Truth Tiles 1
Years 2 - 8


  • Fold a piece of A4 blank paper into half longways, then half again longways.
  • Turn it around and fold it into half shortways, then half again shortways.
  • Open it out and you should have sixteen (16) sections.
  • Cut out all sixteen pieces.
  • Choose nine (9) and write the numbers 1 to 9 - one (1) big number on each piece.
  • Choose five (5) and write one of these symbols on each ... +, -, x, =, =, =
  • You have one spare piece in case you need it.
  • Write the title of this challenge and today's date on a fresh page in your maths journal.

Getting Started

  • Spread the symbols out on the table like the picture. Leave room where the boxes are to put in your number tiles.
  • The first challenge is to put the numbers 1 to 9 in the spaces so that all three (3) equations are true at the same time.
  • Keep trying until you can do it, then write the solution - that means all three equations - in your journal.

The Next Challenge

  • Find two (2) more ways to do it.
    You don't have to find them right now, but you can if you want to.
    Or you can come back to this challenge at another time.
  • Write the solutions in your journal.
Have fun exploring Truth Tiles 1.

The Big Challenge

Now you have found three solutions. Are they really different?
The answer to that depends on how you answer these questions.
  • Do you think 7 + 2 is different from 2 + 7?
  • Do you think 7 - 2 is different from 2 - 7?
  • Do you think 7 x 2 is different from 2 x 7?
Write your answers in your journal and give reasons.
  • Find one more different solution.
There might be more. At this point a mathematician would ask:
  • How many different solutions are there?
  • How will I know when I have found them all?
Look at the strategies on your working like a mathematician page.
  • Which strategy do you think your mathematician might choose to try to find more solutions?
There are at least eight (8) different solutions.
Find as many as you can and record them.
Remember, a solution means all three equations are true at the same time.

Note: If your school is a member of Maths300, your teacher can provide software that will help you explore Truth Tiles 1.

Just Before You Finish

Copy and complete these sentences in your journal.
  • An equation is true when both sides of the equal sign...
  • I can change the order of adding two numbers and the answer is...
  • I can change the order of subtracting two numbers and the answer is...
  • I can change the order of multiplying two numbers and the answer is...
  • If I multiply a number by 1, the answer...
  • If I add 0 to a number the answer...
  • If I have a true subtraction like 8 - 5 = 3, I can swap ... and get another true subtraction.
Read your Working Like A Mathematician page again and write two or more sentences explaining how you worked like a mathematician in this activity.


Answers & Discussion

These notes were originally written for teachers. We have included them to support parents to help their child learn from Truth Tiles 1.

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Maths At Home is a division of Mathematics Centre