Sides, corners and sorting shapes

When you reach for it

A flat shape has parts a child can count and check: its sides (the straight edges) and its corners (the points where two sides meet). A child can also check whether the outline is closed, with no gap, and whether all its sides are the same length. Each of these is a rule for sorting a pile of shapes into groups, and each can be checked with a finger, a sticker or a paper strip.

Reach for this once a child can name circles, triangles, squares and rectangles. The names stay in the background this week: the work is counting and checking, so ask “how many sides?” more than “what is it called?” Each day takes about ten to fifteen minutes with paper cutouts on a table.

Day 1: Sides and corners

You need: paper cutouts of a few straight-sided shapes, like the ones below, and a sheet of small round stickers.

Hold up one cutout. Run a finger slowly along one straight edge and say, “This is a side.” Have the child trace each side and count out loud, one number for each side. Then point to a spot where two sides meet: “This is a corner. Is it pointy?” The child puts one sticker on each corner and counts the stickers.

After two or three shapes, ask, “What do you notice about the sides and the corners?” On every one of these shapes the two counts match, because each corner sits between two sides as you go around. Then hand over a paper circle and ask the child to trace it. There is no straight side to count and nowhere to put a corner sticker.

Practice. Trace and count on each shape in the picture.

1. Shape A. How many sides and corners? Answer: 3 sides and 3 corners.
2. Shape B. How many sides and corners? Answer: 4 sides and 4 corners. It is lopsided, and that does not change the count.
3. Shape C. How many sides and corners? Answer: 5 sides and 5 corners.
4. Shape D. How many sides and corners? Answer: 6 sides and 6 corners.
5. A paper circle. How many straight sides and corners? Answer: none of either.

Day 2: Sorting a pile

You need: eight paper cutouts like the pile below, and four paper plates to sort onto.

Spread the pile out. Say, “Let’s put shapes that belong together on the same plate. Count the sides of each one first.” Let the child decide which plate each shape goes on, then ask, “Why does this one go here?” The answer you hope for is a count: “It has three sides, like that one.” Shapes with no straight sides get a plate of their own.

When the pile is sorted, sweep the shapes back together and say, “Now sort them again by counting corners.” The plates come out the same, which is Day 1’s discovery again. Last, ask the child to invent a sorting rule of their own (curvy or straight edges, for example) and say it out loud.

Practice. Use the pile in the picture.

1. Which shapes go on the plate for 3 sides? Answer: A and E. E is long and thin, and it still has 3 sides.
2. Which shapes go on the plate for 4 sides? Answer: B, F and H.
3. Which shape is alone on its plate? Answer: D, the only one with 5 sides.
4. Which shapes have no corners at all? Answer: C and G.
5. How many plates do you need to sort the whole pile by corners? Answer: 4: for 3 corners, 4 corners, 5 corners and no corners.

Day 3: Open and closed

You need: a long piece of yarn (or a pipe cleaner) and a small toy animal.

Lay the yarn on the table in a loop whose ends touch and put the toy inside. Say, “This is a fence. Can the animal get out without jumping over?” It cannot: the shape is closed. Now pull one end away to leave a gap. “Can it get out now?” Yes, through the gap: the shape is open. Have the child make a closed shape and an open shape with the yarn.

Then trace figures on paper. A closed figure lets a finger go all the way around and land back where it started without lifting off. On an open figure the finger runs off the end. The sides and corners of Day 1 are counted on closed shapes.

Practice. Trace each figure in the picture.

1. Figure A. Open or closed? Answer: closed, and it has 3 sides.
2. Figure B. Open or closed? Answer: open; there is a gap at the top where the lines do not meet.
3. Figure C. Open or closed? Answer: closed; it is wavy, but the finger comes back to its start.
4. Figure D. Open or closed? Answer: open; the animal walks out through the gap on the right.

Day 4: Sides the same length

You need: a paper square, a paper rectangle that is long and thin, other paper cutouts like the ones below, and a narrow strip of paper.

Lay the strip along one side of the square and make a pencil mark on the strip where the side ends. Move the strip to the next side and ask, “Is this side the same length as the mark?” Check all four sides. They all match, so the square has all its sides the same length. Do the same with the long rectangle: the long side and the short side do not match.

Make two groups on the table, “all sides the same” and “not all the same”, and let the child check each shape with the strip before placing it.

Practice. Check each shape in the picture with a paper strip.

1. Shape A. Are all its sides the same length? Answer: yes, all 4 sides match.
2. Shape B. Are all its sides the same length? Answer: no; 2 sides are long and 2 are short.
3. Shape C. Are all its sides the same length? Answer: yes, all 3 sides match.
4. Shape D. Are all its sides the same length? Answer: no; the 2 long sides match each other, but the bottom side is much shorter.

Exercises

1. Look at P, Q and R. Which are closed? For each closed one, how many sides and how many corners does it have?
2. Which shape in the picture has all its sides the same length? Check with a paper strip.

Where this goes next

Counting sides and corners leads to building shapes from sticks and clay, where each stick is a side and each clay ball a corner. The next step after that is deciding what makes a shape a triangle: a closed shape with 3 straight sides, whatever its color, size or turn. Closed shapes with straight sides, named by how many sides they have, are Polygons, and sides of equal length come back when shapes are put together and taken apart in composing and decomposing shapes.