Comparing And Ordering Fractions

Overview

Lesson 3 of 15 in Number Connections: Fractions, Decimals, Percentages. Students compare and order fractions using benchmark fractions, number lines and common denominators, explaining their reasoning with models and mathematical language.

Learning intentions

• WALT compare fractions using benchmarks such as 0, ½ and 1.
• WALT use number lines and common denominators to compare and order fractions.
• WALT use <, > and = accurately.
• WALT justify a comparison with a model or mathematical explanation.

Success criteria

• I can place halves, quarters, tenths and hundredths on a number line.
• I can compare two fractions and choose <, > or =.
• I can order a set of fractions from least to greatest.
• I can explain my strategy using a model, benchmark or common denominator.

Curriculum links

• Number: recognise, represent, compare and order fractions, including fractions with related and unlike denominators.
• Number: identify and use equivalent fractions to support comparison.
• Mathematical practices: use representations, symbols and precise mathematical language to communicate reasoning.
• Problem solving and reasoning: select a strategy, justify conclusions and consider more than one method.

Lesson structure (45 minutes)

1. 0–5 minutes – Hook and prior knowledge Open with the fraction comparison hook and display: “Which is greater: 3/10 or 1/4? How could you prove it?” Students think independently, then share with a partner. Invite several estimates and record strategies without confirming the answer yet.

2. 5–13 minutes – Connect to benchmarks Use the benchmark fraction examples to revisit 0, ½ and 1. Model placing 1/2, 1/4, 3/4, 2/10 and 8/10 on a number line. Emphasise that fractions closer to 1 are greater, and that the denominator names the equal-sized parts. Students rehearse the sentence stem: “I know ___ is greater because it is closer to ___.”

3. 13–21 minutes – Model two strategies Demonstrate comparing 3/4 and 5/8 using a fraction wall and number line. Use the fraction wall and strip cards for a visual model, then show that 3/4 = 6/8, so 6/8 > 5/8. Next compare 7/10 and 68/100 by converting 7/10 to 70/100. Stress that equivalent fractions must represent the same amount.

4. 21–25 minutes – Guided class practice Display the guided questions in the worked examples and discussion prompts: 2/5? 1/2, 9/10? 85/100, and 3/4? 6/8. Students show <, > or = on mini-whiteboards, then justify one answer using a benchmark or common denominator. Address misconceptions, especially “larger denominator means larger fraction”.

5. 25–38 minutes – Differentiated MNP practice Distribute the differentiated fraction comparison worksheet. Students work independently first, then explain selected answers to a partner. Support learners use labelled number lines, benchmark cards and paired rehearsal; work with a small teacher group on halves, quarters and tenths. Core tasks compare and order familiar fractions. Extension tasks include unlike denominators and require students to defend two different strategies.

6. 38–43 minutes – Reasoning share Return to the strategy share prompts. Select two students with different methods for the same comparison, such as 4/5 and 75/100. Ask: “Which representation makes the comparison clearest? Are both strategies valid?” Record precise vocabulary including equivalent, numerator, denominator, benchmark and common denominator.

7. 43–45 minutes – Exit check and reflection Show the plenary and exit question: order 1/2, 45/100 and 3/10 from least to greatest, and explain one comparison. Students submit their response or share it as they leave. Revisit the success criteria and identify which strategy helped most.

Resources

• the complete lesson slide deck
• the differentiated fraction comparison worksheet
• the fraction wall and strip cards
• Mini-whiteboards and pens
• Large floor or board number line
• Fraction benchmark cards: 0, ½ and 1
• Rulers, pencils and highlighters
• Prepared small-group number lines

Assessment

• Listen for accurate use of <, > and = during whiteboard responses and partner explanations.
• Check worksheet representations and explanations, not just final answers.
• Use the exit response to identify students needing further support with benchmarks, equivalent fractions or denominator reasoning.

Differentiation

• Support: provide labelled number lines, benchmark cards and fraction strips; begin with halves, quarters and tenths before introducing hundredths.
• Language and learning support: use visuals, repeated sentence stems and paired rehearsal; read task instructions aloud and reduce the number of questions while retaining the reasoning demand.
• Core: compare and order fractions with denominators of 2, 4, 5, 10, 20 and 100 using a model or written explanation.
• Extension: order fractions with unlike denominators, including examples greater than one half, and defend the answer using both a number line and equivalent fractions.