Halves, thirds, and fourths of shapes
In 2nd grade, children learn to split circles and rectangles into two, three, or four equal shares; to name them halves, thirds, or fourths; and to see that equal shares can have different 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 2nd 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
How many fourths does it take to make one whole shape?
- Two
- Three
- Four
Why this matters
Cutting shapes into equal shares is your child's first real step into fractions, one of the main topics of 3rd, 4th, and 5th grade. Seeing that two halves of a square can be different shapes yet the same size teaches them to focus on the amount, not the appearance. In 3rd grade, they write these shares with numbers, such as 1/3, and place fractions on a number line.
Where kids can get stuck
- Calling any three pieces thirds, even when they are clearly different sizes.
- Believing two halves cut different ways cannot both be halves, such as a triangle half and a rectangle half of a square.
- Thinking a third is bigger than a half because 3 is bigger than 2.
How you can help
- Cut sandwiches, tortillas, or brownies into halves, thirds, and fourths at mealtimes, and ask your child to name the pieces and check that they are equal.
- Cut two identical squares of bread or paper into halves in different ways, one straight and one corner to corner, and talk about whether the halves are the same amount.
- Share a snack among two, three, or four people, and ask your child how to cut it so everyone gets an equal share and what each share is called.
The kid-friendly video below is a nice one to watch together. For more, Bobby's Math Club has free practice at your child’s level.
Kid-friendly explanation
Questions parents ask
Why is my child learning that equal shares can have different shapes?
Equal shares are about amount, not appearance. A square cut in half with a straight line or corner to corner gives two equal halves either way. Understanding this helps your child focus on how much each part is, which is the main idea behind fractions in 3rd grade.
When will my child start writing fractions like 1/3?
In 2nd grade, children describe equal shares with words like halves, thirds, and fourths. Writing fractions with numbers, such as 1/2 and 1/3, begins in 3rd grade, along with placing fractions on a number line. This year builds the understanding those symbols will rest on.
Why are thirds harder than halves and fourths?
Halves and fourths can be made by folding or cutting in half and in half again. Thirds require dividing into three equal parts, which is harder to do evenly and cannot be made by repeated folding in half. Practicing with paper strips or cutting food into thirds helps your child see what equal thirds look like.
Make learning math fun
Bobby's Math Club turns 2nd grade math practice into something fun to do together.
- Free, unlimited practice for every child in your family
- A few minutes a day, at just the right level
- 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 2.G.A.3: “Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.” Learn how Bobby's Math Club can help your students grow. (Common Core 2.G.3)