## Mrs Trimmer's String

Mrs Trimmer's class had been drawing different shapes with straight sides. On Tuesday the sun was shining and Mrs Trimmer took all twenty-four of the children out into the playground. She also took some long loops of string.

Mrs Trimmer held up one of the string loops. "How many of you will we need to make a triangle?" she asked. She chose Ellie, Winston and Andy. They held the string tight and so made a beautiful triangle.

Then other children made triangles, squares, rectangles, pentagons and hexagons. Some made regular polygons and others made more irregular shapes.

Six of the class made a shape. Nick pointed at it. "That's nearly a triangle!" he laughed. Mrs Trimmer came up. "It's still a hexagon," she explained, "It's got six sides and six people holding the corners."
After a while Mrs Trimmer called all the twenty-four children together. "Now we are all going to make triangles," she said, "So get into threes." They made lots of different ones. Some looked like these:

If all the children were making a triangle, how many triangles did they make altogether?

Then the children made four-sided shapes.
What different shapes could they have made?
Can you draw some of them?
How many four-sided shapes did the class make altogether if all the children were involved?

Then the children made hexagons and then octagons.

How many hexagons and how many octagons could the class make?

"We haven't made pentagons yet, Mrs Trimmer," complained Nick.
How do you think they managed to make five good pentagons?

### Why do this problem?

This problem gives children opportunities to explore the properties of $2$D shapes but also to apply their knowledge of dividing into equal groups.

### Possible approach

The activity could be introduced by involving the whole class in the story of Mrs Trimmer and her children. The questions in the story could be raised in a simliar order. You will need plenty of room and a large loop of rope or string for the whole class. After that the children could be practically engaged in small groups of three to six children each with a loop of string about $3$ metres in length and consider the questions themselves as well as ways of recording their answers. 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. Their answers will depend on the number of children who held the string to make the shapes and this can lead into discussions about the underlying mathematics of factors by considering how many triangles/quadrilaterals could be made with this number of children. Encourage the children to use accurate descriptive language to explain what they see so the vocabulary of sides, corners (vertices) and angles can be introduced.

(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? What is the same/different about these two triangles/quadrilaterals/shapes?
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.