nNow,
          \nThe representation of the given information in the form of a bar diagram is:
          \n\"\"
          \nHence, from the above,
          \nWe can conclude that
          \nThe total number of rows of sopranos is: 4 rows<\/p>\n

          Question 2.
          \nSamantha has $600 saved for a trip. She buys an airline ticket for $120 and reserves a hotel room for $55 each night for 4 nights. If Samantha’s trip lasts for 5 days and she spends the same amount each day, how much can Samantha spend each day?
          \nAnswer:
          \nIt is given that
          \nSamantha has $600 saved for a trip. She buys an airline ticket for $120 and reserves a hotel room for $55 each night for 4 nights and Samantha’s trip lasts for 5 days and she spends the same amount each day
          \nNow,
          \nThe amount of money Spent by Samantha = (The amount of money spent to buy an airline ticket) + (The amount of money spent to reserve a hotel room for 4 nights)
          \n= $120 + ($55 \u00d7 4)
          \n= $120 + (50 + 5) \u00d7 4
          \n= 120 + (50 \u00d7 4) + (5 \u00d7 4)
          \n= 120 + 200 + 20
          \n= $120 + $220
          \n= $340
          \nSo,
          \nThe amount of money spent by Samantha for 5 days = $340 \u00d7 5
          \n= (300 + 40) \u00d7 5
          \n= (300 \u00d7 5) + (40 \u00d7 5)
          \n= 1,500 + 200
          \n= $1,700
          \nBut,
          \nSamantha can buy the airline ticket only once
          \nSo,
          \nThe amount of money Samantha spent for 5 days = $1,700 – $120
          \n= $580
          \nSo,
          \nThe amount of money spent by Samantha each day = \\(\\frac{$580}{5}[latex]
          \n= $116
          \nHence, from the above,
          \nWe can conclude that the amount of money spent by Samantha each day is: $116<\/p>\n

          Set C pages 241-244<\/strong><\/p>\n

          There are 13 girls and 14 boys signed up to join volleyball. Each team needs 6 players. How many teams can be formed, and how many more players are needed to form one more team?
          \nFind the total number of players signed up.
          \n13 + 14 = p
          \n27 = p
          \nDivide to find the number of teams that can be formed.
          \n27 \u00f7 6 = t
          \n4 R 3 = t
          \nThere are 3 students left not on a team. Subtract to find the number of players still needed to make a team.
          \n6 – 3 = p
          \n3 = p
          \n4 teams can be formed. 3 more players are needed to make one more team.<\/p>\n

          Remember<\/strong> to draw the bar diagrams to help if needed.<\/p>\n

          Solve each multi-step problem. Write equations to show how you solve.
          \nQuestion 1.
          \nKevin made $96 in necklace sales and half that amount in bracelet sales. How much money did Kevin make in necklace and bracelet sales?
          \nAnswer:
          \nIt is given that
          \nKevin made $96 in necklace sales and half that amount in bracelet sales
          \nSo,
          \nThe amount made by Kevin in bracelet sales = (The amount made by Kevin in necklace sales) \u00f7 2
          \n= [latex]\\frac{96}{2}\\)
          \n= $48
          \nSo,
          \nThe amount of money made by Kevin in necklace and bracelet sales = (The amount of money made by Kevin in necklace sales) + (The amount of money made by Kevin in bracelet sales)
          \n= $96 + $48
          \n= $144
          \nHence, from the above,
          \nWe can conclude that
          \nThe amount made by Kevin in necklace and bracelet sales is: $144<\/p>\n

          Question 2.
          \nA dog and cat rescue use 40 pounds of dog food and 15 pounds of cat food to feed its animals each day. How many pounds of dog and cat food do they use in seven days?
          \nAnswer:
          \nIt is given that
          \nA dog and cat rescue use 40 pounds of dog food and 15 pounds of cat food to feed its animals each day
          \nSo,
          \nThe number of pounds of dog and cat food they use each day = (The number of pounds of dog food) + (The number of pounds of cat food)
          \n= 40 + 15
          \n= 55 pounds
          \nSo,
          \nThe number of pounds of dog and cat food they use in 7 days = 7 \u00d7 (The number of pounds of dog and cat food they use each day)
          \n= 7 \u00d7 55
          \n= 7 \u00d7 (50 + 5)
          \n= (7 \u00d7 50) + (7 \u00d7 5)
          \n= 350 + 35
          \n= 385 pounds
          \nHence, from the above,
          \nWe can conclude that
          \nThe number of pounds of dog and cat food they use in 7 days is: 385 pounds<\/p>\n

