The distributive property with numbers

What it looks like when your child can do it

• — Asked for 6 x 14, your child thinks 6 x 10 = 60 and 6 x 4 = 24, then adds to get 84.
• — Your child works 3 x (4 + 5) both ways, 3 x 9 = 27 and 12 + 15 = 27, and sees that they match.
• — Your child pulls out a shared number: 5 x 7 + 5 x 3 is 5 x 10, which is 50.

How to teach it at the kitchen table

1. 01

   Start with bags of fruit

   Three bags each hold 4 apples and 5 oranges. Count the fruit two ways: 3 bags of 9 pieces is 27, or 12 apples plus 15 oranges is 27. The same total both ways is the whole idea.

2. 02

   Write both ways down

   3 x (4 + 5) = 3 x 4 + 3 x 5. The 3 outside the parentheses multiplies the 4, and it multiplies the 5. Say it together: every piece inside gets multiplied.

3. 03

   Use it for mental math

   Split a hard number into friendly pieces. 7 x 23 is 7 x 20 plus 7 x 3, which is 140 + 21 = 161. Plenty of adults already do this at the store without knowing its name.

4. 04

   Run it backward too

   When two products share a number, pull it out. 4 x 6 + 4 x 9 is 4 x (6 + 9), which is 4 x 15 = 60. Check by working the first form: 24 + 36 = 60.

You will need: Two kinds of small objects, like buttons and beans · Graph paper

Try it together

1. Try 1

   Work out 5 x (3 + 8) two ways: add inside the parentheses first, then use the distributive property.

   Listen for  55 both ways. 5 x 11 = 55, and 15 + 40 = 55. If the second way gives 23, the 5 only multiplied the 3.

2. Try 2

   Find 8 x 26 in your head by splitting 26 into 20 and 6.

   Listen for  208. 8 x 20 = 160 and 8 x 6 = 48, and 160 + 48 = 208. Ask your child to say both pieces out loud before adding.

3. Try 3

   Rewrite 6 x 7 + 6 x 3 with the 6 pulled out, then find the total.

   Listen for  6 x (7 + 3) = 6 x 10 = 60. Check: 42 + 18 = 60. This backward direction is harder, so a slower start here is normal.

4. Try 4

   Is 6 x (2 + 5) equal to 6 x 2 + 5?

   Listen for  No. The left side is 6 x 7 = 42. The right side is 12 + 5 = 17. The 6 has to multiply the 5 as well, which gives 12 + 30 = 42.

Watch for

• — Multiplying only the first number inside, so 3 x (4 + 5) becomes 12 + 5. Three bags means three of everything in the bag.

If it is not there yet

• — Go back to real groups, like plates each holding two kinds of snacks, and count the total both ways until the match feels expected.
• — Draw a rectangle 3 squares tall and 9 wide, split it into a part 4 wide and a part 5 wide, and count the squares in each part and in the whole.

A few days of this is normal, and it is time well spent. The lesson will still be there, and it will go faster.

Where this skill comes up

• Grade 6 Math Practice Workbook · Lesson 18

  Rewriting an Expression Without Changing It

  Needs it because the same property now carries a letter.