# Mental Mondays #2

This Mental and Oral activity focuses on developing children's use and understanding of number properties.

Children work in pairs, using a mini-whiteboard or a scribble pad in order to determine the identity of two 'secret' numbers. The information you give them about these numbers is related to addition and multiplication, for example:

I'm thinking of two single-digit, secret numbers. The product of the two numbers is 15; the sum is 8. What are the numbers?

The children then have a minute to use their knowledge of the multiplication facts and addition to discover what the numbers could be. When the children have done this, ask them to explain their methods to everyone else. In this instance a good strategy would to determine what the factors of 15 were, and then check which two factors added together to make 8.

The solution is 3 and 5:

3 x 5 = 15 3 + 5 = 8

The challenge can be adapted by giving more initial information about the two 'secret' numbers:

I'm thinking of two single-digit, secret numbers; they are both smaller than 4. The product of the two numbers is 6; the sum is 5. What are the numbers?

There are only three factors of 6 that are smaller than 4; solution:

2 x 3 = 6 2 + 3 = 5

or...

I'm thinking of two single-digit, secret numbers; they are both multiples of 3. The product of the two numbers is 54; the sum is 15. What are the numbers?

Again, there is only a small number of factors of 54 that are themselves multiples of 3; solution:

6 x 9 = 54 6 + 9 = 15

It may also be helpful to display the information so the children can remind themselves of the facts while working on the solution. This could be in simple note-form:

Two numbers.

Product is 54. Sum is 15.

The challenge can be made more difficult by using a greater range of numbers.

Here are some other number combinations that have proven useful:

• Two even numbers -  with a product of 32 and a sum of 12      (4 & 8)
• Two odd numbers -  with a product of 35 and a sum of 12       (5 & 7)
• Two odd numbers -  with a product of 63 and a sum of 16       (7 & 9)
• Two prime numbers -  with a product of 14 and a sum of 9       (2 & 7)
• Two consecutive numbers -  with a product of 30 and a sum of 11       (5 & 6)
• Two consecutive numbers -  with a product of 56 and a sum of 15       (7 & 8)
• Two numbers -  with a puzzling product of 9 and a strange sum of 10      (1 & 9)

As a final layer, the children could be asked to calculate clues for their own 'secret' numbers and challenge their partners to determine what the numbers are.

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