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Chapter 48: Probability Language

Learn Grade 4 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.

Grade 4Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
Estimated reading time0% read
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Chapter Overview

This chapter teaches Probability Language in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

48.1 Impossible events

Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: A bag has 4 red and 6 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 2

Problem: A bag has 3 red and 3 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: equally likely

Worked Example 3

Problem: A bag has 3 red and 5 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 4

Problem: A bag has 6 red and 6 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: equally likely

Worked Example 5

Problem: A bag has 1 red and 5 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 6

Problem: A bag has 3 red and 5 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 7

Problem: A bag has 5 red and 3 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 8

Problem: A bag has 5 red and 2 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 9

Problem: A bag has 5 red and 6 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 10

Problem: A bag has 3 red and 2 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Practice Exercise

Create and solve one new example of Impossible events. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

48.2 Unlikely events

Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: A bag has 5 red and 4 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 2

Problem: A bag has 4 red and 3 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 3

Problem: A bag has 1 red and 4 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 4

Problem: A bag has 1 red and 6 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 5

Problem: A bag has 5 red and 6 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 6

Problem: A bag has 2 red and 2 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: equally likely

Worked Example 7

Problem: A bag has 5 red and 4 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 8

Problem: A bag has 2 red and 4 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 9

Problem: A bag has 6 red and 3 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 10

Problem: A bag has 6 red and 1 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Practice Exercise

Create and solve one new example of Unlikely events. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

48.3 Equally likely outcomes

Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: A bag has 1 red and 4 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 2

Problem: A bag has 2 red and 5 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 3

Problem: A bag has 6 red and 5 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 4

Problem: A bag has 6 red and 5 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 5

Problem: A bag has 3 red and 5 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 6

Problem: A bag has 1 red and 2 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 7

Problem: A bag has 1 red and 2 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 8

Problem: A bag has 4 red and 2 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 9

Problem: A bag has 4 red and 6 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 10

Problem: A bag has 1 red and 1 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: equally likely

Practice Exercise

Create and solve one new example of Equally likely outcomes. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

48.4 Likely events

Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: A bag has 3 red and 4 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 2

Problem: A bag has 5 red and 2 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 3

Problem: A bag has 2 red and 5 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 4

Problem: A bag has 5 red and 2 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 5

Problem: A bag has 4 red and 4 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: equally likely

Worked Example 6

Problem: A bag has 3 red and 3 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: equally likely

Worked Example 7

Problem: A bag has 3 red and 5 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 8

Problem: A bag has 6 red and 6 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: equally likely

Worked Example 9

Problem: A bag has 1 red and 1 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: equally likely

Worked Example 10

Problem: A bag has 4 red and 3 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Practice Exercise

Create and solve one new example of Likely events. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

48.5 Certain events

Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: A bag has 2 red and 3 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 2

Problem: A bag has 4 red and 4 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: equally likely

Worked Example 3

Problem: A bag has 6 red and 3 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 4

Problem: A bag has 2 red and 2 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: equally likely

Worked Example 5

Problem: A bag has 3 red and 2 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 6

Problem: A bag has 2 red and 3 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 7

Problem: A bag has 5 red and 1 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 8

Problem: A bag has 4 red and 2 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 9

Problem: A bag has 2 red and 3 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 10

Problem: A bag has 4 red and 2 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Practice Exercise

Create and solve one new example of Certain events. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

48.6 Ordering events by likelihood

Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: A bag has 4 red and 4 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: equally likely

Worked Example 2

Problem: A bag has 5 red and 6 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 3

Problem: A bag has 6 red and 6 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: equally likely

Worked Example 4

Problem: A bag has 5 red and 6 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 5

Problem: A bag has 2 red and 6 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 6

Problem: A bag has 6 red and 6 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: equally likely

Worked Example 7

Problem: A bag has 6 red and 2 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 8

Problem: A bag has 1 red and 3 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 9

Problem: A bag has 1 red and 1 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: equally likely

Worked Example 10

Problem: A bag has 1 red and 4 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Practice Exercise

Create and solve one new example of Ordering events by likelihood. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

48.7 Comparing two events

Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: A bag has 3 red and 6 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 2

Problem: A bag has 2 red and 1 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 3

Problem: A bag has 4 red and 2 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 4

Problem: A bag has 4 red and 6 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 5

Problem: A bag has 6 red and 3 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 6

Problem: A bag has 3 red and 4 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 7

Problem: A bag has 6 red and 1 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 8

Problem: A bag has 5 red and 4 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 9

Problem: A bag has 1 red and 4 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 10

Problem: A bag has 2 red and 3 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Practice Exercise

Create and solve one new example of Comparing two events. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

48.8 Making a prediction

Making a prediction is an important Grade 4 mathematics idea in Probability Language. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Create a simple Grade 4 example about Making a prediction using the numbers 6 and 15.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Making a prediction.

Worked Example 2

Problem: Create a simple Grade 4 example about Making a prediction using the numbers 13 and 14.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Making a prediction.

Worked Example 3

Problem: Create a simple Grade 4 example about Making a prediction using the numbers 13 and 7.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Making a prediction.

