{"id":6332,"date":"2023-12-28T17:21:20","date_gmt":"2023-12-28T11:51:20","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=6332"},"modified":"2023-12-29T14:41:52","modified_gmt":"2023-12-29T09:11:52","slug":"envision-math-common-core-grade-3-answer-key-topic-6","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-3-answer-key-topic-6\/","title":{"rendered":"enVision Math Common Core Grade 3 Answer Key Topic 6 Connect Area to Multiplication and Addition"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 3 Answer Key<\/a>\u00a0Topic 6 Connect Area to Multiplication and Addition<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

enVision Math Common Core 3rd Grade Answers Key Topic 6 Connect Area to Multiplication and Addition<\/h2>\n

Essential Question:<\/strong>
\nHow does area connect to multiplication and addition?
\n\"Envision<\/p>\n

enVision STEM Project: Design Solutions<\/strong>
\nDo Research There are different designs that help protect against weather, such as as lightning rods, flood-defense barriers, and wind-resistant roofs. Use the Internet or another source to gather information about these kinds of designs and how they work.<\/p>\n

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

    \n
  • Tell how some window or door designs can help protect against weather.<\/li>\n
  • Use a grid to draw one of the window or door designs. Count the number of unit squares your design measures. Label your drawing to show how the design works to protect against weather.<\/li>\n<\/ul>\n

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

    Vocabulary<\/strong>
    \nChoose the best term from the box. Write it on the blank.
    \n\u2022 addend
    \n\u2022 equal groups
    \n\u2022 multiply
    \n\u2022 array<\/p>\n

    Question 1.
    \nWhen you skip count to get the total number, you ________.
    \nAnswer:
    \nWhen you skip count to get the total number, you __add<\/strong>______.<\/p>\n

    \"Connect<\/p>\n

    Question 2.
    \nDividing apples so everyone gets the same number of apples is an example of making __________.
    \nAnswer:
    \nDividing apples so everyone gets the same number of apples is an example of making _equal groups<\/strong>____.<\/p>\n

    Question 3.
    \nWhen you display objects in rows and columns, you make a(n). ___________.
    \nAnswer:
    \nWhen you display objects in rows and columns, you make a(n).\u00a0multiply<\/strong><\/p>\n

    Division as Sharing<\/strong><\/p>\n

    Question 4.
    \nChen has 16 model cars. He puts them in 4 rows. Each row has an equal number of cars. How many columns are there?
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition-Division-as-Sharing-Question-4\"<\/p>\n

    Question 5.
    \nJulie has 24 glass beads to give to 4 friends. Each friend gets an equal share. How many glass beads does each friend get?
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition-Division-as-Sharing-Question-5\"<\/p>\n

    Arrays<\/strong><\/p>\n

    Question 6.
    \nWrite an addition equation and a multiplication equation for the array shown at the right.
    \n\"Envision
    \nAnswer:
    \nNumber of rows = 6
    \nNumber of columns = 5
    \nWe add columns value as many times as rows.
    \nWe add 6 times 5.
    \nAddition equation = 5 + 5 + 5 + 5 + 5 + 5 = 30
    \nMultiplication equation= Rows \u00d7 Columns = 6 \u00d7 5 = 30.<\/p>\n

    Relating Multiplication and Division<\/strong><\/p>\n

    Question 7.
    \nThere are 12 team members. They line up in 3 equal rows. Which multiplication equation helps you find how many are in each row?
    \nA. 2 \u00d7 6 = 12
    \nB. 1 \u00d7 12 = 12
    \nC. 3 \u00d7 4 = 12
    \nD. 3 \u00d7 12 = 36
    \nAnswer:
    \nTotal number of team members = 12
    \nNumber of rows = 3
    \nNumber of members in each row = 12 \u00f7 3
    \n12 \u00f7 3 = 4
    \nThere are 4<\/strong> members in each row.
    \n3 \u00d7 4 = 12.
    \nOption C. 3 \u00d7 4 = 12.<\/p>\n

    Question 8.
    \nThere are 20 bottles of juice lined up in 4 equal rows. Explain how you can use a multiplication equation to find out how many bottles of juice are in each row.
    \nAnswer:
    \nNumber of juice bottles = 20
    \nNumber of row the juice bottles lined up = 4
    \nNumber of bottles in each row = 20 \u00f7 4
    \n20 \u00f7 4 = 5
    \n4 \u00d7 5 = 20.
    \nThere are 5 juice bottles in each row.<\/p>\n

    \"Connect<\/p>\n

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

    PROJECT 6A
    \nHow are cities built?
    \nProject: Plan a Dog Park
    \n\"Envision<\/p>\n

    PROJECT 6B
    \nWhat are community gardens?
    \nProject: Design a Community Garden
    \n\"Envision<\/p>\n

    PROJECT 6C
    \nWhat are carpenters?
    \nProject: Draw a School Floor Plan
    \n\"Envision<\/p>\n

    PROJECT 6D
    \nHow do you play the game?
    \nProject: Make an Area Game
    \n\"Envision<\/p>\n

    +<\/h3>\n

    Lesson 6.1 Cover Regions<\/h3>\n

    Solve & Share<\/strong>
    \nLook at Shapes A-C on Area of Shapes Teaching Tool. How many square tiles do you need to cover each shape? Show your answers below. Explain how you decided.
    \nI can … count unit squares to find the area of a shape.
    \n\"Envision<\/p>\n

    Look Back! Can you be sure you have an accurate answer if there are gaps between the tiles you used? Explain.<\/p>\n

    Essential Question<\/strong>
    \nHow Do You Measure Area?<\/p>\n

    Visual Learning Bridge
    \nEmily made a collage in art class. She cut shapes to make her design. What is the area of this shape?
    \n\"Envision<\/p>\n

    Count the unit squares that cover Emily’s shape. The count is the area of the shape.
    \n\"Envision
    \n36 unit squares cover the shape. The area of the shape is 36 square units.<\/p>\n

    Sometimes you can estimate the area. You can combine partially filled squares to estimate full squares.
    \nCount the unit squares that cover this shape.
    \n\"Envision About 27 unit squares cover the shape.
    \nThe area of the shape is about 27 square units.<\/p>\n

    Convince Me! Construct Arguments Karen says these shapes each have an area of 12 square units. Do you agree with Karen? Explain.
    \n\"Envision
    \nAnswer:
    \nI don’t agree with Karen statement that areas of these shapes is 12 square units each. Because the area of the shape 1
    \nThat is circle is approximately 10 square units and the area of the Second shape is 12 square units.
    \nBoth the shape have different areas.<\/p>\n

    Another Example!<\/strong>
    \nEmily wants to cover this octagon.
    \n\"Envision
    \nIf she tries to cover it using unit squares, there will be gaps or overlaps.
    \nEmily can break the square into two same-size triangles. She can cover the shape completely using this triangle:
    \n\"Envision
    \nFourteen triangles cover the octagon. The area of the octagon is 7 square units.<\/p>\n

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

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nHow do you know the area of the octagon is 7 square units?
    \nAnswer:
    \nThe squares are divided into two equal triangles.
    \nThe unit square is 1 unit long
    \n\"Envision
    \nThere are 14 triangles filling the Octagon
    \n14 triangles
    \n2 triangles makes 1 square unit
    \n14 \u00f7 2 = 7.
    \nThe area of the octagon = 7 square unit<\/p>\n

    Question 2.
    \nExplain how finding the area of a shape is different from finding the length of a shape.
    \nAnswer:
    \nArea of a shape
    \nThe area of a shape is the number of unit squares that cover the surface of a closed figure. Area is measured in square units.
    \nLength of a shape
    \nLength is a measurement of the distance around something.<\/p>\n

    Do You Know How?<\/strong>
    \nIn 3 and 4, count to find the area. Tell if the area is an estimate.
    \nQuestion 3.
    \n\"Envision
    \nAnswer:
    \n\"Envision
    \nIn the above image each square represents 1 unit long
    \nA rectangular shape is represented.
    \nThe shape covers 4 rows and 5 columns
    \nNumber of square = 5 + 5 + 5 + 5 = 20 units.
    \nArea of the shape\u00a0 = 5 \u00d7 4 = 20 square unit.<\/p>\n

    Question 4.
    \n\"Envision
    \nAnswer:
    \nIn the above image each square represents 1\u00a0 unit long
    \nA Triangle shape is represented in the square table.
    \nThe shape covers approximately 5 squares.
    \nArea of the shape\u00a0 = 5 square units.<\/p>\n

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

    In 5-7, count to find the area. Tell if the area is an estimate.
    \nQuestion 5.
    \n\"Envision
    \nAnswer:
    \n\"Envision
    \nThe shape showed in the image\u00a0 is a T shaped.
    \nHere each square is 1 square unit
    \nNumber of squares covered in the horizontal line of T = 4 + 4 = 8 unit
    \nNumber of squares covered in the vertical line of T = 2 + 2 = 4
    \nArea of the shape = 8 + 4 = 12 square units.<\/p>\n

    Question 6.
    \n\"Envision
    \nAnswer:
    \n\"Envision
    \nHere each square represents 1 unit long.
    \nAn oval shape is represented in the table.
    \nNumber of squares covered by the shape = 15 squares.
    \nArea of the shape = 15 square units.<\/p>\n

