Activities

1. Complete the following problem using the distributive property:  2(4 + 9) = (___ x 4) + (___ x 9)

2. Complete the following problem using the distributive property:  8(3 + ___) = (8 x 3) + (___ x 7)

3. Apply the distributive property to 16 + 24 as a multiple of a sum of two whole numbers with no common factor.

4. The sum of 28 + 14 can be rewritten in three ways using the distributive property.  They would be 7(4 + 2), 2(14 + 7) or 14(2 + 1).  Rewrite the sum of 24 + 30 in at least two different ways.

5. Write an equivalent statement to 5(4 + 8) using the distributive property. Tell what you did.

6. Use the bank of numbers and symbols below to complete parts A and B:

A.) Write an expression of two whole numbers whose sum equals 24

B.) Use the Distributive Property to re-write the expression as a multiple of a sum of two whole numbers with no common factor.

7. Determine which statement below is correctly showing an example of the distributive property and why.  Explain why the other statement is incorrect, and fix it.

A) 55 + 40 = 5(11 +8)

B) 24 + 20 = 2(4 + 0)

Answer Key/Rubric

1. 2(4 + 9) = (_2_ x 4) + (_2_ x 9)
   
   
2. 8(3 + _7_) = (8 x 3) + (_8_ x 7)
   
   
3. 8(2 + 3)
   
   
4. Possible answers are

6(4 + 5) or 2(12 + 15) or 3(8 + 10)

5. 20 + 40

       Acceptable explanation may include, but is not limited to:

• Distributed the 5 to the sum inside the parentheses
• Multiplied 5 times 4 to get 20
• Multiplied 5 times 8 to get 40

6. Acceptable answers may include, but are not limited to:

       Part A

• 8 +16
• 3 + 21
• 9 + 15

       Part B (keeping the order from above)

• 8(1 + 2)
• 3(1 + 7)
• 3(3 + 5)

7. Statement A is correct.

       Acceptable answers may include, but are not limited to

• A is correct because they found the common factor of 5 and divided 55 by 5 to get 11 and 40 by 5 to get 8
• Students solve both sides of the equation to see if they are equal
• Students might explain that when correctly applying the distributive property to express a sum of two whole numbers you have to find a common factor to multiply by. 
• Statement B is incorrect

• A common factor of 2 was found correctly
• The factors listed in the parentheses are not correct, they are just the digits from the ones place of the original numbers
• Statement B should be 24 + 20 = 4(6 + 5)