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1st Grade · 2nd Grade · 1.G.A.3 · 2.G.A.3

Halves and quarters in 1st and 2nd grade

Halves and quarters are what you get when you cut a whole shape into 2 or 4 equal parts. In 1st grade, your child splits circles and rectangles into halves and fourths. In 2nd grade, your child adds thirds and learns that equal shares can have different shapes.

What the standards say

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

1.G.A.3 Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

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.

What it means, in plain words

Halves and quarters in 1st grade 1.G.A.3

Partitioning shapes means cutting them into parts. In 1st grade, children cut circles and rectangles into equal parts, also called equal shares. Equal shares are exactly the same size. Two equal shares are halves. Four equal shares are fourths, and a fourth is also called a quarter.

Your child uses the words "half of", "fourth of" and "quarter of". Your child also describes the whole as two halves or four fourths. One slice of a pizza cut into 4 equal slices is one fourth of the pizza, or a quarter of it.

The big idea is that more shares means smaller shares. A sandwich cut into fourths gives smaller pieces than the same sandwich cut into halves. Many children expect the opposite, because 4 is more than 2.

Your child should be able to:

  • Split a circle or a rectangle into 2 or 4 equal shares
  • Use the words half of, fourth of and quarter of
  • Say that two halves or four fourths make the whole
  • Explain that fourths of a shape are smaller than halves of the same shape

Example

A round pizza is cut into 4 equal slices. What do you call one slice, and how many slices make the whole pizza?

  1. The 4 slices are equal shares, so each slice is one fourth of the pizza.
  2. One fourth is also called one quarter.
  3. All 4 slices together make the whole pizza.
  4. One slice is a fourth (a quarter) of the pizza. It takes 4 slices to make the whole pizza.

Halves and quarters in 2nd grade, plus thirds 2.G.A.3

In 2nd grade, your child also cuts circles and rectangles into three equal shares, called thirds. Your child says "a third of" and describes the whole as three thirds. Fractions written with numbers come later, in 3rd grade.

2nd grade adds a new idea: equal shares of the same whole do not have to be the same shape. A square sandwich cut straight down the middle gives two rectangles. The same sandwich cut from corner to corner gives two triangles. Both ways make halves, because each piece is exactly half of the sandwich.

Your child should be able to:

  • Split a circle or a rectangle into 2, 3 or 4 equal shares
  • Name the shares halves, thirds or fourths
  • Describe the whole as two halves, three thirds or four fourths
  • Explain why two pieces with different shapes can both be halves of the same whole

Example

A square sandwich is cut from one corner to the opposite corner. Are the two pieces halves?

  1. The cut makes two triangles.
  2. One triangle fits exactly on top of the other, so the two pieces are the same size.
  3. Two equal shares are halves.
  4. Yes, the pieces are halves, even though they are triangles and not rectangles.

Where children usually get stuck

  • Your child cuts a rectangle into a big piece and a small piece and calls each one a half.

    In everyday talk, "half" can mean any piece, as in "you take the bigger half". In math, halves must be equal.

    What helps. Fold a sheet of paper so the two parts match exactly, then make a fold that does not match. Compare the two folds together.

  • Your child says a quarter of a pizza is bigger than a half, because 4 is more than 2.

    The child compares the number of pieces, not the size of each piece.

    What helps. Cut two slices of bread of the same size, one into halves and one into fourths. Lay a half next to a fourth and compare.

  • Your child says a square cut into two triangles is not in halves, because halves are rectangles.

    Most pictures of halves show one straight cut down the middle, so the child links the word to that one shape.

    What helps. Fold a paper square from corner to corner and cut along the fold. Lay one triangle on top of the other to show that they match.

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.

  1. 1Warm-up
    James says, 'I split my shape into halves.' Look at James's work and choose the statement that best describes it.
    A
    James's work shows halves — two equal parts.
    B
    James's work does not show halves — the two parts are not the same size.
    C
    James's work does not show halves — there are four parts, not two.
    D
    James's work does not show halves — there are three parts, not two.
    Show the answer and how to solve it

    James's work shows halves because there are two equal parts.