    \"Connect<\/p>\n

    Question 7.
    \n\"Envision
    \nAnswer:
    \n\"Envision
    \nHere each square is 1 unit long.
    \nA square is divided into 2 equal triangles.
    \nIn the shape above
    \nNumber of squares covered = 8 units
    \nNumber of triangle covered = 2
    \n2 equal triangles is equal to 1 square.
    \nArea of the shape = 8 units + 1 unit = 9 square units.<\/p>\n

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

    Question 8.
    \nMaggie buys 4 sketch pads. She pays with a 20-dollar bill. How much change does Maggie get back?
    \n\"Envision
    \nAnswer:
    \nNumber of sketch pads Maggie bought = 4
    \nCost of each sketch pads = $3
    \nCost of all the sketch pads = 4 \u00d7 $3 = $12
    \n$3 + $3 + $3 + $3 = $12
    \nMoney she paid = 20 dollar bill.
    \nAmount of change she got back = $20 – $12 = $8.
    \nMaggie got $8 cash back.<\/p>\n

    Question 9.
    \nCritique Reasoning<\/strong> Janet covers the red square with square tiles. She says, \u201cI covered this shape with 12 unit squares, so I know it has an area of 12 square units.\u201d Do you agree with Janet? Explain.
    \n\"Envision
    \nAnswer:
    \nAs we can see the tiles covers more area than the red square. I don’t agree with Janet’s saying \u201cI covered this shape with 12 unit squares, so I know it has an area of 12 square units.\u201d
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Lesson-6.1-Cover-Regions-Problem-Solving-Question-9\"<\/p>\n

    Question 10.
    \nHigher Order Thinking<\/strong> Chester drew this picture of a circle inside a square. What would be a good estimate of the green-shaded area of the square? How did you calculate your answer?
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Lesson-6.1-Cover-Regions-Problem-Solving-Question-10\"<\/p>\n

    Question 11.
    \nNumber Sense<\/strong> Arthur puts 18 erasers into equal groups. He says there are more erasers in each group when he puts the erasers in 2 equal groups than when he puts the erasers in 3 equal groups. Is Arthur correct? Explain.
    \nAnswer:
    \nTotal number of erasers Arthur has = 18 erasers.
    \nDividing the 18 erasers into 2 equal groups = 18 \u00f7 2 = 9 erasers.
    \nDividing the 18 erasers into 3 equal groups = 18 \u00f7 3 = 6 erasers.
    \nArthur says there are more erasers in each group when he puts the erasers in 2 equal groups than when he puts the erasers in 3 equal groups.
    \nI agree with the Arthur’s sayings that there will be more erasers in 2 equal groups than in 3 equal groups.
    \nThere are 9 erasers in 2 groups and 6 erasers in 3 groups
    \nThe difference between the 2 groups and 3 groups = 9 – 6 = 3.
    \nThere are 3 more erasers in group 2.<\/p>\n

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

    Question 12.
    \nDaryl draws this shape on grid paper. Estimate the area of the shape Daryl draws.
    \n\"Envision
    \nA. About 4 square units
    \nB. About 5 square units
    \nC. About 6 square units
    \nD. About 7 square units
    \nAnswer:
    \nTotal number of squares = 6 \u00d7 5 = 30 squares.
    \nNumber of uncovered squares = 22 squares.
    \nNumber of covered squares = total squares – uncovered squares
    \n30 – 22 = 8 squares.
    \nThere are 8 covered squares.
    \nBut there is white area in the covered shape squares.
    \nSo, The area of the Daryl shape is about 7 square units.<\/p>\n

    Lesson 6.2 Area: Nonstandard Units<\/h3>\n

    Solve & Share<\/strong>
    \nFind the area of the postcard on each grid. What do you notice about the size of the postcard on each grid? What do you notice about the area of the postcard on each grid? Explain.
    \nI can … count unit squares to find the area of a shape.
    \n\"Envision<\/p>\n

    Look Back! Are the measurements of the areas of the postcard shown above the same? Explain.
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Lesson-6.2-Area-Nonstandard-Units-Solve-&-Share\"
    \nExplanation:
    \nImage 1
    \nNumber of squares = 6 \u00d7 10 = 60 squares.
    \nNumber of uncovered squares = 36 squares
    \nNumber of postcard covered squares = 60 – 36 = 24 squares.
    \nArea of the postcard = 24 square units.<\/p>\n

    Image 2
    \nNumber of squares = 3 \u00d7 5 = 15 squares.
    \nNumber of uncovered squares = 9 squares
    \nNumber of postcard covered squares = 15 – 9 = 6 squares.
    \nArea of the postcard = 6 square units.<\/p>\n

    1 Square in image 2 is equal to 4 squares in image 1
    \nAs shown in the image above.
    \nSo, both the postcards have the same area in both the images.<\/p>\n

    Essential Question<\/strong>
    \nHow Can You Measure Area Using Non-Standard Units?<\/p>\n

    Visual Learning Bridge
    \nTran designs a bookmark for a book. How can he use unit squares to find the area of the bookmark?
    \n\"Envision<\/p>\n

    You can count the number of unit squares.
    \n\"Envision
    \nThere are 32 unit squares.
    \nArea = 32 square units<\/p>\n

    You can use a different unit square.
    \n\"Envision<\/p>\n

    Convince Me! Reasoning How are the areas of these two squares alike and how are they different?
    \n\"Envision<\/p>\n

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

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nWhich of these shapes has an area of 5 square units? How do you know?
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Lesson-6.2-Area-Nonstandard-Units-Guided-Practice-Question-1\"<\/p>\n

    Do You Know How?<\/strong>
    \nQuestion 2.
    \nDraw unit squares to cover the figures and then find the area. Use the unit squares shown.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Lesson-6.2-Area-Nonstandard-Units-Guided-Practice-Do-You-Know-How-Question-2\"<\/p>\n

    \"Connect<\/p>\n

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

    In 3-5, draw unit squares to cover the figures and find the area. Use the unit squares shown.
    \nQuestion 3.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Lesson-6.2-Area-Nonstandard-Units-Independent-Practice-Question-3\"<\/p>\n

    Question 4.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Lesson-6.2-Area-Nonstandard-Units-Independent-Practice-Question-4\"<\/p>\n

    Question 5.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Lesson-6.2-Area-Nonstandard-Units-Independent-Practice-Question-5\"<\/p>\n

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

    Question 6.
    \nBen finds that the area of this figure is 14 square units. Draw unit squares to cover this figure.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Lesson-6.2-Area-Nonstandard-Units-Problem-Solving-Question-6\"<\/p>\n

    Question 7.
    \nLuke eats 6 grapes from the bowl. Then Juan and Luke equally share the grapes that are left. How many grapes does Juan eat? Show how you used reasoning to solve the problem.
    \n\"Envision
    \nAnswer:
    \nTotal number of grapes = 24 grapes.
    \nNumber of grapes Luke ate = 6 grapes.
    \nNumber of remaining grapes in the bowl = 24 grapes – 6 grapes = 18 grapes.
    \nLuke and Juan eat the remaining grapes equally.
    \nNumber of grapes Juan and Luke eat equally are = 18 \u00f7 2 = 9 grapes.
    \nJuan and Luke eat 9 grapes<\/strong> each.<\/p>\n

    Question 8.
    \nConstruct Arguments<\/strong> Riaz estimates that the area of this figure is 45 square units. Martin estimates the area is 48 square units. Whose estimate is closer to the actual measure? Explain.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Lesson-6.2-Area-Nonstandard-Units-Problem-Solving-Question-8\"<\/p>\n

    Question 9.
    \nHigher Order Thinking<\/strong> Theo wants to cover the top of a small table with square tiles. The table is 12 square tiles long and 8 square tiles wide. How many tiles will Theo need to cover the table?
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Lesson-6.2-Area-Nonstandard-Units-Problem-Solving-Question-9\"<\/p>\n

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

    Question 10.
    \nRick used the smaller unit square and found that the area of this shape is 18 square units. If he used the larger unit square, what would the area of the shape be?
    \n\"Envision
    \nA. 1 square unit
    \nB. 2 square units
    \nC. 3 square units
    \nD. 4 square units
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Lesson-6.2-Area-Nonstandard-Units-Assessment-Practice-Question-10\"<\/p>\n

    Lesson 6.3 Area: Standard Units<\/h3>\n

    Solve & Share<\/strong>
    \nDraw a square to represent 1 unit square. Use your unit square to draw a rectangle that has an area of 8 square units. Compare your shape with a partner’s shape. What is the same? What is different?
    \nI can … measure the area of a shape using standard units.
    \n\"Envision<\/p>\n

    Look Back! Are the sizes of your and your partner’s shapes something that is the same or something that is different? Explain.<\/p>\n

    Essential Question<\/strong>
    \nHow Can You Measure Area Using Question Standard Units of Length?<\/p>\n

    Visual Learning Bridge
    \nMeg bought this sticker. What is the area of the sticker in square centimeters?
    \n\"Envision<\/p>\n

    \"Envision<\/p>\n

    Count the unit squares.
    \n\"Envision
    \n6 unit squares cover the sticker. The sticker is measured in square centimeters.
    \nSo, the area of the sticker is 6 square centimeters.<\/p>\n

    Convince Me! Be Precise If square inches rather than square centimeters were used for the problem above, would more unit squares or fewer unit squares be needed to cover the shape? Explain.<\/p>\n

