Not by rote but by heart. How to learn multiplication facts.

Posted in Uncategorized by icttalk on September 23, 2010

It’s important to know multiplication and, for that matter, other number facts. It saves you from having to put a problem to one side while you grapple with a calculation. But not by rote, by heart. Ask a question of a child who has learned by rote and you will see their mouth moving like a little Sun reader as they silently recite the whole lot until they arrive at the one they want.

Before you start there are one or two important things to consider. First of all there is no need to learn tables up to 12, unless you think the government is going to revoke decimal currency. If you’re my age this means you can berate your class for having it so easy! Next remember to introduce commutativity early; this cuts the job in half. Also introduce the idea of inverse, an invaluable concept in all sorts of other areas. Lastly include zero and don’t fall into the trap of dismissing multiplication by ten as adding a zero.

Now for some activities. 20 years ago we saw the excellent Cockcroft Report and its paragraph 243 which said:

Mathematics teaching at all levels should include opportunities for:

·      exposition by the teacher

·      discussion between teacher and pupils and between pupils themselves

·      appropriate practical work

·      consolidation and practice of fundamental skills and routines

·      problem solving including the application of mathematics to everyday situations

·      investigational work

It’s as true today as it was then and holds good for multiplication facts too. See how many you can spot in the following activities.

1.     Group physical objects. ‘Lots of…’ Their product (a useful piece of vocabulary) can be seen as continuous addition. Displays can be made and photographs taken.

2.     A card game for two players. (See image 1 below) You need a pack of cards numbered 0 – 9, shuffled and placed face down. Choose a ‘table’ to practice. Players take turns to take a card of the top of the pack and find the product of the number on it and the ‘table’ in question. When all ten cards are gone total the products for each player. Highest total wins. By the way, using a calculator is fine. No one will bother using it if they know the answer and if they don’t it’s essential.

3.     Put a multiplication square on the board. With the class or individuals cross off any facts that they consider easy. Amazingly you’re often left with very few to learn especially when you invoke commutativity.

4.     With the set of 0 – 9 cards shuffle and place face down. Player A has a calculator on which (s)he must work out the answer while player B must use his or her memory. Choose the ‘table’ to be practiced. Player B turns over the top card. The first one to say the product of the number on it and the ‘table’ keeps the card. The cards kept by the calculator player are the facts the other needs to work on. I once played this with a boy who laughed hysterically all the way through. I asked what the problem was and he said he’d been cheating. I was aghast. “How?” “I’ve been remembering the answers from last time!”

5.     You can play a similar game with these cards to practise particular facts. (See image 2 below)

6.     Watch ITV. Yes! During each commercial break the challenge is to write out a particular list of facts as many times as possible. Not just multiples, you must write the whole thing like 1 x 6 = 6 etc.

7.     Pelmanism. Get the class to make their own cards.

8.     Issue 100 squares. Shade different multiples. What patterns do you get? What if the numbers to 100 were written in, say, 6 columns instead of 10?

9.     There are dozens of websites like http://www.multiplication.com/interactive_games.htm

10. I once know a boy who couldn’t remember 6 x 7. I wrote it on an A4 pice of card which I would hold up at random points during the day at which he had to say “42”. I even carried it round with me in case I bumped into him. In the end he simply said “42” instead of “good morning”!

11. This shape is called a pentomino and it’s made by placing five squares side against side. There are twelve different ones, a little activity in itself is finding them all without rotations. I’m practicing x4, x6, x7, x8, x9. Multiply adjacent squares and total the answers. Which pentomino and arrangement of the numbers gives the greatest total? (See image 3 below)

12. Small, partially completed multiplication squares like:

13. Get a multiplication square and draw a pentomino cross around a group of five numbers. Sum vertically and horizontally leaving out the number in the middle. Patterns? What about a square of four numbers and adding diagonally? Lots of possibilities.

14. The ‘Torture test’. You need
something that learners can get on with quietly when they’ve finished. They draw a 6 x 6 square on cm squared paper. Call out 3, 4, 6, 7, 8, 9 randomly to put along the top and 0, 4, 6, 7, 8, 9 randomly to go down the side. Left handers put the numbers down the right hand side so their writing hand does not obscure them. On ‘Go!” start a stopwatch while they fill in the randomized multiplication square as quickly as possible and they call out “Stop” when complete. You must give them their time which they write down. When everyone is done swap to mark and add a 10 second penalty for each wrong or incomplete square. Do it weekly. Pupils get quite excited by records and personal bests.




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