Equal Parts and Halves

Overview

In this first lesson of the five-lesson unit Fractions: Equal Parts, students build the idea that a fraction describes equal parts of one whole. They investigate halves by folding, drawing, sorting and explaining, while developing precise mathematical language and confidence in justifying their thinking.

Learning intentions

• WALT recognise and make equal parts, especially halves.
• WALT describe fractions using the words whole, half, equal and unequal.
• WALT explain why two parts must be equal to be halves.
• WALT represent one-half using pictures and the notation 1/2.

Success criteria

• I can explain that a whole is divided into equal parts.
• I can identify and make two equal halves.
• I can use the words whole, half, equal and unequal.
• I can explain why unequal pieces are not halves.

Curriculum links

• Mathematics and Statistics — Mathsteasers: rich mathematical thinking and higher-order questions appropriate for deepening understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: challenge connected to classroom mathematics learning.
• Mathematics and Statistics — Additional resources for advanced learners: opportunities to reason, represent, compare and explain mathematical ideas.
• NZ Curriculum Refresh emphasis: students use representations, mathematical language, discussion and justification to make sense of a mathematical idea.

Lesson structure (60 minutes)

1. 0–8 min · Hook and notice. Open with the opening sharing question and show a paper rectangle. Ask, “If two people share this fairly, what must happen?” Fold one rectangle into two matching parts, then show an unequal division. Students turn and talk, then give thumbs-up, sideways or down to show whether each example shows halves.

2. 8–18 min · Build the idea. Use the whole-and-halves examples to define whole, part, equal and unequal. Demonstrate that the dividing line may be vertical, horizontal or diagonal, but the two parts must cover the whole and be the same size. Record the words and introduce the notation 1/2. Students help explain why each demonstration is, or is not, one-half.

3. 18–30 min · Make and draw halves. Give each pair scrap paper and pencils, and distribute the equal-parts investigation sheet. Students fold paper rectangles and other simple shapes to make two equal parts, open them, trace the fold and draw at least two examples. Partners check: “Do the parts cover the whole?” and “Are they equal?” Students label each part 1/2 where appropriate.

4. 30–38 min · Share strategies. Bring the eight students together. Invite pairs to show different folds and drawings, including halves that look different. Record student explanations on the board using the sentence frame, “Each part is one-half of the whole because …” Discuss why a long, thin half can still be equal to a short, wide-looking half when the whole shape is different.

5. 38–52 min · Sort and justify. In two groups of four, students use the shape sketches on the equal-parts investigation sheet to sort examples into whole, halves and not halves. Some sketches should show unequal pieces, parts that do not make the whole, or a shape divided into more than two parts. Students must agree on a reason before placing each example. Confer with each pair, asking, “What is the whole?”, “How many parts are there?” and “How do you know the parts are equal?”

6. 52–60 min · Independent check and reflection. Students independently draw one shape divided into two equal halves on the final section of the equal-parts investigation sheet and complete: “These are halves because …” Invite two students to share. Revisit the success criteria and ask students to show thumbs-up, sideways or down for each one.

Resources

• the Equal Parts and Halves slide deck
• the equal-parts investigation sheet
• Scrap paper for folding
• Pencils and coloured pencils
• One paper rectangle for teacher modelling
• Whiteboard and markers
• A few simple shape sketches
• Optional document camera or visualiser

Assessment

• Listen for students explaining that halves must be equal parts of one complete whole, rather than simply noticing that pieces have the same shape.
• Use thumbs-up, sideways and down during demonstrations to identify misconceptions and respond immediately with another fold or drawing.
• Collect the independently drawn half and explanation from each student. Check that the shape is divided into two parts, both parts belong to the whole, and the student can justify equality.

Differentiation

• Support learners with pre-drawn rectangles and circles, partially marked fold lines, folding alongside an adult, and the sentence frame: “Each part is ___ of the whole because ___.”
• Use familiar sharing contexts such as half a sandwich, apple or piece of toast. Accept oral explanations, pointing, folding and drawing as valid ways to communicate understanding.
• Pair students deliberately so that a confident explainer can model vocabulary without completing the task for a peer. Rehearse whole, part, equal, unequal and half orally before recording.
• Extend advanced learners by asking them to create two different shapes divided into halves and explain how the pieces can look different but still be equal. Ask, “Can you make a half without a straight dividing line?”