Ratio Beginnings

Overview

In this first lesson of the unit “Mathematics Mixed Bag,” students begin learning what ratios mean by comparing quantities in simple visuals and contexts. They will identify ratios and write them using correct notation (for example, 2:3).

Learning intentions

• Understand ratios as comparisons between two quantities.
• Identify the quantities being compared in simple ratio pictures or object sets.
• Write ratios to describe relationships shown in visuals.
• Use language (for example, “for every…”) to explain what a ratio means.

Success criteria

• I can state which two quantities are being compared in a ratio.
• I can write a ratio from a simple diagram or group of objects.
• I can explain my ratio using “for every” language.
• I can check whether my ratio matches the visual by counting accurately.

Curriculum links

• Students develop understanding of rates and ratios as comparisons of quantities.
• Students represent mathematical ideas using words, diagrams, and ratios.
• Students solve problems by reasoning from given information.
• Students communicate mathematical thinking clearly, including using appropriate notation.

Lesson structure (60 minutes)

1. 0–5 min: Warm-up with noticing

• Display a quick mixed picture (e.g., 3 apples and 5 oranges). Ask: “What comparison can we make between these?”
• Invite a couple of students to share comparisons in words before introducing the ratio word.

2. 5–15 min: Mini-lesson—What a ratio is

• Write: “A ratio compares two quantities.” Point to the apple and orange counts.
• Model how to write a ratio as “apples: oranges,” using counted totals (e.g., 3:5). Emphasise that the order matters.
• Teach “for every” language: “For every 3 apples, there are 5 oranges.”

3. 15–30 min: Emerging practice—Objects and pictures

• Give students small sets or cards with simple visuals (for example, counters in two colours or sticker groups).
• Prompt: “Count each type, then write the ratio of one to the other.”
• Teacher circulates and asks: “Which quantity is first? Which is second? What does your ratio tell us?”

4. 30–40 min: Developing—Real-life ratio starters

• Present short, teacher-read scenarios with visuals or simple collections (e.g., “A snack bag has 4 crackers and 6 cheese bites.”).
• Students write the ratio shown, then write one sentence using “for every.”
• Quick share: select 3–4 responses and confirm correct order and counts.

5. 40–50 min: Proficient—Word problem to ratio

• Display one problem on the board: “In a class art corner, there are 2 blue markers and 3 red markers. Write the ratio of blue to red markers.”
• Students work individually, then pair-check.
• Teacher models a “count → write → explain” routine and asks pairs to justify their ratio in a sentence.

6. 50–57 min: Formative check—Ratio quick-sort

• Provide 6–8 ratio cards and 6–8 visual cards. In groups of 3, students match each visual to its written ratio.
• As students match, teacher listens for correct comparisons and common mistakes (swapped order, incorrect counts).

7. 57–60 min: Closure—Exit ticket

• Students answer: “A game box has 5 green pieces and 2 red pieces. Write the ratio of green to red, and tell what it means using ‘for every’.”
• Collect to gauge accuracy and understanding.

Resources

• Mixed picture slides/printed images showing two groups (simple counts up to 10 each)
• Two-colour counters or small objects (e.g., red and yellow) for each student or pair
• Ratio cards (e.g., 2:3, 4:5, 1:4) and matching visual cards
• Scenario cards for developing practice with brief contexts
• Whiteboards or paper for ratio writing and “for every” explanations
• Anchor chart: “Count → Write ratio (first:second) → Explain using ‘for every’”
• Teacher-made checklist for quick formative notes (order, counts, notation, explanation)
• Timer and group roles (counter, writer, checker)

Assessment

• Observation during guided and independent tasks: correct counting and correct ratio order.
• Formative quick-sort matching: accuracy in pairing visuals with written ratios.
• Exit ticket: ratio notation plus a clear explanation using “for every.”

Differentiation

• Support: Provide a partially completed example (counts listed, ratio frame with blanks). Use fewer objects (e.g., totals up to 6) and offer sentence starters: “For every __, there are __.”
• Support: Use colour-coded first/second indicators on visuals to reduce order confusion.
• Extension: Ask students to compare two ratios from different visuals and state which one has “more of the first quantity” (without requiring unit rates yet).
• EAL/SEN: Allow oral responses to be recorded by a partner; provide word banks for “first,” “second,” “for every,” “there are,” and “ratio.”

Curriculum competencies focus

• Communicate mathematical thinking using words, diagrams, and ratio notation.
• Reason and problem solve by counting quantities accurately and making consistent comparisons.
• Connect representations by matching visuals to written ratios and explaining the meaning.