Fractions on Number Lines

Overview

In this lesson, students compare and order common fractions (halves, thirds and quarters) by representing them on the same number line. Students justify their ordering using equivalence, fraction position, and benchmarks.

Learning intentions

Students will:

• represent halves, thirds and quarters on a number line
• compare fractions by using their relative position on the same number line
• order mixed sets of fractions and explain their reasoning clearly
• use equivalence to justify why one fraction is greater than another

Success criteria

Students can:

• place fractions accurately on a shared number line and explain where they come from
• compare pairs of fractions (including halves vs quarters; thirds vs quarters where relevant) using number line evidence
• order at least 4 fractions from least to greatest with a written justification
• use words like “because”, “equivalent”, “same size parts”, and “benchmark (half/quarter/third)” in explanations

Curriculum links

• Number — apply knowledge of equivalence to compare, order and represent common fractions including halves, thirds and quarters on the same number line and justify their order
• Number — represent fractions on a shared number line, paying attention to their relative position and using it to explain relationships between denominators

Lesson structure (60 minutes)

1. 0–7 min · Hook (fraction benchmarks). Teacher displays three fraction cards: 1/2, 1/3, 1/4, and a blank number line from 0 to 1. Students discuss in pairs where each card “should” go using benchmarks (half/quarter/third). Teacher collects quick reasons.

2. 7–18 min · Direct teach (one number line, multiple denominators). Teacher models drawing one number line from 0 to 1, first partitioned into quarters (0, 1/4, 1/2, 3/4, 1). Teacher then shows how thirds land relative to 1/2 by estimating using equivalence: 1/3 is a bit less than 1/2, because thirds don’t reach 1/2 at the same point. Students watch, then on mini-whiteboards show rough positions for 1/3 compared to 1/2.

3. 18–30 min · Guided practice (equivalence moves). Teacher introduces “equivalence stepping” using overlays or fraction strips:

• Show that 1/2 = 2/4 by matching two quarter parts to one half part.
• Show that 2/3 = 4/6 (if sixths are used as a bridge) to support ordering, but keep the final cards limited to halves, thirds, quarters. Students work in groups of 4 with fraction cards and strips to place these onto a number line on paper: 1/4, 2/4, 3/4, 1/2, 1/3, 2/3 (teacher provides the exact set for the group). Each group writes a one-sentence justification for the first two placements they made.

4. 30–43 min · Partner task (order the sets). Teacher distributes three order-challenge strips (each has 4–5 fraction cards). Students must:

• order from least to greatest on the same drawn number line
• underline a comparison statement using “because” Example stems on the worksheet: “_____ is greater than _____ because …” and “They are equal because …” Teacher circulates, prompting students to refer to relative position and equivalence (e.g., “How do you know that card is at the same point?”).

5. 43–52 min · Whole-class discussion (proof by position). Teacher selects 2–3 groups with different strategies (number line-only vs equivalence-first). Students explain their ordering to the class. Teacher checks misconceptions by asking:

• “What benchmark did you use?”
• “Where do you see the fraction sitting on the number line?”
• “What equivalent fraction helped you?”

6. 52–60 min · Exit ticket (quick assessment). Students complete an exit ticket:

• Part A: Place 2 fractions (e.g., 3/4 and 1/2) on a provided 0–1 number line with quarter marks.
• Part B: Write one justification comparing 1/3 and 1/2 (e.g., “____ is greater because ____.”) using position or equivalence language.

Resources

• Fraction strips/overlays showing quarters and halves (paper or plastic)
• Number line templates from 0 to 1 (with quarter marks for some tasks)
• Fraction card set: halves (1/2, 1), thirds (1/3, 2/3, optionally 1), quarters (1/4, 2/4, 3/4)
• Mini-whiteboards and markers
• Group recording sheets with number line and justification sentence frames
• Exit ticket slips and a teacher checklist for misconceptions
• Optional: digital fraction tools or interactive whiteboard number line (no required links)

Assessment

• Formative: teacher observations during group work (accurate placement, use of benchmarks, use of equivalence language)
• Formative: check mini-whiteboard responses in the guided teach segment (especially 1/3 vs 1/2)
• Summative (for the lesson): exit ticket accuracy and quality of justification (must reference number line position or equivalence)

Differentiation

• Support: provide sentence starters and a partially partitioned number line (quarter marks) for students who need structure; use fraction strips with colour-coding for halves and quarters; allow extra time for placement before writing.
• Support for reasoning: give a checklist prompt: “I used a benchmark / I matched equivalent parts / My fractions are in the right order because…”
• Extension: include one extra card per group (e.g., 5/4 or mixed fraction representation as a challenge) only if the main set is mastered; ask students to compare two fractions in different denominators and explain the equivalence strategy they chose.
• EAL/SEN: visual models (strips/overlays), keep vocabulary consistent (“quarter”, “half”, “third”, “equal parts”, “greater than”, “less than”, “equivalent”); offer an option to explain reasoning orally to a teacher or partner before writing.