Symmetric Shapes
Years 3 - 10

Preparation

  • Print this Construction Sheet and cut out the rectangle at the top. Save the rest for later.
  • Inside the rectangle there are six (6) shapes. 2 F shapes, 2 rectangles and 2 squares. Cut out the six pieces.
  • You need one of each shape. The other set is for a partner if you have one. If not store them in an envelope.
  • Print this Recording Sheet.
  • Write the title of this challenge and today's date on a fresh page in your maths journal.
You will be drawing your answers on the Recording Sheet. Stick in your journal when you finish the activity.

Investigating Symmetric Shapes

  • Open this Symmetric Shapes Starter.
    You can read it on screen or print it.
  • Investigate Symmetric Shapes using the challenges on the Starter.
    It begins with easy ones, but the later ones are a bit tricky.
    Take a break if you need to and come back later. Mathematicians don't usually figure out a problem straight away. If they did, it wouldn't be a problem.
    f you really, really need to, there is a hint a the bottom of the page.
Have fun exploring Symmetric Shapes.
When you have drawn all your answers on the Recording Sheet, think about the clues and what you know about reflection and symmetry that helped you solve the problems. Explain your thoughts on your sheet.

Digging Deeper

  • Choose another block capital letter and draw it on the Construction Sheet. It must be five (5) squares high and three (3) squares wide.
  • Cut it out and use it instead of the F. Can you make any symmetric shapes with your letter and the rectangle and square? Record.
  • Repeat for one other block capital letter and record what you find.
  • A Trisquare, or Tromino, is made from three squares joined side to side. There are two (2) of them. Draw them on the Construction Sheet and cut them out.
  • Use them one at time with the rectangle and square to try to make symmetric shapes. Record and report.
  • What happens if you use both Trominoes and the rectangle and square.
  • A Quadsquare, or Tetromino, is made from four (4) squares joined side to side. There are two (2) of them. Draw them on the Construction Sheet and cut them out.
  • (If you need more construction paper, print this Grid Paper.)
  • Use them one at time with the rectangle and square to try to make symmetric shapes. Record and report.

Rotational Symmetry

This shape

has rotational (or point) symmetry.

You could draw its outline, pin it in the middle, then rotate it 180 and it would fit back into its outline.
Rotate it another 180 and it would be in the outline again and back where it started.
So this shape has rotational symmetry of order 2.
This shape does not have any line symmetry.
This shape

has rotational (or point) symmetry.

You could draw its outline, pin it in the middle, then rotate it 9 and it would fit back into its outline.
Rotate it another 90 and it would be in the outline again.
Do this two more times it would be back where it started.
So this shape has rotational symmetry of order 4.
This shape also has several line symmetries.
  • Go back to the F, rectangle and square. Using just those three can you make any shapes that have rotational symmetry?
  • Try with each of your capital letters and the rectangle and the square.
  • Try with the trominoes and the tetrominoes.

Just Before You Finish

For this part you need your maths journal and your Working Like A Mathematician page.
  • Read again what it means to work like a mathematician.
  • How did you work like a mathematician during this investigation?
  • What mathematics do you know now that you didn't know when you started this investigation?

 

Answers & Discussion

Hint: The Starter doesn't say the line of symmetry has to be horizontal or vertical. Perhaps it is in another direction.

These notes were originally written for teachers. We have included them to support parents to help their child learn from Symmetric Shapes.

Send any comments or photos about this activity and we can start a gallery here.

 

Maths At Home is a division of Mathematics Centre