          Set D pages 245-248<\/strong><\/p>\n

          Think about these questions to help you make sense of the problem.
          \nThinking Habits<\/p>\n

            \n
          • What do I need to find?<\/li>\n
          • What do I know?<\/li>\n
          • What’s my plan for solving the problem?<\/li>\n
          • What else can I try if I get stuck?<\/li>\n
          • How can I check that my solution makes sense?
            \n\"Envision<\/li>\n<\/ul>\n

            Remember<\/strong> to make sense of the problem before starting to solve it.<\/p>\n

            At a local shelter, each large dog can be adopted for $10 and each small dog for $5. There are 17 large dogs up for adoption. If all the dogs are adopted, the shelter will make $215. How many small dogs were at the shelter?
            \nQuestion 1.
            \nFind the hidden questions. Write equations to solve each.
            \nAnswer:
            \nIt is given that
            \nAt a local shelter, each large dog can be adopted for $10 and each small dog for $5. There are 17 large dogs up for adoption. If all the dogs are adopted, the shelter will make $215.
            \nSo,
            \nThe hidden questions for the given problem are:
            \na. What is the cost for the adoption of 17 large dogs?
            \nb. What is the cost for the adoption of the small dogs?<\/p>\n

            Question 2.
            \nHow many small dogs are at the shelter?
            \nAnswer:
            \nIt is given that
            \nAt a local shelter, each large dog can be adopted for $10 and each small dog for $5. There are 17 large dogs up for adoption. If all the dogs are adopted, the shelter will make $215.
            \nNow,
            \nLet the number of small dogs be x
            \nSo,
            \nThe total cost for the adoption of all dogs = (The total cost for the adoption of large dogs) + (The total cost for the adoption of small dogs)
            \n$215 = [(The number of large dogs) \u00d7 (The cost for the adoption of each large dog)] + [(The number of small dogs) \u00d7 (The cost for the adoption of each small dog)]
            \n$215 = (17 \u00d7 $10) + (x \u00d7 $5)
            \n$215 = (17 \u00d7 1 \u00d7 10) + (x \u00d7 $5)
            \n$215 = $170 + (x \u00d7 $5)
            \nx \u00d7 $5 = $215 – $170
            \nx \u00d7 $5 = $45
            \nx = \\(\\frac{45}{5}\\)
            \nx = 9
            \nHence, from the above,
            \nWe can conclude that the total number of small dogs is: 9 small dogs<\/p>\n

            Topic 6 Assessment Practice<\/h3>\n

            Question 1.
            \nJason and his 3 brothers want to buy a gift for their mother. They have $314 saved. Each of them will save $17 a week until they have at least $515 for her gift. How much money will they save after 3 weeks? Will they have enough money to buy the gift?
            \nA. What are the hidden questions?
            \nAnswer:
            \nIt is given that
            \nJason and his 3 brothers want to buy a gift for their mother. They have $314 saved. Each of them will save $17 a week until they have at least $515 for her gift
            \nHence,
            \nThe hidden questions for the given problem are:
            \na. How much money Jason and his 3 brothers will save each week?
            \nb. How much amount of money do Jason and his brothers need to save?<\/p>\n

            B. Write an equation that can be used to answer each hidden question. Then solve.
            \nAnswer:
            \nIt is given that
            \nJason and his 3 brothers want to buy a gift for their mother. They have $314 saved. Each of them will save $17 a week until they have at least $515 for her gift
            \nNow,
            \nThe amount of money jason and his 3 brothers will save each week = 4 \u00d7 $17
            \n= 4 \u00d7 (10 + 7)
            \n= (4 \u00d7 10) + (4 \u00d7 7)
            \n= 40 + 28
            \n= $68
            \nNow,
            \nThe amount of enough money Jason and his 3 brothers will have to save = $515 – $314
            \n= $201
            \nHence, from the above,
            \nWe can conclude that
            \nThe amount of money Jason and his 3 brothers will save each week is: $68
            \nThe amount of enough money Jason and his 3 brothers will have to save is: $201<\/p>\n

