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## 'Weights' printed from http://nrich.maths.org/

### Why do this problem?

This
problem offers students an opportunity to add positive and
negative numbers while challenging them to work
systematically.

### Possible approach

Introduce the scenario as it appears in the problem. Negative
weights could be seen as strong helium balloons lifting up the pan
of the weighing scales.

Students could suggest a few examples for the class to work through
and clarify the procedure. Ask about the largest total and the
smallest total, giving time for students to explain to their
partners why $20$ and $^-60$ are correct.

Set the class working on the main task:

Can you make all the numbers in between? Can you show us how?

Is there always a unique way of producing a total, or can different
combinations produce the same total?

There are different strategies for tackling this problem so if you
observed that students approached the task in different ways, ask
(carefully selected) students to describe how they did it. This
could lead to a discussion of the merits of the different
approaches.

### Key questions

Can you make all the numbers in between? Can you show us how?

Is there always a unique way of producing a total, or can different
combinations produce the same total?

### Possible extension

The extension task in the main problem is suitable here.

Some students may learn from seeing how other students have
thought about this, and how they have explained their ideas. Direct
them to the solutions page for this problem.

### Possible support

Organise students into small teams with a big central sheet of
paper. Teams can write the numbers from $20$ to $^-60$, and then
students can fill in any sum that they find. Ask students to pass
their suggested sum to a team mate for checking before it is
written on the team sheet. If appropriate, the teams could be
racing each other to get as many totals as possible, but organise a
penalty system for errors (thus really encouraging the checking
process!).

Teachers may like to take a look at the article

Adding
and Subtracting Negative Numbers