Building bigger shapes from smaller ones
In 1st grade, children learn to put flat shapes or solid shapes together to make new, larger shapes.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 1st grade practice. Tap the speaker to hear one read aloud, or the light bulb for a hint, and talk about the answer together.
Question 1 of 3
If you cut a rectangle exactly in half straight down the middle, what two shapes do you make?
- Rectangles
- Circles
- Triangles
Why this matters
Fitting shapes together is playful work that builds your child's spatial reasoning, the skill of moving shapes around in their mind, which helps with puzzles, building, and reading maps. It also sets up later math: two half-circles making a whole leads into fractions, and covering a rectangle with small squares leads to area in 3rd grade.
Where kids can get stuck
- Overlapping shapes or leaving gaps between them, then being unsure what new shape has been made.
- Missing a familiar shape once it is built from smaller pieces, like not seeing that two triangles make a square.
- Naming a combined shape after its pieces, calling a rectangle made of two squares "two squares."
How you can help
- Cut paper or cereal boxes into squares, triangles, and half-circles, and challenge your child to make a house, a fish, or a rocket by fitting the pieces together.
- Build with blocks, cans, and boxes from the pantry. Ask your child what shape two stacked cubes make, or what happens when a cone sits on a cylinder.
- Fold a square napkin corner to corner to show two triangles, then unfold it and ask your child how two triangles made one square.
If it’s helpful, you can watch the kid-friendly video below, or sign up for free, adaptive practice in Bobby's Math Club.
Kid-friendly explanation
Questions parents ask
Why is my child learning to put shapes together?
Combining shapes builds spatial reasoning, the ability to imagine how shapes fit and move. This skill supports later ideas like fractions, where a whole is made of equal parts, and area, where a shape is covered with squares. It also gives children practice describing shapes with careful words.
What shapes should my child know by the end of 1st grade?
In this skill, children work with flat shapes like rectangles, squares, triangles, trapezoids, half-circles, and quarter-circles; and solid shapes like cubes, rectangular prisms such as boxes, cones, and cylinders. They do not need formal definitions, but they should recognize these shapes and use them to build new ones.
What does compose a shape mean?
To compose a shape means to put two or more shapes together to make a new, larger shape. For example, putting two squares side by side composes a rectangle. Children then use that new shape as part of a bigger design, which is called composing new shapes from the composite shape.
Make learning math fun
Bobby's Math Club turns 1st grade math practice into something fun to do together.
- Unlimited practice, completely free
- Practice that starts where your child is and grows with them
- Hints when they are stuck, and a celebration when it clicks
Written by Robert “Bobby” Barnett
Bobby is an award-winning math teacher, the author of Meet Every Learner’s Needs, and the father of two elementary-school math learners. He uses Bobby’s Math Club with his own kids a few times every week. Learn more or contact Bobby.
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Join the clubNote for teachers: This skill is covered by Common Core math standard 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.” Learn how Bobby's Math Club can help your students grow. (Common Core 1.G.2)