Reasoning with shape

This week is all about reasoning. The first activity extends the skills of identifying squares in different positions on a coordinate grid. What follows is a sequence of activities using properties of shape to solve problems, followed by a review of symmetry. First, by using a Venn diagram to look at line and rotational symmetry together and then by exploring Rangoli patterns. At the end there are a few other puzzles for you to try out.


Following on from the Square It strategy game in Exploring shape properties, in this activity based on a coordinate grid, see if you can find all of the Hidden Squares.

2D shape

In this activity, What shape am I?, nine descriptions of 2D shapes are given in the grid below. For each description, give the full name of the shape and draw it.

For the next activity, you need to use clues and logic to help you to work out which shape should go where in a 3 x 3 grid (similar to the activity above). Each box should contain one of the following nine shapes: kite, rhombus, pentagon, square, parallelogram, trapezium, equilateral triangle, rectangle and isosceles triangle.

Here is the set of clues to help you to work out which shape goes where:

  1. The equilateral shapes are all in different columns.
  2. Each shape in the middle row has two sets of parallel lines.
  3. The shapes in the top two corners each have exactly one line of symmetry.
  4. One of the rows contains a total of 10 sides.
  5. The square is in a corner below the parallelogram.
  6. The shape in the centre has all angles the same, but its diagonals do not intersect at right angles.
  7. The shape with two pairs of equal adjacent sides is not in the same column as the square.
  8. The shape with the most sides is in the bottom right hand corner.

The next activity consists of two puzzles using Pentominoes. If you haven’t come across a pentomino before, consider what a domino is (there are also triominoes and tetrominoes). Write an explanation of what pentominoes are in your own words.

Here is some extra information to help you get you started:

  1. The green slider, top right, needs to be on 1 or 2 (two different puzzles)
  2. The larger blue dot is what you use to move the pentominoes to different positions
  3. The smaller white dot rotates the pentominoes (they can turn around)
  4. The blue slider on the pentominoes reflects the shape (they can be flipped over)

Symmetry review

Decide where each of the following twelve shapes should be placed on the Venn diagram. Check to see if someone else agrees with you if you are able to. Then draw an extra shape of your own that should belong in each of the four regions of the diagram.

Now try this Rangoli pattern activity. Rangoli patterns are symmetrical designs used by Hindu and Sikh families to decorate their homes for important festivals. To follow the instructions step by step, you will need to use a pencil, eraser and ruler on square dotty paper (you can download that here). Otherwise you can use the squared paper in your maths book.

Send your finished Rangoli patterns in to Student Showcase

Further ideas

If you can find some counters (or something else that you could use instead), try out each of these four Counter puzzles.

This is a series of matchstick puzzles using squares. Pause the clip each time to try it yourself first. Use strips of scrap paper (equal in size) or draw it out if you haven’t got matchsticks.

ANSWERS – Click below


Hidden Squares solution here

2D shape

Counter puzzles