Worked Example 4

Problem: Create a simple Grade 4 example about Making a prediction using the numbers 6 and 15.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Making a prediction.

Worked Example 5

Problem: Create a simple Grade 4 example about Making a prediction using the numbers 4 and 6.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Making a prediction.

Worked Example 6

Problem: Create a simple Grade 4 example about Making a prediction using the numbers 11 and 6.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Making a prediction.

Worked Example 7

Problem: Create a simple Grade 4 example about Making a prediction using the numbers 15 and 19.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Making a prediction.

Worked Example 8

Problem: Create a simple Grade 4 example about Making a prediction using the numbers 12 and 2.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Making a prediction.

Worked Example 9

Problem: Create a simple Grade 4 example about Making a prediction using the numbers 18 and 3.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Making a prediction.

Worked Example 10

Problem: Create a simple Grade 4 example about Making a prediction using the numbers 7 and 15.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Making a prediction.

Practice Exercise

Create and solve one new example of Making a prediction. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

48.9 Using data to support a prediction

Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: A data set is [9, 8, 15, 9, 13]. What is the greatest value?

  1. Read all the values.
  2. Choose the largest number.

Very beginner explanation: Data questions should be answered from the recorded values or display.

Answer: 15

Worked Example 2

Problem: A data set is [2, 15, 6, 7, 14]. What is the greatest value?

  1. Read all the values.
  2. Choose the largest number.

Very beginner explanation: Data questions should be answered from the recorded values or display.

Answer: 15

Worked Example 3

Problem: A data set is [6, 5, 4, 15, 6]. What is the greatest value?

  1. Read all the values.
  2. Choose the largest number.

Very beginner explanation: Data questions should be answered from the recorded values or display.

Answer: 15

Worked Example 4

Problem: A data set is [2, 11, 4, 7, 7]. What is the greatest value?

  1. Read all the values.
  2. Choose the largest number.

Very beginner explanation: Data questions should be answered from the recorded values or display.

Answer: 11

Worked Example 5

Problem: A data set is [15, 7, 11, 8, 2]. What is the greatest value?

  1. Read all the values.
  2. Choose the largest number.

Very beginner explanation: Data questions should be answered from the recorded values or display.

Answer: 15

Worked Example 6

Problem: A data set is [14, 11, 2, 2, 13]. What is the greatest value?

  1. Read all the values.
  2. Choose the largest number.

Very beginner explanation: Data questions should be answered from the recorded values or display.

Answer: 14

Worked Example 7

Problem: A data set is [14, 11, 15, 4, 6]. What is the greatest value?

  1. Read all the values.
  2. Choose the largest number.

Very beginner explanation: Data questions should be answered from the recorded values or display.

Answer: 15

Worked Example 8

Problem: A data set is [15, 3, 12, 13, 15]. What is the greatest value?

  1. Read all the values.
  2. Choose the largest number.

Very beginner explanation: Data questions should be answered from the recorded values or display.

Answer: 15

Worked Example 9

Problem: A data set is [7, 4, 3, 8, 2]. What is the greatest value?

  1. Read all the values.
  2. Choose the largest number.

Very beginner explanation: Data questions should be answered from the recorded values or display.

Answer: 8

Worked Example 10

Problem: A data set is [9, 8, 2, 4, 5]. What is the greatest value?

  1. Read all the values.
  2. Choose the largest number.

Very beginner explanation: Data questions should be answered from the recorded values or display.

Answer: 9

Practice Exercise

Create and solve one new example of Using data to support a prediction. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

48.10 Using likelihood to make a decision

Using likelihood to make a decision is an important Grade 4 mathematics idea in Probability Language. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Create a simple Grade 4 example about Using likelihood to make a decision using the numbers 4 and 15.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Using likelihood to make a decision.

Worked Example 2

Problem: Create a simple Grade 4 example about Using likelihood to make a decision using the numbers 16 and 4.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Using likelihood to make a decision.

Worked Example 3

Problem: Create a simple Grade 4 example about Using likelihood to make a decision using the numbers 9 and 9.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Using likelihood to make a decision.

Worked Example 4

Problem: Create a simple Grade 4 example about Using likelihood to make a decision using the numbers 18 and 12.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Using likelihood to make a decision.

Worked Example 5

Problem: Create a simple Grade 4 example about Using likelihood to make a decision using the numbers 16 and 15.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Using likelihood to make a decision.

Worked Example 6

Problem: Create a simple Grade 4 example about Using likelihood to make a decision using the numbers 7 and 15.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Using likelihood to make a decision.

Worked Example 7

Problem: Create a simple Grade 4 example about Using likelihood to make a decision using the numbers 4 and 14.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Using likelihood to make a decision.

Worked Example 8

Problem: Create a simple Grade 4 example about Using likelihood to make a decision using the numbers 19 and 6.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Using likelihood to make a decision.

Worked Example 9

Problem: Create a simple Grade 4 example about Using likelihood to make a decision using the numbers 14 and 19.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Using likelihood to make a decision.

Worked Example 10

Problem: Create a simple Grade 4 example about Using likelihood to make a decision using the numbers 14 and 3.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Using likelihood to make a decision.

