Probability with Fractions

Overview

In this lesson, students connect probability to fractions and use their own experimental results to calculate simple probabilities. They compare expected outcomes using “fraction of the total” language and check that answers match the data.

Learning intentions

• Students will be able to describe probability as “how likely” an outcome is.
• Students will be able to record outcomes from a simple chance experiment and tally results.
• Students will be able to calculate probability as a fraction using experimental data.
• Students will be able to explain their reasoning using probability and fraction language.

Success criteria

• I can identify whether an outcome is more or less likely using our experiment results.
• I can represent probability as a fraction (favourable outcomes out of total outcomes).
• I can calculate probabilities for at least two outcomes correctly from a table.
• I can check my answers by comparing them to the tally counts and totals.

Curriculum links

• Chance experiments, collecting data, and describing likelihood of outcomes.
• Representing probability using simple fractions and relating it to the frequency from experiments.
• Using mathematics to communicate reasoning with counts, totals, and outcomes.
• Applying number sense to work with small whole numbers and fractions.

Lesson structure (45 minutes)

1. 5 minutes – Warm-up: Likely or unlikely? Show 3 short scenarios (e.g., “rain today”, “coin lands heads”, “spinner stops on red”). Students vote with thumbs (likely/less likely/uncertain) and explain using one sentence: “In our classroom experience/data…”.
2. 8 minutes – Model: Probability as a fraction of outcomes Teacher displays an example tally for rolling a die 12 times (or spinning colours with 12 spins). Highlight:

• total outcomes = number of trials
• favourable outcomes = count of the outcome being asked about
• probability = favourable ÷ total as a fraction (e.g., 3 out of 12). Connect to fraction ideas: numerator = favourable count, denominator = total.

3. 20 minutes – Experiment: Collect fresh data In pairs, students complete a short trial set using a fair spinner or bag of counters (teacher chooses one consistent model for the whole class). Aim for 20 trials per pair. Students must:

• record each outcome in a tally table
• calculate totals for each outcome
• keep the fraction connection visible (favourable count written next to the question). Teacher circulates, checking that tallies are correct and that students record totals accurately.

4. 8 minutes – Calculate probabilities from data Students answer 3 teacher prompts in their maths book:

• “What is the probability of Outcome A?” (write as a fraction using their tallies)
• “What is the probability of Outcome B?”
• “Which is more likely and why?” (use fraction comparison or “has a larger count out of the same total”). Encourage students to simplify fractions if they can (e.g., 5/20 to 1/4) and explain simplification in terms of equal parts.

5. 4 minutes – Share and check reasoning Invite 2–3 pairs to share their calculations and reasoning. Class checks using the totals: students verify that probabilities use the same denominator (the total number of trials).

Resources

• Paper or student recording sheets with a tally table and space for calculations
• Spinner and pointer (or bag and counters) with 2–4 possible outcomes
• Counters/chips for recording outcomes (optional)
• Projector/board to model tally totals and fraction probability
• Worked example (teacher reference only) showing favourable and total outcomes
• Pencil, eraser, and maths notebook for each student
• Timer for trial rounds

Assessment

• Teacher observation during experimenting: correct tallying, accurate totals, and correct use of “favourable outcomes out of total”.
• Maths book checks: probability fractions match tallies and use the correct denominator.
• Exit explanation: one sentence identifying the more likely outcome and referencing the fraction or counts.

Differentiation

• Support: Provide sentence starters (“The total number of trials is…”, “The favourable outcomes are…”, “So the probability is favourable/total.”) and a partially completed tally table.
• Support: Offer a bank of common denominators based on trial number (e.g., if 20 trials: 0/20, 1/20, 2/20…).
• Extension: Ask students to compare experimental probability with a “fair” expectation (e.g., if outcomes are equal parts, which fraction should be expected) and comment on differences due to chance.
• EAL/SEN: Allow oral responses and pictorial supports; use consistent language for “favourable” (the outcome we want) and “total” (all trials). Provide extra time for calculating fractions.