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

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nIf Meg’s sticker on the previous page measured 2 inches by 3 inches, what would its area be?
    \nAnswer:
    \nThe measurement of Meg’s sticker are = 2 inches by 3 inches.
    \nArea = 2 inches \u00d7 3 inches = 6 inches.
    \nArea of Meg’s sticker is 6 inches.<\/p>\n

    Question 2.
    \nZoey paints a wall that measures 8 feet by 10 feet. What units should Zoey use for the area of the wall? Explain.
    \nAnswer:
    \nMeasurements of Zoey paint on the wall = 8 feet by 10 feet
    \nArea of the paint on the wall = 8 feet \u00d7 10 feet\u00a0 = 80 square feet.<\/p>\n

    Do You Know How?<\/strong>
    \nIn 3 and 4, each unit square represents a standard unit. Count the shaded unit squares. Then write the area.
    \nQuestion 3.
    \n\"Envision
    \nAnswer:
    \nNumber of shaded unit squares = 4 \u00d7 3 = 12 squares.
    \nArea of the shaded squares = 12 square ft.
    \nsquare ft because 1 square is measure is ft.<\/p>\n

    Question 4.
    \n\"Envision
    \nAnswer:
    \nNumber of shaded squares = 6 \u00d7 2 = 12 squares.
    \nArea of the shaped squares = 12 square m.
    \nsquare m because 1 square is measure is m.<\/p>\n

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

    In 5-10, each unit square represents a standard unit. Count the shaded unit squares. Then write the area.
    \nQuestion 5.
    \n\"Envision
    \nAnswer:
    \nNumber of shaded unit squares = 4 \u00d7 4 = 16 unit squares.
    \nArea of shaded unit squares = 16 squares in.
    \nsquare in because 1 square is measure is in.<\/p>\n

    Question 6.
    \n\"Envision
    \nAnswer:
    \nNumber of shaped unit squares = 3 \u00d7 3 = 9 unit squares.
    \nArea of the shaded unit squares = 9 square ft.
    \nsquare ft because 1 square is measure is ft.<\/p>\n

    Question 7.
    \n\"Envision
    \nAnswer:
    \nNumber of shaded unit squares = 6 \u00d7 3 = 18 unit squares.
    \nArea of shaded unit squares = 18 square in.
    \nsquare in because 1 square is measure is in.<\/p>\n

    Question 8.
    \n\"Envision
    \nAnswer:
    \nNumber of shaded unit squares = 9 \u00d7 7 = 63 unit squares.
    \nArea of the shaded unit squares = 63 square m.
    \nsquare m because 1 square is measure is m.<\/p>\n

    Question 9.
    \n\"Envision
    \nAnswer:
    \nNumber of shaded unit squares = 7 \u00d7 5 = 35 unit squares.
    \nArea of the shaded unit squares = 35 square cm.
    \nsquare cm because 1 square is measure is cm.<\/p>\n

    Question 10.
    \n\"Envision
    \nAnswer:
    \nNumber of shaded unit squares = 4 \u00d75 = 20 unit squares.
    \nArea of the shaded unit squares = 20 square ft.
    \nsquare ft because 1 square is measure is ft.<\/p>\n

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

    Question 11.
    \nReasoning<\/strong> Mr. Sanchez grows three types of vegetables in his garden. What is the area of the garden that Mr. Sanchez uses to grow lettuce and cucumbers? Explain how to use the units in this problem.
    \n\"Envision
    \nAnswer:
    \nNumber of squares covered Cucumbers = 4 \u00d7 2 = 8 squares
    \nArea of garden used to grow Cucumber= 8 square ft.
    \nNumber of square covered to grow Lettuce = 3 \u00d7 6 = 18 squares
    \nArea of garden used to grow Lettuce = 18 square ft.
    \nTotal area used to grow Lettuce and cucumber in Mr. Sanchez garden = 8 square ft + 18 square ft = 26 square ft.
    \nArea used to grow Lettuce and cucumber is 26 square ft.<\/strong><\/p>\n

    Question 12.
    \nLisa received 34 text messages on Monday and 43 text messages on Tuesday. She received 98 text messages on Wednesday. How many more text messages did Lisa receive on Wednesday than on Monday and Tuesday combined?
    \nAnswer:
    \nNumber of text messages Lisa received on Monday = 34
    \nNumber of text messages Lisa received on Tuesday = 43
    \nNumber of text messages Lisa received on Wednesday = 98
    \nTotal number of text messages Lisa received on Monday and Tuesday combined = 34 + 43 = 77 text messages.
    \nNumber of more text messages did Lisa receive on Wednesday than on Monday and Tuesday combined are = 98 – 77 = 21
    \nLisa receive 21 more text messages<\/strong> \u00a0on Wednesday than on Monday and Tuesday combined.<\/p>\n

    Question 13.
    \nMonica buys a postage stamp. Is the area of the stamp more likely to be 1 square inch or 1 square meter? Explain.
    \nAnswer:
    \nGenerally the dimensions of the postage stamp are in inches.
    \nSo , the area of the postage stamp Monica bought is 1 square inch.<\/p>\n

    Question 14.
    \nAlgebra Which operation can you use to complete the equation below? 8 = 56 \u2610 7
    \nAnswer:
    \nTo complete the given equation we use division.
    \n56 \u00f7 7 = 8
    \n8 \u00d7 7 = 56
    \nSo, we use Division.<\/p>\n

    Question 15.
    \nHigher Order Thinking<\/strong> Brad says a square that has a length of 9 feet has an area of 18 square feet. Is Brad correct? Why or why not?
    \nAnswer:
    \nNo, Brad is not\u00a0 correct.
    \nThe area of a square is side \u00d7 side
    \nHere the length of the square = 9 feet
    \nArea of the square = 9 ft\u00a0 \u00d7 9 ft = 81 square ft.
    \nSo, what Brad said is wrong the area of the square is 81 square ft not 18 square ft.<\/p>\n

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

    Question 16.
    \nEach of the unit squares in Shapes A-C represent 1 square foot. Select numbers to tell the area of each shape.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition-Lesson-6.3-Area-Standard-Units-Guided-Assessment-Practice-Question-16\"<\/p>\n

    Lesson 6.4 Area of Squares and Rectangles<\/h3>\n

    Solve & Share<\/strong>
    \nJorge is carpeting two rooms. One room is a square with a side that measures 6 meters. The other room is a rectangle with sides that measure 3 meters and 12 meters. How many square meters of carpet does Jorge need?
    \nI can … find the area of squares and rectangles by multiplying.
    \n\"Envision<\/p>\n

    Look Back! What do you notice about the lengths of the sides and the areas of the two rooms Jorge is carpeting?<\/p>\n

    Essential Question<\/strong>
    \nHow Can You Find the Question Area of a Figure?<\/p>\n

    Visual Learning Bridge
    \nMike paints a rectangular wall in his room green. The picture shows the length and width of Mike’s wall. A small can of paint covers 40 square feet. Does Mike need more than one small can to paint the wall of his room?
    \n\"Envision<\/p>\n

    One Way<\/strong>
    \nCount the unit squares to find area.
    \n\"Envision
    \nThere are 48 unit squares. The area of Mike’s wall is 48 square feet.<\/p>\n

    Another Way<\/strong>
    \nCount the number of rows and multiply by the number of squares in each row. There are 8 rows and 6 squares in each row.
    \n\"Envision
    \nThe area of Mike’s wall is 48 square feet. He will need more than one small can of paint.<\/p>\n

    Convince Me! Model with Math Mike plans to paint a wall in his living room blue. That wall measures 10 feet tall and 8 feet wide. What is the area of the wall Mike plans to paint blue? How many cans of paint will he need?<\/p>\n

    Another Example!<\/strong>
    \nThe area of another wall in Mike’s room is 56 square feet. The wall is 8 feet high. How wide is the wall?
    \n\"Envision
    \n56 = 8 \u00d7 ?
    \nYou can use division: 56 \u00f7 8 = ?
    \n56 \u00f7 8 = 7
    \nThe wall is 7 feet wide.<\/p>\n

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

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nSuji’s garden is 4 yards long and 4 yards wide. What is the area of Suji’s garden?
    \nAnswer:
    \nLength of Suji’s garden = 4 yards
    \nWidth of Suji’s garden = 4 yards
    \nArea of Suji’s garden = length \u00d7 width = 4 yards \u00d7 4 yards = 16 square yards.<\/p>\n

    Question 2.
    \nThe area of Michi’s garden is 32 square feet. The garden is 8 feet long. How wide is Michi’s garden?
    \n\"Envision
    \nAnswer:
    \nArea of Michi’s garden = 32 square feet
    \nLength of the garden = 8 feet
    \nwidth of the garden = ? feet
    \nArea = length \u00d7 width
    \n32 = 8 \u00d7 width
    \nwidth = 32 \u00f7 8 = 4 feet.
    \n8 ft \u00d7 4 ft = 32 square ft
    \nMichi’s garden is 4 ft wide.<\/strong><\/p>\n

    Do You Know How?<\/strong>
    \nIn 3 and 4, find the area of each figure. Use grid paper to help.
    \nQuestion 3.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition-Lesson-6.4-Area-of-Squares-and-Rectangles-Guided-Practice-Do-You-Know-How-Question-3\"<\/p>\n

