Decimal Percentage Connections

Overview

Students connect fractions, decimals and percentages as equivalent representations, then use these connections to solve practical Year 8 problems involving discounts, increases and comparisons. The lesson builds on prior work with place value, fractions and proportional reasoning, with emphasis on explaining strategies and checking whether answers are reasonable.

Learning intentions

• WALT connect fractions, decimals and percentages.
• WALT convert between representations accurately.
• WALT apply decimal and percentage knowledge to solve real-world problems.
• WALT explain and justify our mathematical thinking.

Success criteria

• I can convert a fraction to a decimal and percentage, and explain my method.
• I can recognise that a percentage is a proportion out of 100.
• I can calculate a percentage of an amount using an efficient strategy.
• I can check whether my answer is reasonable and communicate my reasoning clearly.

Curriculum links

• Number: understanding and using rational numbers, including fractions, decimals and percentages.
• Number: applying multiplicative and proportional reasoning in meaningful contexts.
• Mathematical communication: representing, explaining and justifying strategies.
• Mathematics and Statistics — Mathsteasers: using challenging, higher-order problems to deepen understanding and extend advanced learners.

Lesson structure (60 minutes)

1. 0–7 min · Hook and retrieval. Display a supermarket price tag showing “25% off $80” and ask, “What could 25% mean, and how might we find the sale price?” Open with the hook and retrieval slides. Students estimate the discount, record a possible method independently, then compare with a partner; invite several strategies without confirming an answer yet.

2. 7–17 min · Connect representations. Use the slides to model that ( \frac14 = 0.25 = 25% ), linking division by 4, place value and “out of 100”. Teacher highlights that the decimal and percentage describe the same proportion, not two separate calculations. Students complete quick-response conversions on mini-whiteboards, including ( \frac12 ), ( \frac34 ), 0.2 and 0.08, and explain one answer to a partner.

3. 17–27 min · Model percentage strategies. Demonstrate finding 15% of $60 by calculating 10% plus 5%, then compare this with multiplying by 0.15. Model both a discount and an increase, carefully distinguishing “amount changed” from “new total”. Students annotate the worked examples on the decimal and percentage problem-solving worksheet and answer two checkpoint questions. Pause to address common errors, such as subtracting the percentage number rather than the percentage amount.

4. 27–45 min · Paired problem solving. Distribute the worksheet to pairs, with one copy or workspace per student as appropriate. Students solve a graduated set of shopping, sports-statistics and population problems, showing at least one representation and a checking strategy for each. Teacher circulates, asking: “What does the percentage refer to?”, “Could you use a benchmark such as 10% or 50%?”, and “How do you know your answer is sensible?” Students must agree on reasoning before recording a final response.

5. 45–53 min · Mathsteaser challenge and discussion. Show the challenge: “A jacket is reduced by 20%, then the sale price is increased by 20%. Is it back to its original price? Prove your answer with an example and an explanation.” Students work independently for three minutes, then discuss in groups of three. Groups present different representations; teacher draws attention to the changing base amount and accepts multiple valid examples or algebraic explanations.

6. 53–60 min · Plenary and exit check. Return to the opening price tag using the plenary and exit-check slides. Students complete the final worksheet question independently: “A $120 item is reduced by 15%. Find the discount and sale price, and explain why your answer is reasonable.” Collect responses, then ask students to share one connection between a fraction, decimal and percentage.

Resources

• the decimal-percentage lesson deck
• the decimal and percentage problem-solving worksheet
• Whiteboard or projector
• Mini-whiteboards and pens
• Calculators for checking, not replacing, reasoning
• Exercise books and pencils
• Timer
• Highlighters for identifying the original amount and percentage change

Assessment

• Check mini-whiteboard responses during representation and conversion work; note whether students understand percentage as “out of 100”.
• Confer with pairs during problem solving, listening for accurate identification of the base amount and clear explanations.
• Use the independent exit response to identify students needing support with conversion, percentage calculation or interpreting increase and decrease.

Differentiation

• Support learners with a reference strip showing ( \frac12 = 0.5 = 50% ), ( \frac14 = 0.25 = 25% ), ( \frac34 = 0.75 = 75% ), and ( \frac1{10} = 0.1 = 10% ). Provide sentence starters: “The percentage refers to…”, “I know this is reasonable because…”.
• Begin some learners with whole-number percentages and benchmark strategies such as 10%, 25% and 50%, before moving to less familiar percentages. Allow calculators for checking after the method is recorded.
• For EAL learners, pre-teach “original amount”, “discount”, “increase”, “percentage of” and “sale price”, using the visual examples on the slides and partner rehearsal before written explanations.
• Provide structured partner roles—reader, calculator, explainer and checker—rotated during the task. Challenge confident learners to solve a problem in two ways and compare the efficiency and reliability of each method.
• Use enlarged print, uncluttered worksheet sections, extra processing time and teacher scribing or speech-to-text where required for students with learning or physical needs.