Primary Maths | Chance and Probability: An Introduction (for tutors) | the 0 to 1 scale, 3 red 5 blue 2 green, 10 exercises

2026-11-13

Tutor lesson-prep guides · Primary Maths

Data handling at P6 is easily taught as guessing which outcome is more likely. This lesson replaces the guess with a number: a scale from 0 to 1 where impossible and certain sit at the ends, a bag of balls to turn chance into a fraction, and a test of fairness based on whether both sides have the same probability.

Objectives — Students can: (1) use 0 for impossible and 1 for certain and place everyday events on that scale; (2) write a probability as a fraction using favourable outcomes over all outcomes, for example 3 red 5 blue 2 green in a bag of 10 gives 3/10 for red; (3) express 3/10 as 0.3 and 30%, and state that not drawing red is 7/10; (4) judge whether a game is fair by comparing the two probabilities, so 0.3 against 0.5 is unfair.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Meaning of a fraction	What does 3/10 mean?	Split into 10 equal parts and take 3
Fraction to percentage	What is 3/10 as a percentage?	30%
Equal shares	Does each quarter of a spinner have the same chance?	Yes, one quarter each

02 Lesson flow (45 minutes)

Time	Stage	Tutor does	Student does
0-5 min	The 0 to 1 scale	Write impossible and certain and give two examples of each	Answer orally and place them on the scale
5-15 min	Count, then write the fraction	Model 3 red 5 blue 2 green giving 3/10	Count the bag and write each fraction
15-25 min	Three forms of one number	3/10 to 0.3 to 30%, and 7/10 for the complement	Convert four values
25-35 min	Fair and unfair	Model a two player game at 0.3 against 0.5	Judge three games and give the reason
35-42 min	With and without replacement	Show the denominator dropping to 9 after one ball is removed	Do two items and state the new denominator
42-45 min	Exit check	Five oral questions	Leave only with all five correct

03 Teaching script (read it out)

Scene 1: Turn chance into a scale from 0 to 1

Draw a line on the board: 0 means impossible at the left end, 1 means certain at the right. Place events on it: the sun rising in the east goes to 1, rolling a 7 on an ordinary die goes to 0, rain tomorrow sits somewhere in the middle, an odd number on a die sits at 0.5.

Students must know that every probability lies between 0 and 1; an answer of 1.2 or minus 0.3 is wrong by inspection. That boundary does more work than any formula, because it lets students check themselves.

Ask the reverse question: what does a probability of 0.5 mean? It means an even chance, not a guarantee that one of each happens in two tries. Say this explicitly, because treating probability as a promise is the most common P6 misunderstanding.

Scene 2: Count before calculating

A bag holds 3 red, 5 blue and 2 green, ten in total. The probability of red is 3/10, which is 0.3 or 30%. Two steps only: count all of them, count the ones you want, write the fraction.

Then ask for the probability of not drawing red. Students answer 7/10, because 10 minus 3 is 7. Add the useful property: 3/10 plus 7/10 equals 1. The two probabilities always add to one, which gives a free check and a way to work backwards.

Contrast with and without replacement: if one red is taken out and not returned, nine balls remain and only two are red, so the next draw gives 2/9. The denominator changed, and that is the step P6 students most often skip.

Scene 3: Judge fairness by the numbers

Write the game clearly: roll a die, a 6 wins for A, anything else wins for B. A has 1/6, B has 5/6. Is it fair? No, and the reason is that the two probabilities differ.

Give an operational definition: fair means both sides have the same probability of winning. A coin toss and odd against even on a die (1/2 each) are fair; a 6 against the other five faces is not. Require the sentence to carry the numbers, not a feeling.

Finish with a spinner: four equal sectors, one red, so red is 1/4 or 25% and not red is 3/4 or 75%. Paint a second sector red and it becomes 2/4, an even chance, and the game becomes fair. Letting students repaint the spinner themselves is the strongest ending.

04 Question types and worked steps

Type	Example	Steps	Answer
Judging chance	What is the chance of rolling a 7 on a die?	Locate the event on the 0 to 1 scale	0, because it is impossible
Calculating probability	A bag has 3 red 5 blue 2 green. Probability of blue?	Favourable over total	5/10, which is 1/2 or 50%
Complement	What is the probability of not drawing green?	One minus the probability of green	1 minus 2/10, which is 8/10 or 80%
Fairness	A 6 wins for A, anything else for B. Is it fair?	Compare the two probabilities	No, 1/6 against 5/6

Sanity check (teach this): Three checks before collecting answers. First, is the value between 0 and 1? An answer of 1.5 or 30 means percentages and probabilities have been mixed. Second, is the denominator the total? For 3 red 5 blue 2 green it must be 10 unless the question says otherwise. Third, does the answer match the event asked? Giving the probability of drawing when the question asked for not drawing is a reading error, not a calculation error, and the two need separate correction.

05 Independent practice (3 questions)

Question	Answer	What to watch
1. Write two events with probability 0 and two with probability 1.	Two impossible, two certain	A vague answer such as very unlikely is not accepted
2. A bag has 3 red 5 blue 2 green. Write the probability of each colour.	3/10, 5/10, 2/10	The three fractions must add to 1
3. Write 3/10 as a decimal and as a percentage.	0.3 and 30%	Answering 3% shows a place value error
4. One red is removed and not replaced. Probability of red on the next draw?	2/9	Answering 3/10 means replacement was ignored
5. Is a 6 against the rest fair? Give the reason.	No, 1/6 against 5/6	A verdict without a reason is not accepted

06 Common mistakes and what to say

Mistake	Student writes	Say this
Treating probability as a promise	It is 50%, so one of two tries must succeed	An even chance describes the long run, not two tries. The wording to teach is the more trials, the closer to the expected share.
Using the wrong denominator	A bag of 3 red 5 blue 2 green gives 3/7 for red	The denominator is all ten balls, not the other colours. Count the whole bag first.
Writing a probability above 1	Answering 30 or 1.5	The maximum is 1. Ask the check question: is this number bigger than one? If so, a percentage has been written as a probability.
Ignoring without replacement	Keeping the old denominator after a ball is removed	When the question says not replaced, both the denominator and the numerator drop. Circle those two words while reading.

07 Homework (paper, section and question numbers)

Primary maths prep index — Open the line graph and average chapter and compare what graphs show with what probability predicts
Probability exercises — Exercises 1 to 3: write the three fractions and check that they add to 1
Fairness exercises — Exercises 4 and 5: state both probabilities and justify the verdict in one sentence

08 Exit check (last 5 minutes)

Question	Answer	Decision
Which numbers represent impossible and certain?	0 and 1	Very unlikely or very likely is not a number
A bag has 3 red 5 blue 2 green. Probability of red?	3/10, which is 30%	Answering 3/7 means the denominator is wrong
What do the probabilities of an event and its complement add to?	1	Answering 100 means percentages are confused with probabilities
How do you decide whether a game is fair?	Both sides have the same probability	A feeling is not a method
What happens to the denominator when a ball is not replaced?	It drops from 10 to 9	Answering that it stays the same means the condition was missed

09 Tutor FAQ

Does P6 need a formula?

No. Favourable outcomes over all outcomes is enough. The formal rule belongs to secondary school; P6 assesses understanding and explanation.

My student insists red is due because it appeared three times already. What do I say?

Use a coin: each toss is independent and earlier results do not change the next. Twenty recorded tosses persuade far better than an argument.

Must the fraction be simplified?

Yes, but write the percentage as well. Having both 3/10 and 30% makes marking and self checking easier.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.