Percentage Connections

Overview

Lesson 13 of 15 in Number Connections: Fractions, Decimals, Percentages. Students use known fraction and division relationships to find common percentages of quantities, applying their strategies to money, discounts and everyday contexts.

Learning intentions

• WALT find 10%, 50%, 25% and related percentages of quantities.
• WALT connect percentages with fractions, decimals and division.
• WALT explain an efficient strategy and check whether an answer is reasonable.
• WALT apply percentage strategies to money and discount problems.

Success criteria

• I can find 10%, 50% and 25% of a quantity.
• I can use related facts to find percentages such as 20%, 5%, 75% and 15%.
• I can explain my method using words, equations or a bar model.
• I can check that my answer is sensible, especially when solving a discount problem.

Curriculum links

• Number: use multiplicative thinking, fractions, decimals and percentages to solve problems.
• Number: recognise and apply equivalence between common fractions, decimals and percentages.
• Algebraic thinking: identify and use relationships between operations and quantities.
• Mathematical communication and reasoning: choose efficient strategies, explain thinking and evaluate the reasonableness of answers.

Lesson structure (45 minutes)

1. 0–5 minutes – Hook and connect

Open with the hook and learning intention slides. Display: “A $40 game is 25% off. How much money is the discount?” Students make a quick estimate, then discuss what they already know about 25%, one-quarter and division by four. Share the WALT and success criteria.

2. 5–13 minutes – Teacher modelling

Use the percentage connections slides to model a 100-square or bar model. Establish:

• 10% means divide by 10.
• 50% means one-half, or divide by 2.
• 25% means one-quarter, or divide by 4.

Model finding 20% as two lots of 10%, 5% as half of 10%, 75% as 50% + 25%, and 15% as 10% + 5%. Include examples such as 10% of 80, 25% of 60 and 15% of $40. Emphasise explaining the relationship rather than simply using a rule.

3. 13–17 minutes – Partner reasoning

Present two examples from the guided practice slides: “Find 25% of 120” and “Find 75% of 80”. Partners solve using a bar model, fraction, division or known percentage fact. Invite several students to explain different efficient methods and compare them.

4. 17–32 minutes – Independent and supported practice

Distribute the percentage quantities and money worksheet. Students complete the core questions individually, then compare selected answers with a partner. Questions should include common percentages of quantities, fraction and decimal connections, and money discounts.

Work with a support group using counters, paper strips or drawn bar models. Begin with quantities that partition easily, such as 40, 60, 80 and 120. Allow calculator checking only after students have shown their reasoning. Circulate and ask, “What does 10% mean here?” and “How could you use a percentage you already know?”

5. 32–39 minutes – Challenge and application

Return to the discount and challenge slides. Students choose or are assigned a challenge:

• Find 35% of 200 using 30% + 5%.
• A jacket costs $80 and is 25% off. What is the sale price?
• A quantity increased by 10% is 66. What was the original quantity?
• A $50 item has a 20% discount, followed by a 10% increase. Is it back to $50?

Students must show a method and explain why their answer is reasonable. Encourage advanced learners to compare two strategies.

6. 39–45 minutes – Plenary and assessment

Use the reflection and exit prompt slides. Students complete the prompt: “Find 15% of 60. Show how 10% and 5% help.” Invite two contrasting solutions. Discuss common errors, including confusing the discount with the final price. Students self-assess against the success criteria using a traffic-light response or fingers 1–3.

Resources

• the complete percentage connections slide deck
• the percentage quantities and money worksheet
• Counters, linking cubes or paper strips for bar models
• Mini-whiteboards and pens
• Calculators for checking, not initial solving
• Projector or interactive whiteboard
• Pencils, rulers and highlighters
• Optional fraction wall or 100-square display

Assessment

• Listen to partner explanations and note whether students connect 10%, 50% and 25% with division and fractions.
• Check worksheet strategies, not only answers, particularly the use of bar models and decomposed percentages.
• Use the plenary response to identify students needing further support with percentage–fraction connections or discount language.

Differentiation

• Support learners with concrete materials, bar models, a 100-square and quantities that divide evenly. Provide sentence frames: “I found ___% by…”, and read money problems aloud where needed.
• Reduce the number of questions while maintaining the key ideas. Pair students strategically and check understanding after each modelled example.
• Support EAL learners with visual examples and explicitly teach terms such as percentage, of, discount, sale price and reasonable. Accept oral explanations, labelled diagrams or equations.
• Extend confident learners with unfamiliar percentages, reverse problems and successive discount-and-increase contexts. Ask them to prove whether two methods always give the same result.