Splitting shapes into equal parts
In 3rd grade, children learn to split shapes into parts with equal area and to name each part as a unit fraction, such as 1/4 for each of 4 equal parts.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 3rd 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
A pizza is cut into 8 equal slices. What fraction represents one slice of the pizza?
- 1/4
- 8
- 1/8
Why this matters
Cutting shapes into equal parts gives your child something concrete to hold on to when they think about fractions: each of 4 equal parts is 1/4, even when the parts look different. Focusing on equal area rather than matching looks prepares your child to compare and add fractions in 4th grade. It also helps with everyday fairness, like cutting a pan of brownies into equal servings, and supports later work with area and geometry.
Where kids can get stuck
- Splitting a shape into parts of different sizes and still calling each part 1/4, because there are four of them.
- Thinking equal parts must look alike, so two differently shaped halves with the same area do not count.
- Writing the number of parts instead of a fraction, such as 4 instead of 1/4.
How you can help
- Fold a square napkin into 4 equal parts in two different ways, such as strips and smaller squares, and ask your child whether each part is still 1/4.
- Cut a sandwich or brownie into equal pieces and ask your child what fraction of the whole each piece is and how they know the pieces are fair.
- Ask your child to draw lines splitting a rectangle on paper into 3 or 6 equal parts and name the fraction each part shows.
For more, Bobby's Math Club has free practice at your child’s level.
Questions parents ask
Why does my child say parts that look different can still be equal?
Equal parts must cover the same amount of space, but they do not have to be the same shape. A square can be cut into two rectangles or two triangles, and each piece is still 1/2 because it covers half the area. Understanding this helps your child focus on how much space a part covers, which is what fractions measure.
What is a unit fraction?
A unit fraction has 1 on top, such as 1/2, 1/3, or 1/8. It names one part when a whole is split into equal parts. If a pizza is cut into 6 equal slices, each slice is a unit fraction, 1/6. Unit fractions are the building blocks your child uses to understand all other fractions.
How does splitting shapes help my child with fractions?
Splitting shapes gives your child a picture of what a fraction is. When they cut a rectangle into 8 equal parts, they can see that each part is 1/8 and that 8 of them make the whole. This picture supports comparing fractions, finding equal fractions and, in 4th grade, adding fractions with the same bottom number.
Make learning math fun
Bobby's Math Club turns 3rd grade math practice into something fun to do together.
- Unlimited practice, completely free
- A few minutes a day, at just the right level
- Level-ups, badges, and a cheer for every win
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 3.G.A.2: “Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.” Learn how Bobby's Math Club can help your students grow. (Common Core 3.G.2)