    Question 4.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition-Lesson-6.4-Area-of-Squares-and-Rectangles-Guided-Practice-Do-You-Know-How-Question-4\"<\/p>\n

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

    In 5 and 6, find the area. In 7, find the missing length. Use grid paper to help.
    \nQuestion 5.
    \n\"Envision
    \nAnswer:
    \nLength of the figure = 3 cm
    \nWidth of the figure = 1 cm
    \nArea of the figure = 3 cm \u00d7 1 cm = 3 square cm.<\/p>\n

    Question 6.
    \n\"Envision
    \nAnswer:
    \nLength of the figure = 4 ft
    \nWidth of the figure = 9 ft
    \nArea of the figure = 4 ft \u00d7 9 ft = 36\u00a0 square ft.<\/p>\n

    Question 7.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition-Lesson-6.4-Area-of-Squares-and-Rectangles-Guided-Practice-Independent-Practice-Question-7\"<\/p>\n

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

    Question 8.
    \nJen’s garden is 4 feet wide and has an area of 28 square feet. What is the length of Jen’s garden? How do you know?
    \nAnswer:
    \nArea of Jen’s garden = 28 square ft
    \nwidth of Jen’s garden = 4 ft
    \nLength of Jen’s garden = area \u00f7 width
    \n28 sq ft \u00f7 4 ft = 7 ft.
    \nLength of Jen’s garden = 7 ft.<\/p>\n

    Question 9.
    \nMake Sense and Persevere Briana has 2 grandmothers. She mailed 2 cards to each of them. In each card she put 6 photographs. How many photographs did Briana mail in all?
    \nAnswer:
    \nNumber of grandmothers Briana has = 2 grandmothers
    \nNumber of cards she mailed to them = 2 each
    \ntotal number of cards she mailed = 2 + 2 = 4
    \nNumber of photographs in each card = 6 photographs
    \nTotal number of photographs Briana mailed in all = 4 \u00d7 6 = 24 photographs.<\/strong><\/p>\n

    Question 10.
    \nKevin thinks he found a shortcut. He says he can find the area of a square by multiplying the length of one side by itself. Is Kevin correct? Why or why not?
    \nAnswer:
    \nArea of a square is side \u00d7 side = side square.
    \nKevin says he can find the area of a square by multiplying the length of one side by itself.
    \nI agree with Kevin’s saying.
    \nMultiplying the length of one side by itself is same as multiplying side \u00d7 side.
    \nBecause the length of all the side of a square are same.<\/p>\n

    Question 11.
    \nHigher Order Thinking<\/strong> Ryan measures a rectangle that is 9 feet long and 5 feet wide. Teo measures a rectangle that has an area of 36 square feet. Which rectangle has the greater area? Explain how you found the answer.
    \nAnswer:
    \nLength of Ryan rectangle = 9 ft
    \nWidth of Ryan rectangle = 5 ft
    \nArea of rectangle = length \u00d7 width = 9 ft\u00a0 \u00d7 5 ft = 45 ft.
    \nArea of the rectangle Teo measured = 36 square ft.
    \nRyan rectangle has the greater area.
    \nOn comparing the areas of both the rectangles. Ryan rectangle area is 45 square ft and Teo rectangle area is 36 square ft
    \n45 – 36 = 9 square ft greater.
    \nRyan rectangle area is 9 square ft greater than Teo’s rectangle area.<\/p>\n

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

    Question 12.
    \nMarla makes maps of state preserves. Two of her maps of the same preserve are shown. Select all the true statements about Marla’s maps.
    \n\"Envision
    \n\u2610 You can find the area of Map A by counting the unit squares.
    \n\u2610 You can find the area of Map B by multiplying the side lengths.
    \n\u2610 The area of Map A is 18 square feet.
    \n\u2610 The area of Map B is 18 square feet.
    \n\u2610 The areas of Maps A and B are NOT equivalent.
    \nAnswer:
    \n\u2610 You can find the area of Map A by counting the unit squares.
    \n\u2610 You can find the area of Map B by multiplying the side lengths.
    \n\u2610 The area of Map A is 18 square feet.
    \n\u2610 The area of Map B is 18 square feet.
    \nAll the above mentioned statements are true.<\/p>\n

    Lesson 6.5 Apply Properties: Area and the Distributive Property<\/h3>\n

    Solve & Share<\/strong>
    \nThe new reading room floor is a rectangle that is 8 feet wide by 9 feet long. Mrs. Wallace has a rectangular rug that is 8 feet wide by 5 feet long. What area of the reading room floor will not be covered by the rug?
    \nI can … use properties when multiplying to find the area of squares and rectangles.
    \n\"Envision<\/p>\n

    Look Back! Does your strategy change if the rug is in the corner of the room or in the center? Explain why or why not.<\/p>\n

    Essential Question<\/strong>
    \nHow Can the Area of Rectangles Represent Question the Distributive Property?<\/p>\n

    Visual Learning Bridge
    \nGina wants to separate this rectangle into two smaller rectangles. Will the area of the large rectangle equal the sum of the areas of the two small rectangles?
    \n\"Envision<\/p>\n

    Separate the 8-unit side into two parts.
    \n\"Envision<\/p>\n

    7 \u00d7 8 = 7 \u00d7 (5 + 3) = (7 \u00d7 5) + (7 \u00d7 3)
    \n\"Envision
    \nSo, the area of the large rectangle is equal to the sum of the areas of the two small rectangles.<\/p>\n

    Convince Me! Generalize Find another way to separate this rectangle into two smaller parts. Write an equation you can use to find the areas of the two smaller rectangles. Is the area of the large rectangle still the same? What can you generalize?
    \n\"Envision<\/p>\n

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

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nDescribe a way to separate a 6×6 square into two smaller rectangles.
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition-Lesson-6.5-Apply-Properties-Area-and-the-Distributive-Property-Guided-Practice-Question-1\"<\/p>\n

    6 \u00d7 6 = 36
    \n6 \u00d7 6 = 6 \u00d7 (2 + 4 ) = 6 \u00d7 2 + 6 \u00d7 4 = 12 + 24 = 36.<\/p>\n

    Question 2.
    \nWhat multiplication facts describe the areas of the two smaller rectangles you identified in Exercise 1?
    \nAnswer:
    \n6 \u00d7 6 = 36
    \n6 \u00d7 6 = 6 \u00d7 (2 + 4 ) = 6 \u00d7 2 + 6 \u00d7 4 = 12 + 24 = 36.<\/p>\n

    Do You Know How?<\/strong>
    \nComplete the equation that represents the picture.
    \nQuestion 3.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition-Lesson-6.5-Apply-Properties-Area-and-the-Distributive-Property-Guided-Practice-Question-3\"
    \nExplanation:
    \nGiven 6 \u00d7 5
    \nUsing distributive property to find the product of 6 \u00d7 5.
    \nBy breaking one of the facts to get the product.
    \nHere we break 5 in to 2 and 3
    \nThen the equation will be
    \n6 \u00d7 (2 + 3 )= (6 \u00d7 2 ) + (6 \u00d7 3)<\/p>\n

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

    In 4 and 5, complete the equation that represents the picture.
    \nQuestion 4.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition-Lesson-6.5-Apply-Properties-Area-and-the-Distributive-Property-Question-4\"
    \nExplanation:
    \nGiven 5 \u00d7 7
    \nUsing distributive property to find the product of 5 \u00d7 7
    \nBy breaking one of the facts to get the product.
    \nHere 7 is broken into 4 and 3
    \nThen the equation will be
    \n5 \u00d7 7 = 5 \u00d7 (4 + 3) = (5 \u00d74) + (5 \u00d7 3 ) = 20 + 15 = 35.<\/p>\n

    Question 5.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition-Lesson-6.5-Apply-Properties-Area-and-the-Distributive-Property-Question-5\"
    \nExplanation:
    \nGiven 3 \u00d7 8
    \nUsing distributive property to find the product of 3 \u00d7 8
    \nBy breaking one of the facts to get the product.
    \nHere 8 is broken into 4 and 4
    \nThen the equation will be
    \n3 \u00d7 8 = 3 \u00d7 (4 + 4) = (3 \u00d74) + (3 \u00d7 4 ) = 12 + 12 = 24..<\/p>\n

    In 6, write the equation that represents the picture.
    \nQuestion 6.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition-Lesson-6.5-Apply-Properties-Area-and-the-Distributive-Property-Question-6\"
    \nExplanation:
    \nGiven 4 \u00d7 6
    \nUsing distributive property to find the product of 4\u00d7 6
    \nBy breaking one of the facts to get the product.
    \nHere 6 is broken into 2 and 4
    \nThen the equation will be
    \n4 \u00d7 6 = 4 \u00d7 (2 + 4) = (4 \u00d72) + (4 \u00d7 4 ) = 8 + 16 = 24<\/p>\n

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

    Question 7.
    \nAmit sold 3 shells last week for $5 each and 2 more shells this week for $5 each. Show two ways to determine how much money Amit made in the two weeks.
    \nAnswer:
    \nNumber of shells Amit sold last week = 3 shells
    \nCost of each shell he sold = $5 each
    \nTotal Money Amit made in last week = 3 \u00d7 $5 = $15
    \nNumber of shells he sold this week = 2 shells
    \nCost of each shell he sold = $5 each.
    \nTotal money Amit made this week = 2 \u00d7 $5 = $10
    \nTotal money Amit made in two weeks = $15 + $10 =$25.
    \nOther way
    \nTotal number of shells he sold in two weeks = 3 + 2
    \nCost of each shell = $5
    \nTotal money Amit earned in two weeks =
    \n=$5 \u00d7 (3 + 2)
    \n= ($5 \u00d7 3) + ($5 \u00d7 2 )
    \n= $15 + $10
    \n= $25.<\/p>\n

