EASYTUTORGUIDE

Practical tutorials, tools, courses, digital skills, and business promotion.

Free Learning
Google Translate — English / فارسی / العربية
EasyTutorGuide LogoLearn, Build, & Grow

Chapter 40: Mathematical Modelling Process

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
Advertisement area — AdSense / Auto Ads

Chapter Overview

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

40.1 What mathematical modelling means

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 [10, 10, 5, 2, 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: 10

Worked Example 2

Problem: A data set is [14, 9, 8, 3, 10]. 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 3

Problem: A data set is [12, 2, 10, 6, 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 4

Problem: A data set is [15, 5, 14, 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 5

Problem: A data set is [12, 8, 13, 6, 8]. 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: 13

Worked Example 6

Problem: A data set is [2, 8, 12, 5, 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: 12

Worked Example 7

Problem: A data set is [3, 15, 3, 10, 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: 15

Worked Example 8

Problem: A data set is [4, 9, 15, 14, 12]. 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 [2, 9, 2, 12, 11]. 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: 12

Worked Example 10

Problem: A data set is [4, 4, 15, 7, 9]. 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

Practice Exercise

Create and solve one new example of What mathematical modelling means. 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.

40.2 Understanding the real problem

Understanding the real problem is an important Grade 4 mathematics idea in Mathematical Modelling Process. 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 Understanding the real problem using the numbers 12 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 Understanding the real problem.

Worked Example 2

Problem: Create a simple Grade 4 example about Understanding the real problem using the numbers 7 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 Understanding the real problem.

Worked Example 3

Problem: Create a simple Grade 4 example about Understanding the real problem using the numbers 3 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 Understanding the real problem.

Worked Example 4

Problem: Create a simple Grade 4 example about Understanding the real problem using the numbers 11 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 Understanding the real problem.

Worked Example 5

Problem: Create a simple Grade 4 example about Understanding the real problem using the numbers 11 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 Understanding the real problem.

Worked Example 6

Problem: Create a simple Grade 4 example about Understanding the real problem using the numbers 11 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 Understanding the real problem.

Worked Example 7

Problem: Create a simple Grade 4 example about Understanding the real problem using the numbers 15 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 Understanding the real problem.

Worked Example 8

Problem: Create a simple Grade 4 example about Understanding the real problem using the numbers 13 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 Understanding the real problem.

Worked Example 9

Problem: Create a simple Grade 4 example about Understanding the real problem using the numbers 18 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 Understanding the real problem.

Worked Example 10

Problem: Create a simple Grade 4 example about Understanding the real problem using the numbers 5 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 Understanding the real problem.

Practice Exercise

Create and solve one new example of Understanding the real problem. 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.

40.3 Identifying useful information

Identifying useful information is an important Grade 4 mathematics idea in Mathematical Modelling Process. 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 Identifying useful information using the numbers 11 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 Identifying useful information.

Worked Example 2

Problem: Create a simple Grade 4 example about Identifying useful information using the numbers 11 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 Identifying useful information.

Worked Example 3

Problem: Create a simple Grade 4 example about Identifying useful information using the numbers 2 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 Identifying useful information.

Worked Example 4

Problem: Create a simple Grade 4 example about Identifying useful information using the numbers 18 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 Identifying useful information.

Worked Example 5

Problem: Create a simple Grade 4 example about Identifying useful information using the numbers 14 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 Identifying useful information.

Worked Example 6

Problem: Create a simple Grade 4 example about Identifying useful information using the numbers 8 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 Identifying useful information.

Worked Example 7

Problem: Create a simple Grade 4 example about Identifying useful information using the numbers 13 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 Identifying useful information.

Worked Example 8

Problem: Create a simple Grade 4 example about Identifying useful information using the numbers 8 and 20.

  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 Identifying useful information.

Worked Example 9

Problem: Create a simple Grade 4 example about Identifying useful information using the numbers 18 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 Identifying useful information.

Worked Example 10

Problem: Create a simple Grade 4 example about Identifying useful information using the numbers 13 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 Identifying useful information.

Practice Exercise

Create and solve one new example of Identifying useful information. 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.

