Chapter 47: Averages and Comparing Data Sets
Learn Grade 4 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Averages and Comparing Data Sets in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.
47.1 Meaning of an average
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, 13, 4, 4, 3]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 13
Worked Example 2
Problem: A data set is [6, 14, 9, 3, 2]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 3
Problem: A data set is [9, 5, 11, 15, 15]. What is the greatest value?
- Read all the values.
- 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 [6, 12, 5, 9, 8]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 12
Worked Example 5
Problem: A data set is [4, 13, 5, 6, 7]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 13
Worked Example 6
Problem: A data set is [2, 15, 12, 7, 2]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 7
Problem: A data set is [8, 4, 12, 4, 12]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 12
Worked Example 8
Problem: A data set is [6, 12, 3, 14, 11]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 9
Problem: A data set is [4, 8, 15, 12, 10]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 10
Problem: A data set is [8, 6, 6, 14, 9]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Practice Exercise
Create and solve one new example of Meaning of an average. 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.
47.2 Finding a simple mean with whole numbers
Finding a simple mean with whole numbers is an important Grade 4 mathematics idea in Averages and Comparing Data Sets. 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 Finding a simple mean with whole numbers using the numbers 16 and 3.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding a simple mean with whole numbers.
Worked Example 2
Problem: Create a simple Grade 4 example about Finding a simple mean with whole numbers using the numbers 4 and 9.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding a simple mean with whole numbers.
Worked Example 3
Problem: Create a simple Grade 4 example about Finding a simple mean with whole numbers using the numbers 5 and 5.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding a simple mean with whole numbers.
Worked Example 4
Problem: Create a simple Grade 4 example about Finding a simple mean with whole numbers using the numbers 7 and 12.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding a simple mean with whole numbers.
Worked Example 5
Problem: Create a simple Grade 4 example about Finding a simple mean with whole numbers using the numbers 17 and 11.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding a simple mean with whole numbers.
Worked Example 6
Problem: Create a simple Grade 4 example about Finding a simple mean with whole numbers using the numbers 13 and 7.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding a simple mean with whole numbers.
Worked Example 7
Problem: Create a simple Grade 4 example about Finding a simple mean with whole numbers using the numbers 13 and 20.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding a simple mean with whole numbers.
Worked Example 8
Problem: Create a simple Grade 4 example about Finding a simple mean with whole numbers using the numbers 6 and 2.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding a simple mean with whole numbers.
Worked Example 9
Problem: Create a simple Grade 4 example about Finding a simple mean with whole numbers using the numbers 20 and 10.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding a simple mean with whole numbers.
Worked Example 10
Problem: Create a simple Grade 4 example about Finding a simple mean with whole numbers using the numbers 10 and 7.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding a simple mean with whole numbers.
Practice Exercise
Create and solve one new example of Finding a simple mean with whole numbers. 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.
47.3 Using a median to find a middle value
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 [8, 14, 9, 6, 8]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 2
Problem: A data set is [9, 14, 12, 4, 8]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 3
Problem: A data set is [7, 9, 7, 8, 6]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 9
Worked Example 4
Problem: A data set is [14, 7, 2, 8, 14]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 5
Problem: A data set is [10, 7, 9, 15, 10]. What is the greatest value?
- Read all the values.
- 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 [6, 9, 3, 13, 15]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 7
Problem: A data set is [10, 7, 11, 8, 10]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 11
Worked Example 8
Problem: A data set is [9, 10, 2, 11, 5]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 11
Worked Example 9
Problem: A data set is [10, 10, 13, 5, 9]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 13
Worked Example 10
Problem: A data set is [10, 6, 14, 13, 9]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Practice Exercise
Create and solve one new example of Using a median to find a middle value. 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.
47.4 Using a mode to find a common value
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 [11, 10, 4, 4, 6]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 11
Worked Example 2
Problem: A data set is [11, 15, 13, 12, 14]. What is the greatest value?
- Read all the values.
