Mathematical Explorers: Building Foundations · 2nd Class

Active learning ideas

Finding Halves and Quarters of Numbers

Active learning works well for halves and quarters because students need to see, touch, and manipulate quantities to truly understand equal sharing. Partitioning numbers into equal groups requires concrete experiences before moving to abstract calculations, and these activities build that foundation through movement, discussion, and hands-on tasks.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Geometry and Trigonometry - G.3.1

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Think-Pair-Share
• 25 min · Pairs

Manipulative Sharing: Counter Division

Give pairs 20 counters and number cards up to 20. Students share into two equal groups to find halves, then halve one group again for quarters. Record results on charts and compare patterns across numbers. End with a share-out of strategies.

How do you find half of an even number by sharing into two equal groups?

Facilitation Tip

During Counter Division, circulate with pre-prepared counters so every pair gets an even number first, then introduce odd totals to prompt questions about remainders.

What to look for

Present students with number cards (e.g., 8, 14, 20). Ask them to write down the number that represents half of each number. Then, ask them to write down the number that represents a quarter of the same numbers, showing their working if possible.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 02

• Think-Pair-Share
• 35 min · Whole Class

Halving Relay: Whole Class Race

Divide class into teams. Call an even number up to 20; teams race to show half using personal counters or drawings on mini-whiteboards. For quarters, call for second halving. Correct as a group and note successful methods.

How can you find a quarter of a number by halving and halving again?

Facilitation Tip

For Halving Relay, assign clear roles like 'counter holder' and 'recorder' so all students participate and stay focused on halving strategies.

What to look for

Give each student a small card. Ask them to draw 12 counters, then partition them into two equal groups to show half of 12. On the back, they should write the answer to 'half of 12' and 'a quarter of 12'.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• Think-Pair-Share
• 20 min · Pairs

Quarter Fold: Paper Partitioning

Students fold square papers into halves, then quarters, labeling each part with numbers like 1/4 of 16=4. Shade sections and connect to sharing problems. Pairs check each other's work against number facts.

Can you find half and one quarter of numbers up to 20?

Facilitation Tip

In Quarter Fold, demonstrate folding slowly and labeling each part with both the fraction and the numerical value to reinforce the connection between visual and numeric understanding.

What to look for

Ask students: 'Imagine you have 16 sweets to share equally between two friends. How many sweets does each friend get? Now, imagine you only have 8 sweets and want to give a quarter of them to one friend. How many sweets does that friend receive? Explain how you figured it out.'

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 04

• Think-Pair-Share
• 30 min · Small Groups

Sharing Shop: Role-Play Scenarios

Set up small group shops with toy items totaling multiples of 4 up to 20. Customers request halves or quarters; sellers divide and give change. Rotate roles and discuss fair sharing.

How do you find half of an even number by sharing into two equal groups?

Facilitation Tip

During Sharing Shop, provide labeled price tags and role cards so students practice asking for specific fractions, like 'Can I have a quarter of your 12 pencils?'

What to look for

Present students with number cards (e.g., 8, 14, 20). Ask them to write down the number that represents half of each number. Then, ask them to write down the number that represents a quarter of the same numbers, showing their working if possible.

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Start with concrete tools like counters and paper shapes to build understanding before introducing symbols. Model language like 'share equally' and 'split into two groups', and avoid rushing to written methods too soon. Encourage students to explain their thinking out loud, as verbalizing steps helps solidify the process. Research shows that repeated halving builds stronger fraction sense than direct division into four, so emphasize the sequence of halving twice.

Students will confidently partition numbers up to 20 into two or four equal parts using counters, paper folds, or role-play. They will explain their steps aloud, use precise language like 'half' and 'quarter', and connect visual representations to numerical answers.

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Watch Out for These Misconceptions

• During Counter Division, watch for students assuming all numbers can be split evenly into halves.

  Provide sets of odd numbers like 15 counters and ask students to partition them, then discuss why some numbers leave a remainder and how to describe this in words such as 'half of 15 is 7 with 1 left over'.

• During Quarter Fold, watch for students dividing the total by four directly instead of halving twice.

  Ask students to fold their paper in half, unfold to label, then fold in half again before unfolding to label quarters, reinforcing the repeated halving process with clear visual steps.

• During Sharing Shop, watch for students thinking quarters only apply to shapes, not numbers.

  Provide items labeled with quantities (e.g., '8 blocks') and ask students to share a quarter of the blocks, then write the numerical answer on a sticky note to link the visual sharing to the number fact.

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Methods used in this brief

• Think-Pair-Share