AC9M2N03_E1
Create halves of collections by sharing each collection into 2 equal groups and compare halves of differently sized collections.
About This Year 2 Maths Topic
In this unit, children learn that a fraction describes equal parts of a whole. The word equal is essential. A shape or collection has not been divided into halves unless it has been separated into two parts of the same size or amount.
Children first explore one-half by sharing collections into two equal groups and dividing objects, shapes and measurements into two equal parts.
They then use repeated halving to connect halves, quarters and eighths:
- a half is one of 2 equal parts;
- a quarter is one of 4 equal parts;
- an eighth is one of 8 equal parts;
- a quarter is half of a half;
- an eighth is half of a quarter.
Children should explore fractions using real objects before moving to pictures and written symbols. Folding paper, sharing counters, dividing playdough and measuring water give meaning to the fraction names.
These activities support Australian Curriculum Version 9.0 content descriptor AC9M2N03 and its associated elaborations.
Australian Curriculum Alignment
AC9M2N03
Recognise and describe one-half as one of 2 equal parts of a whole and connect halves, quarters and eighths through repeated halving.
AC9M2N03_E2
Create halves using measurement attributes by folding, dividing or separating a whole into 2 equal parts and naming one part as one-half.
AC9M2N03_E3
Use repeated halving to make halves, quarters and eighths and recognise that a quarter is half of a half and an eighth is half of a quarter.
AC9M2N03_E4
Divide shapes into equal parts and connect the number of equal parts with the unit fraction, such as one-quarter or one-eighth.
The Big Idea for Parents
Fractions must show equal parts of the same whole.
The parts may have different shapes, but they must represent the same amount of the whole.
One-half of a large object may be larger than one-half of a small object. The fraction name describes the relationship between the part and its own whole.
For example, half of 12 counters is 6 counters, while half of 8 counters is 4 counters. Both groups represent one-half because each original collection was divided into 2 equal groups.
Learning Intentions
Children will learn to:
- recognise one-half as one of 2 equal parts;
- share a collection into 2 equal groups;
- find one-half of an even collection;
- divide shapes and objects into equal halves;
- compare halves of different wholes;
- explain why unequal parts are not halves;
- use repeated halving to make quarters;
- use repeated halving to make eighths;
- recognise one-quarter as one of 4 equal parts;
- recognise one-eighth as one of 8 equal parts;
- connect a quarter with half of a half;
- connect an eighth with half of a quarter;
- identify unit fractions in divided shapes;
- explain how the denominator relates to the number of equal parts.
Student Success Criteria
I can share a collection into 2 equal groups.
I can find one-half of a collection.
I can divide a shape into 2 equal parts.
I can explain why the parts must be equal.
I can identify one-half of a whole.
I can halve a half to make quarters.
I can halve a quarter to make eighths.
I can identify one-quarter of a shape.
I can identify one-eighth of a shape.
I can name a unit fraction from the number of equal parts.
I can compare the sizes of halves, quarters and eighths.
I can explain my fraction using words, objects or drawings.
Key Vocabulary
fraction
whole
part
equal
equal parts
share
divide
one-half
half
halves
one-quarter
quarter
quarters
one-eighth
eighth
eighths
unit fraction
repeated halving
collection
measurement
Teacher Guide for Parents
Teachers normally introduce fractions with real objects and practical actions before using written fraction symbols.
At home, follow this sequence: share it, check it, name it, halve it again and explain it.
1. Begin with Fair Sharing
Give your child an even collection of objects such as 8 buttons, 10 counters or 12 blocks.
Ask them to share the collection fairly between 2 people or 2 plates by placing one object in each group in turn.
When both groups contain the same number, explain that each group is one-half of the complete collection.
What to say
“The whole collection has been divided into 2 equal groups. Each equal group is one-half.”
2. Check That the Groups Are Equal
Children may divide a collection into 2 groups but forget that the groups must contain the same amount.
Ask your child to count both groups and compare them.
For example:
- 5 objects and 5 objects are equal halves of 10;
- 6 objects and 4 objects are not equal halves of 10.
Teacher tip
Use the expression “two groups” only when describing the number of groups. Use “two equal groups” when describing halves.
3. Compare Halves of Different Collections
Show half of 12 counters and half of 8 counters.
- half of 12 is 6;
- half of 8 is 4.
Explain that both 6 and 4 can represent one-half because they are halves of different wholes.
Important idea
A fraction cannot be understood without knowing the whole. Half of a larger whole may be larger than half of a smaller whole.
4. Make Halves by Folding Paper
Give your child a paper strip or rectangular sheet.
Ask them to fold it so that both ends and edges match. Open the paper and trace the fold line.
Explain that the fold created 2 equal parts. Each part is one-half of the paper.
Fold another sheet incorrectly so the parts are unequal. Compare the two examples and discuss why the unequal parts are not halves.
5. Make Halves with Playdough
Roll a lump of playdough into a ball or sausage shape.