            C. Write and solve an equation to find how much money they will save after 3 weeks. Will they have enough to buy the gift? Explain.
            \nAnswer:
            \nFrom part (a),
            \nWe can observe that
            \nThe amount of money Jason and his 3 brothers will save each week is: $68
            \nSo,
            \nThe amount of money Jason and his 3 brothers will save in 3 weeks = 3 \u00d7 $68
            \n= 3 \u00d7 (60 + 8)
            \n= (3 \u00d7 60) + (3 \u00d7 8)
            \n= 180 + 24
            \n= $204
            \nSo,
            \nThe amount of money Jason and his 3 brothers will save after 3 weeks = $204 – $201
            \n= $3
            \nSo,
            \nThe amount of money Jason and his 3 brothers will have = $515 + $3
            \n= $518
            \nHence, from the above,
            \nWe can conclude that Jason and his 3 brothers will have enough money to buy the gift<\/p>\n

            Question 2.
            \nMarco ordered 2 reclining chairs for $230 each and a coffee table for $350. The shipping cost is $100. Marco is going to pay off his bill in 5 equal payments. How much is each of Marco’s payments?
            \nAnswer:
            \nIt is given that
            \nMarco ordered 2 reclining chairs for $230 each and a coffee table for $350. The shipping cost is $100. Marco is going to pay off his bill in 5 equal payments
            \nSo,
            \nThe total payment made by Marco = (The payment made by Marco for 2 reclining chairs) + (The payment made by Marco for a coffee table) + (The shipping cost)
            \n= (2 \u00d7 230) + 350 + 100
            \n= [(2 \u00d7 23) \u00d7 10] + 450
            \n= 460 + 450
            \n= $910
            \nNow,
            \nThe payment made by Marco in each equal installment = \\(\\frac{$910}{5}\\)
            \n= $182
            \nHence, from the above,
            \nWe can conclude that each of Marco’s payments is: $182<\/p>\n

            Question 3.
            \nMitchell wants to beat the record for the most points scored in a season. This season, he has scored 51 points. If he scores 27 points at each of the next 7 games, he will break the record by 1 point. How many total points will break the record by 1 point?
            \n\"Envision
            \nMitchell will break the record by 1 point if he scores a total of ________ points.
            \nAnswer:
            \nIt is given that
            \nMitchell wants to beat the record for the most points scored in a season. This season, he has scored 51 points. and if he scores 27 points at each of the next 7 games, he will break the record by 1 point.
            \nNow,
            \nThe number of points scored by Mitchell in the next 7 games = 27 \u00d7 7
            \n= (20 + 7) \u00d7 7
            \n= (20 \u00d7 7) + (7 \u00d7 7)
            \n= 140 + 49
            \n= 189 points
            \nSo,
            \nThe total number of points scored by Mitchell in this season = 189 + 51
            \n= 240 points
            \nSo,
            \nThe representation of the given situation in the form of a bar diagram is:
            \n\"\"
            \nHence, from the above,
            \nWe can conclude that
            \nMitchell will break the record by 1 point if he scores a total of 240 points.<\/p>\n

            Question 4.
            \nSelect all the sentences that describe a comparison using multiplication.
            \n\u2610 9 is 3 times as many as p.
            \n\u2610 27 more than r is 41.
            \n\u2610 A bus can travel 3 times as fast as a boat.
            \n\u2610 It costs d dollars for 9 packages.
            \n\u2610 There are 4 times as many girls as boys.
            \nAnswer:
            \nThe sentences that describe a comparison using multiplication are:
            \n\"\"<\/p>\n

            Question 5.
            \nChoose the correct word from the box to complete each statement.
            \n\"Envision
            \nAnswer:
            \nThe completed statements with the suitable word from the given box are:
            \n\"\"<\/p>\n

            Question 6.
            \nDee has $120 to spend. She went to the grocery store and spent $55. She then bought 3 potted flowers for $18 each at the nursery. How much money did Dee have left? Select each correct equation or set of equations that could be used to solve the question.
            \n\u2610 $120 – $55 = M; M \u2013 (3 \u00d7 $18)
            \n\u2610 $120 \u2013 $55 \u2013 (3 \u00d7 $18) = M
            \n\u2610 (3 \u00d7 $18) \u2013 $55 – $120 = M
            \n\u2610 ($120 \u2013 $55) \u2013 (3 \u00d7 $18) = M
            \n\u2610 $120 + $55 – (3 \u00d7 $18) = M.
            \nAnswer:
            \nIt is given that
            \nDee has $120 to spend. She went to the grocery store and spent $55. She then bought 3 potted flowers for $18 each at the nursery.
            \nNow,
            \nThe cost of the 3 potted flowers = 3 \u00d7 $18
            \n= 3 \u00d7 (10 + 8)
            \n= (3 \u00d7 10) + (3 \u00d7 8)
            \n= 30 + 24
            \n= $54
            \nSo,
            \nThe amount of money spent by Dee = $55 + $54
            \n= $109
            \nSo,
            \nThe amount of money Dee left = (The amount of money Dee has to spend) – (The amount of money Dee has spent)
            \n= $120 – $109
            \n= $11
            \nHence, from the above,
            \nWe can conclude that
            \nEach correct equation or set of equations that could be used to solve the given question is:
            \n\"\"<\/p>\n

