Equivalent Fractions Decimals

Overview

In this 45-minute lesson, students identify equivalent fractions and decimals, and practise matching them using group tasks and Think Boards. They will connect fractions, decimals, and values in everyday contexts.

Learning intentions

• Students will identify equivalent fractions (same value) by using visual models.
• Students will recognise decimals that match familiar fractions (for example, halves, quarters, tenths).
• Students will explain their reasoning when matching and converting between representations.

Success criteria

• I can match equivalent fractions using pictures, number lines, or fraction strips.
• I can identify which decimal equals a given fraction using a model.
• I can justify my matching using fraction language (numerator, denominator, tenths, halves, quarters).

Curriculum links

• Number: developing understanding of fractions and decimals as numbers and their place on number lines.
• Measurement and everyday contexts: interpreting decimals and fractions in real situations.
• Mathematical reasoning: using representations and explaining strategies for solutions.

Lesson structure (45 minutes)

1. 0–5 min | Warm-up: Fraction–Decimal Flash

• Display quick prompts such as “Which is the same value? 1/2 or 0.5” and “Which is the same? 1/4 or 0.25”.
• Students record answers on mini-whiteboards and share one reason (e.g., “0.5 means five tenths, which is the same as a half.”).

2. 5–12 min | Whole-class modelling: Building equivalence

• Use a fraction strip and a place value chart (tenths) to show how halves and quarters relate to decimals.
• Teacher models one worked example: show 1/2 as two of four quarters, then link to 0.5 using tenths on a number line.

3. 12–27 min | Group activity: Match and explain

• Put students into 4 groups (about 4 per group). Give each group a set of cards:
• Fraction cards (e.g., 1/2, 1/4, 2/4, 3/4).
• Decimal cards (e.g., 0.5, 0.25, 0.75).
• Representation cards (pictures of shaded areas or a simple number line with jumps).
• Task: Students sort into equivalence sets (same value) and write a brief explanation on a group sheet using sentence starters:
• “These are equivalent because…”
• “I know 1/4 equals 0.25 because…”
• Teacher circulates, prompting students to use appropriate fraction and place value language.

4. 27–38 min | Think Board: Individual practise

• Students complete Think Boards (four prompts total), such as:
• Match 2/4 with its equivalent decimal.
• Place 3/4 on a number line that is labelled in tenths (students choose the correct position).
• Circle the decimal that matches 1/4.
• Explain in one sentence how you know two representations show the same value.
• Students are encouraged to show thinking with diagrams (shaded models, number lines, or fraction strips).

5. 38–45 min | Closure: Reasoning share

• Select 2–3 students to share one Think Board answer and their explanation.
• Teacher summarises key idea: equivalent means “same value,” even though the numbers look different (fraction vs decimal).

Resources

• Fraction strips (halves and quarters) and/or simple fraction models for shading
• Place value charts for tenths (0 to 1) and a labelled number line
• Equivalence card sets (fraction, decimal, and representation cards)
• Group recording sheet with sentence starters
• Mini-whiteboards, markers, and erasers for warm-up
• Individual Think Boards (four prompts) and pencils
• Teacher checklist for observing reasoning and correct matching

Assessment

• Formative: Observe group sorting for correct equivalence sets and listen for the reasoning students give.
• Formative: Review Think Board responses for accuracy and evidence of explanation (not just the answer).
• Quick check: Warm-up boards to confirm prior knowledge of halves/quarters and decimals to tenths.

Differentiation

• Support:
• Provide extra fraction strips and a completed example card showing one fraction–decimal match.
• Offer a partially completed Think Board (students choose from two options first).
• Extension:
• Include an extra equivalence challenge using mixed representation (e.g., 2/4, 0.5, and a shaded model) and ask for a second method (fraction strip plus number line).
• EAL learners:
• Use consistent sentence starters and word banks (half, quarter, tenths, equivalent, same value).
• Allow verbal explanations alongside written responses.
• SEN (additional needs):
• Reduce the number of cards per equivalence set or provide two stages (first match fractions, then match decimals).
• Offer guided prompts during group work to keep students on track.