Problem Teachers' Notes Hint

This activity is one in which the pupils can easily become engaged while showing very different ways of viewing the calculation. It is an activity that enables the teacher to have opportunities to observe just how their pupils are considering a problem, this may be somehwhat different to what the teacher expects. Pupils may have been taught one approach but actually have their own ways of working.

It is important in this activity to ensure that there is no presumption on the child's part that there is one way and one way only to see the calculation that may be required. So working with a group and tackling one problem at a time would seem to be appropriate in this instance. It will be then easier for pupils to discuss how they have approached each problem. They may decide to transfer the problem to a calculation which they would record horizontally. More examples can be found here (doc .,pdf ) the first six increase in difficulty for pupils based on some research evidence, (Children's Symbolic Representation of Addition and Subtraction Word Problems,  Author(s): Harriett C. Bebout, Source: Journal for Research in Mathematics Education, Vol. 21, No. 2 (Mar., 1990), pp. 123- 131, Published by: National Council of Teachers of Mathematics).

In participating in this activity with pupils you may observe things that give rise to some reflection on how pupils deal with these kinds of problems.

Tell me about how you are working this out.

What do you think of _____'s way of doing this?

Is the way you've done this different from the way you do other additions/subtractions?

Ask the pupils to create stories that involve calculations for their partners to do.

Give the pupils a written form of an addition/subtraction eg [] - 5 = 12 and challenge them to create a story around  it.

Some pupils may need to have some small toys/dolls that allow them to enact the situation before being able to think about the calculation. For instance the final balloom problem might be modelled using Lego figures and counters as the balloons.