Year 2 Fractions: Halves, Quarters and Eighths

A fraction names equal parts of one whole. In this unit, students build and describe halves, quarters and eighths with shapes, objects, lengths, capacities and collections. The emphasis is on equal parts: two pieces are not halves unless they are the same size or amount.

• Recognise one-half as 1 of 2 equal parts and write it as 1/2.
• Share an even collection into 2 equal groups and identify either group as one-half of the collection.
• Make quarters by halving each half, and make eighths by halving each quarter.
• Connect the number of equal parts to the unit fraction: 4 equal parts make quarters and 8 equal parts make eighths.
• Explain why the same fraction can look different when the whole has a different shape, size or quantity.

The denominator tells how many equal parts the whole has been divided into. The numerator 1 tells us that one of those parts is being named.

Always compare fractions using the same whole. One-half of a large pizza can be larger than one-half of a small pizza, even though both pieces represent 1/2 of their own whole.

1. Start with equal and unequal shares. Fold paper, cut playdough or pour water into 2 containers. Ask whether the shares are equal and how students know.
2. Build halves of shapes and collections. Shade half of a rectangle, then share 12 counters into 2 equal groups. Connect both models to 1/2.
3. Halve each half. Fold the same paper strip again. Four equal parts are quarters, so one part is 1/4.
4. Halve each quarter. Fold once more. Eight equal parts are eighths, so one part is 1/8.
5. Name, compare and explain. Students describe the repeated-halving relationship: a quarter is half of a half, and an eighth is half of a quarter.

Half of a collection

Share 12 counters equally between 2 groups. Each group has 6 counters, so half of 12 is 6. Each group is 1/2 of the original collection.

Repeated halving

Begin with one paper strip. Fold it into 2 equal parts to make halves. Fold each half into 2 equal parts to make 4 quarters. Fold each quarter into 2 equal parts to make 8 eighths.

Whole → 2 halves → 4 quarters → 8 eighths

Different-looking halves

A rectangle can be split vertically, horizontally or diagonally. Each split can show halves when the two regions have equal area, even though the pieces have different orientations.

Key idea: Fraction parts must be equal parts of the same whole. Halving once makes halves, halving again makes quarters and halving again makes eighths.

Remember

• Identify equal parts
• Describe one-half
• Connect halves and quarters
• Connect quarters and eighths
• Explain repeated halving

Quick questions

• Show one half of a rectangle.
• How are quarters made from halves?
• Are four unequal pieces quarters? Explain.
• Which is smaller: a quarter or an eighth?

If an answer is uncertain, return to the model and explain what each part represents before calculating or drawing a conclusion.

• Counting parts but ignoring equality: two parts are not automatically halves. Ask students to compare the size or amount of each part.
• Changing the whole: fraction comparisons are only fair when students identify the whole being divided.
• Thinking more parts means larger pieces: for the same whole, eighths are smaller than quarters because the whole is divided into more equal parts.
• Confusing the number of parts with the fraction: four equal parts are quarters, but one selected part is one-quarter.
• Halving odd collections without a suitable context: begin with even collections so equal whole-number groups can be formed before discussing split objects.

• Support: use foldable paper shapes, playdough, counters and matching cards labelled whole, 1/2, 1/4 and 1/8.
• Core: move between a concrete model, a drawing, fraction words and fraction notation.
• Extension: ask students to create two different models of the same fraction and justify why both are correct.

Content description: recognise and describe one-half as one of 2 equal parts of a whole and connect halves, quarters and eighths through repeated halving.

• E1: create halves of collections by sharing into 2 equal groups and compare halves of different-sized collections.
• E2: create halves using measurement attributes, including folded paper, playdough, capacity and collections, and explain that a half is 1 of 2 equal parts.
• E3: repeatedly halve shapes and objects to make corresponding halves, quarters and eighths, and explain the relationships between them.
• E4: divide a shape into equal parts and relate the number of parts to the unit fraction: 4 equal parts are quarters and 8 equal parts are eighths.

1. Draw a shape divided into 2 equal parts and shade one-half.
2. Share 16 counters into 2 equal groups. How many counters are in one-half?
3. Explain why a shape divided into 2 unequal pieces does not show halves.
4. Complete the sentence: one-quarter is half of ______.
5. Complete the sentence: one-eighth is half of ______.
6. Which is larger for the same whole: 1/4 or 1/8? Explain.

Use the topic guide for planning, present the static Teacher Slides for explicit instruction, then choose the worksheet, supported Practice or independent Test. Return to concrete equal-part models whenever a student can name a fraction but cannot explain why the parts are equal.

The Australian Curriculum code below is exact. Other entries are broad planning equivalents because each jurisdiction organises early fraction learning differently.

Curriculum equivalents for And describe one-half as one of 2 equal parts of...

Mapped skill: recognise and describe one-half as one of 2 equal parts of a whole and connect halves, quarters and eighths through repeated halving

These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.

Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.

• Australian Curriculum Version 9.0
• Victorian Curriculum F–10
• NSW Curriculum
• England National Curriculum
• New Zealand Curriculum

• AC9M2N01: Numbers to at least 1000
• AC9M2N02: Place value, regrouping and renaming numbers
• AC9M2N04: Addition and subtraction strategies
• AC9M2N05: Equal groups, arrays, multiplication and division
• AC9M2M02: Halves, quarters and eighths in measurement