1st Grade · 1.G.A.2

Composite shapes in 1st grade

Composite shapes are shapes made by putting smaller shapes together, like a house drawn from a square and a triangle. In 1st grade, your child builds composite shapes from flat shapes and from solid shapes such as cubes and cones. Your child also uses a shape already built as one piece of a bigger shape.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

1.G.A.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

What it means, in plain words

Composite means made of parts. A composite shape is one shape made from two or more smaller shapes that touch with no gaps. Two squares side by side make a rectangle. Two half-circles make a whole circle.

Composite shapes in 1st grade use two kinds of pieces. Flat shapes are rectangles, squares, triangles, half-circles, quarter-circles and trapezoids. A trapezoid is a four-sided shape with one pair of sides that run the same way, like the red block in a pattern block set. Solid shapes are cubes, boxes, cones and cylinders. A cylinder is shaped like a can. Your child does not need formal names: "box" is enough.

The second step is to use a new shape as a building block. Your child puts two squares together to make a rectangle, then adds a triangle on top of that rectangle to make a house. Joining and splitting shapes like this prepares your child for halves, fourths and area in later grades.

Your child should be able to:

Put flat shapes together to make a new shape, such as two squares into a rectangle
Join solid shapes, such as cubes and cylinders, to build a new figure
Use a shape already built as one piece of a bigger shape
Name the smaller shapes that make up a composite shape

Example

How can you make a rectangle from two squares of the same size?

Put the two squares side by side.
Push them together so one full side of each square touches, with no gap and no overlap.
The new shape has 4 square corners and is twice as long as it is tall, so the two squares make a rectangle.

Example

You have 4 square tiles of the same size. How can you make one big square from them?

Put 2 tiles side by side to make a rectangle.
Make a second rectangle the same way.
Put one rectangle on top of the other, long sides touching.
The 4 tiles make one big square, 2 tiles across and 2 tiles down.

Where children usually get stuck

Your child leaves a gap between two pieces, or lets them overlap, and says the result is a rectangle.
The child matches the rough outline and does not check that the edges touch along a full side.
What helps. Trace around the pieces on paper. If the outline has a notch or a bump, the pieces do not fit together yet.
Your child calls a square built from two triangles "two triangles" and does not see one new square.
Young children see the pieces before the whole. Seeing the outline as one shape comes after building and naming many shapes.
What helps. After your child builds something, trace only the outside edge with a finger and ask what shape that outline is.
Your child tries to stand a cube on the point of a cone and gives up when it falls.
The child has not yet looked at which faces are flat. A point or a curved face cannot hold another block.
What helps. Build towers with cans, boxes and a paper cone. Before each one, ask which side is flat enough to stack on.

Try four practice questions

Real 1st grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
Maria has the blocks shown below. Which model uses all of her blocks?
A
B
C
D
Show the answer and how to solve it
Maria can build the model with 1 cube and 1 cone. That model uses every block from her set, with no extra blocks and no missing blocks.
1. 1First, look at Maria's blocks. Count each shape.
2. 2Maria has 1 cube and 1 cone.
3. 3Now look at each model. Find the one that uses 1 cube and 1 cone — no extra blocks and no missing blocks.
4. 4The correct model has 1 cube and 1 cone stacked together. Maria can build that one using every block in her set.
Common mistake. A common mistake is to confuse a cone with a cylinder. A cone has a pointed top, but a cylinder has flat ends. Make sure each shape in the model matches a shape in the set.
The idea underneath. A model needs the same blocks as the set — the same shapes AND the same number of each.
2On level
Aisha built a tower from 3D solids. James took the tower apart and tried to make a new tower with what he had.
Aisha's tower:
James's tower:
Select the statement that best describes James's tower.
A
James used the right pieces.
B
James used a cylinder where a sphere belongs.
C
James used an extra cylinder.
D
James left out a cone.
Show the answer and how to solve it
James's tower has all 3 of Aisha's pieces (cube, cone, sphere) plus one extra cylinder on top. The best description is "James used an extra cylinder."
1. 1Look at Aisha's tower. It has 3 pieces: a cube on the bottom, a cone in the middle, and a sphere on top.
2. 2Look at James's tower. It has 4 pieces: a cube, a cone, a sphere, AND a cylinder on top.
3. 3James has all the pieces Aisha had, plus one more piece. The extra piece is the cylinder. James used an extra cylinder.
Common mistake. A common mistake is missing the change because James still has all of Aisha's pieces. To spot an extra, count the pieces in each tower: Aisha has 3, but James has 4.
The idea underneath. When you compare two towers, count the pieces first. If one tower has more pieces, look for what was ADDED. If one tower has fewer pieces, look for what's MISSING. Order doesn't matter — the pieces themselves do.
3On level
Liam built the tower shown below using 3 solids.
Use the same 3 solids to build the new tower shown by the dashed outline.
Tap or click a shape, then tap the building area to stack it. Tap a shape in the tower to remove it.
Cube
Cone
Cylinder
Show the answer and how to solve it
Liam's new tower is built by stacking the cylinder on the bottom, the cube in the middle, and the cone on top — using the same 3 solids Liam used.
1. 1Look at Liam's tower. From bottom to top, it has a cube, a cone, and a cylinder.
2. 2Now look at the dashed outline of the new tower. It needs a cylinder on the bottom, a cube in the middle, and a cone on top. The same 3 solids — just in a new order!
3. 3Drag the cylinder onto the workspace first. Then stack the cube on top of the cylinder. Last, place the cone on top of the cube.
4. 4The new tower matches the dashed outline: cylinder, cube, cone — bottom to top.
Common mistake. A common mistake is keeping the cube on the bottom (the way Liam had it) instead of moving the cylinder there. Look carefully at the dashed outline to see which solid sits at the bottom of the NEW tower.
The idea underneath. The same solids can be stacked in different orders to build different towers. The set of pieces stays the same; only the arrangement changes.
4Stretch
Liam wants to make the shape below.
Liam picked 4 triangles. What should Liam do?
A
Add 1 more piece.
B
Use different pieces.
C
He has the right pieces.
D
Take away 1 piece.
Show the answer and how to solve it
A trapezoid is made of 3 triangles. Liam picked 4, so he should take away 1 piece.
1. 1Look at the shape Liam wants to make. It is a trapezoid.
2. 2A trapezoid is made of 3 triangles. Three triangles fit together to make one trapezoid.
3. 3Liam picked 4 triangles. That is 1 more than 3. So Liam should take away 1 piece.
Common mistake. A common mistake is thinking 4 triangles fit a trapezoid — a trapezoid is made of exactly 3 triangles, and 4 is one too many.
The idea underneath. Count the pieces, then compare to how many fit together to make the whole shape. A trapezoid takes exactly 3 triangles.