### Use the language of probability

Describe and predict outcomes from data using the language of chance or likelihood.

Get your students engaged with probability scale through the use of Mangahigh’s adaptive quiz ‘Probability scale’. Students will start with ‘Easy’ questions to help introduce new ideas and then move onto ‘Medium’ questions with some scaffolded support. Students then progress onto ‘Hard’ questions that really test their understanding, and the most able will move on to ‘Extreme’ questions that will challenge even the brightest students.

Example of blended learning lesson

Write these 4 statements on the board:

1. A coin landing on heads.

2. A fair dice landing on a 6.

3. My mother being female.

4. My sister being male.

Discuss what the probability of each of these statements is and how it can be shown as a percentage, decimal or fraction. Order these statements from likely to unlikely and discuss what the probability numbers look like.

1. A coin landing on heads.

2. A fair dice landing on a 6.

3. My mother being female.

4. My sister being male.

Discuss what the probability of each of these statements is and how it can be shown as a percentage, decimal or fraction. Order these statements from likely to unlikely and discuss what the probability numbers look like.

Set the Mangahigh activity ‘Probability scale’. Each time students play through the activity they will answer 10 questions. Encourage students to make at least three attempts, i.e. attempt at least 30 questions. Students will receive a bronze medal award and thus demonstrate they have a secure understanding if they can prove their competency at the hard questions. The most able students might achieve a silver or gold medal by answering extreme questions. Move through the class offering help where needed and challenge students to explain their solutions. Use your Mangahigh analytics platform to check progress and support struggling students.

Play through the activity ‘Probability scale’ from your Mangahigh teacher platform on the whiteboard with the whole class. Challenge students to explain their solutions.

Students return to the ‘Probability Scale’. For the most able, set an additional activity ‘Experimental probability’. Use your Mangahigh analytics platform to identify any students who have struggled with the first activity ‘Probability Scale’ and support them or encourage them to work with their peers.

Write the following statements on the board:

1. A coin landing on tails.

2. A fair dice not landing on a 6.

3. My father being female.

Ask the students to attempt on paper:

1. Write the probability of each event as a decimal

2. Write the probability of each event as a fraction

3. Write the probability of each event as a percentage.

Bonus question:

4. I am certain that if I rolled a dice I would get a 1, true or false?

5. Explain your reasoning for your answer to the last question

1. A coin landing on tails.

2. A fair dice not landing on a 6.

3. My father being female.

Ask the students to attempt on paper:

1. Write the probability of each event as a decimal

2. Write the probability of each event as a fraction

3. Write the probability of each event as a percentage.

Bonus question:

4. I am certain that if I rolled a dice I would get a 1, true or false?

5. Explain your reasoning for your answer to the last question

Introduce your students to calculating the probability of single events through the use of Mangahigh’s adaptive quiz ‘Probability of single events’. Students will start with ‘Easy’ questions to help introduce new ideas and then move onto ‘Medium’ questions with some scaffolded support. Students then progress onto ‘Hard’ questions that really test their understanding, and the most able will move on to ‘Extreme’ questions that will challenge even the brightest students.

Example of blended learning lesson

On the whiteboard draw a bag with 10 marbles in: Discuss and colour in the marbles using the definitions that: half the marbles are blue, 10% of the marbles are red and 0.4 marbles are green. Then continue by asking what the probability of taking out a red marble is and how many different ways can you write this mathematically.

Set the Mangahigh activity ‘Probability of single events’. Each time students play through the activity they will answer 10 questions. Encourage students to make at least three attempts, i.e. attempt at least 30 questions. Students will receive a bronze medal award and thus demonstrate they have a secure understanding if they can prove their competency at the hard questions. The most able students might achieve a silver or gold medal by answering extreme questions. Move through the class offering help where needed and challenge students to explain their solutions. Use your Mangahigh analytics platform to check progress and support struggling students.

Play through the activity ‘Probability of single events’ from your Mangahigh teacher platform on the whiteboard with the whole class. Challenge students to explain their solutions.

Students return to ‘Probability of single events’. For the most able, set an additional activity ‘The probability of events not happening’. Use your Mangahigh analytics platform to identify any students who have struggled with the first activity ‘Probability of single events’ and support them or encourage them to work with their peers.

Using the whiteboard write down this statements:

1. There are 10 marbles in a bag, 3 red, 3 blue and 4 green, what is the probability that blue is chosen?

2. There are 12 marbles in a bag, half are red, a quarter are blue and a quarter are green, how many blue marbles are in the bag?

3. There are 20 marbles in a bag, 7 red, 10, blue and 3 green, there is a probability of 0.5 that I will pick out a blue marble, true or false? Explain your reasoning.

Students attempt to write down the correct answer for each event.

1. There are 10 marbles in a bag, 3 red, 3 blue and 4 green, what is the probability that blue is chosen?

2. There are 12 marbles in a bag, half are red, a quarter are blue and a quarter are green, how many blue marbles are in the bag?

3. There are 20 marbles in a bag, 7 red, 10, blue and 3 green, there is a probability of 0.5 that I will pick out a blue marble, true or false? Explain your reasoning.

Students attempt to write down the correct answer for each event.

Curriculum-aligned activities

Describe and predict outcomes from data using the language of chance or likelihood.

Understand what is meant by random (i.e. different results may occur from repeating the same experiment) and bias events and recognize them in a practical context.

Draw a tree diagram for conditional events. Find the probability of more than one successive event occurring using the branches of the tree diagram. Include multiplication of both decimals or fractions with and without a calculator. Find the probability of more than one mutually exclusive overall outcome occurring by summing the required results.

Calculate the relative frequency of an event for a changing number of trials. Understand that the relative frequency gives an estimation of the probability of an event. Calculate the expected number of outcomes for an event based on a fixed number of trials. Draw and interpret a graph showing the relative frequency plotted against the number of trials. Understand that the variations will settle down as the number of trials increase.

Calculate probabilities of successive independent or dependent events using p(A and B) = p(A) × p(B) or p(A and B) = p(A) × p(B if A has happened) without reference to tree diagrams. The formula notation is not needed. Use the multiplication formula to prove/disprove events are independent. Restrict examples to only one overall outcome, i.e. do not sum separate overall events.

List all possible equally likely outcomes for successive events including using a 2 way table. The terms sample space, possibility space, probability space need to be known. Include tossing coins and combinations from a menu and 2 dice rolls.

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