Multiplying whole numbers

What it looks like when your child can do it

• — Given 36 x 14, your child breaks it into 36 x 10 and 36 x 4, gets 360 and 144, and adds them to make 504.
• — Faced with 4 x 4 x 4, your child does 4 x 4 = 16 first, then 16 x 4 = 64, two numbers at a time.
• — Before multiplying 48 x 21, your child says the answer should be close to 50 x 20, which is 1000.

How to teach it at the kitchen table

1. 01

   Start with a real case of cans

   A case holds 24 cans and the pantry has 15 cases. Before anyone writes anything, ask about how many cans that is. A little more than 20 x 15, which is 300, is a good target to aim at.

2. 02

   Split one number into tens and ones

   24 x 15 is 24 x 10 plus 24 x 5. That is 240 plus 120, so 360. The standard written method does the same two pieces in a tidier layout.

3. 03

   Keep the columns lined up

   In the written method the second row starts with a zero, because it is multiplying by tens. Turn lined paper sideways so each digit gets its own column. Many wrong answers at this age are a digit that slid over, not a fact that was wrong.

4. 04

   Multiply long chains two at a time

   For 9 x 9 x 9, multiply the first pair, 9 x 9 = 81, then multiply that answer by the last 9: 81 x 9 = 729. The book works every power this way, left to right.

5. 05

   Check the size with an estimate

   Round and multiply in your head. If 36 x 14 comes out 5040 on paper, the estimate 40 x 14 = 560 says a zero crept in somewhere.

You will need: Lined paper turned sideways · A pencil

Try it together

1. Try 1

   Work out 36 x 14 together.

   Listen for  504. Watch for 36 x 10 = 360 and 36 x 4 = 144, then 360 plus 144. The estimate 40 x 14 = 560 is a little more, so 504 is sensible.

2. Try 2

   A case holds 24 cans. How many cans are in 15 cases?

   Listen for  360 cans. If your child gets 144, the second row lost its zero: 24 x 1 ten should be written as 240, not 24.

3. Try 3

   Work out 2 x 2 x 2.

   Listen for  8, because 2 x 2 = 4 and 4 x 2 = 8. An answer of 6 means your child added the twos, or multiplied 2 by 3.

4. Try 4

   Work out 8 x 8 x 8.

   Listen for  512, because 8 x 8 = 64 and 64 x 8 = 512. The second step is a two-digit number times a one-digit number, and that is where slips happen.

5. Try 5

   A woodpile holds 4 stacks of 115 pieces each. How many pieces in all?

   Listen for  460. 4 x 100 = 400 and 4 x 15 = 60, so 460. Breaking 115 into 100 and 15 is a strong mental move.

Watch for

• — Leaving the zero off the start of the second row. That row comes out ten times too small, and an estimate catches it.

If it is not there yet

• — Go back to a two-digit number times a one-digit number, like 36 x 6, until it is steady. Every bigger problem is built from those.
• — Draw 24 x 15 as a rectangle split into tens and ones, 20 and 4 across, 10 and 5 down. The four boxes are 200, 40, 100 and 20, and they add to 360.
• — If the slips come from shaky facts rather than layout, spend a week on multiplication facts first.

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 16

  Exponents: Repeated Multiplication

  Needs it because a power is a repeated multiplication.