Ask your child to divide it into 2 parts. Compare the parts by placing them beside each other or weighing them.
Adjust the amounts until both parts are equal, then name each part as one-half.
Teacher tip
Equal fractions describe equal quantities, even when the pieces do not look exactly the same shape.
6. Make Halves with Water
Fill a measuring cup with a safe amount of water. Ask your child to pour the water equally into 2 identical cups.
Place the cups side by side and check that the water levels are equal.
Explain that each cup contains one-half of the original amount.
7. Connect Collections and Shapes
Show half of 10 counters beside half of a paper circle or rectangle.
Ask:
- What is the whole in each example?
- How many equal parts were made?
- How many parts have been selected?
- Why does each example show one-half?
Explain that one example shows half of a collection and the other shows half of a shape, but both show one of 2 equal parts of their respective wholes.
8. Use Repeated Halving to Make Quarters
Fold a paper strip in half. Then fold it in half again.
Open the strip and count the equal sections. There should be 4 equal parts.
Explain:
- the first fold made halves;
- halving each half made quarters;
- each part is one-quarter of the whole;
- a quarter is half of a half.
What to say
“We did not make the whole larger. We divided the same whole into more equal parts, so each part became smaller.”
9. Use Repeated Halving to Make Eighths
Take the paper divided into quarters and halve each quarter again.
Count the 8 equal parts.
Explain:
- each part is one-eighth of the whole;
- an eighth is half of a quarter;
- 2 eighths make 1 quarter;
- 4 eighths make 1 half;
- 8 eighths make 1 whole.
10. Compare the Sizes of Fractional Parts
Use the same-sized paper strips to show halves, quarters and eighths.
Place the strips beside each other and ask which individual parts are largest and smallest.
Children should notice:
- one-half is larger than one-quarter;
- one-quarter is larger than one-eighth;
- as the number of equal parts increases, each part becomes smaller.
Common confusion
Children may think one-eighth is larger than one-half because 8 is greater than 2. Use equal-sized wholes to show that the denominator tells how many equal parts the whole has been divided into.
11. Connect Equal Parts to Unit Fractions
A unit fraction describes one equal part of a whole.
- 2 equal parts means each part is one-half;
- 4 equal parts means each part is one-quarter;
- 8 equal parts means each part is one-eighth.
Ask your child to count the total number of equal parts before naming one selected part.
Recommended Teaching Sequence at Home
- Share an even collection into 2 equal groups.
- Check that both groups contain the same amount.
- Name each group as one-half.
- Fold or divide an object into equal halves.
- Compare halves of different wholes.
- Halve each half to make quarters.
- Halve each quarter to make eighths.
- Compare the sizes of the fractional parts.
- Connect 2, 4 and 8 equal parts to the unit fractions.
- Ask the child to explain the fraction in their own words.
Common Misconceptions and How Parents Can Help
Calling any two pieces halves
Compare an equally divided shape with an unequally divided shape. Explain that halves must be equal in size or amount.
Counting the selected parts but ignoring the whole
Always identify the complete whole before naming its fractional parts.
Thinking halves must have identical shapes
Show examples where equal areas have different shapes. Explain that the amount must be equal, even when the outlines look different.
Thinking half is always the same amount
Compare half of 8 objects with half of 12 objects. Explain that the size of the half depends on the size of the whole.
Thinking one-eighth is larger than one-quarter
Divide equal-sized paper strips into quarters and eighths. Compare one part from each strip directly.
Counting lines instead of parts
A shape divided by 3 lines may create 4 parts. Ask the child to point to and count the spaces, not the dividing lines.
Making quarters by drawing four unequal sections
Fold the shape or use a grid to check that all 4 parts have the same area.
Using repeated halving without keeping the parts equal
Match edges when folding and compare the resulting sections before naming them as quarters or eighths.
Simple Home Activities for Halves, Quarters and Eighths
Activity 1: Share the Counters
Give your child 8, 10 or 12 counters. Ask them to share the collection fairly between 2 plates.
Count each group and name each group as one-half.
Focus: AC9M2N03_E1.
Activity 2: Compare Two Halves
Find half of 12 buttons and half of 8 blocks.
Ask why the two halves contain different numbers even though both represent one-half.
Focus: Comparing fractions of different wholes.
Activity 3: Fold a Paper Strip
Fold a paper strip into 2 equal sections. Colour one section and name it one-half.
Repeat with different paper shapes.
Focus: One-half as 1 of 2 equal parts.
Activity 4: Playdough Halves
Divide a lump of playdough into 2 equal amounts.
Compare the parts and adjust them until both represent one-half.
Focus: AC9M2N03_E2.
Activity 5: Water Halves
Pour one cup of water equally into 2 identical containers.
Compare the water levels and explain why each amount is one-half of the original whole.
Focus: Measurement and equal quantities.
Activity 6: Half of a Snack
Use a safe food item that can be divided, such as a sandwich or piece of fruit.
Ask how it could be divided fairly between 2 people.
Focus: Fractions in everyday contexts.
