Locate, Compare and Order

Overview

In this second lesson of Equivalent Fractions in Action, students use fraction walls and number lines to locate, compare and order fractions. They connect equivalent fractions to equal lengths and use benchmarks such as 0, 1/2 and 1 to justify their thinking.

Learning intentions

• WALT locate unit and related fractions on open and labelled number lines.
• WALT compare fractions using models, equivalence and benchmark fractions.
• WALT order a set of fractions and explain our reasoning clearly.
• WALT listen to and respond to a partner’s mathematical explanation.

Success criteria

• I can locate a fraction on a number line.
• I can compare fractions using a model, equivalent fractions or benchmark fractions.
• I can order fractions from least to greatest and explain my reasoning.
• I can make a claim, show a model and explain how my model proves my claim.

Curriculum links

• Partitioned fractions — represent and compare halves, quarters, thirds and fifths, including related fractions formed by halving, as lengths on a number line.
• Partitioned fractions — model equivalent fractions and represent fractional quantities equal to and greater than one.
• Representing numbers using place value — make connections between fractions and decimal notation where appropriate.
• Mathematical reasoning — communicate and justify strategies using representations, mathematical language and clear explanations.

Lesson structure (60 minutes)

1. 0–7 min · Revisit equivalence. Teacher opens the hook and equivalence slides with the question, “Which is greater: 1/2 or 4/8, and how could you prove it?” and briefly revisits that equivalent fractions name the same length. Students complete a quick partner card sort using the Equivalent Fractions Dominoes, matching visual and numerical representations, then explain one match using the sentence frame: “These fractions are equivalent because…”.

2. 7–17 min · Locate fractions. Teacher models a number line from 0 to 1, first partitioning it into equal intervals and then placing 1/2, 1/4, 3/4 and related fractions such as 2/8 and 6/8; emphasise that the denominator tells the number of equal intervals and the numerator tells how many intervals to count. Students use the Fraction Wall and Strip Cards to build and check fractions, then place selected fractions on open and labelled number lines shown in the number-line modelling slides.

3. 17–27 min · Compare fractions. Teacher demonstrates <, > and = using fraction strips and number-line distance, beginning with like denominators and familiar benchmarks before comparing examples such as 3/8 and 1/2 or 2/3 and 4/6. Students complete the first section of the fraction comparison and ordering worksheet, drawing or referring to a model and recording a comparison sentence for each example.

4. 27–42 min · Collaborative investigation. Teacher places groups of four and displays the investigation instructions in the group investigation slides. Each group receives a set of fractions, including halves, quarters, thirds, fifths, sixths, eighths and tenths, and orders them from least to greatest on a large number line. Students must agree on the order, identify any equivalent fractions and prepare one “claim, model, explanation” to defend a decision. Encourage roles such as reader, organiser, model builder and reporter.

5. 42–52 min · Peer explanation and revision. Teacher pairs groups to compare orders and conferences with groups, asking, “What is your benchmark?”, “How does your model prove this?” and “Could you use an equivalent fraction?” Students present one comparison to their partner group, give feedback using the prompts “Your claim is…” and “Your model shows…”, then revise their order or explanation if needed.

6. 52–60 min · Independent check and plenary. Teacher displays the final prompts in the plenary slides and distributes the final section of the fraction comparison and ordering worksheet. Students independently place 3/5, 6/10 and 7/8 on a number line, compare 3/5 and 6/10, and order 1/4, 1/2, 3/4 and 2/8. They write one sentence explaining their strategy, then share one useful idea in a brief whole-class discussion.

Resources

• the complete introduction, modelling, investigation and plenary slide deck
• the fraction comparison and ordering worksheet
• the Equivalent Fractions Dominoes
• the Fraction Wall and Strip Cards
• Large number lines from 0 to 1, including open and labelled versions
• Mini-whiteboards and markers
• Pencils, rulers and coloured pencils
• Group fraction cards prepared by the teacher

Assessment

• During modelling and group work, conference with students: check whether they partition number lines into equal intervals and distinguish numerator from denominator.
• Review journal or worksheet reasoning for accurate use of models, equivalent fractions and benchmarks; note whether explanations include a claim, model and explanation.
• Use peer feedback to identify misconceptions, especially the belief that a larger denominator always means a larger fraction.

Differentiation

• Support students with pre-partitioned number lines, fraction strips, colour-coded visual comparison prompts and vocabulary cards for fraction, numerator, denominator, equivalent, compare, greater than, less than and equal to.
• Begin with like denominators and familiar benchmarks such as 0, 1/2 and 1; then move to less familiar comparisons such as 3/8 and 1/2.
• Provide EALD learners with oral rehearsal, partner discussion, gesture and sentence frames: “___ is greater than ___ because…”, “I know this because…”, and “___ is equivalent to ___.”
• Allow students to show thinking through annotated diagrams, manipulatives or oral explanations before writing. Extension students order fractions with different denominators without a supplied model, create two fractions between given benchmarks, and explain more than one comparison strategy.

Extension

• Order 1/3, 3/8, 1/2, 5/8 and 2/3 without using a supplied fraction wall, then justify every placement.
• Create two different fractions between 1/2 and 3/4 and prove that both belong between the benchmarks.
• Compare one pair using a number line and a second method using equivalent fractions or a benchmark.