Problem

Materials:

  • paper
  • pencil

This is a number balance.

A balance with an arm that is balanced labelled with numbers going from 10 on the left hand side to 1 in the middle then 1 from the middle to 10 on the right hand side. There is a peg under each number.

It has weights.3 blue weights with holes in them at the top.

The weights are hung on pegs under the numbers and it balances when both sides are equal like this:

A balance with an arm that is balanced with one blue weight hanging under the number 10 on the left side, one blue weight hanging under the 2 on the right side and one blue weight hanging under the 8 on the right side. Under the balance is the equation 10 = 2 + 8.

We can represent this number balance with an equation:

10 = 2 + 8

Where would you put the weight to make this one balance? Write an equation that represents this number balance.

A balance with an arm that is lower on the left side with one blue weight hanging under the number 9 on the left side, one blue weight hanging under the 3 on the right side, one blue weight hanging under the 4 on the right side and one blue weight to the side of the balance.

Where would you put the weight to make this one balance? Write an equation that represents this number balance.

A balance with an arm that is lower on the right side with one blue weight hanging under the number 6 on the left side, one blue weight hanging under the 4 on the right side, one blue weight hanging under the 9 on the right side and one blue weight leaning against the bottom of the balance.

What if you had to use two more weights to make this one balance, where could you put them? Write an equation that represents this balance.

Is there more than one way? How many can you find?

A balance with an arm that is slightly lower on the left side with one blue weight hanging under the number 9 on the left side, one blue weight hanging under the 6 on the left side, one blue weight hanging under the 4 on the right side, one blue weight hanging under the 10 on the right side and two blue weights leaning against the bottom of the balance.

Adapted from nrich.maths.org