Activity 7: Repeated Halving
Fold a strip in half, then halve each part to make quarters, and halve each quarter to make eighths.
Label one-half, one-quarter and one-eighth.
Focus: AC9M2N03_E3.
Activity 8: Fraction Strip Comparison
Make three equal-length strips showing halves, quarters and eighths.
Compare one part from each strip and order the parts from largest to smallest.
Focus: Comparing unit fraction sizes.
Activity 9: Fraction Shape Hunt
Look for objects that can be divided into equal parts, such as windows, tiles, chocolate-bar patterns or paper shapes.
Ask how each whole could be divided into halves, quarters or eighths.
Focus: Recognising fractions in the environment.
Activity 10: Name the Unit Fraction
Draw a shape divided into 2, 4 or 8 equal parts.
Ask your child to name one part and explain how the total number of equal parts helped them decide.
Focus: AC9M2N03_E4.
Questions Parents Can Ask
- What is the whole?
- How many equal parts have been made?
- Are all the parts the same size or amount?
- How can you check that the groups are equal?
- Which part represents one-half?
- How many objects are in each half?
- Why can two different amounts both represent one-half?
- Can you show one-half another way?
- What happens when you halve a half?
- What happens when you halve a quarter?
- How many quarters make one whole?
- How many eighths make one whole?
- Which is larger: one-half or one-quarter?
- Which is smaller: one-quarter or one-eighth?
- What happens to the size of each part when the whole is divided into more parts?
- Why is this shape not divided into quarters?
- What unit fraction names one of these equal parts?
- Can you prove that the parts are equal?
Mathematical Sentence Starters
The whole is _____.
I divided the whole into _____ equal parts.
Each part is called _____.
One-half means _____.
The groups are equal because _____.
This does not show halves because _____.
Half of _____ is _____.
A quarter is half of _____.
An eighth is half of _____.
There are _____ quarters in one whole.
There are _____ eighths in one whole.
One-half is larger than one-quarter because _____.
The more equal parts we make, the _____ each part becomes.
This part is one-_____ because the whole has _____ equal parts.
Supporting Different Learners at Home
Children Who Need More Support
- begin only with one-half;
- use small even collections;
- share objects one at a time between 2 groups;
- use identical plates or containers;
- fold shapes instead of estimating division lines;
- compare equal and unequal examples;
- use the same whole when comparing fraction sizes;
- introduce quarters only after halves are secure;
- introduce eighths only after quarters are secure;
- allow oral explanations before written answers.
Children Ready for Extension
- find halves of larger collections;
- identify half of collections arranged in unusual patterns;
- divide irregular shapes into equal areas;
- find several ways to divide the same shape equally;
- compare unit fractions using equal-sized wholes;
- explain why larger denominators create smaller unit fractions;
- identify 2 quarters as equivalent to one-half;
- identify 4 eighths as equivalent to one-half;
- create true and false fraction examples;
- design fraction puzzles for another person.
Quick Parent Check
Use these questions to check whether your child understands the main ideas.
- Share 12 counters into 2 equal groups.
- State how many counters are in one-half of 12.
- Explain why 5 counters and 3 counters are not equal halves of 8.
- Fold a strip of paper into 2 equal parts.
- Colour one-half of the strip.
- Halve each half to make quarters.
- Halve each quarter to make eighths.
- Explain why a quarter is half of a half.
- Identify one-quarter of a shape divided into 4 equal parts.
- Identify one-eighth of a shape divided into 8 equal parts.
A child shows secure understanding when they can create the fraction, check that the parts are equal and explain the relationship between the part and the whole.
Quick Exit Ticket
- Draw a shape divided into 2 equal halves.
- Show how repeated halving creates quarters.
- Complete: an eighth is half of a _____.
Printable Teacher, Parent and Student Resources
Use the buttons below to open the AC9M2N03 teaching materials and printable worksheets in a new browser tab.
Dividing Shapes into Equal Parts
Equal Parts and Unit Fractions
Finding Half of Collections
Halves, Quarters and Eighths Exit Ticket
Halves, Quarters and Eighths of Shapes
Halves, Quarters and Eighths Worksheets
Identifying One-Eighth of a Shape
Identifying One-Quarter of a Shape
Making Halves with Paper, Playdough and Water
One-Half as Two Equal Parts
Repeated Halving Fractions
Repeated Halving to Make Quarters and Eighths
Sharing Sets into Two Equal Groups
Resources open in a new tab. Browser PDF settings may determine whether a file opens in the browser or downloads automatically.
Home Learning Summary
Fractions are best learned through short practical experiences. Begin with sharing real collections and dividing familiar objects before completing picture-based worksheets.
Use this simple routine:
- identify the whole;
- divide it into equal parts;
- count the total number of equal parts;
- select one part;
- name the unit fraction;
- explain how the child knows the parts are equal.
Related Foundation and Year 1 Maths Topics
Children who need additional support can revisit these earlier equal-sharing, grouping and number-partitioning topics.