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Halves and Quarters of Shapes

A 40-minute Grade 1 lesson on splitting circles and rectangles into two and four equal shares, where the word doing all the work is 'equal'.

Halves and Quarters of Shapes is a free 40-minute Grade 1 maths lesson plan for Common Core standard 1.G.A.3 — split shapes into halves and quarters. It is timed across 5 sections, gives the exact wording to use where the wording carries the mathematics, names 3 misconceptions with the teaching move that addresses each, and ends with an exit ticket and a printable worksheet with its answer key.

Grade:
Grade 1
Length:
40 minutes
Standard:
1.G.A.3

Grade 1 · Geometry

1.G.A.3

Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters.

Objective

Students will be able to partition circles and rectangles into two or four equal shares and name the shares as halves, fourths or quarters.

Students are successful when they can

  • Splits a shape into two equal parts and names each a half.
  • Rejects a split into two unequal parts as not halves.
  • Says that four quarters make the whole.

What you need

  • Paper circles and rectangles, several per pupil
  • Scissors
  • Pre-cut examples of correct and incorrect splits
  • The printable practice sheet linked at the end of this plan

The lesson

Warm-up — fair shares

5 min
  1. Show a paper rectangle split into two very unequal parts and offer a pupil either piece.
  2. Ask whether that was fair, and get the word 'equal' into the room from them rather than from you.

Teach — halves must match

12 min
  1. Fold a paper circle in half and cut. Lay one piece on the other. They match exactly, which is what makes them halves.
  2. Fold a rectangle in half two different ways — across and down. Both give halves, and the halves are different shapes.
  3. Show a rectangle split into two unequal parts. Ask if these are halves. Lay one on the other; they do not match.
  4. Fold in half again to make quarters. Four pieces, all matching.
  5. Put the four quarters back together into the whole. Say the sentence: four quarters make one whole.
  6. Show a circle cut into four unequal wedges and ask whether those are quarters.
“Two pieces is not enough. Two equal pieces is halves. If one is bigger, they are just two pieces.”

Guided practice — fold, cut, check

11 min
  1. Pairs fold and cut shapes into halves, then quarters, and check by stacking the pieces.
  2. Then they find a second way to split the same shape into quarters.
  3. A rectangle can be quartered in at least three ways, and finding more than one is the task.

Independent practice

9 min
  1. Students complete a halves and quarters page.
  2. Watch for a shape split into four visibly unequal parts labelled quarters — that is the diagnostic error.

Close

3 min
  1. Hold up a half and ask how many make a whole. Then a quarter.
  2. Ask which is bigger, a half or a quarter, and let the pieces answer.

What goes wrong, and why

Each of these is a reasoning error rather than carelessness. The fix addresses the reasoning.

Calls any two pieces halves.

Why: The word half has been learned as 'one of two pieces', which is how it is used loosely in speech — half the biscuit, whichever bit you got.

Fix: Stack the pieces. Matching is the test, and it either works or it does not without an adult adjudicating.

Says a quarter is bigger than a half because four is bigger than two.

Why: Whole number reasoning is being applied to the name of the part. Four has always meant more than two.

Fix: Put the two pieces side by side. More pieces means each is smaller, and holding both makes it settle in a way that explanation does not.

Splits a rectangle into halves one way and insists that is the only way.

Why: The first successful method becomes the definition of the task, and nothing has suggested a second exists.

Fix: Ask for a different fold that still passes the stacking test. Finding it themselves is what breaks the single-method assumption.

If they are not there yet

  • Fold rather than draw. Folding produces equal parts automatically, so 'equal' is achieved before it has to be judged.
  • Work with halves alone until the equal-parts test is secure, then introduce quarters.

If they finish early

  • Split a shape into quarters in three different ways.
  • Shade three of four quarters and describe what is shaded.
  • Split a shape into thirds by folding, which is genuinely hard and shows what equal costs.

Exit ticket

Here are two rectangles. One is split into two equal parts, one into two unequal parts. Circle the one showing halves and say why.

What to look for: The equal split, with a reason using 'the same' or 'equal'. Circling both means the word half is still being used for any two pieces.

Printable practice for 1.G.A.3

Free to print and copy, answer key included. Each sheet can generate a fresh set of problems for a retake.

Questions about Halves and Quarters of Shapes

How long does the Halves and Quarters of Shapes lesson take?

40 minutes, split across 5 timed sections: warm-up 5 min, teach 12 min, guided practice 11 min, independent practice 9 min, close 3 min. The minutes are stated per section and add up to the stated length, so the plan can be cut or extended at a section boundary rather than abandoned halfway.

Which standard does Halves and Quarters of Shapes teach?

CCSS.MATH.CONTENT.1.G.A.3 — 1.G.A.3, Geometry for Grade 1: “Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters.” In plain terms, split shapes into halves and quarters.

What do I need to teach this lesson?

Paper circles and rectangles, several per pupil, scissors, pre-cut examples of correct and incorrect splits and the printable practice sheet linked at the end of this plan. Everything listed is either ordinary classroom equipment or a free printable from this site — there is nothing to buy and nothing to prepare beyond photocopying.

What mistakes should I expect in this lesson?

Three, each a reasoning error rather than carelessness: calls any two pieces halves; says a quarter is bigger than a half because four is bigger than two and splits a rectangle into halves one way and insists that is the only way. The plan gives the thinking behind each one and the teaching move that addresses the thinking rather than the symptom.

How do I know whether the lesson worked?

The exit ticket asks: “Here are two rectangles. One is split into two equal parts, one into two unequal parts. Circle the one showing halves and say why.” The equal split, with a reason using 'the same' or 'equal'. Circling both means the word half is still being used for any two pieces. That tells you whether the class needs a reteach or a thirty-second conversation before you plan tomorrow.

Is there a worksheet to go with Halves and Quarters of Shapes?

Yes — 2 printable 1.G.A.3 worksheets, linked at the end of the plan and free like the rest of the site. Each one comes with an answer key and 25 versions, so the practice after the lesson can be a different paper on every desk.

Is Halves and Quarters of Shapes free to use?

Yes. The plan, its printables and their answer keys are free to read, print and photocopy for your own class, with no account and no email capture. It was last reviewed on 5 September 2026. Please do not resell it or republish it as your own.

Last reviewed 2026-09-05. Aligned to 1.G.A.3 of the Common Core State Standards for mathematics.