Ordering Fractions

Overview

Students will order unit fractions (fractions with numerator 1) on a number line using hands-on tools, then extend to ordering other equivalent/related fractions. The lesson builds understanding that fraction size depends on the size of the “whole” parts.

Learning intentions

• Students will order unit fractions on a number line using reasoning about equal-sized parts.
• Students will explain why one unit fraction is larger than another.
• Students will represent fractions using practical materials (pegs and paper strips/“food”).
• Students will order non-unit fractions using connections to unit fractions and equivalence.

Success criteria

• I can place unit fractions in correct order on a line with correct intervals.
• I can justify my ordering by referring to the number of equal parts and the size of each part.
• I can convert between equivalent representations (for example, using equivalent unit fractions) to help order.
• I can complete an independent practice task showing fractions in order.

Curriculum links

• Number — AC9M7N04: find equivalent representations of rational numbers and represent rational numbers on a number line (ordering fractions by representing them on an appropriate number line).
• Number — AC9M7N04: use fraction equivalence reasoning to compare and order fractions.
• Mathematical reasoning (general capability): justify ordering using models, diagrams and explanations.
• Literacy (general capability): communicate explanations using correct mathematical language (numerator, denominator, unit fraction, interval).

Lesson structure (60 minutes)

1. 0–5 min · Hook (practical reveal). Teacher displays 4 peg cards showing unit fractions: 1/2, 1/3, 1/4, 1/5. Students predict (without placing) which is biggest and which is smallest, then share one reason with a partner.

2. 5–15 min · Mini-teach: unit fractions on a “whole” strip. Teacher shows a paper “whole” strip and models dividing it into equal parts for a chosen denominator (e.g., halves, then fourths). Students build a small fraction strip in pairs for one denominator using pre-cut templates (halves, thirds, quarters, fifths) and hold up the unit part, discussing: “Each piece is 1 equal part; smaller denominator means larger piece.”

3. 15–28 min · Hands-on number line ordering with pegs. Teacher draws a number line from 0 to 1 with tick intervals labelled (as a generic template with placeholders), then models placing 1/2, 1/3, 1/4, 1/5 using fraction strips as “measuring sticks”. Students work at their tables:

• Each group receives a laminated number line (0 to 1) and peg cards for unit fractions.
• Students place pegs for 1/2, 1/3, 1/4, 1/5 in order and check intervals using the physical strips (match the unit piece size to the interval). Teacher moves between groups asking: “How do you know this peg interval matches the unit fraction size?”

4. 28–35 min · Whole-class discussion: compare and explain. Teacher uses two fraction comparisons from students’ placements (e.g., 1/3 vs 1/4). Students explain using the sentence frame: “Because the whole is divided into ___ equal parts, 1/___ is ___ the size of 1/___, so it comes before/after on the line.”

5. 35–48 min · Extend: ordering other fractions using equivalence and unit anchors. Teacher introduces a practical “food” option using paper shapes representing pizzas/circles (no real food required) or safe paper “cookie” cuts. Task: Order these fractions on the same 0–1 line: 2/4, 3/6, 1/3, 1/4. Students:

• Use cutting lines to show that 2/4 equals 1/2, 3/6 equals 1/2 (or similar equivalent links provided on the worksheet).
• Place the fractions using pegs, but justify placements by linking them to unit fractions (e.g., identify the “same size” as a unit fraction you already ordered). Teacher prompts: “Which unit fraction are these fractions equivalent to? How does that help with ordering quickly?”

6. 48–58 min · Independent practice (quiet, hands-on supported). Students complete a worksheet + mini-number-line at their desk:

• Part A: Order unit fractions: 1/2, 1/3, 1/6, 1/4.
• Part B: Order mixed fractions of the form 2/3, 3/4, 4/6, 1/2 (include at least one equivalent pair so students use equivalence reasoning). They must show their work by either pegs on a small desk number line or drawing tick intervals and writing an equivalence statement (e.g., “4/6 is the same size as 2/3”).

7. 58–60 min · Exit ticket (quick check). Students answer one prompt: “Place 1/3 and 1/5 on the line from 0 to 1 and explain which is larger using words.” Teacher collects for formative assessment.

Resources

• Pre-cut fraction strips/templates for 2, 3, 4, 5, 6 equal parts
• Laminated number line cards (0 to 1) with peg-friendly ticks/intervals
• Peg cards or clothes pegs with attached fraction labels
• Paper circles/pizzas divided into equal parts (for equivalent fraction modelling)
• Ordering worksheets (unit fraction ordering + non-unit ordering with equivalence prompts)
• Sentence starters for explanations
• Timer for transitions, teacher flip-chart or board
• Small manipulatives per table (fraction strips, peg cards, paper “foods”)

Assessment

• Formative checks during peg placement: teacher listens for correct reasoning about equal-sized parts and interval matching.
• Use teacher questioning in Steps 3–5 to assess understanding of “denominator as the number of equal parts.”
• Exit ticket in Step 7 to confirm students can order two unit fractions and justify with a brief explanation.

Differentiation

• Support:
• Provide pre-labelled interval templates (e.g., for halves/thirds/fourths/fifths) so students focus on ordering rather than drawing.
• Offer sentence starters and word bank: numerator, denominator, equal parts, smaller, larger, comes before, comes after.
• Allow use of fraction strips at the desk during independent practice.
• Targeted intervention:
• For students who struggle to compare, require them to match each unit fraction to its strip and then place the peg (no skipping to abstract ordering).
• Extension:
• Add one extra challenge fraction (e.g., 2/5) and ask students to place it by relating it to the unit fraction 1/5 (doubling the interval).
• EAL/SEN considerations:
• Keep language consistent: “bigger piece” vs “more smaller parts.” Use visuals and model one full example before group work.