## 1089

#### Summary

Beginning with any three-digit number and performing a simple subtraction followed by an addition, the answer is almost always 1089. Students are asked to explore the reason why this occurs and to work out which of the three-digit numbers produce this interesting result.

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## 2 Litre Balloon Problem

#### Summary

Challenge each student to blow up a balloon to a volume of 2 litres. This simple, physical, personal starting point becomes an investigation with many potential extensions and challenges. Firstly, what can we measure on a balloon to check the volume and find which student was closest? A computer program can quickly check results for students. Then extensions open up such as 'By how much do we need to increase the radius to get a volume of 3 litres?'

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## 4 Arm Shapes

#### Summary

Children are asked to use tiles to make four paths coming into a central intersection tile:

This is a very tactile concrete counting challenge that quickly exposes patterns which may be described algebraically. The context introduces a strong visual as well as tactile dimension to the learning. The small group work of collection and then discussion of the data is also a strong feature. It is suitable for several grade and ability levels.