Unit 5 · Shapes and Equal Shares

Look at a slice of pizza. It has three straight edges. A shape with three straight sides is a triangle. Where two sides meet, there is a corner. A triangle has three corners too.

Now look at a cracker. It has four sides. All four are the same length. All four corners are square, like the corner of a book. That shape is a square.

A door has four sides too. But two sides are long and two are short. That shape is a rectangle. To name a shape, count the sides. Then look at the corners.

Look at a honeycomb. Each little room has six sides. A shape with six straight sides is a hexagon. It has six corners too. Count them: 1, 2, 3, 4, 5, 6.

Now look at a clock face or a coin. It is round. It has no straight sides. It has no corners. That shape is a circle. Every spot on the edge is the same distance from the middle.

Here is a common mistake. Some kids think a big triangle is a different shape than a small one. It is not. Size does not change the name. Only the sides and corners do.

A drawing of a square is flat. A dice is not flat. You can hold it. It is a solid shape. Solid shapes take up space. A dice is a cube. Every face is a square.

Count the faces on a dice. Top, bottom, front, back, left, right. That is 6 faces. A cube has 6 square faces. It stacks well because the faces are flat.

A ball is a solid shape too. It is round all over. It has no flat faces and no corners. That shape is a sphere. A sphere rolls any way you push it.

Look at a can of soup. The top is a circle. The bottom is a circle. The side is curved. That solid shape is a cylinder. A cylinder stacks on its flat end. It rolls on its side.

Now look at a party hat or an ice cream cone. The bottom is a circle. The top comes to a point. That shape is a cone. A cone stands on its circle. It cannot stack on its point.

Some kids mix up a cylinder and a cone. Check the ends. Two circles means a cylinder. One circle and a point means a cone.

Take two squares that are the same size. Put them side by side. Now you have one long shape. It has four sides. Two are long and two are short. Two squares make a rectangle.

Take a square and cut it from corner to corner. You get two triangles. Put them back together. The square is back. Shapes can split apart and join up again.

Try this with six triangles. Put their points in the middle. They make a hexagon. Building shapes from shapes is how blocks make a city.

Ms. Lee says, "Draw a shape with four sides." You could draw a square. You could draw a rectangle. Both have four sides. Both are right. The rule tells you what counts.

Now she says, "Draw a shape with three corners." That is a triangle. It can be tall or short. It can point up or sideways. It is still a triangle if it has three sides and three corners.

Here is a trap. A shape with four sides but one side bent is not a square. Sides must be straight. Check each side with a ruler if you are not sure.

Walk down a street in Chicago. A stop sign has eight sides. A window is a rectangle. A manhole cover is a circle. Shapes are on every block.

Look at a floor made of tiles. The tiles are often squares. They fit with no gaps. Squares fit together well because their corners are square. Hexagon tiles fit too.

Look up at a tall building. Its sides are rectangles. A roof may be a triangle. Now find a solid. A trash can is a cylinder. A ball in the park is a sphere.

Take a paper circle. Fold it so the edges match. Open it up. The fold cuts the circle into two parts. The two parts are the same size. They are equal. Each part is one half.

Now take a paper square. Cut it into two parts. But make one part big and one part small. Are those halves? No. Halves must be equal. Two unequal pieces are not halves.

Two halves make one whole. Put the two halves of the circle back together. The whole circle is back. Say it like this: one half and one half make one whole.

Take two paper squares the same size. Cut the first one straight down the middle. You get two tall rectangles. Each one is a half.

Cut the second square from corner to corner. You get two triangles. Each one is a half too. A rectangle half and a triangle half look different. But they came from the same square. They are the same size.

Here is the rule. Halves of the same whole are always equal in size. Their shape can be different. Kids often think the triangle half is smaller. Check by cutting. It is not.

Three friends share one granola bar. They cut it into three equal pieces. Each piece is one third. Each friend gets one third of the bar.

To cut a rectangle into thirds, make two cuts. Not three. Two cuts make three pieces. Make the pieces the same size. Check by laying one piece on another.

Three thirds make one whole. Put the three pieces back. The bar is whole again. A common mistake is to make three cuts. That gives four pieces, not three.

Four kids share a small pizza. They cut it into four equal slices. Each slice is one fourth. Another name for one fourth is one quarter. Both words mean the same thing.

To cut a square into fourths, fold it in half. Then fold it in half again. Open it. You see four equal squares. Four fourths make one whole.

Fourths are smaller than halves. Think about the pizza. Cut it in half, and you get a big slice. Cut it in fourths, and you get a smaller slice. More parts means smaller parts.

Look at a chocolate bar. It is made of small squares. The squares go across in rows. They go up and down in columns. Count the rows: 2. Count the squares in each row: 3.

Now count all the squares. Row one has 3. Row two has 3. That is 3 + 3 = 6 squares. You can also add the columns: 2 + 2 + 2 = 6. Same answer.

Try a bigger bar. It has 3 rows. Each row has 4 squares. Add: 4 + 4 + 4 = 12. The bar has 12 squares. Counting by rows is faster than counting one by one.

Two kids share one pancake. Cut it into halves. Each kid gets one half. Three kids share one pancake. Cut it into thirds. Each kid gets one third.

Four kids share one pancake. Cut it into fourths. Each kid gets one fourth. Count the people. Cut that many equal parts. That is a fair share.

Watch out for this mistake. Ben cut a pancake into two big pieces and one small one for three kids. Three pieces, but not equal. That is not thirds. Not fair.