Unit 6, Lesson 10: The Distributive Property, Part 2
GRADE 6 MATHEMATICSNAMEDATEPERIODUnit 6, Lesson 10: The Distributive Property, Part2Let's use rectangles to understand the distributive property with variables.10.1: Possible Areas1. A rectangle has a width of 4 units and a length ofunits. Write an expression for thearea of this rectangle.2. What is the area of the rectangle ifis 3 units? 2.2 units? unit?3. Could the area of this rectangle be 11square units? Why or why not?10.2: Partitioned Rectangles When Lengths are Unknown1. Here are two rectangles. The length and width of one rectangle are 8 and 5. Thewidth of the other rectangle is 5, but its length is unknown so we labeled it . Writean expression for the sum of the areas of the two rectangles.2. The two rectangles can be composed into one larger rectangle as shown. Whatare the width and length of the new, large rectangle?3. Write an expression for the total area of the large rectangle as the product of itsUnit 6: Expressions and Equations Lesson 10: The Distributive Property, Part 21
GRADE 6 MATHEMATICSNAMEDATEPERIODwidth and its length.Unit 6: Expressions and Equations Lesson 10: The Distributive Property, Part 22
GRADE 6 MATHEMATICSNAMEDATEPERIOD10.3: Areas of Partitioned RectanglesFor each rectangle, write expressions for the length and width and two expressions forthe total area. Record them in the table. Check your expressions in each row with yourgroup and discuss any disagreements.widthlengtharea as a product ofwidth times lengtharea as a sum of the areasof the smaller rectanglesAre you ready for more?Here is an area diagram of a rectangle.1. Find the lengths, , , and , and the area . All values are whole numbers.2. Can you find another set of lengths that will work? How many possibilities are there?Unit 6: Expressions and Equations Lesson 10: The Distributive Property, Part 23
GRADE 6 MATHEMATICSNAMEDATEPERIODLesson 10 SummaryHere is a rectangle composed of two smaller rectangles A and B.Based on the drawing, we can make several observations about the area of the rectangle: One side length of the large rectangle is 3 and the other is, so its area is. Since the large rectangle can be decomposed into two smaller rectangles, A andB, with no overlap, the area of the large rectangle is also the sum of the areas ofrectangles A and B:or. Since both expressions represent the area of the large rectangle, they are equivalentto each other.is equivalent to.We can see that multiplying 3 by the sumis equivalent to multiplying 3 by 2 andthen 3 by and adding the two products. This relationship is an exampleof the distributive property.Unit 6: Expressions and Equations Lesson 10: The Distributive Property, Part 24
GRADE 6 MATHEMATICSNAMEDATEPERIODUnit 6, Lesson 10: The Distributive Property, Part 21. Here is a rectangle.a. Explain why the area of the large rectangle isb. Explain why the area of the large rectangle is2. Is the area of the shaded rectangle.or?Explain how you know.3. Choose the expressions that do not represent the total area of the rectangle. Select all that apply.A.B.C.D.E.4. Evaluate each expression mentally.a.b.c.(from Unit 6, Lesson 9)5. Select all the expressions that are equivalent to.Unit 6: Expressions and Equations Lesson 10: The Distributive Property, Part 21
GRADE 6 MATHEMATICSNAMEDATEPERIODA.B.C.D.E.(from Unit 6, Lesson 8)6. Solve each equation. Show your reasoning.a.c.b.d.e.(from Unit 6, Lesson 4)7. Andre ranlaps of a track in 8 minutes at a constant speed. It took Andreminutes to run each lap.Select all the equations that represent this situation.A.B.C.D.E.F.(from Unit 6, Lesson 2)Unit 6: Expressions and Equations Lesson 10: The Distributive Property, Part 22
Unit 6, Lesson 10: The Distributive Property, Part 2 Let's use rectangles to understand the distributive property with variables. 10.1: Possible Areas 1.A rectangle has a width of 4 units and a length of units. Write an expression for the area of this r
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