Percent In Context

Overview

Lesson 5 of 10 in the unit Rational Number Knowledge Practices. Students connect percentages with fractions and decimals, then interpret and calculate percentages of whole-number quantities and measures in meaningful contexts such as shopping, water conservation and fundraising.

Learning intentions

• WALT connect benchmark percentages to fractions and decimals.
• WALT find percentages of whole-number quantities and measures.
• WALT explain whether a percentage is taken of the whole.
• WALT use estimation and benchmark percentages to check answers.

Success criteria

• I can find 10%, 25%, 50% and other familiar percentages.
• I can explain my strategy using fractions, decimals or proportional scaling.
• I can decide whether my answer should be less than, equal to or greater than the whole.
• I can check whether my answer is reasonable.

Curriculum links

• Understand and use rational numbers, including equivalent fractions, decimals and percentages.
• Apply multiplication, division and proportional reasoning to solve problems involving quantities and measures.
• Use mathematical language, representations and diagrams to explain thinking.
• Develop mathematical practices: make connections, choose efficient strategies, justify solutions and check reasonableness.

Lesson structure (60 minutes)

1. 0–5 minutes – Hook and retrieval

Open with the hook and retrieval slides. Display a supermarket discount or water-saving statistic and ask: “What might 25% mean here?” Students briefly discuss with a partner, then recall that 100% means the whole. Record benchmark links: 50% = 1/2 = 0.5, 25% = 1/4 = 0.25, 10% = 1/10 = 0.1.

2. 5–15 minutes – Teacher modelling

Use the benchmark percentage slides and a 100 grid to model several representations. Think aloud: “25% of $80 is one quarter of $80, so $20.” Then model 15% of $80 as 10% + 5%: $8 + $4 = $12. Emphasise that “of” identifies the whole and that percentages below 100% usually produce an answer less than the whole.

3. 15–25 minutes – Guided problem solving

In groups of three, students solve problems from the guided percentage contexts worksheet using 100 grids, play money or mental strategies. Include examples such as:

• A school saves 20% of 50 litres of water.
• A fundraiser earns 25% of $120 for a local project.
• 10% of 40 kilograms of local produce is donated.

Pause after each problem to ask: “What is 100%? Which benchmark is efficient? Is your answer less or greater than the whole?” Invite groups to explain different methods.

4. 25–40 minutes – Pair challenge design

Pairs use the supermarket circulars, sustainability data and play money to design a fair-shopping or conservation challenge. Their challenge must include a whole quantity, a familiar percentage and a clear question. For example: “A $60 jacket is discounted by 25%. What is the discount and sale price?” or “A school uses 200 litres and reduces use by 15%. How many litres are saved?”

Pairs solve their own challenge and swap with another pair. Use the pair challenge instructions to reinforce that students must show two representations where possible and check whether the answer is reasonable.

5. 40–50 minutes – Share and compare strategies

Select two or three solutions to discuss. Compare fraction, decimal, benchmark and proportional-scaling methods. Ask students to identify the most efficient strategy for each example and explain why. Address common errors, such as finding a percentage of the wrong quantity or treating 15% as 15 whole units.

6. 50–56 minutes – Independent practice

Students complete the remaining selected questions on the independent practice section. Include percentages of money, water, mass and whole-number quantities. Students may use a calculator only to check, not replace, their explanation. Circulate and record who can identify the whole, select a benchmark and estimate first.

7. 56–60 minutes – Exit ticket and reflection

Finish with the plenary and exit-ticket slide. Students complete: “Find 35% of 200 and show two methods.” Encourage 30% + 5%, or 0.35 × 200, and ask students to write one reason their answer is reasonable. Collect responses for next-lesson grouping.

Resources

• the complete percentage lesson deck
• the percentage contexts and practice worksheet
• 100 grids, one per student or pair
• Play money
• Supermarket circulars or catalogues
• Sustainability data about water, energy or waste
• Mini-whiteboards and pens
• Calculators for checking
• Fraction and decimal reference notes

Assessment

• During guided work, listen for correct identification of the whole, suitable benchmark selection and explanations using percentage, fraction and decimal language.
• Review pair challenges for accurate calculations, realistic contexts and reasonableness checks.
• Use the exit ticket to identify whether students can calculate 35% in two ways and connect percentages with proportional reasoning.

Differentiation

• Support learners with concrete play money, 100 grids, benchmark percentage cards and reduced numerical load, such as 10%, 25% and 50% of multiples of 10.
• Provide sentence stems: “The whole is…”, “I chose… because…”, and “My answer is reasonable because…”. Pre-teach and display percentage, percent of, whole, benchmark, discount, increase and decrease.
• Allow calculators for checking, paired rehearsal and oral explanation. Offer enlarged grids, clear visual spacing and scribing or speech-to-text where appropriate.
• Extend confident learners by calculating percentage increases and decreases, comparing two strategies, or solving reverse problems such as finding the original price when 25% equals $15.