Learn more about shapes. Count shapes.

If you have been reading my posts (thank you!), you probably know I am reluctant to dictate or impose my reasoning. Sometimes though, it is necessary because we need to *define* things.

### Task

Supplies:paper, pencil, scissors. Draw shapes on (triangles, squares, rectangles, quadrilaterals). You can cut them out if you want.What to do:1) Explain to your child that sometimes, we need to explain words or terms so everyone knows what we are talking about. It's called a definition. A good way to introduce the notion is through homonym (words that sound alike), for example, say "flower" and "flour". 2) Invite your child to find other examples. Then ask him/her to explain or define each of the meaning. 3) Then move to math and define - a triangle: A shape with 3 sides. - a quadrilateral: A shape with 4 sides. Depending on the reactions, the definitions might need to be refined: closed shape or straight sides, etc. 4) Explain what a right angle is by showing a lot of examples. And say that "A rectangle is defined to be a shape with 4 right angles". Then ask them to draw different rectangles. Or sort or count how many rectangles there are in the pictures drawn. 5) There are 3 rectangles in the picture below. Can you find them?

6) How many rectangles are there?

7) How many triangles in the picture below?

### How it went

For 1) Bel came up with “fair”. Then Nia wanted to have a turn and said “Megaman” (we have some figurines around) and “fan”. I pounced on “fan” and said it was a good example. Bel came up with “box” and “bound”. Then Nia wanted to participate and said “backpack” as in a bag you put on your back and something you fill with things (?). I wasn’t quite sure.

I told that in math, we need definitions too and gave them the one for triangle and quadrilateral. I showed them what a right angle was by pointing at the corner of a sheet of paper and told them that a rectangle was a quadrilateral – what is a quadrilateral again? – with four right angles.

When they got the first picture, I asked them how many rectangles they saw. Bel immediately said “3!”, which surprised me. I asked her to show me and she correctly added the large one around everything. Nia said 2.

In the next picture, Nia went first and said 5. She would not show me the rectangles. She counted the four small ones and I didn’t understand which one was her fifth one. I asked her to trace around it but she did not do it. I asked her to color them, she colored the four little ones with four different colors.

Finally, I asked her how many rectangles were in this picture and she correctly told me there were 5 rectangles and traced them. I think that she sees the little ones and then tries to get the ones around the outer borders. In the case below, she could get the last two ones.

Bel figured out that the answer was 9 and was moving on to making her own crazy problems. We both had it wrong at first: I was missing the 1×3 rectangles, and she was missing the 2×2 ones. Then I showed her how to do it systematically: count the

- the smaller “1×1” rectangles (6)
- the “1×2” which are two squares next to each other (4)
- the “2×1” which are two squares stacked on each other (3)
- the “1×3”
- the “2×2”
- the “2×3”

We did not get to do the triangle one.

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