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Shapely Lines

Stage: 1 Challenge Level: Challenge Level:1

Shapely Lines


For this activity, you'll need:

  • a piece of paper
  • a pencil
  • a ruler
  • some coloured pencils or pens

Using your pencil and ruler, draw some straight lines on your piece of paper to make an interesting pattern. You can draw as many or as few as you like. This is what I drew:



Can you describe what you see in your own pattern?
Can you find any shapes which have three sides?
How about any with four sides?
Which shape or shapes have the most sides?

Using your coloured pencils or pens, decorate all the three-sided shapes in some way. You could colour them all in using a particular colour or you could cover them with a special design or pattern.

Can you decorate all the four-sided shapes in another, different, way?
How about the five-sided/six-sided ... shapes?

This activity is based on an idea in Mathematics Through Art and Design published by Collins Educational.


Why do this problem?

This activity gives children practice in drawing straight lines with a ruler and offers opportunities for learners to identify and talk about properties of shapes. The creative aspect of the task means that children must make their own decisions and thus the finished product becomes their own.

Possible approach

You could introduce this task by beginning to create an image on the board, working as a whole group. You might ask individuals to draw lines in turn (either using a straight-line function on the interactive whiteboard, or using a suitable ruler) and then, once there are a good number of lines, invite everyone to look carefully at the image that has been created. Suggest that pairs talk about what they see and then open it out to a wider discussion (think-pair-share).

Listen out for children who describe the shapes. Some may recognise and be able to name 2D shapes with which they are familiar but this could be a good opportunity to introduce correct vocabulary if children are describing shapes using the number of sides or corners (vertices). You could shade all the triangles, for example, in the same way and ask learners if they could work out how you have decided what to shade.

At this stage, encourage the pupils to create their own pictures, drawing the lines for themselves and deciding upon their own way of colouring/decorating the shapes. You can take this opportunity to observe them as they work and to talk to some of them about their pictures.

Leave time for all the children to look at everyone else's work and invite them to comment or ask questions of each other. The pictures would make a lovely classroom display.

Key questions

Tell me about your picture.
What shapes can you see?
Which shapes are there most of?
Which shapes are there fewest of?
How will you colour/decorate all the triangles/quadrilaterals ...?


Possible extension

Some children might be motivated to create pictures which satisfy certain criteria. For example, can they create more triangles than their first picture, or a shape with more sides than any on their first picture? They could produce a 'key' to accompany their picture.

Possible support

Some children might find it helpful to write the number of sides of each shape lightly in pencil in the centre of each one.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.