Fraction Ordering

Overview

Today students extend their understanding of fractions by comparing and ordering them using reasoning about like and unlike denominators. The lesson builds toward later work with rational numbers by strengthening fraction equivalence and unit-fraction thinking.

Learning intentions

• Students will be able to compare fractions with the same numerator or the same denominator by reasoning about the size of the parts.
• Students will be able to compare fractions with different numerators and denominators by using benchmarks or equivalent fractions.
• Students will be able to order a set of fractions from least to greatest or greatest to least with justification.
• Students will be able to explain their reasoning using fraction models, number lines, or common denominators.

Success criteria

• I can compare fractions that share the same numerator or the same denominator and explain why the larger part is larger.
• I can compare fractions with different denominators using a benchmark fraction (like 1/2) or by making equivalent fractions.
• I can order at least 4 given fractions correctly and justify the order with a model or number line.
• I can check my work by using equivalences (same whole) and correct reasoning.

Curriculum links

• Ratios and proportional relationships: unit-rate ideas support later fraction reasoning across contexts (Grade 7 RP).
• The number system: multiplication/division of rational numbers connects to operating with fractions (Grade 7 NS).
• Number and operations with fractions: comparing fractions with the same numerator or denominator using visual models (Grade 3 NF progression).
• Number and operations with fractions: comparing fractions with different numerators and denominators using common denominators/numerators or benchmarks (Grade 4 NF progression).

Lesson structure (45 minutes)

1. 0–5 min · Launch (context + prediction). Teacher displays four fractions (e.g., 2/3, 3/4, 5/6, 7/8) and asks students to predict which is largest and smallest without computing a decimal; students do a quick think-pair-share and give one reason.

2. 5–15 min · Mini-lesson: comparison strategies. Teacher models two cases on the board:

• Case A (same numerator or same denominator): show how fixing one part (e.g., same denominator means same-sized slices) changes the size.
• Case B (different numerators and denominators): show two methods: using a benchmark (1/2, 3/4) and finding equivalent fractions (common denominators). Students take guided notes in a three-step “Compare → Model/Benchmark → Explain” template.

3. 15–25 min · Guided practice: comparing fractions. Teacher gives 6 comparison prompts in pairs (each pair shares a strategy tag: “benchmark” or “common denominator”). Students solve on whiteboards, then hold up answers; teacher selects two solutions to discuss how the reasoning matches the model.

4. 25–35 min · Practice: ordering fractions (least to greatest). Teacher posts 3 sets, each with 4 fractions (e.g., Set 1: 1/2, 2/5, 3/8, 4/9). Students work in small groups to order each set, using either fraction strips, area models, or number lines; groups must include one justification sentence for each set.

5. 35–42 min · Whole-class share + misconception check. Teacher calls on groups to present one ordered set; class compares two different reasoning approaches and resolves conflicts. Teacher emphasizes: comparisons are valid only when fractions refer to the same whole, and students must use consistent partitioning or equivalent fractions.

6. 42–45 min · Exit ticket (quick assessment). Students complete 3 tasks independently:

• Compare: 3/5 vs 4/7 (choose benchmark or convert to compare).
• Compare with same denominator: 2/9 vs 7/9.
• Order: 1/3, 5/6, 2/3 from least to greatest with brief justification.

Resources

• Fraction strips or paper folding templates (1/2 to sixths/eighths and tenths if available)
• Area/rectangle model sheets (same-whole visual)
• Number line handouts (0 to 1 partitioned into common denominators)
• Whiteboards and markers
• Student “Compare → Model/Benchmark → Explain” note sheet
• Exit tickets (three problems, same format as practiced prompts)

Assessment

• Formative checks during guided practice: whiteboard thumbs-up/side-by-side comparison of strategies
• Teacher monitors group ordering work using a quick rubric: correct order + justification tied to model/benchmark
• Exit ticket: correctness of comparisons and ordering plus a brief explanation statement

Differentiation

• Support: provide sentence starters (“I used a benchmark of 1/2, so…,” “Because the denominators are the same,…” “These fractions refer to the same whole by…”) and a partially completed number line for one of the ordering sets.
• Support for visual learners: allow fraction strips/area models as the default tool; require students to mark the fraction locations before writing the final order.
• Extension: include one “trick” set where students must choose the correct method (e.g., comparing fractions that are close to the benchmark but require careful equivalence), and ask for an alternative strategy explanation.
• EAL/SEN: reduce the number of items on the exit ticket to one comparison plus one ordering if needed, while maintaining the justification requirement; keep all fraction visuals consistent to reduce language load.