Turning The Tables
Filling in a standard multiplication table is boring, and children quickly realize they can fill it using repeated addition rather than multiplication. To really practice multiplication, as well as practicing problem solving and factoring, create a mixed-up multiplication table.
How to create
Make these tables by moving the rows and columns around, and then leaving out most of the headings and entries in the middle.
Example
Here is an example using headings of 2 through 9:
How to solve
Start with the distinctive entries.
The 20 forces its row to be multiplying by 4, and then the 36 makes its column be 9.
The 49 forces its column and row to be multiplying by 7. The 9 forces its column and row to be multiplying by 3.
Continue the detective work in this way and fill in the entries as the headings are discovered.
Variations
Level of difficulty: Increase or decrease the difficulty by leaving out more or less of the numbers. In this example, the ‘5’ in the 5 column could have been left out – there must be a factor of 5 in 20, and that factor cannot come from 20’s row because there is a 36 in that row.
Your child can make them: Challenge your child to make one of these puzzles for you. A lot of good thought can go into creating one of these!
Helping your child
Puzzles are meant to be challenging and to take time, so please don’t ruin the fun by telling your child how to do them. These puzzles are chosen so that you can create them easily and then have fun solving them together.
If your child gets stuck on a puzzle, you have several options. You can, of course, give very small hints, if you can think of things that won’t give away the puzzle. You can suggest looking at smaller or simpler versions of the puzzle. Encourage your child to be bold in their ideas, even if sometimes they lead to dead ends. We all learn a lot from our mistakes and dead ends! Let your child know that it is perfectly okay not to solve a puzzle on the first (or second or third) try, and that useful ideas may occur to them if they leave the puzzle alone for a day or two.
These puzzles are meant to be fun and to teach problem solving. One of the greatest mathematical pleasures is that AHA moment, after many false starts and much wrestling with a problem, when the answer is finally discovered – be sure to let your child experience that feeling of discovery as many times as you can!