40.4 Choosing variables and quantities

Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal. 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: Solve n + 5 = 19.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 14

Worked Example 2

Problem: Solve n + 6 = 12.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 6

Worked Example 3

Problem: Solve n + 2 = 12.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 10

Worked Example 4

Problem: Solve n + 8 = 11.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 3

Worked Example 5

Problem: Solve n + 9 = 20.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 11

Worked Example 6

Problem: Solve n + 6 = 16.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 10

Worked Example 7

Problem: Solve n + 7 = 20.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 13

Worked Example 8

Problem: Solve n + 1 = 7.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 6

Worked Example 9

Problem: Solve n + 4 = 10.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 6

Worked Example 10

Problem: Solve n + 4 = 6.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 2

Practice Exercise

Create and solve one new example of Choosing variables and quantities. 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.

40.5 Making reasonable assumptions

Addition combines quantities. Align place values, regroup when needed, and estimate first to predict a reasonable answer. 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 reasonable assumptions using the numbers 19 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 reasonable assumptions.

Worked Example 2

Problem: Create a simple Grade 4 example about Making reasonable assumptions using the numbers 20 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 reasonable assumptions.

Worked Example 3

Problem: Create a simple Grade 4 example about Making reasonable assumptions using the numbers 6 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 Making reasonable assumptions.

Worked Example 4

Problem: Create a simple Grade 4 example about Making reasonable assumptions using the numbers 5 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 Making reasonable assumptions.

Worked Example 5

Problem: Create a simple Grade 4 example about Making reasonable assumptions using the numbers 4 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 Making reasonable assumptions.

Worked Example 6

Problem: Create a simple Grade 4 example about Making reasonable assumptions using the numbers 13 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 Making reasonable assumptions.

Worked Example 7

Problem: Create a simple Grade 4 example about Making reasonable assumptions using the numbers 13 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 Making reasonable assumptions.

Worked Example 8

Problem: Create a simple Grade 4 example about Making reasonable assumptions using the numbers 13 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 Making reasonable assumptions.

Worked Example 9

Problem: Create a simple Grade 4 example about Making reasonable assumptions using the numbers 8 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 reasonable assumptions.

Worked Example 10

Problem: Create a simple Grade 4 example about Making reasonable assumptions using the numbers 5 and 20.

  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 reasonable assumptions.

Practice Exercise

Create and solve one new example of Making reasonable assumptions. 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.

40.6 Choosing a representation

Choosing a representation is an important Grade 4 mathematics idea in Mathematical Modelling Process. 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 Choosing a representation using the numbers 5 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 Choosing a representation.

Worked Example 2

Problem: Create a simple Grade 4 example about Choosing a representation using the numbers 15 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 Choosing a representation.

Worked Example 3

Problem: Create a simple Grade 4 example about Choosing a representation using the numbers 6 and 8.

  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 Choosing a representation.

Worked Example 4

Problem: Create a simple Grade 4 example about Choosing a representation using the numbers 5 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 Choosing a representation.

Worked Example 5

Problem: Create a simple Grade 4 example about Choosing a representation using the numbers 12 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 Choosing a representation.

Worked Example 6

Problem: Create a simple Grade 4 example about Choosing a representation using the numbers 17 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 Choosing a representation.

Worked Example 7

Problem: Create a simple Grade 4 example about Choosing a representation using the numbers 9 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 Choosing a representation.

Worked Example 8

Problem: Create a simple Grade 4 example about Choosing a representation 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 Choosing a representation.

Worked Example 9

Problem: Create a simple Grade 4 example about Choosing a representation using the numbers 8 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 Choosing a representation.

Worked Example 10

Problem: Create a simple Grade 4 example about Choosing a representation using the numbers 19 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 Choosing a representation.

Practice Exercise

Create and solve one new example of Choosing a representation. 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.

