What Is a Percentage?

Overview

This is lesson 1 of 3 in Percentages on the Grid. Learners develop the idea that percentage means “out of 100”, using a hundreds grid to connect percentage, fraction and decimal representations.

Learning intentions

• WALT understand percentage as parts per hundred.
• WALT represent percentages on a hundreds grid.
• WALT connect percentage, fraction and decimal notation.
• WALT explain how different representations can show the same amount.

Success criteria

• I can explain that percent means “out of 100”.
• I can shade and label a percentage on a hundreds grid.
• I can write a percentage as a fraction and decimal where appropriate.
• I can match equivalent percentage, fraction and decimal representations.

Curriculum links

• Number: recognise, represent and compare fractions, decimals and percentages.
• Number: use place value to connect tenths and hundredths with decimal notation.
• Algebraic thinking: identify and explain equivalent representations of the same quantity.
• Mathematical practices: use materials, diagrams, symbols and mathematical language to communicate reasoning and justify answers.

Lesson structure (30 minutes)

1. 0–5 min – I do: Introduce “out of 100”

Open with the introduction and modelling slides and display a large hundreds grid. Ask: “If the whole grid is 100 squares, how many squares would 10% represent?” Model shading 10 squares, then record:

• 10% = 10/100 = 0.10
• 25% = 25/100 = 0.25
• 50% = 50/100 = 0.50

Think aloud about the connection between the shaded squares, the fraction and the decimal. Emphasise that the denominator is 100 because percent means “per hundred”.

2. 5–8 min – Notice and discuss

Ask learners to turn and talk: “How could you shade 25% quickly?” and “What fraction of the grid is 50%?” Invite responses such as using quarters, halves, rows of ten or known fractions. Clarify that 50/100 is equivalent to 1/2 and 25/100 is equivalent to 1/4.

3. 8–18 min – We do: Build examples

In pairs, distribute hundreds grids and counters or base-ten materials. Use the fraction-decimal-percentage matching cards to support the matching discussion. Call out or display examples such as 10%, 25%, 50%, 20% and 75%; learners build or shade each amount and explain what they notice.

Support discussion with prompts:

• “How many out of 100 are shaded?”
• “What fraction does this show?”
• “What decimal records the same amount?”
• “How do you know your representations are equivalent?”

Year 4 learners focus on 10%, 25% and 50%. Year 5 learners record equivalent fractions and decimals. Year 6 learners extend examples to tenths and hundredths, including 31% = 31/100 = 0.31.

4. 18–28 min – You do: Represent and match

Distribute the percentage grid and matching worksheet. Learners independently shade and label given percentages, then match percentage, fraction and decimal representations. Include differentiated items:

• Year 4: 10%, 25% and 50%, with visual grids.
• Year 5: 10%, 25%, 50%, 20% and 75%, including simplified fractions and decimals.
• Year 6: include 31%, 45%, 62% and 90%, recording each as a fraction over 100 and a decimal.

Circulate and ask learners to justify one answer rather than simply checking it. Invite early finishers to create a percentage that has more than one equivalent fraction.

5. 28–30 min – Review and share

Return to the discussion and plenary slides. Ask selected pairs to share a strategy for finding 25%, 50% or 31%. Finish with the prompt: “What does the word percent tell us about the whole?” Restate the key idea: percentage describes how many parts there are out of 100.

Resources

• the introduction and modelling slides — one deck used throughout the lesson
• the percentage grid and matching worksheet
• the fraction-decimal-percentage matching cards
• Hundreds grids, one per learner or pair
• Counters or base-ten materials
• Coloured pencils or highlighters
• Board or visualiser
• Prepared examples: 10%, 25%, 50%, 20%, 75% and 31%

Assessment

• Listen for accurate use of “out of 100”, “equivalent” and “whole”.
• Check whether learners shade the correct number of squares and connect it to fraction and decimal notation.
• Collect or scan the worksheet, noting misconceptions such as treating 25% as 25/10 or writing 0.25 as 0.025.

Differentiation

• Support: use a grid labelled in rows of ten; begin with 10%, 50% and 25%; provide sentence frames such as “___% means ___ out of 100”.
• Support for EAL and learners needing additional scaffolding: pre-teach whole, part, hundred, fraction, decimal with gestures and visuals; allow learners to explain using materials before recording symbols.
• Extension: ask learners to find two equivalent fractions for 25%, 50% and 75%, or explain why 31% is greater than 0.3.
• Challenge: ask Year 6 learners to order 31%, 0.45, 1/2 and 62/100, explaining their method.