Ratio Forms Connect

Overview

In this ninth lesson of the “Mapping Data and Change” unit, students connect equivalent ratios written in different forms, including 1:2, “1 to 2”, and `1/2”. They use models, tables and discussion to decide which representation communicates a proportional relationship most clearly.

Learning intentions

• WALT recognise that different ratio forms can describe the same relationship.
• WALT convert ratios between colon, comparative and fractional forms.
• WALT use models and equivalent ratios to justify our thinking.
• WALT select a useful representation for communicating a proportional relationship.

Success criteria

• I can read and write a ratio in at least three forms.
• I can explain what each number in a ratio represents.
• I can use a model, table or multiplication to prove that two ratios are equivalent.
• I can choose a representation and explain why it is useful.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that deepen mathematical understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: challenge connected to familiar textbook and classroom content.
• Mathematics and Statistics — Additional resources for advanced learners: reasoning, representation and communication for students ready for further challenge.
• Mathematical competencies: representing relationships, reasoning, communicating and justifying mathematical ideas.

Lesson structure (45 minutes)

1. 0–5 min · Hook and prior knowledge. Teacher opens with the ratio comparison hook showing a class drink mixed with 1 cup of concentrate and 2 cups of water, then asks, “Which statement tells the story best: 1:2, 1 to 2, or 1/2?” Students think independently, share with a partner and explain what they believe each form means.

2. 5–12 min · Make the connection. Teacher uses the representation teaching slides to model that 1:2, “1 to 2” and 1/2 compare the same two quantities when the first quantity is compared with the second; clarify that the fraction is a comparison, not necessarily a part of one whole. Students annotate three linked examples and identify the first and second quantities in each.

3. 12–20 min · Concrete modelling. Teacher gives pairs the fraction circles cut-out pack and displays the modelling prompt. Model the comparison of 2 red pieces to 4 blue pieces, recording 2:4, “2 to 4” and 2/4”, then simplify the fraction and discuss the equivalent ratio 1:2`. Students build or sketch examples, match equivalent representations and explain how halving or doubling both quantities preserves the relationship.

4. 20–32 min · Guided practice. Teacher distributes the ratio forms practice sheet and works through the first question with the class, prompting students to use a ratio table or drawing before converting. Students complete questions independently, checking selected answers with a partner. They convert examples such as 3:5, “4 to 8” and `6/10” into connected forms, and identify whether a statement is correct.

5. 32–39 min · Choose and communicate. Teacher displays the representation choice challenge and presents three communication situations: describing a red-to-blue counter comparison, comparing two quantities in a report, and showing a recipe relationship. Students choose the most useful form for each situation, record it on the worksheet and justify their choices using mathematical language. Invite two or three pairs to compare different valid choices.

6. 39–45 min · Plenary and exit check. Teacher returns to the hook using the plenary and exit prompt and asks students to complete the final worksheet question: “A pattern has 4 black tiles for every 6 white tiles. Write the relationship in three forms and explain which form you would use to compare the quantities.” Students submit their response and share one misconception or useful strategy they noticed.

Resources

• the ratio forms teaching deck
• the ratio forms practice sheet
• the fraction circles cut-out pack
• Board and markers
• Pencils and coloured pencils
• Pair discussion spaces
• Visual timer

Assessment

• During modelling, listen for whether students identify the order of the quantities and understand that both parts of a ratio must be changed by the same factor.
• Check worksheet responses for accurate conversions, equivalent ratios and explanations rather than answers alone.
• Use the final question as an exit check: identify students who need further support with fraction notation, simplifying or selecting an appropriate representation.

Differentiation

• Support students with a colour-coded model: use one colour for the first quantity and another for the second, and provide the sentence stem, “The ratio compares ___ with ___.”
• Allow students to draw counters or use fraction circles before writing symbols; pair students strategically for oral rehearsal.
• For EAL learners, pre-teach and display “compare”, “ratio”, “equivalent”, “first quantity” and “second quantity”; accept spoken explanations alongside written work.
• Extend confident students by asking them to create three different-looking but equivalent ratios, prove equivalence in two ways and explain when a fractional form may be misleading or less useful.