Make a record of all the rectangles that you can find in this shape.

Which rectangles are exactly the same (congruent)?

Which rectangles are similar?

Notes for Teachers – Is a Square a Rectangle?

Is a Square a Rectangle – Template

This problem is adapted from the NRICH task with the same name with permission of the University of Cambridge. All rights reserved.

4 Responses to Grades 5 to 10 Is a Square a Rectangle?

  1. toni toni says:

    Can you write anything that would help other teachers? What did your learners learn through doing this activity? Did they already know the word rectangle? Did most learners find all 14 rectangles? If not how did you help them to find them all? Did you teach your learners about shapes being the same (congruent) and shapes being similar and was this discussed in class at all? Why did you decide to discuss this with your learners or not to discuss it? Do your learners now understand that a square is a special rectangle? Have the class discussed the similarities and differences between squares and rectangles? Read the Notes for Teachers and make sure that your learners get full benefit from doing this activity.

  2. Msuthu Mdleleni says:

    I gave my learners a copy each in grade 5.I first told them that there are many rectangles in the copy so they must look for those rectangles. On the first day we managed to calculate many rectangles and I helped them by showing them that even two rectangles can form one rectangle. On the second day learners were then comparing rectangles looking for the ones that are equal. We did this by measuring the rectangles after we have identified them. They enjoyed this activity.

  3. Sagree Pillay says:

    Being a teacher of Grade 4 learners I would first explain the concepts “similar” and “congruent”, thereafter, I would give learners the problem and ask them to then identify the similar rectangles and the congruent ones. So, what do you think? Would you do it a little differently in a Grade 5 or 6 class?

  4. sinobia says:

    This lesson is a really good way of introducing young learners to congruency and similarity. Secondary school teachers would be delighted to know that these concepts are introduced at primary school. It is much harder to teach using triangles which is what most secondary teachers tend to do. Using triangles in the first instance may not encourage understanding of these concepts. It’s always a good idea to start with what the learners know!

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