Building shapes from sticks and clay
How many sticks and clay balls does it take to build a triangle, a square, a rectangle or a cube, and how does a built shape turn into a drawing?
Where you are 15 in Two-dimensional shapes
When you reach for it
A flat shape is made of straight sides that meet at corners. Build one with craft sticks for the sides and small balls of clay for the corners, and both parts can be held, counted and moved: a triangle takes 3 sticks and 3 balls, a square or rectangle 4 and 4. Reach for this once a child can count the sides and corners of a shape; building is the same counting done with the hands, and it ends with drawing the shape on paper.
You need, all week: craft sticks or drinking straws (some cut in half, so there are long and short ones), and play dough or clay rolled into balls about the size of a marble. Each day takes ten to fifteen minutes.
Day 1: Building a triangle
Show how a ball holds two stick ends together: push one stick into each side of the ball. Say, “The ball is a corner. The sticks are sides.” Then build a triangle together, one stick and one ball at a time, and close it by pushing the last stick into the first ball.
Ask, “How many sticks did we use? How many balls?” Count each with a finger. Then let each child build a triangle from any three sticks: a long one, a short one, whatever is at hand. Line the triangles up and ask what is the same about all of them. Every one has 3 sticks and 3 balls, however tall, wide or turned it is.
Practice.
- Triangle A. How many sticks and balls? Answer: 3 sticks and 3 balls.
- Triangle B. How many sticks and balls? Answer: 3 sticks and 3 balls, even though it is tall and thin.
- Triangle C. How many sticks and balls? Answer: 3 sticks and 3 balls.
- You have 3 sticks but only 2 balls. Can you build a triangle? Answer: Not yet. One corner has nothing to hold it, so you need 1 more ball.
- Build a triangle from two long sticks and one short stick. Answer: It works: a tall, thin triangle, still with 3 sticks and 3 balls.
Day 2: Squares and rectangles
Give each child four sticks the same length and four balls. Ask them to build a shape with all four sticks. Some will make a lopsided shape; gently push the corners until each one is square, like the corner of a sheet of paper. That is a square.
Now hand out two long sticks and two short sticks. Ask, “Where do the long sticks go?” Try it: the long sticks go across from each other, and so do the short ones. Square up the corners and the shape is a rectangle. Stand it up the other way and ask whether it is still a rectangle. It is: same sticks, same balls, only turned.
Practice.
- Shape A. How many sticks and balls? Answer: 4 sticks and 4 balls.
- Shape B. How many sticks and balls? Answer: 4 sticks and 4 balls.
- Shape C. How many sticks and balls? Answer: 4 sticks and 4 balls, the very same sticks as Shape B, standing up.
- Which shape has all four sticks the same length? Answer: Shape A, the square.
- You have two long sticks and two short sticks. Can you build a square? Answer: No. A square needs four sticks the same length. These make a rectangle.
Day 3: A cube frame
A shape that is not flat can be built the same way. This is a group build; it needs 12 sticks the same length and 8 balls.
Start with a square lying flat on the table: 4 sticks, 4 balls. Push a stick straight up out of each ball and put a ball on top of each stick. Then join the top balls with 4 more sticks. Lift the frame and ask, “What shape did we build?” It is a cube. Count the balls together, then the sticks, and ask, “Are there as many sticks as balls?” On a flat shape there always were. On the cube there are more sticks, because 3 sticks meet at every ball. Point at one ball and count its sticks to see it.
Practice.
- Stage A. How many sticks and balls? Answer: 4 sticks and 4 balls.
- Stage B. How many sticks and balls? Answer: 8 sticks and 8 balls.
- Stage C. How many sticks and balls? Answer: 12 sticks and 8 balls.
- How many balls are on top of the finished cube? Answer: 4.
- How many squares can you find on the finished cube? Trace each one with a finger. Answer: 6: bottom, top, front, back and the two sides.
Day 4: Drawing what you built
Lay a built triangle on a sheet of paper. Press a pencil dot next to each ball, lift the triangle away, and join the dots with straight lines, one line for each stick. Ask, “How many dots? How many lines?” The drawing has 3 of each, just like the model: a dot for every ball and a line for every stick. Do the same with a rectangle.
Then turn it around: show a drawing and ask the child to build it. They count the dots to know how many balls to roll and the lines to know how many sticks to take.
Practice. For each drawing, how many sticks and balls do you need to build it?
- Drawing A. Answer: 3 sticks and 3 balls.
- Drawing B. Answer: 4 sticks and 4 balls; two of the sticks are long.
- Drawing C. Answer: 5 sticks and 5 balls.
- Drawing D. Answer: 4 sticks and 4 balls.
- Which two drawings need the same number of sticks? Answer: B and D, 4 each. They take the same number of sticks but are different shapes.
Exercises
- Look at the model. How many sticks and how many clay balls does it take to build it? Then draw it.
- Kai wants to build a triangle and a square side by side, not touching. How many sticks and how many balls does Kai need?
Answers
- 6 sticks and 6 balls. The drawing has 6 dots and 6 straight lines, closed all the way around. A child who has it counts the balls once each, without starting the count again.
- 7 sticks and 7 balls, because the triangle takes 3 of each and the square 4 of each, and 3 and 4 make 7.
Where this goes next
Building with sides and corners leads into Composing and decomposing shapes, where whole shapes become the pieces and are put together into bigger shapes. Counting the sticks a shape needs is the start of naming Polygons by how many sides they have, and drawing a shape from its parts grows into drawing a shape that must have a given number of sides or corners.