Exploring shape properties

This week is all about properties of shape. The first activity is a fun strategy game to encourage you to identify squares in different positions on a grid. Then a sequence of activities to explore to remind you about the properties of quadrilaterals but also to check that you know how mathematical notation works on diagrams. At the end there are a few other ideas and puzzles if you want to take these ideas a little further.

This strategy game Square It helps you to look for squares in different orientations.

You can play with two players or one.
Play interactively or print out dotty paper to play away from the screen if there are two of you.


Ways to identify specific parts of diagrams

Write down the angle name for each one. The first two have been completed for you.

We would use this same convention to identify shapes from a diagram too. Try to complete these statements

  • Triangle AEC is congruent to triangles ABE, BDE and _____
  • The triangle with red, blue and purple angles is triangle _____
  • The pentagon with two smallest angles shown in brown and purple is pentagon _____
  • Four small triangles together make the square _____

More practice of this sort of naming convention later, with quadrilaterals.

Ways of showing information on diagrams

In maths, lots of geometrical information is shown on diagrams. Here is an example:

Picking out two of the pieces of information from this diagram, we can see the way that equal angles are indicated:

Can you write out two more pairs of pieces of information used in the diagram about the pairs of equal sides and the pairs of parallel sides? If you can’t remember which of the other symbols shows those pieces of information, take a look at the next section on quadrilaterals (the BBC bitesize link should help you to work it out. Hint: look at the trapezium diagram and information.)


Colour each of the quadrilaterals

If you need a reminder of what all of the properties of the quadrilaterals are, there’s a full description of each one on BBC Bitesize here. Write yourself some notes about the quadrilaterals that you are less confident about.

This is a diagram showing some tangled quadrilaterals. You need to identify the different quadrilaterals using their vertices (corners) – list them in a clockwise direction around the shape starting with the first of those letters alphabetically. For example, the square would be HOSM.

List the following quadrilaterals from this diagram:

  • square
  • trapezium
  • rhombus
  • rectangle
  • kite
  • parallelogram

Then identify the one letter on the diagram that has not been used (Hint: I is not the answer).

Do the same for each of the following three diagrams.

Challenge task: Can you design a diagram like this yourself and see if someone else is able to identify all of the quadrilaterals and the one letter that you haven’t used? Send it in to the Student Showcase.

In these Shape Search puzzles (from Japan, also called Zukei Sagashi) you need to identify the specific triangles or quadrilaterals from the points given on the grids.

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This last interactive activity contains five questions. You may know some of the answers from what you already know about quadrilaterals but you can also investigate by using the applet:

Further ideas

Can you explain what shapes are being created between the squares and how they change?
How about this one? What’s the same and what’s different?

Challenge task: What pieces of music would you choose as a soundtrack to these moving images and why?

The Tangram is an ancient Chinese puzzle. Here is a clip telling you more about it and an interactive activity to try.

Can you make each of these six animals?

ANSWERS – click below

  • Triangle AEC is congruent to triangles ABE, BDE and EDC
  • The triangle with red, blue and purple angles is triangle BDE
  • The pentagon with two smallest angles shown in brown and purple is pentagon AEBDC
  • Four small triangles together make the square ABDC