Warm- Up Answer Key (Master copies on page 7): 3) Yes: Repetitive addition of the quantity 10+4 (14).

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1 Grade Level/Course: Grade Lesson/Unit Plan Name: Factoring Expressions and Variable Expressions Rationale/Lesson Abstract: Students will learn to compare common factors of whole number and variable expressions and re- write equivalent expressions using the distributive property. Timeframe: 0-90 minutes Common Core Standard(s):.NS.: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 1. Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express + 8 as (9 + )..EE.: Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression ( + x) to produce the equivalent expression + x; apply the distributive property to the expression x + 18y to produce the equivalent expression (x + y); apply properties of operations to y + y + y to produce the equivalent expression y. Instructional Resources/Materials: 1) - sided counters (0 counters for every students) ) Copies of Warm- Up (If passing out. Warm- Up may also be shown on a document camera.) Warm- Up Answer Key (Master copies on page 7): Key to Warm- Up: 1) : The sum of the products 0 and. ) : or 10( + ) ) : Repetitive addition of the quantity 10+ (1). ) : 1 5 5) : Generic rectangle showing partial products 0 and representing a product (area) of 8. ) : Bar model showing repetitive addition of the quantity 1. Page 1 of 7 MCC@WCCUSD 10/10/1

2 Activity/Lesson: Example 1 (I Do): Use the distributive property to factor out the GCF and write an expression equivalent to Sided Counters: *Create arrays that represent and 1. The area represents the value and the two dimensions are the factors of the value. *Build the arrays so that they share the largest common dimension possible. NOTE: is a common factor, but not the greatest common factor. Allow students to build the arrays until they discover the largest common dimension possible. *Find the GCF of and 1. This will be the common dimension of the rectangle.?? 1 *The partial areas represent the products of and two other factors. The other factors must be 1 and. 1 + *Decompose and 1 to prime factors. *Use the associative property to group all common prime factors of and 1. te: 1 is a factor of every number. *The product of all common prime factors is the GCF. 1 The GCF is. 1 *Use the distributive property to re- write an equivalent expression. Equivalent expression Page of 7 MCC@WCCUSD 10/10/1

3 Activity/Lesson continued: Example : (Partner Do) - Sided Counters: The GCF is. *Allow students to create as many arrays as needed to find the largest common dimension. * The GCF of 18 and 1 is.?? *Decompose 18 and 1 to prime factors. *Use commutative and associative properties to re- group all common prime factors. *Use distributive property to re- write an equivalent expression. Example : (Partner Do) * The GCF of, 9, and 15 is..??? 5 The GCF is Example : (You Do) *te: Students may have difficulty including 1 as a factor when re- writing an equivalent expression. Remind students that 1 is a factor of every number (identity property of multiplication). The GCF of 8 and 1 is 8.?? Page of 7 MCC@WCCUSD 10/10/1

4 Activity/Lesson continued: Example 5: (We Do) - Sided Counters: *Point out to students that this approach is not an efficient method for this problem due to the values of each term. *Remind students to decompose each term to prime factors to find the GCF *te: Students have already decomposed each term into a product of its primes. Have students demonstrate proper syntax when re- writing the expression Example (You Do) Page of 7 MCC@WCCUSD 10/10/1

5 Activity/Lesson continued: Example 7: Connection to Algebra (We Do) Example 8: (You Do) Page 5 of 7 MCC@WCCUSD 10/10/1

6 Assessment: Ticket out the Door Problems: Give students scratch paper and write both problems on the board. Check for student understanding before students leave the room. Use the distributive property to write an equivalent expression. Do each problem ways. 1) ) Page of 7 MCC@WCCUSD 10/10/1

7 Warm- Up: Select "" for all choices that represent the multiplication problem 1 and "" for choices that do not. For all "" choices, write the correct multiplication problem. 1) ( 10) + ( ) ) ) ( 10 ) + ( 10 + ) + ( 10 + ) + ( 10 + ) + ( 10 + ) + ( 10 + ) + ) ) ) Select "" for all choices that represent the multiplication problem 1 and "" for choices that do not. For all "" choices, write the correct multiplication problem. 1) ( 10) + ( ) ) ) ( 10 ) + ( 10 + ) + ( 10 + ) + ( 10 + ) + ( 10 + ) + ( 10 + ) + ) ) ) Page 7 of 7 MCC@WCCUSD 10/10/1

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