Go back to L3 online home page.

This is the course page for your Level 3 mathematics shape and space workshop. You can follow the links below to access the resources you need for this session.

Please have your ILP to hand as you work through these activities.

Session PowerPoint

The link to the session’s PowerPoint is below:

Shape and space presentation Apr18v3

R1 Pentominoes

What is a pentomino?

  • A collection of five equal squares so that at least one side of each square is coincident with that of an adjacent square.
  • pentominoRotations, reflections and translations are not permitted.
  • How many different arrangements can you find?
  • Compare with a partner and challenge any arrangements you disagree with.
  • Make notes of any points you want to raise about terminology, area / perimeter of the pentominoes you discover, challenges you faced.
  • Look at the solution sheet and try some of the other challenges

This resource is reproduced with the kind permission of the Centre for Innovation in Mathematics Teaching (CIMT) based at Plymouth University www.cimt.org.uk

R 1- Pentominoes answers

R2 Classifying shapes

R3 – Dissecting a square

Dissecting a square

What fraction and percentage of the whole square are the other pieces?

Note your answers in a table like the one below:

Screen Shot 2016-07-21 at 01.12.00

Check that your answers add up to a whole unit or 100%

R 3- Dissecting a square answers

From the Standards Unit materials – session SS3

R4 Transformations

On a copy of the sheet below, draw the image of the L-shape after the following transformations:

  • Screen Shot 2016-07-21 at 01.24.48Shape A: reflection in x axis
  • Shape B: reflection in y axis
  • Shape C: reflection in the line y = x
  • Shape D: reflection in the line y = -x
  • Shape E: translation of -4 units vertically
  • Shape F: rotation of 90º clockwise about the origin

Screen Shot 2016-07-21 at 01.24.56

R4 Transformations question

R 4- Transformations answers


  • Make up your own, more complex, transformations, record the image and label it with the transformation (for example, use a vector translation (xy), use shapes which straddle the line of reflection, use a point of rotation other than the origin).
  • Use the blank grid below to explore with more complex shapes.

From the Standards Unit materials (session SS7)

R6 – 7 Evaluating statements about area and perimeter (no R5)


R8 Pythagoras’ theorem – consolidation question

1. A ladder, 5m long, is resting against a wall as shown.

The base of the ladder is 1.5m from the wall.

How far up the wall does the ladder reach?Screen Shot 2016-07-21 at 01.49.06

2. A plane is coming in to land. It is flying at 4000ft and is currently 2 miles south of the runway.

What is the actual distance the plane has left to fly before it lands?  (1 mile = 5280 ft)


3. A square has a diagonal 14.14cm long.

What is the area of the square?

R9 Trigonometry calculations – practice questions

R10 The sine rule

R11 Using geometry to solve problems

R12 Using trigonometry to solve problems

R13 When the boat comes in

R14 Bearings