Half With Rods

Overview

Ākonga explore one half as an equal sharing of a whole using hands-on Cuisenaire rods (rākau Ātaarangi). In groups of 3–4, they find and record different ways to make half of the orange, brown, dark green and pink rods, then investigate whether odd-length rods can be halved and justify their conclusions.

Learning intentions

• WALT use Cuisenaire rods to show one half of a whole.
• WALT find more than one way to represent the same half.
• WALT explain why two parts are equal.
• WALT record mathematical thinking with pictures, words and equations.

Success criteria

• I can identify the whole rod and find its half by making two equal lengths.
• I can show different combinations of rods that make half of a whole.
• I can record my combinations clearly on the worksheet.
• I can prove whether an odd-length rod can be divided into two equal whole-rod lengths.

Curriculum links

• Mathematics and Statistics — Number: part–whole relationships, equal sharing and fractions.
• Mathematics and Statistics — Number: use additive strategies and combinations to make a given quantity.
• Mathematics and Statistics — mathematical reasoning and communication through diagrams, materials and equations.
• Mathsteasers: challenging questions that deepen understanding for advanced learners and encourage more than one possible solution.

Lesson structure (60 minutes)

1. 0–7 min · Notice and wonder. Teacher displays the orange 10 rod and asks, “What would half of this rod look like?” Open with the hook and learning intention slides. Students silently estimate, discuss with a partner, and explain what “half” must mean. Emphasise that the two parts must be equal and together make the whole.

2. 7–15 min · Explicit teaching. Teacher models placing two equal 5 rods along the orange 10 rod, then shows that half can also be represented by combinations such as 4 + 1 or 3 + 2. Record each as a drawing and equation: 10 ÷ 2 = 5, 4 + 1 = 5, and 3 + 2 = 5. Explain that the equal sign means both sides have the same value. Students build, check and describe one example with a partner. Refer to the modelling and vocabulary slides.

3. 15–30 min · Group investigation 1. Teacher places students in mixed groups of 3–4 and assigns roles: builder, recorder, checker and reporter. Distribute the Cuisenaire half investigation sheet and rods. Students solve in order: half of the orange 10 rod, the brown 8 rod, the dark green 6 rod and the pink 4 rod. For each, they must find as many different combinations as possible, place them against the whole, draw the coloured rods on the matching picture, and record an equation. Teacher prompts: “How do you know it is half?” and “How can you be systematic so you do not miss a combination?” Use the group task instructions and prompts.

4. 30–43 min · Odd-number challenge. Teacher introduces the 9, 7, 5 and 3 rods and asks, “Can you show half using whole Cuisenaire rods?” Students test each rod physically and record either a construction or a proof that it cannot be made exactly with whole rods. Encourage them to notice that an odd number cannot be split into two equal whole-number lengths. Students may show a fractional half with a strip or explain that it lies between two whole-rod lengths, but must distinguish this from an exact whole-rod construction. Capture useful examples on the board. Refer to the odd-number challenge slide.

5. 43–52 min · Share, compare and feedback. Teacher selects groups to present one even-rod combination and one odd-rod conclusion. Class checks each response by matching both parts to the whole and gives feedback using: “I agree because…” or “I would check…”. Students add a star to their clearest representation and improve one explanation on their sheet. Photograph strong group work for upload as evidence in Hero, with student names or group members recorded.

6. 52–60 min · Plenary and exit check. Teacher asks students to complete the final prompt on the Cuisenaire half investigation sheet: “Half of 8 is ____. Show two different ways and explain how you know.” Students hold up their work for a quick scan, then share one new idea. Teacher collects sheets and notes who can model, record and justify one half.

Resources

• Cuisenaire rods (one substantial class set, with at least one set per group)
• the one-half exploration slide deck
• the Cuisenaire half investigation sheet
• Pencils, coloured pencils and rulers
• Large demonstration rods or magnetic rods
• Whiteboard and pens
• Camera or tablet for Hero evidence
• Group role cards or labels
• Optional number-line strips for students needing additional visual support

Assessment

• Observe whether students make two equal parts rather than simply selecting a smaller rod. Question groups about how they know their construction is half.
• Check worksheets for accurate drawings, equations, multiple combinations and a justified conclusion about odd-number rods.
• Use the exit prompt to identify students needing further experience with equal sharing, and upload selected work and teacher observations to Hero as evidence of curriculum progress.

Differentiation

• Support: begin with the 4 and 6 rods; provide a half marker, pre-drawn alignment guides and sentence starters such as “Half of ___ is ___ because ___ and ___ are equal.” Allow students to keep rods in place while drawing.
• For dyslexia-friendly access, use a clear sans-serif font, large print, minimal text, high-contrast colours, coloured rod images and read instructions aloud. Pair oral explanation with drawing and manipulatives.
• EAL learners: pre-teach “whole”, “half”, “equal”, “part”, “same” and “prove”; use gestures, modelled language and partner rehearsal before recording.
• Extension: students investigate whether there are other ways to make half of 10 using three or more rods, organise their solutions systematically, or choose a different whole rod and write a rule about when an exact half can be made with whole rods.