- 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 [8, 2, 3, 2, 11]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 11
Worked Example 4
Problem: A data set is [10, 5, 2, 7, 4]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 10
Worked Example 5
Problem: A data set is [11, 7, 12, 5, 4]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 12
Worked Example 6
Problem: A data set is [3, 9, 5, 6, 7]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 9
Worked Example 7
Problem: A data set is [5, 8, 14, 13, 7]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 8
Problem: A data set is [5, 12, 10, 11, 6]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 12
Worked Example 9
Problem: A data set is [5, 14, 6, 3, 9]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 10
Problem: A data set is [4, 3, 6, 14, 6]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Practice Exercise
Create and solve one new example of Using a mode to find a common value. 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.
47.5 Comparing two data sets
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 [2, 2, 10, 12, 13]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 13
Worked Example 2
Problem: A data set is [12, 15, 15, 5, 9]. What is the greatest value?
- Read all the values.
- 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, 11, 7, 11, 13]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 13
Worked Example 4
Problem: A data set is [10, 8, 7, 15, 8]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 5
Problem: A data set is [4, 15, 7, 4, 15]. What is the greatest value?
- Read all the values.
- 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 [15, 9, 5, 13, 6]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 7
Problem: A data set is [11, 8, 6, 5, 13]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 13
Worked Example 8
Problem: A data set is [10, 14, 8, 2, 14]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 9
Problem: A data set is [15, 6, 6, 3, 13]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 10
Problem: A data set is [7, 5, 3, 11, 10]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 11
Practice Exercise
Create and solve one new example of Comparing two data sets. 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.
47.6 Comparing two frequency tables
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 [12, 4, 3, 6, 7]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 12
Worked Example 2
Problem: A data set is [2, 3, 7, 2, 14]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 3
Problem: A data set is [7, 5, 3, 14, 3]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 4
Problem: A data set is [14, 12, 12, 6, 5]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 5
Problem: A data set is [10, 7, 4, 12, 3]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 12
Worked Example 6
Problem: A data set is [12, 9, 5, 4, 9]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 12
Worked Example 7
Problem: A data set is [12, 9, 5, 9, 8]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 12
Worked Example 8
Problem: A data set is [6, 7, 4, 2, 7]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 7
Worked Example 9
Problem: A data set is [3, 8, 15, 15, 3]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 10
Problem: A data set is [5, 8, 7, 4, 15]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Practice Exercise
Create and solve one new example of Comparing two frequency tables. 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.
47.7 Comparing two graphs
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 [14, 8, 4, 2, 2]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 2
Problem: A data set is [4, 3, 6, 4, 3]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 6
Worked Example 3
Problem: A data set is [2, 9, 13, 6, 8]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 13
Worked Example 4
Problem: A data set is [4, 14, 14, 3, 11]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 5
Problem: A data set is [11, 8, 4, 12, 15]. What is the greatest value?
- Read all the values.
- 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 [9, 10, 8, 8, 7]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 10
Worked Example 7
Problem: A data set is [12, 15, 10, 12, 4]. What is the greatest value?
- Read all the values.
- 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 [7, 10, 13, 15, 12]. What is the greatest value?
- Read all the values.
- 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 [12, 15, 12, 9, 11]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 10
Problem: A data set is [3, 10, 13, 12, 2]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 13
Practice Exercise
Create and solve one new example of Comparing two graphs. 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.
47.8 Finding similarities
Finding similarities is an important Grade 4 mathematics idea in Averages and Comparing Data Sets. 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 Finding similarities using the numbers 10 and 11.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding similarities.
Worked Example 2
Problem: Create a simple Grade 4 example about Finding similarities using the numbers 16 and 20.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding similarities.
Worked Example 3
Problem: Create a simple Grade 4 example about Finding similarities using the numbers 6 and 8.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding similarities.
Worked Example 4
Problem: Create a simple Grade 4 example about Finding similarities using the numbers 17 and 17.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding similarities.
Worked Example 5
Problem: Create a simple Grade 4 example about Finding similarities using the numbers 18 and 4.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding similarities.
Worked Example 6
Problem: Create a simple Grade 4 example about Finding similarities using the numbers 10 and 10.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding similarities.
Worked Example 7
Problem: Create a simple Grade 4 example about Finding similarities using the numbers 13 and 4.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding similarities.
Worked Example 8
Problem: Create a simple Grade 4 example about Finding similarities using the numbers 19 and 4.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding similarities.
