Introduction to Fractions: Halves of Quantities

Active learning helps young students grasp the abstract concept of halves by turning it into concrete, hands-on experiences. When children physically share objects, fold paper, or divide real food, they connect the idea of equal shares to their own actions, making the learning more meaningful and memorable.

• Year 1
• Mathematics
• 4 activities
• 20 min–35 min

Learning Objectives

1. Identify the quantity that represents one half of a given even number of objects.
2. Demonstrate how to partition a group of objects into two equal halves.
3. Explain why equal sharing is necessary to find a half.
4. Compare the result of sharing an even number of objects into two equal groups versus an odd number.

Experiential Learning

⏱ 25 min·Pairs

Sharing Circle: Counter Halves

Place 10 counters in the centre. Pairs take turns sharing them equally into two bowls, checking by counting each side. Discuss if they match and record with drawings. Extend to predict halves of 8 or 12.

Prepare & details

Explain how to find half of a group of 10 counters.

Facilitation Tip: During Sharing Circle: Counter Halves, circulate and ask students to explain why their two groups are the same size to reinforce verbal reasoning alongside physical action.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Experiential Learning

⏱ 30 min·Pairs

Fruit Fair Share: Real Food Division

Provide pairs of items like 6 grapes or 4 strawberries. Students wash, then halve by pulling apart or cutting safely with plastic knives. Compare shares visually and taste to confirm equality.

Prepare & details

Predict what happens if you try to find half of an odd number of objects.

Facilitation Tip: During Fruit Fair Share: Real Food Division, encourage students to describe how they divided the fruit so each person gets the same amount, linking language to the activity.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Experiential Learning

⏱ 20 min·Whole Class

Paper Partition: Folding Halves

Give A4 paper rectangles. Students fold in half multiple ways, crease, and cut shapes to make two identical pieces. Whole class shares examples on the board, noting equal areas.

Prepare & details

Justify why sharing equally is important when finding a half.

Facilitation Tip: During Paper Partition: Folding Halves, ask students to hold up their folded paper to show symmetry and discuss how the fold creates two equal parts.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Experiential Learning

⏱ 35 min·Small Groups

Odd One Out: Group Challenge

Distribute odd numbers of objects like 9 beads per small group. Students attempt halving, discuss the leftover, and pair up remainders across groups to make even totals.

Prepare & details

Explain how to find half of a group of 10 counters.

Facilitation Tip: During Odd One Out: Group Challenge, prompt groups to explain their choices and how they confirmed each share was fair.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Teaching This Topic

Teachers should start with concrete materials like counters or real food because young children learn best by doing. Avoid rushing to abstract symbols; let students verbalize their understanding before connecting it to written fractions. Research shows that guided peer discussion during activities strengthens comprehension, so structure time for students to explain their thinking to each other.

What to Expect

Students will confidently partition quantities into two equal groups and explain why the groups are fair. They will use words like 'half' and 'equal share' when describing their actions and results, showing they understand the purpose of equal division in everyday life.

Watch Out for These Misconceptions

Common Misconception

During Sharing Circle: Counter Halves, watch for students who stop at 5 counters for one person without checking the other group or who cannot explain why 5 and 5 are equal.

What to Teach Instead

Ask the student to count each group aloud and compare the totals. Encourage them to move counters one by one until both groups match, reinforcing the idea of equal shares.

Common Misconception

During Paper Partition: Folding Halves, watch for students who fold unevenly or believe any fold creates two halves because the paper looks split in half visually.

What to Teach Instead

Provide a ruler to measure the fold or a small mirror to check symmetry. Have the student refold until the edges align perfectly, then reopen the paper to see the two equal parts.

Common Misconception

During Odd One Out: Group Challenge, watch for students who insist that half always means one exact share, even when the total is odd and cannot be split equally.

What to Teach Instead

Guide the group to physically divide the odd number of items and discuss what happens to the leftover piece. Ask them to explain why equal halves aren’t possible and how they might adjust the share.

Assessment Ideas

Quick Check

After Sharing Circle: Counter Halves, give each student 8 counters and ask them to show how to find half. Observe if they separate the counters into two equal groups of 4 and can explain why each group is a half.

Exit Ticket

After Fruit Fair Share: Real Food Division, provide a worksheet showing 10 apples. Ask students to draw a line to divide the apples into two equal halves and write how many apples are in each half.

Discussion Prompt

During Odd One Out: Group Challenge, present 7 toy cars and ask: 'Can we share these cars equally between two people so each person gets half? Why or why not?' Listen for explanations about odd numbers and the idea of unequal shares or remainders.

Extensions & Scaffolding

• Challenge: Provide groups of 12 or 14 counters and ask them to explore halves, then present their methods to the class.
• Scaffolding: Give students with fine motor challenges pre-divided paper plates or counters pre-grouped into pairs.
• Deeper exploration: Introduce the term 'remainder' when working with odd numbers, connecting it to real-life scenarios like sharing pencils or toys.

Key Vocabulary

Half	One of two equal parts that a whole is divided into. For a quantity, it means splitting it into two groups with the same number of items.
Share Equally	To divide objects or a quantity so that each person or group receives the same amount. This is essential for finding a half.
Group	A collection of objects or items. We find half of a group by dividing it into two equal smaller groups.
Whole	The entire quantity or group of objects before it is divided into halves.