Compose Shapes

Grade 1 · geometry · 41 practice problems · read aloud

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Compose Shapes: Putting Shapes Together! 🧩

Composing shapes means putting smaller shapes together to make a new, bigger shape. It's like building with blocks! This helps us see how shapes work and is super useful for building things, drawing, and solving puzzles.

How to Compose Shapes: Step-by-Step

  1. Look at the Big Shape: What shape are you trying to make? A house? A boat?
  2. Choose Your Small Shapes: Pick shapes like squares, rectangles, triangles, and circles.
  3. Fit Them Together: See how the small shapes can fit side-by-side or on top of each other without gaps.
  4. Check Your Work: Does your new shape look like the one you wanted to make?

Let's Try Some Examples!

Example 1: Make a Rectangle

Can you make a rectangle using two squares? Yes! Put two squares of the same size right next to each other. They fit perfectly to make a longer rectangle! ▢▢

Example 2: Make a Bigger Triangle

Can you make a bigger triangle using smaller triangles? Yes! Put two small triangles together along their long edges. They make a diamond or a bigger triangle! ◤◢

Watch Out! Common Mistakes

Leaving Gaps: Sometimes shapes don't fit together smoothly, leaving empty spaces. Make sure the edges touch completely.

Wrong Shape Choice: Not all shapes can make the big shape you want. A circle can't help you make a square with straight sides!

Tips & Tricks for Success

Think Like a Builder: Imagine you are building a wall with blocks. You wouldn't leave holes!

Trace and Cut: Draw a big shape on paper, then see if you can cut it into smaller shapes that fit back together.

Use Your Toys: Practice with pattern blocks, LEGO bricks, or paper cut-outs. Hands-on learning is the best!

How to Practice

  • Ask a grown-up for a shape puzzle.
  • Use tangrams to make animals and objects.
  • Look around your room! What objects can you see that are made from smaller shapes?

Practice problems

6 of the 41, worked through step by step — try them before opening the answer.

1 Emma has two identical squares. She puts them together along one side. What new 2D shape does Emma make?

Hint: Think about the sides and corners. When you put two squares side by side, the new shape has four sides, but two are longer than the others.

Show the answer

Answer: rectangle

  1. Start with two identical squares. Each square has four equal sides.
  2. Place them side by side so they share one whole side.
  3. Count the sides of the new shape. The top has two square tops making one long top. The bottom has two square bottoms making one long bottom. The left and right sides are the same as before.
  4. The new shape has 4 sides, with opposite sides equal and longer than the other pair. This is a rectangle.

The answer is a rectangle.

2 Hana has 4 square tiles. If she puts all 4 squares together to make one larger shape, what shape can she make?

Hint: Think about how you can arrange the 4 small squares. Try placing them in 2 rows with 2 squares in each row. What shape do you see now?

Show the answer

Answer: a larger square

  1. Start with 4 small squares.
  2. Arrange them in a 2 by 2 grid (2 rows and 2 columns).
  3. When you put them together this way, the outside edges form one big square.
  4. The new shape has 4 equal sides and 4 square corners, just like a square.

The answer is a larger square.

3 Mere has 6 identical square tiles. If she puts them together in a row, side by side, what new 2D shape does she make?

Hint: Think about what happens when you line up squares next to each other. Does the new shape still have all sides the same length?

Show the answer

Answer: a rectangle

  1. Start with 6 square tiles. Each square has 4 equal sides.
  2. When you place them side by side in a row, the top and bottom edges line up to form one long top edge and one long bottom edge.
  3. The left and right ends are still the sides of the first and last square.
  4. The new shape has 2 long sides and 2 short sides. Opposite sides are equal.
  5. A shape with 4 sides and opposite sides equal is a rectangle.

The answer is a rectangle.

4 Mere has 10 small square tiles. She arranges them in 2 equal rows to form a larger shape. What 2D shape does she make?

Hint: Think about what shape you get when you put squares together in rows. Count the sides of the new shape and look at how the sides compare to each other.

Show the answer

Answer: rectangle

  1. Mere has 10 small square tiles. Each tile is a square with 4 equal sides.
  2. She arranges the tiles in 2 equal rows. That means each row has 10 divided by 2 = 5 tiles.
  3. The tiles are placed side by side in each row, and the rows are stacked on top of each other. This forms a shape with 4 sides.
  4. The top and bottom sides are each made from 5 tile edges, so they are the same length. The left and right sides are each made from 2 tile edges, so they are the same length.
  5. A shape with 4 sides where opposite sides are equal is called a rectangle.

The answer is rectangle.

5 Matiu has 12 small square tiles. He puts them together in 3 equal rows to make a larger shape. What 2D shape does he make?

Hint: Think about how the tiles are arranged. When you put squares together in rows, what kind of shape do the outer edges form? Count the number of sides and look at how the sides compare to each other.

Show the answer

Answer: rectangle

  1. Matiu has 12 small square tiles. Each tile is a square with 4 equal sides.
  2. He arranges the tiles in 3 equal rows. That means each row has 12 divided by 3 = 4 tiles.
  3. The tiles are placed side by side in each row, and the rows are stacked on top of each other. This forms a shape with 4 sides.
  4. The top and bottom sides are each made from 4 tile edges, so they are the same length. The left and right sides are each made from 3 tile edges, so they are the same length.
  5. A shape with 4 sides where opposite sides are equal is called a rectangle.

The answer is rectangle.

6 Kaia has 9 small square tiles. She wants to put them together to make one big square. How many tiles will she have left over?

Hint: Think about how many rows and columns you need to make a square. Try drawing small squares in your mind, making each row the same length as the column.

Show the answer

Answer: 0 tiles left over (she can make a 3 by 3 square)

  1. To make a square, the number of tiles in each row must equal the number of rows.
  2. Try 2 rows of 2 tiles = 4 tiles, but 9 is bigger than 4.
  3. Try 3 rows of 3 tiles = 9 tiles.
  4. 9 tiles exactly makes a 3 by 3 square.
  5. 9 - 9 = 0, so no tiles are left over.

The answer is 0 tiles left over.

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