Lesson 6: Distributive Property of Multiplication

Day 2

Activity 3: Using the Distributive Property of Multiplication

Materials: calculator, fine point dry-erase marker (kit), Interactive Notebook (kit), whiteboard (kit)
Write 12×5 on the whiteboard, and review the steps of the distributive property of multiplication with your child by saying and writing the following:
  1. "First, I'm going to break 12 down into two easier factors: 5 and 7. Picture breaking a 12 by 5 array down into two smaller arrays."
  2. "Second, I'm going to multiply each of these easier factors by the other factor in 12×5." (Write 5×5= and 7×5=)
  3. "Now, I need to find the products of each of these multiplication problems." (Write 25 and 35 with their corresponding problems)
  4. "Next, I will find the sum of 25 and 35." (Write a vertical addition sentence for 25+35=60)
  5. "Finally, I'm going to check my answer using a calculator. Is 12×5 equal to 60?" (YES!)
Next, repeat this process, breaking 12 down into two other factors: 10 and 2. Say, "When you break a large factor down, you have options about how you do that." With 12x5 still on the whiteboard, say and write the following:
  1. "First, I'm going to break 12 down into two easier factors: 10 and 2. Again, picture a large array becoming two smaller ones."
  2. "Second, I'm going to multiply each of these smaller factors by the other factor in 12x5." (Write 10x5= and 2x5=)
  3. "Now, I need to find the products of each of these multiplication problems." (Write 50 and 10 with their corresponding problems)
  4. "Next, I will find the sum of 50 and 10." (Write a vertical addition sentence for 50+10=60)
  5. "Once again, I have a product of 60. So, I've broken 12x5 down using the Distributive Property in two different ways and have found the same product both times."
Now, say, "Remember that we use parentheses to tell us what to do first in math problems. I'm going to show you how we use parentheses when applying the distributive property." Write the following on the whiteboard:
Tell your child to talk about the steps in the distributive property as she points to the numbers on the board. Ask the following questions as needed:
  • Which number sentence represents a large array? (6×9)
  • Which number sentence represents two smaller arrays? [(6×4)+(6×5)]
  • What did I do at each step?
Say, "While you may already know 6×9 easily, you're definitely going to come across multiplication problems that are harder for you, and using the distributive property can help you find the answers."

Leaving the previous numbers on the whiteboard so that your child can refer to them and the steps they represent, write the following multiplication problems on a sheet of paper, and ask your child to follow the steps to find their products. Encourage her to use multiplication facts that she knows as she works. For example, if she knows her 10 facts well, then she can break the larger number down into 10 and another number (for example, 10 and 4 for the first problem) and then work from there. Also, remind your child that she can use the commutative property of multiplication to first switch the order of the factors so that she can break down the second factor in each sentence.
  • 14×3 (42)
  • 15×6 (90)
Your child will complete the "Distributive Property of Multiplication" sheet. There are two options for this sheet. The first option is more concrete, while the second is slightly more abstract. Both provide support for your child, so you may want to ask your child to complete both, starting with Option 1 and then moving to Option 2 if you feel that your child needs additional work with this property. She can use the "Understanding the Distributive Property of Multiplication" sheet for reference as needed and then place the page in her Interactive Notebook.

Option 1

On the Option 1 sheet, the first row provides a model for completing the other rows. The missing answers for the other rows are as follows:
  • 2nd row: 15+30, 45
  • 3rd row: (4×3)+(4×5), 12+20, 32
  • 4th row: (7×4)+(7×5), 28+35, 63
  • 5th row: (4×5)+(4×10), 20+40, 60
  • 6th row: approaches will vary, but the product is 39
  • 7th row: approaches will vary, but the product is 108

Option 2

On the Option 2 sheet, your child should work with the factors 10 and 2 in the first box: (4×10)+(4×2), 40+8, 48. The approaches will vary in the other three boxes, but the products are as follows:
  • 4×12=48
  • 14×5=70
  • 3×15=45
  • 6×12=72

Activity 4: Basic Skills Review

Your child will complete the "Basic Skills Review #9" sheet. Give her scratch paper to use, and allow her to refer to her Interactive Notebook as needed.
Answer Key:
  1. Katarina started cleaning her room at 3:05 and stopped at 4:15. How long did she clean her room? (1 hour and 10 minutes)
  2. Cliff starts looking for tadpoles at 8:20. If he continues looking for 45 minutes, what time will he be finished? (9:05)
  3. Mrs. Moneybags had $4.25 in her purse. Her friend borrowed 2 quarters. How much does she have in her purse now? ($3.75)
  4. Mrs. Moneybags has 11 coins in her purse that total $1.36. Which coins does she have in her purse? (3 quarters, 5 dimes, 2 nickels, 1 penny OR 4 quarters, 1 dime, 5 nickels, and 1 penny — other coin combinations may be possible)
  5. Round 5871 to the nearest 10 and 100. (5870, 5900)
  6. 2277+3109=5386
  7. 8793−2888=5905
  8. Robert needs to fill a two-gallon tank with water. How many cups of water will he need? Circle one: 16 cups or 32 cups (32 cups)