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Can you fill in the matrix (table square) below?
The numbers 2 to 12 were used to generate it with, again, just one number used twice.
You might like to have a go at similar versions of this task using the interactivity below.
For an extra challenge, you could try this 6 by 6 version of the grid.
You may like to try Missing Multipliers once you've had a go at this task.
One way to encourage children to be more curious is to present them with challenges to be solved, or intriguing contexts that require explanation.
This problem requires learners to apply knowledge of multiplication facts, and stresses the importance of knowing the squares of numbers, particularly the squares of primes. It will increase their familarity with representing multiplication facts as a grid or matrix.
You could start by giving the whole group some numbers such as $18$, $33$, $35$, $48$ and $56$ and asking for the multiplication facts that generate them. Include some squares such as $25$, and even $49$, if you feel the group might have a problem identifying it.
After this learners could work in pairs on the problem itself so that they are able to talk through their ideas with a partner. They could use this sheet which has two copies of the matrix on it.
At the end of the lesson the whole group could come together again to discuss, not only the answers, but how they worked them out and which multiplication tables they needed to know well in order to do a problem such as this.
The interactivity could be used to round off the lesson. Can the class use their knowledge of times tables and the strategies they have developed to work out the headings of the rows and columns?
The interactivity could also be used in its own right during subsequent lessons, perhaps with learners working in pairs on a computer or tablet.
Learners could make a similar challenge with the least amount of information given so that it can still be done. They could then swap with someone else. Missing Multipliers would make a great follow-up to this one.
Some learners might find it helpful to start by looking for the number which is used twice. A multiplication square would support those who are struggling to remember table facts. Tables Teaser includes a similar interactivity to Missing Multipliers, but only the 2, 5 and 10 times tables are used.