Worked Example 9
Problem: Create a simple Grade 4 example about Finding similarities using the numbers 3 and 8.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding similarities.
Worked Example 10
Problem: Create a simple Grade 4 example about Finding similarities using the numbers 7 and 16.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding similarities.
Practice Exercise
Create and solve one new example of Finding similarities. 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.
47.9 Finding differences
Subtraction finds what remains or the difference between quantities. Addition is a useful way to check. 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 Finding differences using the numbers 3 and 3.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding differences.
Worked Example 2
Problem: Create a simple Grade 4 example about Finding differences using the numbers 17 and 10.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding differences.
Worked Example 3
Problem: Create a simple Grade 4 example about Finding differences using the numbers 19 and 7.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding differences.
Worked Example 4
Problem: Create a simple Grade 4 example about Finding differences using the numbers 8 and 14.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding differences.
Worked Example 5
Problem: Create a simple Grade 4 example about Finding differences using the numbers 10 and 19.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding differences.
Worked Example 6
Problem: Create a simple Grade 4 example about Finding differences using the numbers 3 and 5.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding differences.
Worked Example 7
Problem: Create a simple Grade 4 example about Finding differences using the numbers 6 and 16.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding differences.
Worked Example 8
Problem: Create a simple Grade 4 example about Finding differences using the numbers 2 and 18.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding differences.
Worked Example 9
Problem: Create a simple Grade 4 example about Finding differences using the numbers 14 and 12.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding differences.
Worked Example 10
Problem: Create a simple Grade 4 example about Finding differences using the numbers 6 and 11.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Finding differences.
Practice Exercise
Create and solve one new example of Finding differences. 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.
47.10 Drawing a conclusion
Drawing a conclusion is an important Grade 4 mathematics idea in Averages and Comparing Data Sets. 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 Drawing a conclusion using the numbers 4 and 13.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Drawing a conclusion.
Worked Example 2
Problem: Create a simple Grade 4 example about Drawing a conclusion using the numbers 5 and 7.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Drawing a conclusion.
Worked Example 3
Problem: Create a simple Grade 4 example about Drawing a conclusion using the numbers 7 and 12.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Drawing a conclusion.
Worked Example 4
Problem: Create a simple Grade 4 example about Drawing a conclusion using the numbers 14 and 8.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Drawing a conclusion.
Worked Example 5
Problem: Create a simple Grade 4 example about Drawing a conclusion using the numbers 11 and 15.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Drawing a conclusion.
Worked Example 6
Problem: Create a simple Grade 4 example about Drawing a conclusion using the numbers 8 and 4.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Drawing a conclusion.
Worked Example 7
Problem: Create a simple Grade 4 example about Drawing a conclusion using the numbers 17 and 4.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Drawing a conclusion.
Worked Example 8
Problem: Create a simple Grade 4 example about Drawing a conclusion using the numbers 5 and 9.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Drawing a conclusion.
Worked Example 9
Problem: Create a simple Grade 4 example about Drawing a conclusion using the numbers 13 and 18.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Drawing a conclusion.
Worked Example 10
Problem: Create a simple Grade 4 example about Drawing a conclusion using the numbers 9 and 6.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Drawing a conclusion.
Practice Exercise
Create and solve one new example of Drawing a conclusion. 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.
47.11 Supporting an argument with data
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 [13, 8, 6, 12, 15]. What is the greatest value?
- Read all the values.
- 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 [15, 6, 10, 7, 11]. What is the greatest value?
- Read all the values.
- 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 [2, 5, 12, 9, 12]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 12
Worked Example 4
Problem: A data set is [10, 7, 2, 12, 13]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 13
Worked Example 5
Problem: A data set is [12, 14, 10, 8, 11]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 6
Problem: A data set is [8, 7, 7, 9, 3]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 9
Worked Example 7
Problem: A data set is [2, 13, 4, 7, 8]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 13
Worked Example 8
Problem: A data set is [12, 6, 15, 13, 2]. What is the greatest value?
- Read all the values.
- 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 [2, 8, 7, 15, 8]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 10
Problem: A data set is [8, 2, 11, 15, 15]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Practice Exercise
Create and solve one new example of Supporting an argument with data. 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.
