Percent Connections

Overview

Students explore how 10%, 25% and 50% represent the same quantity in three forms: percentage, decimal and fraction. They use visual models and benchmark percentages to connect prior learning about fractions and place value with proportional reasoning.

Learning intentions

• WALT represent 10%, 25% and 50% as fractions, decimals and percentages.
• WALT explain how equivalent representations show the same amount.
• WALT use visual models and known fractions to solve percentage problems.
• WALT communicate our mathematical thinking clearly.

Success criteria

• I can convert 10%, 25% and 50% to a fraction and a decimal.
• I can use a hundred grid or other model to prove my answer.
• I can explain why different representations can have the same value.
• I can solve a simple problem involving one of these percentages.

Curriculum links

• Mathematics and Statistics: Number — recognising and representing fractions, decimals and percentages.
• Mathematics and Statistics: proportional reasoning — connecting different representations of the same quantity.
• Mathematics and Statistics: mathematical communication — explaining strategies and justifying answers.
• Mathsteasers — using challenging questions to deepen understanding and problem-solving.

Lesson structure (40 minutes)

1. 0–5 min · Hook and prior knowledge. Open with the hook and learning intention slides showing three identical 100-square grids shaded 10, 25 and 50 squares, and ask, “Which number tells us how much is shaded?” Students make predictions, discuss with a partner and share any fraction, decimal or percentage they recognise.

2. 5–13 min · Explicit teaching. Use the conversion teaching slides to model that percent means “out of 100”. Record:

• 10% = 10/100 = 1/10 = 0.1
• 25% = 25/100 = 1/4 = 0.25
• 50% = 50/100 = 1/2 = 0.5 Teacher shades each amount on a hundred grid and models simplifying the fractions. Students copy the three equivalence chains and explain one connection to a partner.

3. 13–18 min · Guided reasoning. Display the prompts in the guided questions slides: “How many tenths is 50%?”, “How many quarters is 25%?” and “Why is 10/100 the same as 1/10?” Students use mini-whiteboards to answer, hold them up, and correct their thinking after discussion. Emphasise that decimals describe tenths and hundredths using place value.

4. 18–30 min · Independent practice. Distribute the percentage conversion and reasoning worksheet. Students complete matching, conversion and visual-model questions independently, then compare selected answers with a partner. Teacher works with a focus group, using a hundred grid and fraction strips to support students who need concrete representations.

5. 30–36 min · Challenge and discussion. Use the problem-solving and challenge slides to present: “A class has 25 students. 50% bring fruit for morning tea. How many students is that?” Students solve using a drawing, fraction or decimal, then tackle a second problem involving 25% of 20 or 10% of 30. Invite several strategies and discuss which representations are most efficient.

6. 36–40 min · Plenary and exit check. Return to the recap and exit-question slide. Students complete a quick exit response: “Convert 25% to a fraction and decimal. Show or describe how you know.” Invite two students to explain different methods, collect responses and revisit any common misconception.

Resources

• the complete percentage connections slide deck
• the percentage conversion and reasoning worksheet
• Hundred grids, one per student or pair
• Fraction strips or fraction circles
• Mini-whiteboards and pens
• Pencils, rulers and coloured pencils
• Display board or interactive whiteboard

Assessment

• Listen for correct use of “out of 100”, “equivalent” and “same value” during partner talk and guided questioning.
• Check mini-whiteboard responses and circulate during the worksheet, noting whether students simplify fractions accurately and connect decimals to place value.
• Use the exit response to identify students who can convert independently and those who need further work with hundred grids or fraction equivalence.

Differentiation

• Support learners with a pre-drawn hundred grid, fraction strips, a conversion table and sentence starters: “___% means ___ out of 100” and “I know this because…”.
• Provide dyslexia-friendly options: clear sans-serif font, large print, uncluttered worksheet sections, minimal text, strong contrast and the option to hear instructions read aloud.
• Pair students strategically for discussion and allow students to show understanding through drawing, pointing, oral explanation or written calculation.
• For advanced learners, ask them to find two different ways to calculate 25% of 36 or 50% of 48, then create a word problem involving 10%, 25% or 50% and explain why their answer is reasonable.