            Question 7.
            \nDarcy ordered 18 boxes of red balloons and 12 boxes of blue balloons for a party. She ordered a total of 240 balloons. How many balloons are in each box?
            \nA. 6
            \nB. 8
            \nC. 7
            \nD. 9
            \nAnswer:
            \nIt is given that
            \nDarcy ordered 18 boxes of red balloons and 12 boxes of blue balloons for a party. She ordered a total of 240 balloons
            \nSo,
            \nThe total number of balloons present in 2 boxes = (The number of red balloons) + (The number of blue balloons)
            \n= 18 + 12
            \n= 30 balloons
            \nSo,
            \nThe number of balloons present in each box = \\(\\frac{The total number of balloons}{The total number of balloons present i 2 boxes}\\)
            \n= \\(\\frac{240}{30}\\)
            \n= 8 balloons
            \nHence, from the above,
            \nWe can conclude that
            \nThe number of balloons present in each box is:
            \n\"\"<\/p>\n

            Question 8.
            \nSelect all of the sentences that are true for the number 9.
            \n\u2610 18 \u00d7 _____ = 162
            \n\u2610 20 more than _____ = 180
            \n\u2610 _____ times as many as 16 is 145.
            \n\u2610 315 is _____ times as many as 35.
            \n\u2610 16 \u00d7 _______ = 128
            \nAnswer:
            \nThe sentences that are true for the number 9 are:
            \n\"\"<\/p>\n

            Question 9.
            \nSelect all the expressions that are equal to the product of 14 and 9.
            \n\u2610 (2 \u00d7 7) + 9
            \n\u2610 9 times as many as 14
            \n\u2610 14 \u00d7 9
            \n\u2610 14 more than 9
            \n\u2610 9 less than 14
            \nAnswer:
            \nWe know that,
            \nAccording to the Commutative Property of Multiplication,
            \na \u00d7 b = b \u00d7 a
            \nSo,
            \n14 \u00d7 9 = 14 \u00d7 9
            \nHence, from the above,
            \nWe can conclude that
            \nAll the expressions that are equal to the product of 14 and 9 are:
            \n\"\"<\/p>\n

            Question 10.
            \nMaggie collected 63 pounds of paper for recycling. Carl collected 9 pounds. How many times as many pounds did Maggie collect as Carl?
            \nA. 3 times
            \nB. 5 times
            \nC. 7 times
            \nD. 8 times
            \nAnswer:
            \nIt is given that
            \nMaggie collected 63 pounds of paper for recycling. Carl collected 9 pounds
            \nNow,
            \nLet the number of pounds as many times collected be x
            \nSo,
            \nAccording to the given information,
            \n9 \u00d7 x = 63
            \nx = \\(\\frac{63}{9}\\)
            \nx = 7
            \nHence, from the above,
            \nWe can conclude that
            \nThe number of times as many pounds did Maggie collect as Carl are:
            \n\"\"<\/p>\n

            Topic 6 Performance Task<\/h3>\n

            Ski Jumping<\/strong>
            \nJackie and her older brother Robert went skiing. The Ski Jumping table shows their best jumps, including the distance they jumped and the total length of their run.
            \n\"Envision
            \nQuestion 1.
            \nJackie wants to find how much farther Robert’s run was than her run.
            \nPart A
            \nWhat is the total length of Robert’s run? Draw a bar diagram and write and solve an equation to represent the problem. Does this situation use addition or multiplication to compare?
            \nAnswer:
            \nThe given table is:
            \n\"Envision
            \nNow,
            \nFrom the given table,
            \nWe can observe that
            \nThe total length of Robert’s run = 3 \u00d7 (The jump distance of Robert)
            \n= 3 \u00d7 297
            \n= 3 \u00d7 (200 + 90\u00a0 + 7)
            \n= (3 \u00d7 200) + (3 \u00d7 90) + (3 \u00d7 7)
            \n= 600 + 270 + 21
            \n= 891 feet
            \nNow,
            \nThe representation of the given information about Robert in the form of a bar diagram is:
            \n\"\"
            \nSo,
            \nThe given situation uses multiplication to compare
            \nHence, from the above,
            \nWe can conclude that the total length of Robert’s run is: 891 feet<\/p>\n