    1. 1Look at James's work.
    2. 2Count the parts in James's work. The rectangle is split into 2 parts. Both parts are the same size.
    3. 3Halves means EXACTLY two equal parts. James's work has 2 equal parts. So James's work shows halves — two equal parts.

    The idea underneath. Halves means exactly two equal parts. Always count the parts AND check that they are the same size.

  2. 2On level
    Click one piece to shade one third of the rectangle.
    Tap or click a part to shade it. Tap again to clear it.
    Show the answer and how to solve it

    Shading any one of the 3 equal parts shows one third of the rectangle. One third means 1 of 3 equal pieces.

    1. 1Look at the rectangle above. It is cut into 3 equal parts.
    2. 2One third means 1 of 3 equal parts. So you shade just 1 part — not 3.
    3. 3Click any one of the 3 parts to shade it. Each part is the same size, so any one of them shows one third of the rectangle.

    Common mistake. A common mistake is shading 3 parts because the word 'third' sounds like the number 3. Remember, 'one third' means just 1 part out of 3 equal parts.

    The idea underneath. A unit fraction tells you to take 1 piece from a number of equal pieces. 'One half' is 1 of 2 equal pieces, 'one third' is 1 of 3, and 'one fourth' is 1 of 4.

  3. 3On level
    Maya and Liam each have a brownie the same size. The colored piece shows what each one ate.
    Maya:
    Liam:
    Who ate the bigger piece?
    A
    Maya
    B
    Liam
    Show the answer and how to solve it

    Maya ate the bigger piece. When the same-size brownie is split into more equal pieces, each piece gets smaller — so a half is bigger than a fourth.

    1. 1Look at Maya's brownie. It is cut into 2 equal pieces. Each piece is called a half. Maya ate 1 half.
    2. 2Now look at Liam's brownie. It is cut into 4 equal pieces. Each piece is called a fourth. Liam ate 1 fourth.
    3. 3Both brownies are the same size. Liam cut his into more pieces, so each of his pieces is smaller. Maya cut hers into fewer pieces, so each of her pieces is bigger. Maya ate the bigger piece.

    Common mistake. A common mistake is thinking that 4 is bigger than 2, so fourths must be bigger than halves. But the brownies are the same size — cutting one into more pieces makes each piece smaller, not bigger.

    The idea underneath. When you split the same whole into more equal pieces, each piece is smaller. More pieces means smaller pieces.

  4. 4Stretch
    Select all the shapes that show equal shares.
    A
    B
    C
    D
    E
    F
    Show the answer and how to solve it

    Two shapes show equal shares: the circle split into 3 equal sectors and the rectangle split into 4 equal vertical strips.

    1. 1Equal shares means every part of the shape must be the same size. Look at each shape and check whether the parts match.
    2. 2The circle split into 3 sectors: all 3 sectors look the same size. This shape shows equal shares.
    3. 3The rectangle split into 4 vertical strips: all 4 strips have the same width. This shape shows equal shares.
    4. 4The circle split into 3 sectors: the sectors are clearly different sizes — at least one is much bigger than the others. This shape does NOT show equal shares.
    5. 5The rectangle split into 4 vertical strips: the strips have different widths. Even though there are 4 strips, the parts are not the same size. This shape does NOT show equal shares.
    6. 6The circle split into 2 pieces: one piece is clearly larger than the other. This shape does NOT show equal shares.
    7. 7The rectangle split into 3 horizontal strips: the strips have different heights. This shape does NOT show equal shares.

    Common mistake. A common mistake is choosing a shape just because it has the same number of parts as a correct shape. Equal shares means every part must be the same size — the number of cuts alone is not enough.

    The idea underneath. When deciding if a shape shows 'equal shares', the number of parts is not enough — every part has to be the same size as the others. Always check the part sizes, not just the cuts.