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Equal Parts as Unit Fractions

A 45-minute Grade 3 lesson joining geometry to fractions: split a shape into equal areas, and each part is a unit fraction of the whole.

Equal Parts as Unit Fractions is a free 45-minute Grade 3 maths lesson plan for Common Core standard 3.G.A.2 — split shapes into equal parts and name each part as a fraction. 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 3
Length:
45 minutes
Standard:
3.G.A.2

Grade 3 · Geometry

3.G.A.2

Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.

Objective

Students will be able to partition a shape into parts of equal area and express each part as a unit fraction of the whole.

Students are successful when they can

  • Splits a shape into a given number of equal-area parts.
  • Names each part as a unit fraction.
  • Recognises equal-area parts that are different shapes.

What you need

  • Squared paper
  • Paper shapes for folding and cutting
  • Scissors
  • The printable practice sheet linked at the end of this plan

The lesson

Warm-up — how many parts?

5 min
  1. Show shapes already partitioned into 2, 3, 4 and 6 equal parts and ask what one part is called.
  2. A half, a third, a fourth, a sixth. The name comes from the number of parts, and only when they are equal.

Teach — equal area, and the name that follows

14 min
  1. Split a rectangle on squared paper into four equal parts by counting squares, not by eye.
  2. Each part is one fourth of the whole. Write 1/4 on each.
  3. Now split the same rectangle into four equal parts a different way — four strips instead of a two by two grid.
  4. Check both by counting squares. Same area per part, different shapes, both are fourths.
  5. Split a shape into six equal parts and name each a sixth. Ask how many sixths make the whole.
  6. Deliberately split a shape into four unequal parts and ask what one part is called. It has no fraction name, because fractions require equal parts.
“The parts have to be the same amount, not the same shape. Once they are, one part is one over however many parts you made.”

Guided practice — split and name

12 min
  1. Pairs partition shapes on squared paper into a given number of equal parts, checking by counting squares.
  2. They name one part and say how many of them make the whole.
  3. Then they find a second way to split the same shape into the same number of parts.

Independent practice

11 min
  1. Students complete a partitioning page.
  2. Parts labelled with a fraction but visibly unequal are the diagnostic error — the count was met and the equality was not checked.

Close

3 min
  1. Show a shape in eight equal parts and ask what three of them are called.
  2. Three eighths, and the step from unit fractions to the rest is made in one sentence.

What goes wrong, and why

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

Labels four unequal parts as fourths.

Why: The count of parts has been treated as the whole requirement, which is what the fraction name appears to describe.

Fix: Count the squares in each part. Equality becomes a number rather than a judgement, and the mismatch is the pupil's own to find.

Rejects four strips as fourths because they are not the same shape as a two by two split.

Why: Equal has been read as identical, which is true when the split is made by folding a shape symmetrically.

Fix: Count the squares in a strip and in a small square. The same number, so the same area. Shape and area are different questions.

Says one part of a shape split into six is 'one sixth of a sixth' or cannot name it at all.

Why: The link between the number of parts and the fraction name has not been made explicit, only demonstrated on halves and quarters.

Fix: Write the rule as the pupils say it: however many equal parts, that number goes underneath. Then test it on fifths and tenths.

If they are not there yet

  • Work on squared paper with shapes whose area divides exactly by the number of parts.
  • Fold rather than draw for halves and fourths, where folding guarantees equality.

If they finish early

  • Split a shape into eighths and name three of the parts together.
  • Split a triangle into four equal areas.
  • Explain why a shape with area 10 squares cannot be split into three equal whole-square parts.

Exit ticket

Split this rectangle into 6 equal parts. What is each part called? How many make the whole?

What to look for: Six equal-area parts, named sixths, and six making the whole. Unequal parts with the right count mean the equality was not checked by counting.

Printable practice for 3.G.A.2

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

Questions about Equal Parts as Unit Fractions

How long does the Equal Parts as Unit Fractions lesson take?

45 minutes, split across 5 timed sections: warm-up 5 min, teach 14 min, guided practice 12 min, independent practice 11 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 Equal Parts as Unit Fractions teach?

CCSS.MATH.CONTENT.3.G.A.2 — 3.G.A.2, Geometry for Grade 3: “Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.” In plain terms, split shapes into equal parts and name each part as a fraction.

What do I need to teach this lesson?

Squared paper, paper shapes for folding and cutting, scissors 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: labels four unequal parts as fourths; rejects four strips as fourths because they are not the same shape as a two by two split and says one part of a shape split into six is 'one sixth of a sixth' or cannot name it at all. 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: “Split this rectangle into 6 equal parts. What is each part called? How many make the whole?.” Six equal-area parts, named sixths, and six making the whole. Unequal parts with the right count mean the equality was not checked by counting. 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 Equal Parts as Unit Fractions?

Yes — 2 printable 3.G.A.2 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 Equal Parts as Unit Fractions 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 3.G.A.2 of the Common Core State Standards for mathematics.