    Question 8.
    \nenVision\u00ae STEM Claudia wants to replace the roof of a dog house with a new wind-resistant material. The roof has two rectangular sides that are 6 feet by 4 feet. What is the total area of the roof?
    \nAnswer:
    \nNumber of rectangular sides = 2
    \nSizes of the rectangular sides = 6 feet by 4 feet
    \nArea of 1 rectangular sides = 6 ft \u00d7 4 ft = 24 square ft
    \nTotal area of the roof = 2 \u00d7 24 square ft = 48 square ft.<\/p>\n

    Question 9.
    \nUse Structure<\/strong> Chiya has an 8 x 6 sheet of tiles. Can she separate the sheet into two smaller sheets that are 8 x 4 and 8 x 2? Do the two smaller sheets have the same total area as her original sheet? Explain.
    \n\"Envision
    \nAnswer:
    \nThe dimensions of Chiya sheet of tiles = 8 \u00d7 6
    \nArea of the sheet = 8\u00d7 6 = 48.
    \nThe sheet is divided into two smaller sheet
    \nUsing distributive property and dividing into two smaller parts
    \n8 \u00d7 6 = 8 \u00d7(4 + 2) = (8 \u00d7 4) + (8 \u00d7 2) = 32 + 16 = 48.
    \nIn both the cases the area is same.<\/p>\n

    Question 10.
    \nHigher Order Thinking<\/strong> List all possible ways to divide the rectangle at the right into 2 smaller rectangles.
    \n\"Envision
    \nAnswer:
    \nThe dimensions of the picture = 4 rows with 5 squares
    \nTotal number of squares = 4 \u00d7 5 = 20 squares.
    \nUsing distributive property and finding all the possible ways.
    \n4 \u00d7 5 = 4 \u00d7 (1 + 4 )= (4 \u00d7 1) + (4 \u00d7 4) = 4 + 16 = 20
    \n4 \u00d7 5 = 4 \u00d7 (2 + 3 )= (4 \u00d7 2) + (4 \u00d73) = 8\u00a0 + 12 = 20
    \n4 \u00d7 5 = 4 \u00d7 (3 + 2 )= (4 \u00d7 3) + (4 \u00d7 2) =12 + 8 = 20
    \n4 \u00d7 5 = 4 \u00d7 (4 + 1 )= (4 \u00d7 4) + (4 \u00d7 1) = 16 + 4 = 20.<\/p>\n

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

    Question 11.
    \nWhich equation represents the total area of the green shapes?
    \n\"Envision
    \nA. 4 \u00d7 8= 4 \u00d7 (6 + 2) = (4 \u00d7 6) + (4 \u00d7 2)
    \nB. 4 \u00d7 7 = 4 \u00d7 (3 + 4) = (4 \u00d7 3) + (4 \u00d7 4)
    \nC. 4 \u00d7 7 = 4 \u00d7 (4 + 3) = (4 \u00d7 4) + (4 \u00d7 3)
    \nD. 4 \u00d7 7 = 4 \u00d7 (5 + 2) = (4 \u00d7 5) + (4 \u00d7 2)
    \nAnswer:
    \nNumber of rows = 4 with 7 square each
    \nArea of the green shapes = 4 \u00d7 7 = 28 square units.
    \nBreaking 7 into smaller part
    \n7 = 1 + 6
    \n7 = 2 + 5
    \n7 = 3 + 4
    \n7 = 4 + 3
    \n7 = 5 + 2
    \n7 = 6 + 1
    \nthe equations are
    \nB. 4 \u00d7 7 = 4 \u00d7 (3 + 4) = (4 \u00d7 3) + (4 \u00d7 4)
    \nC. 4 \u00d7 7 = 4 \u00d7 (4 + 3) = (4 \u00d7 4) + (4 \u00d7 3)
    \nD. 4 \u00d7 7 = 4 \u00d7 (5 + 2) = (4 \u00d7 5) + (4 \u00d7 2)
    \nwhich represents the green shapes.<\/p>\n

    Lesson 6.6 Apply Properties: Area of Irregular Shapes<\/h3>\n

    Solve & Share<\/strong>
    \nMrs. Marcum’s desk is shaped like the picture below. The length of each side is shown in feet. Find the area of Mrs. Marcum’s desk.
    \nI can … use properties to find the area of irregular shapes by breaking the shape into smaller parts.
    \n\"Envision<\/p>\n

    Look Back! How can you check your answer? Is there more than one way to solve this problem? Explain.<\/p>\n

    Essential Question<\/strong>
    \nHow Can You Find the Area of an Irregular Shape?<\/p>\n

    Visual Learning Bridge
    \nMr. Fox is covering a miniature golf course putting green with artificial grass. Each artificial grass square is 1 square foot. What is the area of the putting green that Mr. Fox needs to cover?
    \n\"Envision<\/p>\n

    One Way<\/strong>
    \nYou can draw the figure on grid paper. Then count the unit squares to find the area.
    \n\"Envision
    \nThe area of the putting green is 56 square feet.<\/p>\n

    Another Way<\/strong>
    \nDivide the putting green into rectangles. Find the area of each rectangle. Then add the areas.
    \n\"Envision
    \nRectangle A 4 \u00d7 3= 12
    \nRectangle B 4 \u00d7 3 = 12
    \nRectangle C 4 \u00d7 8 = 32
    \n12 + 12 + 32 = 56. The area of the putting green is 56 square feet.<\/p>\n

    Convince Me! Use Structure Find another way to divide the putting green into smaller rectangles. Explain how you can find the area of the putting green using your smaller rectangles.
    \n\"Envision
    \nAnswer:
    \n\"Envision
    \nHere dividing the image as per the above image. into 3 rectangles.
    \nRectangle A = 8 ft \u00d7 3 ft = 24 square ft
    \nRectangle B = 8 ft \u00d7 3 ft = 24 square ft
    \nRectangle C = 4 ft \u00d7 2 ft = 8 square ft
    \nTotal area of the image = 24 +24 + 8 = 56 square ft.<\/p>\n

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

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nExplain why you can find the area of the putting green on the previous page using different rectangles.
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition-<\/p>\n

    Question 2.
    \nExplain what operation you use to find the total area of the smaller rectangles.
    \nAnswer:
    \nI used distributive property.
    \nI divide the shape into smaller shapes and then added all the shapes to find the total shape.
    \nTo find the area of the irregular shape find the areas of the smaller area and then add them together.<\/p>\n

    Do You Know How?<\/strong>
    \nIn 3 and 4, find the area of each figure. Use grid paper to help.
    \nQuestion 3.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition-<\/p>\n

    Question 4.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition-<\/p>\n

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

    In 5-8, find the area of each figure. Use grid paper to help.
    \nQuestion 5.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition-<\/p>\n

    Question 6.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition-<\/p>\n

    Question 7.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition-<\/p>\n

    Question 8.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition-<\/p>\n

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

    Question 9.
    \nReasoning<\/strong> Mrs. Kendel is making a model house. The footprint for the house is shown at the right. What is the total area? Explain your reasoning.
    \n\"Envision
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition-
    \nExplanation:
    \nHere to find the area of Mrs. Kendel Model House i divided the model into two sections.
    \nLiving Section and Sleeping Section.
    \nFinding the area of Living Section and Sleeping Section and then adding them gives the total area of the model house.<\/p>\n

    Question 10.
    \nVocabulary Fill in the blanks. Mandy finds the _________ of this shape by dividing it into rectangles. Phil gets the same answer by counting ________.
    \n\"Envision
    \nAnswer:
    \nMandy finds the _Area__<\/strong> of this shape by dividing it into rectangles. Phil gets the same answer by counting _squares__.<\/strong><\/p>\n

    Question 11.
    \nAlgebra Write an equation. Use a question mark to represent the unknown quantity for the phrase “six times a number is 24.” Solve your equation.
    \nAnswer:
    \n“six times a number is 24.”
    \n4 + 4 + 4 + 4 + 4 + 4 = 24
    \nsix times 4 is 24.<\/p>\n

    Question 12.
    \nHigher Order Thinking<\/strong> Mr. Delancy used 3-inch square tiles to make the design at the right. What is the area of the design he made? Explain how you found it.
    \n\"Envision
    \nAnswer:
    \nDimensions of 1 square = 3 in
    \nArea of 1 square = 3 in \u00d7 3 in = 9 square in.
    \nNumber of green squares = 4 squares
    \nNumber of blue squares = 4 squares.
    \nTotal number of squares =4 + 4 = 8 squares.
    \nTotal Area of all squares = 8 \u00d7 9 square in = 72 square in.<\/p>\n

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

    Question 13.
    \nJared drew the figure at the right. Draw lines to show how you can divide the shape to find the area. Then select the correct area for the figure at the right.
    \n\"Envision
    \nA. 6 square inches
    \nB. 24 square inches
    \nC. 30 square inches
    \nD. 33 square inches
    \nAnswer:
    \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition-<\/p>\n