47.12 Making an informed decision
Making an informed decision is an important Grade 4 mathematics idea in Averages and Comparing Data Sets. 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 an informed decision using the numbers 19 and 6.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 an informed decision.
Worked Example 2
Problem: Create a simple Grade 4 example about Making an informed decision using the numbers 13 and 5.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 an informed decision.
Worked Example 3
Problem: Create a simple Grade 4 example about Making an informed decision using the numbers 13 and 4.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 an informed decision.
Worked Example 4
Problem: Create a simple Grade 4 example about Making an informed decision using the numbers 5 and 5.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 an informed decision.
Worked Example 5
Problem: Create a simple Grade 4 example about Making an informed decision using the numbers 2 and 5.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 an informed decision.
Worked Example 6
Problem: Create a simple Grade 4 example about Making an informed decision using the numbers 19 and 20.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 an informed decision.
Worked Example 7
Problem: Create a simple Grade 4 example about Making an informed decision using the numbers 12 and 8.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 an informed decision.
Worked Example 8
Problem: Create a simple Grade 4 example about Making an informed decision using the numbers 7 and 6.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 an informed decision.
Worked Example 9
Problem: Create a simple Grade 4 example about Making an informed decision using the numbers 11 and 8.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 an informed decision.
Worked Example 10
Problem: Create a simple Grade 4 example about Making an informed decision using the numbers 6 and 19.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 an informed decision.
Practice Exercise
Create and solve one new example of Making an informed 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.
30 Review Questions and Answers
Q1. What is important to understand about Meaning of an average?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q2. What is important to understand about Finding a simple mean with whole numbers?
Answer: Finding a simple mean with whole numbers is an important Grade 4 mathematics idea in Averages and Comparing Data Sets. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q3. What is important to understand about Using a median to find a middle value?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q4. What is important to understand about Using a mode to find a common value?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q5. What is important to understand about Comparing two data sets?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q6. What is important to understand about Comparing two frequency tables?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q7. What is important to understand about Comparing two graphs?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q8. What is important to understand about Finding similarities?
Answer: Finding similarities is an important Grade 4 mathematics idea in Averages and Comparing Data Sets. 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 Finding differences?
Answer: Subtraction finds what remains or the difference between quantities. Addition is a useful way to check.
Q10. What is important to understand about Drawing a conclusion?
Answer: Drawing a conclusion is an important Grade 4 mathematics idea in Averages and Comparing Data Sets. 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 Supporting an argument with data?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q12. What is important to understand about Making an informed decision?
Answer: Making an informed decision is an important Grade 4 mathematics idea in Averages and Comparing Data Sets. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q13. How would you explain Meaning of an average?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q14. How would you explain Finding a simple mean with whole numbers?
Answer: Finding a simple mean with whole numbers is an important Grade 4 mathematics idea in Averages and Comparing Data Sets. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q15. How would you explain Using a median to find a middle value?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q16. How would you explain Using a mode to find a common value?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q17. How would you explain Comparing two data sets?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q18. How would you explain Comparing two frequency tables?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q19. How would you explain Comparing two graphs?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q20. How would you explain Finding similarities?
Answer: Finding similarities is an important Grade 4 mathematics idea in Averages and Comparing Data Sets. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q21. How would you explain Finding differences?
Answer: Subtraction finds what remains or the difference between quantities. Addition is a useful way to check.
Q22. How would you explain Drawing a conclusion?
Answer: Drawing a conclusion is an important Grade 4 mathematics idea in Averages and Comparing Data Sets. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q23. How would you explain Supporting an argument with data?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q24. How would you explain Making an informed decision?
Answer: Making an informed decision is an important Grade 4 mathematics idea in Averages and Comparing Data Sets. 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 Meaning of an average?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q26. What should a beginner check when working with Finding a simple mean with whole numbers?
Answer: Finding a simple mean with whole numbers is an important Grade 4 mathematics idea in Averages and Comparing Data Sets. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q27. What should a beginner check when working with Using a median to find a middle value?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q28. What should a beginner check when working with Using a mode to find a common value?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q29. What should a beginner check when working with Comparing two data sets?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q30. What should a beginner check when working with Comparing two frequency tables?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.