Fraction Building

Overview

Today students build a whole number from a given fractional part, then use equivalence to reason about addition and subtraction of fractions. They also compare and order common fractions with related denominators, using Polypad as a visual and interactive tool for the whole class.

Learning intentions

• Students will recognise that fractions can represent division of a whole into equal parts.
• Students will compare and order common fractions (with denominators such as 2, 3, 4, 5, 6, 8, 10) using benchmarks and equivalence.
• Students will find the whole number when a fraction of it is given (halves, quarters, fifths, tenths).
• Students will use fraction equivalence to add and subtract fractional quantities.

Success criteria

• I can explain what the numerator and denominator tell me about equal parts.
• I can compare fractions with related denominators and justify my ordering.
• I can find the missing whole when I know a fractional part.
• I can use equivalent fractions to solve addition/subtraction problems.

Curriculum links

• MA3-RQF-02 — representing quantity fractions B (building up to the whole from a given fractional part; equivalence for addition/subtraction; division meaning of fractions; fractional quantities of wholes).
• MA3-RQF-01 — comparing and ordering fractions with denominators of 2, 3, 4, 5, 6, 8, 10.
• Mathematics reasoning and problem-solving: students communicate strategies, justify comparisons, and select representations to model fraction meaning.

Lesson structure (60 minutes)

1. 0–5 min · Hook (Polypad visual prompt). Teacher displays a “fraction of a whole” situation on the introduction slides (e.g., “3/5 of my class are wearing red—how many students altogether?”) and asks: “How can we use the fraction to find the whole?” Students turn-and-talk with a partner, then share one idea.

2. 5–15 min · Direct teach (fraction as division + building the whole). Teacher uses the introduction slides to model: a rectangle split into equal parts, showing “fraction as division” (denominator = number of equal parts; numerator = number of parts). Then teacher demonstrates two examples:

• If 1/2 of 24 is given, how to find the whole.
• If 3/5 of a number is given as 18 parts total, how to find the whole (show “each fifth” and scale up). Students copy one worked example strategy into notes (steps, not full sentences). Teacher checks understanding with quick thumbs (confident/unsure).

3. 15–27 min · Guided practice (finding wholes from fractional parts). Teacher puts a short set on the introduction slides: 3 problems, increasing complexity, including denominators 2, 4, 5, and 10. Students work individually first (2 minutes), then in pairs to compare methods (5 minutes). Teacher circulates and prompts: “What is one ‘part’? How did you get from the part to the whole?” At 27 minutes, teacher collects answers using Polypad annotations: students are called to the board to highlight the “one part” and the “whole” on the fraction model from the introduction slides.

4. 27–42 min · Polypad rotation: compare and order + equivalence reasoning. Teacher explains task: “Use Polypad to place fractions in order and justify using equivalence.” On the introduction slides, present a Polypad board with fraction strips (e.g., 2/3, 4/6, 3/4, 6/8, 1/2) and sentence frames.

• Students rotate through Polypad (teacher-led batches due to no prior use): 3 groups of 10 at a time.
• Each group must: (a) order 4–5 fractions, (b) show one equivalence connection (e.g., 4/6 = 2/3), and (c) add one justification statement on Polypad. Teacher uses the introduction slides to keep prompts visible and revisits the meaning of equivalence: “Same size of shaded amount, different denominators.”

5. 42–52 min · Independent task (worksheet consolidates). Distribute the whole-building and ordering worksheet. Students complete:

• 2 “find the whole” fraction-of-a-whole questions (focus on halves/quarters/fifths/tenths)
• 2 comparison/ordering questions with related denominators
• 1 mixed reasoning question using equivalence to add/subtract (e.g., “If 3/10 is shaded, what is shaded when you add 2/10?”) Teacher gives 3-minute mid-check: students underline the “one part” they calculated.

6. 52–60 min · Plenary (exit check with Polypad). Teacher projects the final problem from the introduction slides and asks: “What’s the whole? What is one part? Which fractions are equivalent and why?” Students answer in quick-write (1–2 sentences) or via Polypad multiple-choice/drag ordering if available, then teacher reviews 3 responses.

Resources

• the introduction slides (hook scenarios, modelling division meaning, worked examples, Polypad prompts, plenary)
• the whole-building and ordering worksheet (1 page: find whole + compare/order + equivalence reasoning)
• Polypad-enabled board set-up for fractions (shaded strips/circle models; annotation/drag features)
• Fraction models or paper strips (backup if Polypad glitches)
• Coloured pencils/highlighters for “one part” marking
• Timer for group rotations
• Accessibility supports: large-print fraction strips, high-contrast versions, and screen magnification option

Assessment

• Formative during guided practice: teacher checks “one part” reasoning and models shown on Polypad.
• Worksheet-1: evaluates ability to (1) build the whole from a fractional part and (2) justify ordering via equivalence.
• Plenary responses: quick written explanation of “part to whole” and one equivalence link.

Differentiation

• Visual impairment (inclusive access):
• Provide a high-contrast, large-print version of key fraction models on the whole-building and ordering worksheet and on printed fraction strips.
• Seat the student where screen glare/movement is minimal; allow use of device magnification settings for Polypad and ensure buttons/handles are visible.
• Use tactile/physical fraction strips (paper/foam) alongside Polypad so the student can match “shaded amount” with “equal parts”.
• Offer audio read-aloud of Polypad instructions and sentence frames; teacher repeats key steps verbally before each rotation.
• When annotating on Polypad, allow the student to contribute by selecting from a small set of labelled options (e.g., “This is 1/5 of the whole”) rather than freehand drawing.
• Support for all learners:
• Sentence starters on the whole-building and ordering worksheet: “One part is… so the whole is…”
• Provide a worked example “anchor” on the board (from the introduction slides) showing part-to-whole scaling.
• Extension:
• Challenge question on the last worksheet item: find the whole when the given fraction includes tenths (e.g., 7/10 of a number is 35) and explain using equivalence.
• EAL/SEN:
• Pre-teach the wording “equal parts”, “denominator”, “numerator”, “equivalent”, and “whole” using brief examples displayed throughout the introduction slides.