            Part B
            \nHow much farther was Robert’s run than Jackie’s run? Write equations to represent each step of the problem. Tell what your variables represent.
            \nAnswer:
            \nThe given table is:
            \n\"Envision
            \nNow,
            \nFrom the given table,
            \nThe total length of Jackie’s run = 3 \u00d7 (The jump distance of Jackie)
            \n= 3 \u00d7 189
            \n= 3 \u00d7 (100 + 80 + 9)
            \n= (3 \u00d7 100) + (3 \u00d7 80) + (3 \u00d7 9)
            \n= 300 + 240 + 27
            \n= 567 feet
            \nNow,
            \nFrom part (A),
            \nThe total length of Robert’s run is: 891 feet
            \nSo,
            \nThe difference between Robert and Jackie’s length = 891 – 567
            \n= 324 feet
            \nHence, from the above,
            \nWe can conclude that Robert’s run was 324 feet farther than Jackie’s run<\/p>\n

            Question 2.
            \nJackie’s run was the same on two different jumps. In the first, she jumped 145 feet and went an additional 167 feet after the jump. In the second, she jumped 135 feet. How many feet, f, did she go after the jump?
            \nAnswer:
            \nIt is given that
            \nJackie’s run was the same on two different jumps. In the first, she jumped 145 feet and went an additional 167 feet after the jump. In the second, she jumped 135 feet
            \nSo,
            \nThe total run of Jackie in the first jump = (The total run of Jackie before she jumped) + (The additional run of Jackie after she jumped)
            \n= 145 + 167
            \n= 312 feet
            \nNow,
            \nLet the additional run of Jackie after the second jump be x
            \nSo,
            \nAccording to the given information,
            \n312 = 135 + x
            \nx = 312 – 135
            \nx = 177 feet
            \nHence, from the above,
            \nWe can conclude that Jackie had gone 177 feet after her second jump<\/p>\n

            Question 3.
            \nUse the Beginner Jump information to find how much longer the total length of the ski jump hill for an advanced jump is than a beginner jump. The advanced jump distance is 408 feet.
            \n\"Envision
            \nPart A
            \nWhat are the hidden questions you need to answer to solve the problem? Name a variable for each question.
            \nAnswer:
            \nIt is given that
            \nThe advanced jump distance is 408 feet.
            \nNow,
            \nThe given information is:
            \n\"Envision
            \nHence, from the above,
            \nWe can conclude that
            \nThe hidden questions you need to answer to solve the given problem are:
            \na. What is the jump distance of the beginner jump distance?
            \nb What is the total length of a beginner jump?<\/p>\n

            Part B
            \nHow much longer is d, the total length of an advanced jump hill, then a beginner jump hill? Write equations and explain how to solve the hidden questions and the original question.
            \nAnswer:
            \nIt is given that
            \nThe advanced jump distance is 408 feet.
            \nNow,
            \nThe given table is:
            \n\"Envision
            \nNow,
            \nLet the advanced jump distance is x times as the beginner jump distance
            \nSo,
            \nAccording to the given information,
            \nx \u00d7 8 = 408
            \nx = \\(\\frac{408}{8}\\)
            \nx = 51 feet
            \nSo,
            \nThe beginner jump distance is: 51 feet
            \nNow,
            \nAccording to the given information,
            \nx \u00d7 3 = 51
            \nx = \\(\\frac{51}{3}\\)
            \nx = 17 feet
            \nSo,
            \nThe toatl length of a beginner jump is: 17 feet
            \nSo,
            \nThe length of an advanced jump hill, greater than a beginner jump hill = 51 – 17
            \n= 34 feet
            \nHence, from the above,
            \nWe can conclude that
            \nThe length of an advanced jump hill is 34 feet longer than a beginner jump hill<\/p>\n","protected":false},"excerpt":{"rendered":"

            Go through the\u00a0enVision Math Common Core Grade 4 Answer Key\u00a0Topic 6 Use Operations with Whole Numbers to Solve Problems\u00a0regularly and improve your accuracy in solving questions. enVision Math Common Core 4th Grade Answers Key Topic 6 Use Operations with Whole Numbers to Solve Problems Essential Questions: How is comparing with multiplication different from comparing with …<\/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\/9049"}],"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=9049"}],"version-history":[{"count":5,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/9049\/revisions"}],"predecessor-version":[{"id":28061,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/9049\/revisions\/28061"}],"wp:attachment":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media?parent=9049"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/categories?post=9049"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/tags?post=9049"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}