Equal Groups, Equal Parts

Overview

Students find a half or quarter of a set by recognising equal groups and skip-counting patterns, rather than sharing objects one at a time. They connect the meaning of a half as 1 of 2 equal parts with a quarter as 1 of 4 equal parts.

Learning intentions

• WALT identify equal groups in a set.
• WALT find a half or quarter by using groups and patterns.
• WALT explain how halves and quarters are connected.

Success criteria

• I can make 2 or 4 equal groups.
• I can find half by finding 1 of 2 equal groups.
• I can find a quarter by finding 1 of 4 equal groups.
• I can explain my answer using groups or a skip-counting pattern.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking and challenge for advanced learners.
• Mathematics and Statistics — Mathsteasers / Alignment: connecting challenge tasks with relevant mathematical learning.
• Mathematics and Statistics — Mathsteasers: additional resources for advanced learners.
• Te Mātaiaho guidance: a half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts; learners develop the relationship between halves and quarters.

Key vocabulary

Half, quarter, equal groups, equal parts, set, share, groups of 2, groups of 4, skip-count.

Lesson structure (18 minutes)

1. 0–2 min · Hook. Teacher displays 12 counters and asks, “Without dealing them out one at a time, how could we find half of this set?” using the opening hook slide. Students turn and talk, then suggest making two equal groups.

2. 2–6 min · Teacher model. Teacher arranges 12 counters into two rows of 6, explicitly showing that half means 1 of 2 equal groups; then rearranges the same counters into four equal rows of 3 to show that a quarter is 1 of 4 equal groups, supported by the half-and-quarter model slides. Students count in 2s or 4s, identify the equal groups and state: “Half of 12 is 6” and “A quarter of 12 is 3.”

Emphasise: “We are looking for equal groups. We do not need to hand out every counter one at a time.” Ask: “What would happen if one group had more?” and “How many quarters make one whole set?”

3. 6–10 min · Guided practice. Teacher gives each pair 8, 16 or 20 counters and displays the first prompts in the guided-practice slides. Call out “Find half” or “Find a quarter”; support pairs to arrange counters in 2 or 4 equal rows and record the number in one row. Students work with a partner, checking that every group has the same number, then explain their pattern: “I counted 4 groups of 4, so a quarter of 16 is 4.”

4. 10–14 min · Card pattern practice. Teacher gives pairs the skip-counting matching cards and directs them to use the 2s and 4s patterns to check their groups. Students match or order the relevant skip-counting cards, then use the pattern to solve two oral examples, such as half of 18 and a quarter of 20. Reinforce that 18 can be arranged as 2 groups of 9, while 20 can be arranged as 4 groups of 5.

5. 14–17 min · Independent/partner task. Teacher distributes the equal-groups fraction worksheet and models one example without completing the page. Students complete four short tasks: draw equal groups for half of 10, find a quarter of 12, find half of 16, and find a quarter of 20. They write one sentence explaining one answer using “equal groups” or “groups of”.

6. 17–18 min · Plenary and check. Teacher shows the final reflection and exit-question slide and asks students to hold up two fingers for half or four fingers for quarter. Students respond to: “Is 1 of 4 equal groups a half or a quarter? How do you know?” Invite one student to explain the relationship: two quarters make one half.

Resources

• the complete equal-groups slide deck
• the equal-groups fraction worksheet
• the skip-counting matching cards
• Counters, linking cubes or small classroom objects: one set per pair
• Mini-whiteboards and pens
• Pencils and crayons
• Large demonstration counters or magnetic dots
• Prepared sets of 8, 12, 16 and 20 objects

Assessment

• During modelling, ask: “How do you know the groups are equal?” and “Which group shows one quarter?”
• During guided practice, check whether students arrange objects into 2 or 4 equal groups and use skip-counting rather than sharing by ones.
• Collect the worksheet or note responses to the final question. Look for correct answers and an explanation involving equal groups or patterns.

Differentiation

• Support learners with 8 or 12 objects, pre-drawn circles or rows, and sentence frames: “I made ___ equal groups” and “One group is ___, so ___ of ___ is ___.”
• Use concrete objects and clear visual rows before moving to drawings or numerals. Pair learners carefully and allow oral explanations, gestures and pointing.
• For learners needing additional support, focus first on making two equal groups, then introduce four groups; check each group together before asking for the answer.
• Extend confident learners with: “If half of a set is 7, how many are in the whole set?” and “If a quarter is 5, what is half?” Ask them to justify the answers using the relationship between halves and quarters.