Mrs Trimmer's String

Problem | Teachers' Notes | Hint | Solution | Printable page |
Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

Why do this problem?

This problem requires children to apply their of knowledge of factors and multiples, but at the same time it reinforces properties of common $2$D shapes.

Possible approach

Ideally, children would be practically engaged with this problem in the classroom, school hall or outside, using loops of string. You could pose the questions in the problem orally for them to investigate using loops of string, encouraging them to make conjectures and justify them. You could give each group some paper to record their shapes, or you may want to take photographs of the children as they experiment.

You could then return to the classroom to discuss their findings. Of course their answers will depend on the number of children in the whole group and this can lead into discussions about the underlying mathematics of factors and multiples. Depending on the class' experience, you may want to introduce these terms.

(This sheet, which contains all the questions asked but has a shortened introductory part and no illustrations, may be useful if you wish children to have paper copies of the problem as written.)

Key questions

How many children are needed for one triangle? Then how many children would be needed to make two triangles? How many triangles can we make at the same time with our class?
Why don't you use counters to help?
Can you think of the names of any other shapes with four sides?
How many sides has a pentagon got? How many can we make with our class if everyone holds one corner each? Can you think of a way we could make five pentagons?

Possible extension

Learners could try one of these Stage 2 problems, Bracelets or Where Are They?.

Possible support

If it is not possible to work on the problem practically using string, some children might find it useful to make the shapes with some apparatus, such as geostrips. Alternatively, they could draw the triangles and number the corners to show the children or use counters to group together to represent the children or to represent the corners of the shapes.

Published September 2005,November 2009,December 2009.