In how many ways can you half cover one big square using two smaller yellow squares as in diagram A.

What are the similarities and differences between the patterns?


Suppose you half cover four big squares by half covering each square as in diagram B.

Diagram B is unchanged when you rotate it by a quarter turn. How many other 4-square patterns can you find that are unchanged when you rotate the pattern by a quarter turn?

See the Notes for Teachers

(Thanks to Nicky Roberts for inspiration for this problem.

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8 Responses to Years 4 – 10 Quarters

  1. tvanvught says:

    Diagram A : 6 different ways to colour in. Position of diagram A must be fixed. Colour the two blocks on the left, on the right, top two, bottom two, top left and bottom right, bottom left and top right. Similar in that two blocks are coulored next to one another in four cases and it is different positions for instance left, right, top, and bottom.

    Diagram B : 6 different ways to colour to get six symmetrical shapes.

    The learners will enjoy learning about symmetry in this way, since it is learning through play. Will use this as an introduction when I get to transformations with my grade nine groups and when I discuss symmetry in graphs. A great idea!

  2. Stombles Magadlela says:

    We did this activity with grade 6 learners. They shaded two parts in each square, they find that a square can be half covered in 6 ways. We are still looking for the similarities and patterns.

  3. Sari Smit says:

    Seeing that your learners are still busy with this activity it would be good to hear from you what they found about symmetry when working with diagram B.

  4. Thabs Sais says:

    I did the activity in diagram A with the grade 5 and grade 6 learners. They all managed to find 6 different way on their own. They liked the activity.

  5. Stombles Magadlela says:

    Sari its been a long time looking for the similarities and differences can you please help me with them.

  6. Zodwa Shai says:

    I gave the activity to grade 4 learners. They only found the right answer by drawing their own square then they found out that they can use 6 different ways to half cover one square using 2 smaller squares

  7. Tau Tamako says:

    I tried the activity on half square with grade 4 learners. They struggled with instructions, but as soon as I explained the instructions to them, they had no problem in finding the solutions. They enjoyed it.

    • Msuthu Mdleleni says:

      I did this activity with my grade five learners. What I did firstly I asked them to look at diagram A then I asked them to half cover the square in different ways. They were able to half cover the square square horizontally vertically and diagonally and they enjoyed the activity. We looked at the similarities and we found out that horizontal and vertical half square are similar and diagonal half squares are similar.

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