Carnival Probability Conversions

Overview

In this lesson students convert fractions to decimals and percentages, then use these forms to compare quantities linked to carnival game probabilities. They work with short, realistic scenarios (e.g., “chance to win” cards) and represent results in simple tables/graphs.

Learning intentions

• Students will convert between fractions, decimals and percentages for values that represent probability.
• Students will compare quantities using decimal and percentage representations.
• Students will interpret probability information from carnival-style scenarios.
• Students will create and read simple data representations to compare probabilities.

Success criteria

• I can convert common fractions (with denominators such as 2, 4, 5, 10) into decimals and percentages.
• I can match a decimal or percentage to the correct fraction form.
• I can compare two probabilities using decimals and percentages and explain which is larger and why.
• I can use a table or bar plot to represent and compare probabilities from a scenario.

Curriculum links

• Number and Algebra: converting between fractions, decimals and percentages and using them to interpret quantities
• Probability: assigning numerical probabilities to likelihood and using probability language appropriately
• Data representation: using tables and graphs to organise and interpret information

Lesson structure ({total minutes})

1. 5 min — Launch: “Which game is better?” Display two carnival game cards showing win chances as fractions (e.g., 3/5 and 1/2). Students decide quickly which is more likely, but must justify using conversion (not guesses only).

2. 10 min — Mini-lesson: conversion strategies Model 3 worked examples using thinking aloud:

• Convert fraction to decimal by finding an equivalent fraction with denominator 10 (or 100).
• Convert decimal to percentage by multiplying by 100.
• Show both directions: decimal/percentage back to a fraction when possible (especially tenths and fifths). Emphasise: probability written as a value between 0 and 1 can also be a percentage between 0% and 100%.

3. 10 min — Guided practice: conversion and comparison Students work in pairs on a short set of conversions and comparisons (4–6 items). For each item they write: fraction → decimal → percentage, then circle the larger probability. Teacher circulates to check correct placement of “tenths/hundredths” and percent reasoning.

4. 10 min — Data representation activity: compare probabilities Provide a “carnival board” scenario: three games with win probabilities given as fractions/decimals/percentages in mixed forms. Students complete a table with columns: Game, Win probability (fraction), (decimal), (percentage). Then they create a simple bar representation (e.g., one bar per game) using the percentages as heights or scaled ticks on a short axis.

5. 7 min — Whole-class discussion: fairness lens Students share one comparison (e.g., “Game A is 60% while Game B is 50%, so A is more likely to win”). Guide them to make links to fairness: if players pay the same, higher win probability may make a game less fair for the organiser.

6. 3 min — Exit ticket: convert + compare Individually, students answer 2 questions:

• Convert a given fraction to decimal and percentage.
• Compare two given probability values and state which is greater using a complete sentence.

Resources

• Fraction to decimal and decimal to percentage conversion charts (including tenths and common carnival-friendly denominators)
• Game cards/scenario sheets with win probabilities written in mixed forms
• Table template for recording fraction, decimal and percentage
• Graph paper or printed bar-plot templates with a percentage scale (0–100)
• Coloured pencils for highlighting the larger probability
• Student calculators (optional, teacher-managed) for checking tenths/hundredths
• Rulers/tape for drawing quick bar heights
• Dyslexia-friendly worksheets with larger fonts and short lines (or audio-supported read-aloud version)

Assessment

• Formative checks during guided practice (conversion accuracy and correct comparison language)
• Teacher observation of table and bar representation accuracy
• Exit ticket used to diagnose common errors (e.g., percent placement, incorrect equivalence)

Differentiation

• Provide conversion charts at each workstation, including worked examples for converting halves, quarters, fifths, tenths.
• Support students needing scaffolded steps: a “fraction → make denominator 10 → read decimal → multiply by 100” checklist.
• EAL support: sentence starters for justification (e.g., “Because 0.xx is larger than 0.yy, the percentage is larger, so…”).
• Dyslexia-friendly options:
• Print worksheets in larger font with generous spacing and fewer items per page.
• Read scenarios aloud and allow students to answer verbally or with a partner scribe before writing independently.
• Extension for advanced learners:
• Ask students to find and justify equivalent probabilities (e.g., identify fractions that match 0.3 or 40%).
• Include one “trick” comparison where values look similar (e.g., 0.6 vs 60%) and require precise reasoning.
• Extension (time allowing, built into practice): add a challenge item requiring choosing which conversion method is most efficient and explaining why.

Extension (optional)

• Probability puzzles (decimals and percentages): Students solve a mini set where probability is given as a percentage, then they must decide the matching fraction and compare two “win chances” without converting all values fully (only convert strategically, then justify).