Finding Percentages

Overview

In this 30-minute lesson (Lesson 11 of 20) you will practise finding percentages of whole numbers in realistic contexts. Students will model each situation, choose an efficient method, and check their answers for reasonableness.

Learning intentions

Students will:

• calculate a given percentage of a whole number using efficient strategies
• represent percentage calculations using equivalent fractions, known “benchmark” percentages (10%, 20%, 50%), and place value
• interpret solutions in context (e.g., interpreting “15% off” as a discount amount)
• communicate their calculation steps clearly, and verify by estimation or inverse reasoning

Success criteria

Students can:

• find 15% of 200, 20% of 75, and 5% of 180 accurately
• explain how they calculated the percentage (for example, using 10% then combine, or dividing by 100 and multiplying)
• check whether their answer is sensible for the context (larger/smaller than the original, close to an estimate)
• state the meaning of the percentage in the given problem (amount, not just the rate)

Curriculum links

• Mathematics — Number: use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts (formulate problems, choose calculation strategies, interpret solutions, review appropriateness of the model)
• Mathematics — Number: use efficient strategies with rational numbers and apply digital tools where appropriate to support calculations
• Mathematical modelling focus: connect the percentage calculation to the situation and communicate the meaning of the result

Lesson structure (30 minutes)

1. 0–3 min · Retrieval warm-up. Teacher writes three quick prompts: “10% of 60?”, “20% of 40?”, “50% of 18?” Students answer on mini-whiteboards, then teacher checks for correct reasoning (not just answers).

2. 3–10 min · Worked example: percentage as a part. Teacher models two examples on the board. Example A: “A ticket costs $80. What is 15% of $80?” Teacher demonstrates an efficient method: 10% then 5% (or 1% then multiply if needed). Example B: “You have 240 stickers. What is 5%?” Students watch and note the steps in a short, scaffolded working format (given → strategy → calculation → answer in context).

3. 10–18 min · Guided practice: multiple strategies. Teacher assigns 4 short tasks (one at a time). Students work in pairs or individually, then compare methods. Tasks:

• “Find 20% of 75.”
• “Find 15% of 200.”
• “Find 5% of 180.”
• “Find 25% of 88.” Teacher circulates and asks: “Which benchmark percentage did you use?” and “What does your answer represent in the context?” Teacher selects 2 student methods to share (e.g., breaking into 10% + 5%, or using halves/quarters for 25%).

4. 18–26 min · Modelling task: apply and interpret. Teacher gives a context set (choose one to match class interests):

• Option 1 (finance): “A phone plan discount is 15% on $320. How much is the discount, and what is the new price?”
• Option 2 (school context): “A class collection goal is 120 items. 20% have been collected. How many items is that?” Students must write a short model: identify the whole, state what the percentage represents, calculate, and write the final sentence using units. Teacher reminds students to include a check (e.g., estimate: 15% should be less than 20% of the whole).

5. 26–30 min · Exit ticket and reflection. Students complete one timed question: “Find 12.5% of 64 and explain your method in one sentence.” Teacher collects and uses responses to plan the next lesson (consolidation on fractions of 100 and benchmark decomposition).

Resources

• Mini-whiteboards or scrap paper and pens
• Slide/board with warm-up prompts and example worked steps
• Student task sheet with the practice and modelling items
• Calculator available (optional) but students must show the method
• Percent fraction-matching card set (optional: 10% = 1/10, 25% = 1/4, 50% = 1/2)

Assessment

• Formative checks during warm-up using mini-whiteboard responses (accuracy and strategy cues)
• Teacher observation during guided practice: students explaining what the percentage amount represents
• Exit ticket: accuracy plus a one-sentence explanation of method (e.g., using halves/quarters or benchmark decomposition)

Differentiation

• Support:
• Provide a “strategy checklist” (Use 10%? Use 5%? Use halves/quarters?) and sentence starters: “15% of 200 means …” “I used … because …”
• Offer a partially completed worked example template for students to finish (given → break into benchmarks → compute)
• Targeted scaffolds:
• For students who struggle, start from “1% of the number” and build up (divide by 100 then multiply), or restrict choices to one taught method per task
• Extension:
• After completing the main task, students can answer: “How would the result change if the percentage doubled? Explain.” (e.g., double 15% to 30% of the same whole)
• EAL/SEN considerations:
• Keep contexts familiar and repeat the key language: “percentage of” (part of a whole), “discount amount”, “new price”
• Allow responses using words + numbers, not only diagrams