Fraction Probabilities

Overview

In this lesson (Lesson 3 of 8), students learn to calculate probabilities of single events and express answers as fractions on the 0–1 scale. This builds from Lesson 2 where students recorded outcomes and compared equally likely outcomes.

Learning intentions

Students will:

• calculate theoretical probabilities for single events using equally likely outcomes
• represent probability as a fraction (favourable outcomes ÷ total outcomes)
• understand and use appropriate probability language such as “equally likely” and “chance”

Success criteria

Students can:

• list/identify the total number of equally likely outcomes
• count favourable outcomes for the event
• write probability as a simplified fraction
• give a sensible answer between 0 and 1

Curriculum links

• Probability: record, describe and analyse frequency of outcomes, including using appropriate language and the 0–1 probability scale
• Probability: generate theoretical sample spaces and use them to calculate theoretical probabilities
• Probability: understand that probabilities of all possible outcomes sum to 1
• Mathematics KS3: enumerate sets systematically using tables, grids and Venn diagrams (as needed for counting outcomes)

Lesson structure (60 minutes)

1. 0–5 min · Do Now (Review). Teacher displays 2 quick questions from Lesson 2 outcomes (e.g., “How many outcomes in this sample space?” and “Is this event more or less likely?”) and checks answers with brief cold calls. Students face front and stay silent during teacher checks, then write their answers independently.

2. 5–12 min · I Do (Model fractional probability). Teacher models a worked example with a small equally likely sample space (e.g., a fair spinner with 8 equal sectors, or a die roll). Teacher writes:

• total outcomes = 8 (or 6)
• favourable outcomes = number that match the event
• probability = favourable ÷ total Students copy the structure “Total outcomes → Favourable outcomes → Fraction probability”.

3. 12–22 min · We Do (Guided practice). Teacher and class complete 3 example questions together, using the same counting template and simplifying fractions. After each question, teacher asks one “think” question, then uses short turn and talk.

• Q1: “Probability of getting an odd number on a die”
• Q2: “Probability of flipping heads when flipping a coin once”
• Q3: “Probability of choosing a blue counter from a bag with known equal counts” Students work in pairs for 30–40 seconds on each, then return to face front for the class method.

4. 22–35 min · You Do (Independent practice with success checks). Students complete a worksheet of 6 questions (single events only) using equally likely outcomes and fraction form. Teacher circulates using the school’s “stop and focus” routine during teaching points; when students are stuck, they use a checklist: “Have I counted total? Have I counted favourable? Have I written as favourable/total? Have I simplified?” Students mark one self-check question after question 3 using an answer slip at the desk.

5. 35–45 min · Success check round (Target misconceptions). Teacher chooses 2 student answers (anonymised) showing common errors:

• using wrong numerator/denominator
• forgetting to simplify the fraction Teacher asks the class to diagnose the mistake. Students turn and talk briefly (“Which part is wrong and why?”), then teacher confirms the correct method.

6. 45–55 min · You Do (Final practice: mixed context). Students complete 2 final questions: one guaranteed fraction simplification (e.g., 2 favourable out of 6), and one where favourable outcomes equals total (probability 1) or equals 0 (probability 0). Students write answers and a one-sentence justification using probability language (e.g., “There are 0 outcomes that… so probability is 0”).

7. 55–60 min · Exit ticket (Quick assessment). Teacher gives a single exit question: “A spinner has 10 equal sections. Event A: landing on 2 specific sections. What is P(A) as a simplified fraction?” Students answer independently; teacher collects for next-step planning.

Resources

• Worksheet: “Calculating Simple Probabilities” (fraction probability, 8 questions total)
• Spinner/die/counter pictorial cards (optional class examples)
• Fraction counting template (Total → Favourable → Fraction)
• Answer slip for self-check after question 3
• Anonymous misconception examples (prepared on paper)
• Small counters or paper strips for bag/spinner representations
• Dyslexia-friendly reading supports: sentence-by-sentence question cards, larger font, and a “maths glossary” sheet for key words

Assessment

• Formative: teacher circulates during You Do, checks whether students identify total and favourable correctly
• Formative: guided “success check round” targets numerator/denominator and simplification misconceptions
• Exit ticket: assesses ability to compute and simplify fraction probabilities for a single event

Differentiation

• Support:
• sentence starters for justifications: “Total outcomes are ___. Favourable outcomes are ___. So the probability is ___. ”
• number line prompt for 0–1 scale: “0 means impossible, 1 means certain”
• provide a completed example template with blanks for students to fill (Total / Favourable / Probability)
• allow dyslexia-friendly reading cards with reduced text and clear spacing
• Core challenge:
• ensure students write probability as a fraction and simplify when possible
• Extension (advanced learners):
• add a question where the event includes a subset of outcomes (still single event) and require both fraction probability and a quick comparison (e.g., “Is it less than 1/2? Prove it by counting.”)
• ask students to create their own spinner with 12 equal sections and design an event with probability 1/3, then swap and solve using the sample space
• EAL/SEN considerations:
• pre-teach “favourable outcome” with one visual example
• encourage turn and talk using a structured prompt: “I counted __ total and __ favourable”
• accept equivalent fraction forms if not simplified, but require simplification in final two questions for core learners

Success criteria for each lesson

• Do Now: students recall how to identify outcomes and events
• I Do: students match the method structure (Total → Favourable → Fraction)
• We Do: students correctly count favourable outcomes with teacher support
• You Do: students independently produce correct simplified fraction probabilities for single events and justify with brief probability language