    Lesson 6.7 Problem Solving<\/h3>\n

    Look For and Use Structure<\/strong>
    \nSolve & Share<\/strong>
    \nMr. Anderson is tiling his kitchen floor. He will not need tiles for the areas covered by the kitchen island or the counter. How many square meters of tiles does Mr. Anderson need?
    \nI can … use the relationships between quantities to break a problem into simpler parts.
    \n\"Envision
    \nThinking Habits
    \nBe a good thinker! These questions can help you.<\/p>\n

      \n
    • What patterns can I see and describe?<\/li>\n
    • How can I use the patterns to solve the problem?<\/li>\n
    • Can I see expressions and objects in different ways?
      \n\"Envision<\/li>\n<\/ul>\n

      Look Back! Use Structure is the tiled area greater than or less than the total area of the kitchen? Explain.<\/p>\n

      Essential Question<\/strong>
      \nHow Can You Use Structure to Solve Problems?<\/p>\n

      Visual Learning Bridge
      \nJanet is painting a door. She needs to paint the entire door except for the window.
      \nWhat is the area of the part of the door that needs paint?
      \n\"Envision<\/p>\n

      What do I need to do to solve this problem?
      \nI need to find the area of the door without the window.<\/p>\n

      How can I make use of structure to solve this problem?
      \nI can<\/p>\n

        \n
      • break the problem into simpler parts.<\/li>\n
      • find equivalent expressions.<\/li>\n<\/ul>\n

        I will subtract the area of the window from the total area.
        \nHere’s my thinking…)
        \nFind the area of the whole door.
        \n4 feet \u00d7 9 feet = 36 square feet<\/p>\n

        Find the area of the window.
        \n2 feet \u00d7 2 feet = 4 square feet<\/p>\n

        Subtract to find the area that needs paint.
        \n36 \u2013 4 = 32 square feet<\/p>\n

        The area of the part of the door that needs paint is 32 square feet.<\/p>\n

        Convince Me! Use Structure Janet thinks of a different way to solve the problem. She says, \u201cI can divide the area I need to paint into 4 smaller rectangles. Then I will find the area of each smaller rectangle and add the 4 areas.\u201d Does Janet’s strategy make sense? Explain.
        \n\"Envision<\/p>\n

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

        Use Structure<\/strong> Lil glued beads on the border of the frame. What is the area of the part she decorated with beads?
        \n\"Envision
        \nQuestion 1.
        \nHow can you think about the total area of the frame?
        \nAnswer:
        \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

        Question 2.
        \nUse what you know to solve the problem.
        \n\"Envision
        \nAnswer:
        \nGiven a frame and a image
        \nTo find the\u00a0 decorated area we subtract the image area from\u00a0 total area.<\/p>\n

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

        Use Structure<\/strong> A keypad has 10 rubber buttons. Each button is 1 centimeter by 2 centimeters. The rest is made out of plastic. Is the area of the plastic greater than the area of the rubber buttons?
        \n\"Envision
        \nAnswer:
        \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition\u2013Lesson-6.7-Problem-Solving-Independent-Practice\"
        \nQuestion 3.
        \nHow can you break the problem into simpler parts? What is the hidden question?
        \nAnswer:
        \nArea of the buttons is calculated. Then
        \nTotal area of the keypad is calculated.
        \nFinally the area of the plastic is calculated by subtracting buttons area from the total area.<\/p>\n

        Question 4.
        \nHow can you find the area of all the rubber buttons?
        \nAnswer:
        \nThe area of the rubber = Area of the keypad – Area of the 10 buttons
        \n= 70 square cm – 20 square cm
        \n= 50 square cm.<\/p>\n

        Question 5.
        \nUse what you know to solve the problem.
        \nAnswer:
        \nWe know the
        \nDimensions of the button
        \nDimensions of the keypad.
        \nUsing these dimensions area of buttons and keypad are calculated.
        \nSubtracting the button area from keypad area. Plastic area is calculated.<\/p>\n

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

        Performance Task
        \nPlace Mat Genevieve is designing a placemat. The center measures 8 inches by 10 inches. A 2-inch border goes around the center. Genevieve cuts the corners to make the placemat an octagon. She wants to find the area of the placemat.
        \n\"Envision<\/p>\n

        Question 6.
        \nUse Structure What are the lengths and widths of each rectangular border piece?
        \nAnswer:
        \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition\u2013Lesson-6.7-Problem-Solving-<\/p>\n

        Question 7.
        \nUse Appropriate Tools How can Genevieve find the area of the 4 corner pieces using grid paper?
        \n\"Envision
        \nAnswer:
        \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition\u2013Lesson-6.7-Problem-Solving-
        \nArea of the corners is 8 square in.<\/p>\n

        Question 8.
        \nModel with Math What equation can Genevieve use to find the area of the center? Find the area of the center using your equation.
        \n\"Envision
        \nAnswer:
        \nGiven
        \nThe center measures 8 inches by 10 inches.
        \nArea of the center = 8 in \u00d7 10 in = 80 square in.<\/p>\n

        Question 9.
        \nReasoning<\/strong> How are the quantities in this problem related?
        \nAnswer:
        \nThey share one side of the other rectangles.<\/p>\n

        Question 10.
        \nBe Precise<\/strong> Solve the problem. Explain what unit you used for your answer.
        \nAnswer:
        \nWe used inches. to measure the answer.<\/p>\n

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

        Follow the Path<\/strong>
        \nShade a path from START to FINISH. Follow the quotients that are odd numbers. You can only move up, down, right, or left. Once you complete the path, write the fact families for each of the squares you shaded.
        \nI can … multiply and divide within 100.
        \n\"Envision<\/p>\n

        Topic 6 Vocabulary Review<\/h3>\n

        Understand Vocabulary<\/strong>
        \nChoose the best term from the Word List. Write it on the blank.
        \nWord List<\/p>\n

          \n
        • area<\/li>\n
        • column<\/li>\n
        • Distributive Property<\/li>\n
        • estimate<\/li>\n
        • multiplication<\/li>\n
        • product<\/li>\n
        • row<\/li>\n
        • square unit<\/li>\n
        • unit square<\/li>\n<\/ul>\n

          Question 1.
          \nA(n) __________ has sides that are each 1 unit long.
          \nAnswer:
          \nA(n) _unit square__<\/strong> has sides that are each 1 unit long.<\/p>\n

          Question 2.
          \n__________ is the number of unit squares that cover a region or shape.
          \nAnswer:
          \n__Area__<\/strong> is the number of unit squares that cover a region or shape.<\/p>\n

          Question 3.
          \nYou can use the ___________ to break apart facts and find the __________.
          \nAnswer:
          \nYou can use the __Distributive Property<\/strong>__ to break apart facts and find the ___Area_______.<\/strong><\/p>\n

          Question 4.
          \nA unit square has an area of 1 _________.
          \nAnswer:
          \nA unit square has an area of 1 __Square<\/strong>\u00a0unit<\/strong>_______.<\/p>\n

          Question 5.
          \nWhen you __________, you give an approximate answer.
          \nAnswer:
          \nWhen you _multiplicate<\/strong>_________, you give an approximate answer.<\/p>\n

          Write always, sometimes, or never.<\/strong><\/p>\n

          Question 6.
          \nArea is __________ measured in square meters.
          \nAnswer:
          \nArea is __sometimes<\/strong>_______ measured in square meters.<\/p>\n

          Question 7.
          \nMultiplication __________ involves joining equal groups.
          \nAnswer:
          \nMultiplication __sometimes<\/strong>________ involves joining equal groups.<\/p>\n

          Question 8.
          \nThe area of a shape can __________ be represented as the sum of the areas of smaller rectangles.
          \nAnswer:
          \nThe area of a shape can __always<\/strong>________ be represented as the sum of the areas of smaller rectangles.<\/p>\n

          Use Vocabulary in Writing<\/strong>
          \nQuestion 9.
          \nWhat is the area of this rectangle? Explain how you solved the problem. Use at least 3 terms from the Word List in your answer.
          \n\"Envision
          \nAnswer:
          \nNumber of rows = 4
          \nNumber of squares in each row = 6 squares.
          \nArea of the rectangle = 4 \u00d7 6 = 24 square units.<\/p>\n

          Topic 6 Reteaching<\/h3>\n

          Set A pages 209-212<\/strong><\/p>\n

          A unit square has sides that are 1 unit long.
          \nCount the unit squares that cover the shape. The count is the area of the shape.
          \n\"Envision
          \nSeventeen unit squares cover the shape. The area of the shape is 17 square units.
          \nSometimes you need to estimate to find the area. First count the full squares. Then estimate the number of partially filled squares.
          \n\"Envision<\/p>\n

          Remember<\/strong> that area is the number of unit squares needed to cover a region with no gaps or overlaps.<\/p>\n

          In 1 and 2, count to find the area. Tell if the area is an estimate.
          \nQuestion 1.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

          Question 2.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

          Set B pages 213-216<\/strong><\/p>\n

          Unit squares can be different sizes. The size of a unit square determines the area.
          \n\"Envision
          \nThe measurements are different because different sizes of unit squares were used.<\/p>\n

          Remember<\/strong> that you can use unit squares to measure area.<\/p>\n

          Draw unit squares to cover the figures and find the area. Use the unit squares shown.
          \nQuestion 1.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