Practice Exercise

Create and solve one new example of Using likelihood to make a decision. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

48.11 Explaining a probability judgement

Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: A bag has 4 red and 4 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: equally likely

Worked Example 2

Problem: A bag has 4 red and 5 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 3

Problem: A bag has 1 red and 1 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: equally likely

Worked Example 4

Problem: A bag has 6 red and 3 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 5

Problem: A bag has 2 red and 1 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 6

Problem: A bag has 1 red and 2 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 7

Problem: A bag has 2 red and 4 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 8

Problem: A bag has 4 red and 2 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: red

Worked Example 9

Problem: A bag has 1 red and 6 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: blue

Worked Example 10

Problem: A bag has 3 red and 3 blue counters. Which colour is more likely to be drawn?

  1. Compare the numbers of each colour.
  2. More possible outcomes means a greater chance.

Very beginner explanation: Probability compares how likely outcomes are.

Answer: equally likely

Practice Exercise

Create and solve one new example of Explaining a probability judgement. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

48.12 Checking whether a prediction was reasonable

Checking whether a prediction was reasonable is an important Grade 4 mathematics idea in Probability Language. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Create a simple Grade 4 example about Checking whether a prediction was reasonable using the numbers 13 and 13.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Checking whether a prediction was reasonable.

Worked Example 2

Problem: Create a simple Grade 4 example about Checking whether a prediction was reasonable using the numbers 2 and 18.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Checking whether a prediction was reasonable.

Worked Example 3

Problem: Create a simple Grade 4 example about Checking whether a prediction was reasonable using the numbers 4 and 2.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Checking whether a prediction was reasonable.

Worked Example 4

Problem: Create a simple Grade 4 example about Checking whether a prediction was reasonable using the numbers 20 and 16.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Checking whether a prediction was reasonable.

Worked Example 5

Problem: Create a simple Grade 4 example about Checking whether a prediction was reasonable using the numbers 20 and 5.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Checking whether a prediction was reasonable.

Worked Example 6

Problem: Create a simple Grade 4 example about Checking whether a prediction was reasonable using the numbers 12 and 5.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Checking whether a prediction was reasonable.

Worked Example 7

Problem: Create a simple Grade 4 example about Checking whether a prediction was reasonable using the numbers 2 and 10.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Checking whether a prediction was reasonable.

Worked Example 8

Problem: Create a simple Grade 4 example about Checking whether a prediction was reasonable using the numbers 7 and 10.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Checking whether a prediction was reasonable.

Worked Example 9

Problem: Create a simple Grade 4 example about Checking whether a prediction was reasonable using the numbers 2 and 10.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Checking whether a prediction was reasonable.

Worked Example 10

Problem: Create a simple Grade 4 example about Checking whether a prediction was reasonable using the numbers 10 and 11.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Checking whether a prediction was reasonable.

Practice Exercise

Create and solve one new example of Checking whether a prediction was reasonable. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

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30 Review Questions and Answers

Q1. What is important to understand about Impossible events?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q2. What is important to understand about Unlikely events?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q3. What is important to understand about Equally likely outcomes?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q4. What is important to understand about Likely events?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q5. What is important to understand about Certain events?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q6. What is important to understand about Ordering events by likelihood?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q7. What is important to understand about Comparing two events?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q8. What is important to understand about Making a prediction?

Answer: Making a prediction is an important Grade 4 mathematics idea in Probability Language. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q9. What is important to understand about Using data to support a prediction?

Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.

Q10. What is important to understand about Using likelihood to make a decision?

Answer: Using likelihood to make a decision is an important Grade 4 mathematics idea in Probability Language. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q11. What is important to understand about Explaining a probability judgement?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q12. What is important to understand about Checking whether a prediction was reasonable?

Answer: Checking whether a prediction was reasonable is an important Grade 4 mathematics idea in Probability Language. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q13. How would you explain Impossible events?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q14. How would you explain Unlikely events?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q15. How would you explain Equally likely outcomes?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q16. How would you explain Likely events?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q17. How would you explain Certain events?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q18. How would you explain Ordering events by likelihood?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q19. How would you explain Comparing two events?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q20. How would you explain Making a prediction?

Answer: Making a prediction is an important Grade 4 mathematics idea in Probability Language. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q21. How would you explain Using data to support a prediction?

Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.

Q22. How would you explain Using likelihood to make a decision?

Answer: Using likelihood to make a decision is an important Grade 4 mathematics idea in Probability Language. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q23. How would you explain Explaining a probability judgement?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q24. How would you explain Checking whether a prediction was reasonable?

Answer: Checking whether a prediction was reasonable is an important Grade 4 mathematics idea in Probability Language. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q25. What should a beginner check when working with Impossible events?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q26. What should a beginner check when working with Unlikely events?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q27. What should a beginner check when working with Equally likely outcomes?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q28. What should a beginner check when working with Likely events?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q29. What should a beginner check when working with Certain events?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.

Q30. What should a beginner check when working with Ordering events by likelihood?

Answer: Probability describes how likely an event is. Predictions can be checked by carrying out simple experiments and recording outcomes.