40.7 Building a simple model

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, 8, 6, 13, 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: 13

Worked Example 2

Problem: A data set is [11, 3, 5, 15, 3]. 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 [11, 15, 5, 13, 3]. 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 [3, 10, 10, 9, 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: 14

Worked Example 5

Problem: A data set is [10, 8, 12, 10, 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: 12

Worked Example 6

Problem: A data set is [11, 7, 14, 5, 10]. 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 [6, 8, 12, 4, 10]. 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: 12

Worked Example 8

Problem: A data set is [4, 7, 11, 5, 9]. 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 9

Problem: A data set is [3, 12, 12, 5, 12]. 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: 12

Worked Example 10

Problem: A data set is [13, 6, 4, 15, 9]. 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

Practice Exercise

Create and solve one new example of Building a simple model. 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.

40.8 Testing the model

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, 9, 4, 4, 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: 13

Worked Example 2

Problem: A data set is [7, 10, 13, 9, 4]. 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: 13

Worked Example 3

Problem: A data set is [13, 9, 13, 10, 9]. 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: 13

Worked Example 4

Problem: A data set is [12, 3, 15, 3, 8]. 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 5

Problem: A data set is [9, 7, 2, 15, 8]. 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 [5, 5, 14, 7, 9]. 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 [9, 13, 2, 14, 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: 14

Worked Example 8

Problem: A data set is [8, 15, 12, 4, 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 9

Problem: A data set is [7, 6, 14, 12, 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 10

Problem: A data set is [3, 6, 10, 15, 11]. 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

Practice Exercise

Create and solve one new example of Testing the model. 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.

40.9 Comparing model results with the situation

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, 5, 6, 2, 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: 14

Worked Example 2

Problem: A data set is [9, 7, 12, 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: 13

Worked Example 3

Problem: A data set is [5, 6, 8, 2, 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 4

Problem: A data set is [9, 7, 9, 14, 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: 14

Worked Example 5

Problem: A data set is [11, 6, 13, 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: 13

Worked Example 6

Problem: A data set is [10, 9, 15, 10, 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: 15

Worked Example 7

Problem: A data set is [6, 12, 4, 5, 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: 12

Worked Example 8

Problem: A data set is [9, 11, 3, 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: 14

Worked Example 9

Problem: A data set is [12, 14, 7, 14, 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: 14

Worked Example 10

Problem: A data set is [8, 5, 12, 12, 9]. 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: 12

Practice Exercise

Create and solve one new example of Comparing model results with the situation. 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.

40.10 Revising a model

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 [7, 10, 7, 8, 12]. 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: 12

Worked Example 2

Problem: A data set is [9, 2, 2, 5, 4]. 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

Worked Example 3

Problem: A data set is [14, 12, 6, 7, 12]. 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 4

Problem: A data set is [11, 8, 4, 12, 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: 13

Worked Example 5

Problem: A data set is [11, 4, 9, 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: 13

Worked Example 6

Problem: A data set is [13, 12, 5, 14, 3]. 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 [12, 7, 13, 13, 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: 13

Worked Example 8

Problem: A data set is [13, 4, 5, 3, 3]. 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: 13

Worked Example 9

Problem: A data set is [4, 3, 3, 12, 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: 12

Worked Example 10

Problem: A data set is [14, 3, 11, 15, 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: 15

Practice Exercise

Create and solve one new example of Revising a model. 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.

40.11 Communicating a recommendation

Communicating a recommendation is an important Grade 4 mathematics idea in Mathematical Modelling Process. 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 Communicating a recommendation using the numbers 9 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 Communicating a recommendation.

Worked Example 2

Problem: Create a simple Grade 4 example about Communicating a recommendation using the numbers 20 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 Communicating a recommendation.

Worked Example 3

Problem: Create a simple Grade 4 example about Communicating a recommendation using the numbers 16 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 Communicating a recommendation.

Worked Example 4

Problem: Create a simple Grade 4 example about Communicating a recommendation using the numbers 16 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 Communicating a recommendation.

Worked Example 5

Problem: Create a simple Grade 4 example about Communicating a recommendation using the numbers 19 and 20.

  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 Communicating a recommendation.

Worked Example 6

Problem: Create a simple Grade 4 example about Communicating a recommendation using the numbers 17 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 Communicating a recommendation.

Worked Example 7

Problem: Create a simple Grade 4 example about Communicating a recommendation 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 Communicating a recommendation.

Worked Example 8

Problem: Create a simple Grade 4 example about Communicating a recommendation using the numbers 15 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 Communicating a recommendation.