          Question 2.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

          Set C pages 217-220<\/strong><\/p>\n

          The unit squares below represent square inches.
          \nWhat is the area of the figure below?
          \n\"Envision
          \nTwenty-four unit squares cover the figure. The area of the figure is measured in square inches.
          \nSo, the area of the figure is 24 square inches.<\/p>\n

          Remember<\/strong> that you can measure using standard or metric units of area for unit squares.<\/p>\n

          In 1 and 2, each unit square represents a standard unit. Count the unit squares. Then write the area.
          \nQuestion 1.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

          Question 2.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

          Set D pages 221-224<\/strong><\/p>\n

          You can find area by counting the number of rows and multiplying by the number of squares in each row.
          \n\"Envision
          \nThere are 5 rows.
          \nThere are 4 squares in each row.
          \n5 \u00d7 4 = 20
          \nThe area of the figure is 20 square inches.<\/p>\n

          Remember<\/strong> that you can multiply the number of rows by the number of squares in each row to find the area.<\/p>\n

          In 1-3, find the area of each figure. Use grid paper to help.
          \nQuestion 1.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

          Question 2.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

          Question 3.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

          Set E pages 225-228<\/strong><\/p>\n

          Reteaching Continued<\/strong><\/p>\n

          You can use the Distributive Property to break apart facts to find the product.
          \nSeparate the 5 unit side into two parts.
          \n\"Envision
          \nArea of the large rectangle: 6 \u00d7 5 = 30
          \nAreas of the small rectangles:
          \n6 \u00d7 2 = 12
          \n6 \u00d7 3 = 18
          \nAdd the two areas: 12 + 18 = 30
          \nYou can write an equation to show that the area of the large rectangle is equal to the sum of the areas of the two small rectangles.
          \n6 \u00d7 5 = 6 \u00d7 (2 + 3) = (6 \u00d7 2) + (6 \u00d7 3)
          \n\"Envision<\/p>\n

          Remember<\/strong> that you can separate a rectangle into two smaller rectangles with the same total area.<\/p>\n

          In 1-3, write the equations that represent the total area of the red shapes. Find the area.
          \nQuestion 1.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

          Question 2.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

          Question 3.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

          Set F pages 229-232<\/strong><\/p>\n

          Find the area of this irregular shape.
          \n\"Envision
          \nYou can place the shape on grid paper and count the unit squares. The area of the shape is 21 square inches.<\/p>\n

          You also can divide the shape into rectangles. Find the area of each rectangle and add.
          \n5 \u00d7 3 = 15 square inches
          \n3 \u00d7 2 = 6 square inches
          \n15 + 6 = 21 square inches<\/p>\n

          Remember<\/strong> that you can add smaller areas to find a total area.<\/p>\n

          In 1 and 2, find the area of each shape.
          \nQuestion 1.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

          Question 2.
          \n\"Envision
          \nAnswer:
          \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

          Set G pages 233-236<\/strong><\/p>\n

          Think about these questions to help you use structure in solving problems.
          \nThinking Habits<\/p>\n

            \n
          • What patterns can I see and describe?<\/li>\n
          • How can I use the patterns to solve the problem?<\/li>\n
          • Can I see expressions and objects in different ways?
            \n\"Envision<\/li>\n<\/ul>\n

            Remember<\/strong> to look for simpler ways of representing an area.<\/p>\n

            Debra made this design from 1-inch square tiles. What is the area of the blue tiles?
            \n\"Envision
            \nQuestion 1.
            \nHow can you express the area of the blue tiles?
            \nAnswer:
            \nArea of the blue tile = area of the outer rectangle – area of the inner rectangle
            \n= 7 in \u00d7 7 in – 5 in \u00d7 3 in
            \n= 49 square in – 15 square in
            \n= 34 square in.
            \nArea of the blue tile is 34 square in.<\/p>\n

            Question 2.
            \nSolve the problem. Explain how you solved.
            \nAnswer:
            \nArea of the outer rectangle = 7 in \u00d7 7 in = 49 square in
            \nArea of the inner rectangle = 5 in \u00d7 3 in = 15 square in
            \nArea of the blue tile = area of the outer rectangle – area of the inner rectangle
            \n= 49 square in – 15 square in
            \n= 34 square in.
            \nArea of the blue ti,e is 34 square in.<\/p>\n

            Topic 6 Assessment Practice<\/h3>\n

            Question 1.
            \nCount to find the area of the shape. Tell if the area is exact or an estimate.
            \n\"Envision
            \nAnswer:
            \nThere are 10 squares covered by the shape. out of ten 4 are half covered with the shape.
            \nSo, area of the shape is around 8 squares unit.<\/p>\n

            Question 2.
            \nUse the Distributive Property to write the equation that represents the picture. Then give the area of each smaller rectangle and the large rectangle.
            \n\"Envision
            \nAnswer:
            \nArea of the larger rectangle = 3 \u00d7 5 = 15
            \nArea of the smaller rectangles |
            \n3 \u00d7 3 = 9
            \n3 \u00d7 2 = 6
            \nadding them
            \n9 + 6 = 15 .
            \nThe equation
            \n3 \u00d7 5 = 3 \u00d7 (2 + 3) = (3 \u00d7 2) + (3 \u00d7 3 ) = 6 + 9 = 15.<\/p>\n

            Question 3.
            \nLewis says that the figure below has an area of 4 square meters. Is he correct? Explain.
            \n\"Envision
            \nAnswer:
            \nNo, Lewis is wrong. As he says the area of the figure is 4 square m. But the\u00a0 square represent cm.
            \nThe area of the figure is = 7 square cm.
            \nThere are 4 complete squares and 6 half divided squares.
            \nadding them
            \n4 + (6 \u00f7 2 ) = 4 + 3 = 7 square cm.
            \nArea of the figure is 7 square cm.<\/p>\n

            Question 4.
            \nSelect all of the ways to break apart the area of the large rectangle into the sum of the areas of two smaller rectangles. Then give the area of the large rectangle.
            \n\"Envision
            \n\u2610 5 \u00d7 7 = 5 \u00d7 (1 + 5) = (5 \u00d7 1) + (5 \u00d7 5)
            \n\u2610 5 \u00d7 7 = 5 \u00d7 (3 + 4) = (5 \u00d7 3) + (5 \u00d7 4)
            \n\u2610 5 \u00d7 7 = 5 \u00d7 (2 + 3) = (5 \u00d7 2) + (5 \u00d7 3)
            \n\u2610 5 \u00d7 7 = 5 \u00d7 (1 + 6) = (5 \u00d7 1) + (5 \u00d7 6)
            \n\u2610 5 \u00d7 7 = 5 \u00d7 (2 + 5) = (5 \u00d7 2) + (5 \u00d7 5)
            \nArea = \u2610 square inches
            \nAnswer:
            \n7 is divided into two parts
            \n7 = (1 + 6)
            \n7 = (2 + 5)
            \n7 = (3 + 4)
            \n7 = (4 + 3)
            \n7 = (5 + 2)
            \n7 = (6 + 1)
            \nArea of the larger rectangle = 5 in \u00d7 7 in = 35 square in
            \n5 \u00d7 7 = 5 \u00d7 (3 + 4) = (5 \u00d7 3) + (5 \u00d7 4) = 15 + 20 = 35
            \n5 \u00d7 7 = 5 \u00d7 (1 + 6) = (5 \u00d7 1) + (5 \u00d7 6) = 5 + 30 = 35
            \n5 \u00d7 7 = 5 \u00d7 (2 + 5) = (5 \u00d7 2) + (5 \u00d7 5) = 10 + 25 = 35
            \nall these equations are correct.<\/p>\n

            Question 5.
            \nWhat is the total area of the design below?
            \n\"Envision
            \nA. 4 \u00d7 4 = 16 square inches
            \nB. (4 \u00d7 4) + (2 \u00d7 2) = 20 square inches
            \nC. (4 \u00d7 4) + (2 \u00d7 2) + (2 \u00d7 2) = 24 square inches
            \nD. 8 \u00d7 4 = 32 square inches
            \nAnswer:
            \nThe design is divided into 3 rectangles
            \n(4 in \u00d7 4 in) + (2 in \u00d7 2 in) + (2 in \u00d7 2 in)
            \n16 square in + 4 square in + 4 square in
            \n24 square in.
            \nSo the answer is C. (4 \u00d7 4) + (2 \u00d7 2) + (2 \u00d7 2) = 24 square inches.<\/p>\n

            Question 6.
            \nJared draws a rectangle. Explain how to find the area using the Distributive Property.
            \n\"Envision
            \nAnswer:
            \nArea of the rectangle using distributive property
            \nDividing the rectangle into smaller parts
            \n9 ft is divided into 5 ft and 4 ft
            \nArea of the smaller rectangles
            \n5 \u00d7 9 = 5 \u00d7 (5 + 4)
            \n= (5 \u00d7 5) + (5 \u00d7 4)
            \n= 25 + 20
            \n= 45 square ft.
            \nArea of the rectangle Jared drew is 45 square ft.<\/p>\n

