Three-Way Number Connections

Overview

Lesson 14 of 15 in the unit Number Connections: Fractions, Decimals, Percentages. Students connect equivalent fractions, decimals and percentages through sorting, matching, visual models, place value and MNP consolidation tasks.

Learning intentions

• WALT move flexibly between fractions, decimals and percentages.
• WALT use models and place value to explain equivalent representations.
• WALT communicate mathematical thinking clearly and listen to different strategies.

Success criteria

• I can match equivalent fractions, decimals and percentages.
• I can convert common values between the three forms.
• I can justify a connection using a model, hundred grid or place-value explanation.
• I can check whether a representation is reasonable.

Curriculum links

• Number: recognise, represent and connect fractions, decimals and percentages.
• Number: use place value and multiplicative thinking to calculate and compare quantities.
• Mathematical communication: explain, represent and justify mathematical ideas using words, symbols and diagrams.
• Mathematical practices: choose useful tools, notice patterns, connect representations and evaluate whether an answer makes sense.

Lesson structure (45 minutes)

1. 0–5 minutes – Hook and retrieval

Open with the hook and retrieval slides. Display three statements such as “0.5, 1/2 and 50% are different numbers” and ask students to decide whether they agree, disagree or are unsure. Students briefly explain their thinking to a partner, then share examples from earlier lessons.

2. 5–12 minutes – Teacher modelling

Use the representation modelling slides to model one benchmark value, such as one half. Show it as a fraction, a shaded hundred grid, a decimal and a percentage. Explicitly connect 1/2 to 50/100, 0.50 and 50%, highlighting that the value stays the same even though the notation changes.

Model a second example, such as 3/4 = 0.75 = 75%, using a fraction wall or hundred grid. Emphasise that decimal places describe parts of one whole and that “per cent” means “out of one hundred”.

3. 12–20 minutes – Representation sort

Place students in five groups of four. Give each group a mixed set from the fraction-decimal-percentage matching cards. Students sort cards into equivalent groups, using the fraction/decimal/percentage mat to organise their thinking.

Pause halfway for a “notice and wonder”. Ask: “Which values were easy to match? Which needed a model?” Groups must choose one match and prepare a sentence explaining how they know it is correct.

4. 20–31 minutes – Matching-card investigation

Students work in pairs with the same matching cards. One student selects a card and the other finds the two equivalent representations, then both justify the match. Partners swap roles after each turn.

Circulate and ask: “What does the denominator tell you?”, “How could you make this fraction out of 100?”, and “Where can you see the decimal in the percentage?” Encourage students to use a fraction wall, hundred grid or place-value explanation rather than relying only on memory. Invite a few pairs to share different methods using the investigation prompts.

5. 31–41 minutes – MNP consolidation

Distribute the MNP consolidation and workbook task sheet. Students complete selected MNP-style tasks independently: match equivalent forms, convert common values and explain one connection with a diagram or written reason. Prioritise accuracy and explanation over completing every question.

Confer with students who need support. Record common misconceptions, such as confusing 0.4 with 4%, or changing the denominator without changing the numerator consistently.

6. 41–45 minutes – Plenary and formative check

Return to the opening statement using the plenary and exit prompt. Students respond on the worksheet: “Explain why 0.25, 1/4 and 25% are equivalent.” Ask two students to share different justifications, then preview the final lesson, which will apply these connections to problem-solving.

Resources

• the complete lesson slide deck
• the MNP consolidation and workbook task sheet
• the fraction-decimal-percentage matching cards
• Fraction walls and strips for support
• Hundred grids
• Mini-whiteboards and pens
• Pencils, highlighters and group trays
• Optional place-value charts

Assessment

• Listen during the sort and investigation for accurate matching and explanations using models or place value.
• Check the independent task for correct conversions, equivalent representations and a valid justification.
• Use the final explanation to identify students ready for less familiar values or needing further work with benchmark values.

Differentiation

• Support learners with a reference chart, fraction walls, hundred grids and a limited set of benchmark values: 1/2, 1/4, 3/4, 1/10 and 1/100. Provide sentence frames such as “I know these are equal because…”.
• Pair students strategically and allow learners to explain orally before recording. Read instructions aloud, use clear visual examples and reduce the number of cards where working memory or language is a barrier.
• Extend advanced learners with less familiar values such as 3/5, 7/10 or 35/100. Ask them to prove equivalence in two ways and create a three-way matching challenge for classmates, including a plausible distractor.
• For EAL and neurodiverse learners, pre-teach “equivalent”, “out of”, “hundredths” and “percentage”; use colour coding across all three forms and provide predictable turn-taking roles during pair work.