Worked Example 9

Problem: Create a simple Grade 4 example about Communicating a recommendation using the numbers 4 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 Communicating a recommendation.

Worked Example 10

Problem: Create a simple Grade 4 example about Communicating a recommendation using the numbers 8 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 Communicating a recommendation.

Practice Exercise

Create and solve one new example of Communicating a recommendation. 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.

40.12 Recognizing model limitations

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, 7, 2, 14, 12]. 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 2

Problem: A data set is [3, 5, 10, 12, 9]. 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: 12

Worked Example 3

Problem: A data set is [5, 12, 4, 3, 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: 14

Worked Example 4

Problem: A data set is [14, 2, 11, 3, 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: 14

Worked Example 5

Problem: A data set is [6, 4, 11, 11, 11]. 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 6

Problem: A data set is [11, 5, 15, 12, 9]. 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 7

Problem: A data set is [4, 7, 13, 8, 11]. 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: 13

Worked Example 8

Problem: A data set is [13, 7, 12, 7, 11]. 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: 13

Worked Example 9

Problem: A data set is [6, 15, 2, 5, 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 10

Problem: A data set is [10, 10, 9, 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

Practice Exercise

Create and solve one new example of Recognizing model limitations. 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.

Advertisement area — AdSense / Auto Ads

30 Review Questions and Answers

Q1. What is important to understand about What mathematical modelling means?

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 Understanding the real problem?

Answer: Understanding the real problem is an important Grade 4 mathematics idea in Mathematical Modelling Process. 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 Identifying useful information?

Answer: Identifying useful information is an important Grade 4 mathematics idea in Mathematical Modelling Process. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q4. What is important to understand about Choosing variables and quantities?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q5. What is important to understand about Making reasonable assumptions?

Answer: Addition combines quantities. Align place values, regroup when needed, and estimate first to predict a reasonable answer.

Q6. What is important to understand about Choosing a representation?

Answer: Choosing a representation is an important Grade 4 mathematics idea in Mathematical Modelling Process. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q7. What is important to understand about Building a simple model?

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 Testing the model?

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

Q9. What is important to understand about Comparing model results with the situation?

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 Revising a model?

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

Q11. What is important to understand about Communicating a recommendation?

Answer: Communicating a recommendation is an important Grade 4 mathematics idea in Mathematical Modelling Process. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q12. What is important to understand about Recognizing model limitations?

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

Q13. How would you explain What mathematical modelling means?

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 Understanding the real problem?

Answer: Understanding the real problem is an important Grade 4 mathematics idea in Mathematical Modelling Process. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q15. How would you explain Identifying useful information?

Answer: Identifying useful information is an important Grade 4 mathematics idea in Mathematical Modelling Process. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q16. How would you explain Choosing variables and quantities?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q17. How would you explain Making reasonable assumptions?

Answer: Addition combines quantities. Align place values, regroup when needed, and estimate first to predict a reasonable answer.

Q18. How would you explain Choosing a representation?

Answer: Choosing a representation is an important Grade 4 mathematics idea in Mathematical Modelling Process. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q19. How would you explain Building a simple model?

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 Testing the model?

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

Q21. How would you explain Comparing model results with the situation?

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 Revising a model?

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

Q23. How would you explain Communicating a recommendation?

Answer: Communicating a recommendation is an important Grade 4 mathematics idea in Mathematical Modelling Process. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q24. How would you explain Recognizing model limitations?

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

Q25. What should a beginner check when working with What mathematical modelling means?

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 Understanding the real problem?

Answer: Understanding the real problem is an important Grade 4 mathematics idea in Mathematical Modelling Process. 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 Identifying useful information?

Answer: Identifying useful information is an important Grade 4 mathematics idea in Mathematical Modelling Process. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q28. What should a beginner check when working with Choosing variables and quantities?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q29. What should a beginner check when working with Making reasonable assumptions?

Answer: Addition combines quantities. Align place values, regroup when needed, and estimate first to predict a reasonable answer.

Q30. What should a beginner check when working with Choosing a representation?

Answer: Choosing a representation is an important Grade 4 mathematics idea in Mathematical Modelling Process. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.