Multiplication facts through 12

What it looks like when your child can do it

• — Asked 7 x 8, your child says 56 within a couple of seconds, without skip counting up from 7.
• — Your child can turn a fact around: if 6 x 9 = 54, then 54 ÷ 6 = 9 and 54 ÷ 9 = 6.
• — When a fact slips, your child rebuilds it from one they know: 12 x 7 is 10 sevens plus 2 sevens, 70 plus 14, so 84.

How to teach it at the kitchen table

1. 01

   Sort the facts into known and not yet

   Write one fact per index card and make two piles: ones your child answers right away and ones they have to work out. Most children this age know more than they think. The not-yet pile is often a dozen or so cards, which is a job you can finish.

2. 02

   Build hard facts from ones already known

   Times 9 is times 10 minus one group: 9 x 6 is 60 minus 6, so 54. Times 4 is double, then double again. Times 12 is times 10 plus times 2: 12 x 8 is 80 plus 16, so 96.

3. 03

   Say every fact in both directions

   When your child practices 7 x 8 = 56, also say 56 ÷ 8 = 7 and 56 ÷ 7 = 8. Long division asks for facts backwards, so the division has to come as fast as the multiplication.

4. 04

   Five minutes a day beats an hour on Saturday

   Work only the not-yet pile, a few minutes at breakfast or in the truck. When a card comes up right three days running, it moves to the known pile.

5. 05

   Connect the facts to long division

   Ask how many 6s fit in 45. Your child finds 6 x 7 = 42, sees that 6 x 8 = 48 is too big, and says 7 with 3 left over. That is the move every round of long division makes.

You will need: Index cards and a pencil · A handful of dried beans or pennies

Try it together

1. Try 1

   Ask: what is 7 x 8?

   Listen for  56. Watch whether it comes out right away or whether your child counts up by sevens. Counting up to the right answer still means the fact belongs on the practice pile.

2. Try 2

   Ask: what times 9 makes 72?

   Listen for  8, because 9 x 8 = 72. This is the backwards question long division asks, and it is usually slower than the forward one at first.

3. Try 3

   Ask for 12 x 7, and then ask how your child got it.

   Listen for  84. A strong answer sounds like: 10 sevens is 70, and 2 more sevens is 14, so 84. Rebuilding a fact from known ones is a good sign.

4. Try 4

   Ask: how many 8s fit inside 60, and how many are left over?

   Listen for  7, with 4 left over, because 8 x 7 = 56 and 60 minus 56 is 4. If your child says 8, check 8 x 8 = 64, which is more than 60.

5. Try 5

   Ask for 6 x 9 and then 9 x 6, back to back.

   Listen for  54 both times. If one comes fast and the other slowly, your child may not yet trust that the order of the two numbers does not matter.

Watch for

• — The 6, 7 and 8 facts, especially 7 x 8 = 56 and 6 x 8 = 48. These are among the facts most often mixed up, and long division uses them constantly.
• — Quiet counting under the breath. It gets the right answer, but slowly enough that long division turns into a slog.

If it is not there yet

• — Back up to the times 2, 5 and 10 facts until they are instant, then build the rest from them: times 4 from times 2, times 9 from times 10.
• — Lay out dried beans or pennies in 6 rows of 7, so your child can see why 6 x 7 and 7 x 6 are the same and why 42 ÷ 7 = 6.
• — Start long division with a printed times table on the desk. It comes off the desk as the facts settle.

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 1

  Long Division, the Whole Way Through

  Needs it because every step of long division is a multiplication fact read backwards.