Percentages Foundations

Overview

Lesson 10 of 20 focuses on introducing percentages and linking them to fractions and decimals. Students will use efficient mental strategies and represent the same quantity in multiple forms, then interpret solutions back in context.

Learning intentions

• Students will understand that a percentage is “out of 100” and can be represented as a fraction and a decimal.
• Students will convert between percentages, fractions, and decimals using place value and reasoning about equivalence.
• Students will solve simple practical percentage problems by choosing efficient calculation strategies.
• Students will communicate their thinking clearly and check that their answers make sense in context.

Success criteria

• I can explain what 50% means as “50 out of 100”.
• I can write a given percentage as a fraction and a decimal (and vice versa) when the denominator is 100 or can be converted to a hundred.
• I can find a simple percentage of a whole using a strategy (e.g. 10% then combine parts).
• I can review my model by checking the result against the situation (e.g. whether it should be more or less than the whole).

Curriculum links

• Number — recognise and use terminating/recurring decimals as appropriate when linking decimals to fractions.
• Number — use rational number operations with efficient strategies (including working with negative/positive values when needed).
• Number — use mathematical modelling to solve practical problems involving rational numbers and percentages; interpret and communicate solutions in terms of the situation; review appropriateness of the model.
• Mathematical practice — formulation of problems, selection of calculation strategies, and interpreting results in context.

Lesson structure (30 minutes)

1. 0–3 min · Activate prior knowledge (warm-up). Teacher displays three equivalent representations for a small quantity (e.g. 25% / 1/4 / 0.25) in jumbled form and asks: “Which one matches and why?” Student sorts and explains their choice to themselves (then one brief whole-class share if time allows).

2. 3–10 min · Direct teach: Percent as “out of 100”. Teacher draws a 10×10 grid and colours one section, linking it to “__ out of 100” and therefore a percentage; then converts:

• 10 squares = 10% = 10/100 = 0.10
• 25 squares = 25% = 25/100 = 1/4 = 0.25 Students copy the structure (grid → out of 100 → fraction → decimal) and answer quick checks verbally.

3. 10–18 min · Guided practice: Conversions (teacher-led then student-led). Teacher provides 6 cards (e.g. 20%, 40%, 75%, 0.6, 1/2, 3/4) and models two conversions, emphasising efficiency (turn percent to “out of 100”, then simplify the fraction; for decimals, write as tenths/hundredths). Students work through the remaining cards in pairs (or independently if truly 1 student) using a conversion table template: Percentage → fraction → decimal. Teacher circulates and prompts: “What does the ‘100’ represent here?”

4. 18–26 min · Modelling task: Simple percentage of a whole. Teacher gives a realistic scenario: “A $50 voucher. You get 20% bonus value. How much extra do you get?” Teacher models one approach: 10% of 50 is 5, so 20% is 10; extra = 10. Then asks students to check: “Is the bonus more than the original or less?” Students solve the next two scenarios on the same sheet:

• “$80 item with 25% discount: what is the sale price?” (find 25% off using 10%/5% or equivalent)
• “A class recycling bin is 60% full after one hour. If the bin holds 100 kg, how much is it holding?” (interpret 60% as 60 kg) Students must show the model: link percent to part/whole, then compute, then interpret the meaning.

5. 26–30 min · Exit check and review. Teacher displays 3 rapid questions:

• “Convert 30% to a fraction and decimal.”
• “Which is bigger: 0.7 or 70%? Explain.”
• “If something increases by 10%, should the value be larger than the original? Why?” Student answers individually; teacher quickly checks reasoning for equivalence and interpretation.

Resources

• 10×10 hundred grid (print or interactive on screen)
• Coloured counters or markers
• Conversion table worksheet (Percentage ↔ Fraction ↔ Decimal)
• Modelling scenarios sheet (bonus, discount, and “percent full” problem)
• Whiteboard/markers and projector (if available)
• Calculator available only for checking, not for every step
• Exit ticket strip (3 questions)

Assessment

• Formative checks during guided practice: accuracy in linking “out of 100” to correct fraction/decimal representations.
• Teacher questioning during modelling: “What is the whole? What does the percent mean as a part?” and “How do you know your answer fits the situation?”
• Exit ticket to verify conversions and interpretation (big-picture sense-making and correctness).

Differentiation

• Support: Provide a partially completed conversion table (e.g. fill the “out of 100” fraction first), plus sentence starters: “30% means 30 out of 100, so …”
• Support: Use only percentages that convert cleanly to hundredths (10%, 20%, 25%, 40%, 50%, 75%) and decimals that terminate (to avoid non-terminating complications in this introduction).
• Extension (if finished quickly): Ask students to create their own example where a percentage equals a common fraction (e.g. 50% = 1/2) and explain the link.
• EAL/SEN considerations: Keep language consistent (“whole”, “part”, “out of 100”) and allow drawing from the grid to represent quantities, not only writing.