            Question 7.
            \nFran has a square flower bed. One side of the flower bed is 3 feet long. How can you find the area of the flower bed?
            \nAnswer:
            \nShape of Fran flower bed is Square.
            \nSquare have 4 equal sides.
            \nOne side of the flower bed = 3 ft.
            \nArea of a square = side \u00d7 side
            \nArea of the flower bed = 3 ft \u00d7 3 ft = 9 square ft.
            \nFran square flower bed is 9 square ft.<\/p>\n

            Question 8.
            \nFind the missing side length. Then find the area and explain how to find it.
            \n\"Envision
            \nAnswer:
            \nThe opposite side of the missing side has a length of 6 ft.
            \nHere the missing length having 1 ft length above and below it.
            \n6 ft id distributed as
            \n6 = 1 + 1 + ?
            \n? = 6 – 1 – 1
            \n? = 6 – 2
            \n? = 4 ft.
            \nThe missing side length is 4 ft.
            \nOn adding the lengths 1 ft + 4 ft + 1 ft = 6 ft .
            \nsame as the opposite side.<\/p>\n

            Question 9.
            \nThis rectangle has an area of 56 square centimeters. What is the missing length? Use an equation to explain.
            \n\"Envision
            \nAnswer:
            \nGiven
            \nArea of the rectangle is 56 square cm.
            \nArea of a rectangle = length \u00d7 width
            \n56 square cm = 7 cm \u00d7 ? cm
            \n? cm = 56 square cm \u00f7 7 cm
            \n? cm = 8 cm.
            \nThe missing length is 8 cm.
            \n7 cm \u00d7 8 cm = 56 square cm.<\/p>\n

            Question 10.
            \nWhat is the area of Ron’s figure? Explain.
            \n\"Envision
            \nAnswer:
            \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

            Question 11.
            \nMaddie makes a mosaic with 1-inch glass squares, as shown below. Which color of glass has the greatest area in Maddie’s mosaic?
            \n\"Envision
            \nAnswer:
            \nNumber of violet squares = 1 + 3 +5 + 5 + 3 + 1 = 9 + 9 = 18 squares
            \nArea of violet squares = 18 square in
            \nNumber of yellow squares = 2 + 6 + 2 = 10 squares.
            \nArea of yellow squares = 10 square in
            \nNumber of white squares = 4 + 4 = 8 squares.
            \nArea of white squares = 8 square in<\/p>\n

            Violet color squares have greater area.<\/p>\n

            Question 12.
            \nSelect the correct side length for each square given its area.
            \n\"Envision
            \nAnswer:
            \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

            Question 13.
            \nExplain how to find the area of each rectangle and the total area of the rectangles.
            \n\"Envision
            \nAnswer:
            \nNumber of squares Ryan rectangle covers = 6 \u00d7 4 = 24 squares.
            \nArea of Ryan rectangle = 24 square cm
            \nNumber of squares Jodie rectangle covers = 3 \u00d7 2 = 6 squares.
            \nArea of Jodie rectangle = 6 square cm.
            \nTotal area of the rectangles = 24 square cm + 6 square c,m = 30 square cm.<\/p>\n

            Question 14.
            \nSome students in Springfield make a parade float with the letter S on it. Draw lines to divide the shape into rectangles. Then find how many square feet the letter is.
            \n\"Envision
            \nA. 28 square ft
            \nB. 56 square ft
            \nC. 54 square ft
            \nD. 90 square ft
            \nAnswer:
            \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

            Question 15.
            \nMax draws 2 rectangles, each with an area of 24 square centimeters. What could be the side lengths of Max’s rectangles? Show how he could use the Distributive Property to represent the area in each case.
            \nAnswer:
            \nGiven
            \nNumber of rectangles Max draws = 2 rectangles
            \nArea of each rectangles = 24 square cm
            \nThe lengths of the rectangle 1 = 4 cm \u00d7 6 cm
            \nUsing distributive property
            \nto find the area of rectangle 1 =
            \n=\u00a0 4 cm \u00d7 6 cm
            \n= 4 cm \u00d7 (2 cm + 4 cm )
            \n= (4 cm \u00d72 cm) + (4 cm \u00d7 4 cm)
            \n= 8 square cm + 16 square cm
            \n=24 cm
            \nto find the area of rectangle 2 =
            \nThe lengths of the rectangle 2 = 3 cm \u00d7 8 cm
            \n= 3 cm \u00d7 8 cm
            \n= 3 cm \u00d7 (3 cm + 5 cm)
            \n= (3 cm \u00d7 3 cm ) + (3 cm \u00d7 5 cm)
            \n= 9 square cm +15 square cm
            \n= 24 square cm<\/p>\n

            Question 16.
            \nA community center builds a new activity room in the shape shown below. Explain how to find the area of the room, and solve.
            \n\"Envision
            \nAnswer:
            \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

            Question 17.
            \nShow 2 different unit squares that you can use to measure the area of these rectangles. Find the area with your unit squares.
            \n\"Envision
            \nAnswer:
            \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

            Question 18.
            \nEthan wants to know the area of the yellow part of this design.
            \n\"Envision
            \nA. Explain how you can break this problem into simpler problems.
            \nAnswer:
            \nFinding the area of the outer rectangle.
            \nFinding the area of the inner rectangle .
            \nThen subtracting the area of inner rectangle from outer rectangle gives the area of the yellow region.<\/p>\n

            B. Find the yellow area. Show your work.
            \nAnswer:
            \nArea of the outer rectangle = 6 ft \u00d7 4 ft = 24 square ft
            \nArea of the inner rectangle = 3 ft \u00d7 2 ft = 6 square ft
            \nArea of the yellow area = Area of outer rectangle – Area of inner rectangle
            \n= 24 square ft – 6 square ft
            \n= 18 square ft.
            \nThe yellow area is 18 square ft.<\/p>\n

            Topic 6 Performance Task<\/h3>\n

            Banner Design
            \nJessie is designing a banner that has red, blue, and white sections.
            \nThe Banner Details list shows the rules for each color.
            \nThe Jessie’s Banner diagram shows the different sections of the banner.
            \nBanner Details<\/strong><\/p>\n

              \n
            • Red sections must have a total area greater than 5 in. 4in. 3 in. 40 square inches.<\/li>\n
            • Blue sections must have a total area greater than 30 square inches.<\/li>\n
            • The white section must have an area less than 40 square inches.<\/li>\n<\/ul>\n

              Use the Jessie’s Banner diagram to answer Question 1.
              \n\"Envision<\/p>\n

              Question 1.
              \nTo check if his banner fits the rules, Jessie started this table. Complete the table. Use multiplication and addition as needed.
              \n\"Envision
              \nAnswer:
              \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

              Use the table above and the Banner Details list to answer Question 2.<\/p>\n

              Question 2.
              \nIs Jessie’s banner within the totals in the Banner Details list? Explain.
              \nAnswer:<\/p>\n

              Banner Details<\/strong><\/p>\n

                \n
              • Red sections must have a total area greater than 5 in. 4in. 3 in. 40 square inches.<\/li>\n
              • Blue sections must have a total area greater than 30 square inches.<\/li>\n
              • The white section must have an area less than 40 square inches.<\/li>\n<\/ul>\n

                Yes, Jessie banner is not within the totals in the Banner detail list.
                \nTotal red color area = 35 square inches + 21 square inches = 56 square inches.
                \n56 square inches is greater than 40 square inches
                \nTotal White color area = 30 square inches.
                \n30 square inches less than 40 square inches.
                \nTotal blue color area = 9 square inches + 25 square inches = 34 square inches.
                \n34 square inches greater than 30 square inches.<\/p>\n

                Question 3.
                \nJessie makes a square patch to go on top of the banner.
                \nPart A
                \nDraw unit squares to cover the patch. How many unit squares cover the patch?
                \n\"Envision
                \nAnswer:
                \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

                Part B
                \nJessie says if he checks the area by multiplying, the area will be the same as if he counts each unit square. Is he correct? Explain.
                \nAnswer:
                \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition
                \nYes, Jessie is correct.
                \nArea of the patch by multiplying is same as area by counting the squares.<\/p>\n

                Question 4.
                \nJessie uses two colors to make the patch. The colors have different areas.
                \nPart A
                \nExplain how to separate the square into two smaller rectangles with different areas. Use multiplication to find the areas of each of the smaller rectangles.
                \nAnswer:
                \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n

                Part B
                \nIs the area of the square equal to the total area of the two smaller rectangles? Use an equation to explain.
                \nAnswer:
                \n\"Envision-Math-Common-Core-3rd-Grade-Answers-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition<\/p>\n","protected":false},"excerpt":{"rendered":"

                Go through the\u00a0enVision Math Common Core Grade 3 Answer Key\u00a0Topic 6 Connect Area to Multiplication and Addition\u00a0regularly and improve your accuracy in solving questions. enVision Math Common Core 3rd Grade Answers Key Topic 6 Connect Area to Multiplication and Addition Essential Question: How does area connect to multiplication and addition? enVision STEM Project: Design Solutions …<\/p>\n","protected":false},"author":1,"featured_media":25588,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/enVision-Math-Common-Core-Grade-3-Answer-Key-Topic-6-Connect-Area-to-Multiplication-and-Addition.png","_links":{"self":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/6332"}],"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=6332"}],"version-history":[{"count":5,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/6332\/revisions"}],"predecessor-version":[{"id":28164,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/6332\/revisions\/28164"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media\/25588"}],"wp:attachment":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media?parent=6332"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/categories?post=6332"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/tags?post=6332"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}