Chapter 41: Mathematical Modelling Project: Designing a Schoolyard

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

Grade 4Beginner Friendly10 Examples Per Topic30 Q&APractice + Review

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Chapter Overview

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

41.1 Defining the design problem

Defining the design problem is an important Grade 4 mathematics idea in Mathematical Modelling Project: Designing a Schoolyard. 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 Defining the design problem using the numbers 20 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 Defining the design problem.

Worked Example 2

Problem: Create a simple Grade 4 example about Defining the design problem using the numbers 11 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 Defining the design problem.

Worked Example 3

Problem: Create a simple Grade 4 example about Defining the design problem using the numbers 5 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 Defining the design problem.

Worked Example 4

Problem: Create a simple Grade 4 example about Defining the design problem using the numbers 20 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 Defining the design problem.

Worked Example 5

Problem: Create a simple Grade 4 example about Defining the design problem 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 Defining the design problem.

Worked Example 6

Problem: Create a simple Grade 4 example about Defining the design problem using the numbers 10 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 Defining the design problem.

Worked Example 7

Problem: Create a simple Grade 4 example about Defining the design problem using the numbers 9 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 Defining the design problem.

Worked Example 8

Problem: Create a simple Grade 4 example about Defining the design problem using the numbers 17 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 Defining the design problem.

Worked Example 9

Problem: Create a simple Grade 4 example about Defining the design problem using the numbers 15 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 Defining the design problem.

Worked Example 10

Problem: Create a simple Grade 4 example about Defining the design problem using the numbers 9 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 Defining the design problem.

Practice Exercise

Create and solve one new example of Defining the design 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.

41.2 Listing needs and constraints

Listing needs and constraints is an important Grade 4 mathematics idea in Mathematical Modelling Project: Designing a Schoolyard. 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 Listing needs and constraints using the numbers 4 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 Listing needs and constraints.

Worked Example 2

Problem: Create a simple Grade 4 example about Listing needs and constraints using the numbers 16 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 Listing needs and constraints.

Worked Example 3

Problem: Create a simple Grade 4 example about Listing needs and constraints using the numbers 4 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 Listing needs and constraints.

Worked Example 4

Problem: Create a simple Grade 4 example about Listing needs and constraints using the numbers 5 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 Listing needs and constraints.

Worked Example 5

Problem: Create a simple Grade 4 example about Listing needs and constraints using the numbers 4 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 Listing needs and constraints.

Worked Example 6

Problem: Create a simple Grade 4 example about Listing needs and constraints using the numbers 15 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 Listing needs and constraints.

Worked Example 7

Problem: Create a simple Grade 4 example about Listing needs and constraints using the numbers 14 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 Listing needs and constraints.

Worked Example 8

Problem: Create a simple Grade 4 example about Listing needs and constraints using the numbers 7 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 Listing needs and constraints.

Worked Example 9

Problem: Create a simple Grade 4 example about Listing needs and constraints 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 Listing needs and constraints.

Worked Example 10

Problem: Create a simple Grade 4 example about Listing needs and constraints using the numbers 3 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 Listing needs and constraints.

Practice Exercise

Create and solve one new example of Listing needs and constraints. 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.

41.3 Measuring available space

Measuring available space is an important Grade 4 mathematics idea in Mathematical Modelling Project: Designing a Schoolyard. 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 Measuring available space using the numbers 19 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 Measuring available space.

Worked Example 2

Problem: Create a simple Grade 4 example about Measuring available space using the numbers 8 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 Measuring available space.

Worked Example 3

Problem: Create a simple Grade 4 example about Measuring available space using the numbers 9 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 Measuring available space.

Worked Example 4

Problem: Create a simple Grade 4 example about Measuring available space using the numbers 7 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 Measuring available space.

Worked Example 5

Problem: Create a simple Grade 4 example about Measuring available space using the numbers 7 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 Measuring available space.

Worked Example 6

Problem: Create a simple Grade 4 example about Measuring available space using the numbers 13 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 Measuring available space.

Worked Example 7

Problem: Create a simple Grade 4 example about Measuring available space 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 Measuring available space.

Worked Example 8

Problem: Create a simple Grade 4 example about Measuring available space using the numbers 11 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 Measuring available space.

Worked Example 9

Problem: Create a simple Grade 4 example about Measuring available space 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 Measuring available space.

Worked Example 10

Problem: Create a simple Grade 4 example about Measuring available space using the numbers 11 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 Measuring available space.

Practice Exercise

Create and solve one new example of Measuring available space. 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.

41.4 Using whole numbers in a plan

Using whole numbers in a plan is an important Grade 4 mathematics idea in Mathematical Modelling Project: Designing a Schoolyard. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

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

10 Worked Examples with Answers

Worked Example 1

Problem: Create a simple Grade 4 example about Using whole numbers in a plan using the numbers 19 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 Using whole numbers in a plan.

Worked Example 2

Problem: Create a simple Grade 4 example about Using whole numbers in a plan using the numbers 11 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 Using whole numbers in a plan.

Worked Example 3

Problem: Create a simple Grade 4 example about Using whole numbers in a plan 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 Using whole numbers in a plan.

Worked Example 4

Problem: Create a simple Grade 4 example about Using whole numbers in a plan using the numbers 16 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 Using whole numbers in a plan.

Worked Example 5

Problem: Create a simple Grade 4 example about Using whole numbers in a plan using the numbers 19 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 Using whole numbers in a plan.

Worked Example 6

Problem: Create a simple Grade 4 example about Using whole numbers in a plan 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 Using whole numbers in a plan.

Worked Example 7

Problem: Create a simple Grade 4 example about Using whole numbers in a plan using the numbers 2 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 Using whole numbers in a plan.

Worked Example 8

Problem: Create a simple Grade 4 example about Using whole numbers in a plan using the numbers 4 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 Using whole numbers in a plan.

Worked Example 9

Problem: Create a simple Grade 4 example about Using whole numbers in a plan using the numbers 5 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 Using whole numbers in a plan.

Worked Example 10

Problem: Create a simple Grade 4 example about Using whole numbers in a plan 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 Using whole numbers in a plan.

Practice Exercise

Create and solve one new example of Using whole numbers in a plan. 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.

41.5 Using rectangle area

Spatial reasoning uses shape, position, movement, and measurement. Diagrams, coordinates, and measurements make relationships easier to see. 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: Find the area of a 4 cm by 8 cm rectangle.

Use area = length × width.
4 × 8 = 32.

Very beginner explanation: Area measures the surface inside a 2D shape.

Answer: 32 cm²

Worked Example 2

Problem: Find the area of a 7 cm by 3 cm rectangle.

Use area = length × width.
7 × 3 = 21.

Very beginner explanation: Area measures the surface inside a 2D shape.

Answer: 21 cm²

Worked Example 3

Problem: Find the area of a 4 cm by 6 cm rectangle.

Use area = length × width.
4 × 6 = 24.

Very beginner explanation: Area measures the surface inside a 2D shape.

Answer: 24 cm²

Worked Example 4

Problem: Find the area of a 8 cm by 4 cm rectangle.

Use area = length × width.
8 × 4 = 32.

Very beginner explanation: Area measures the surface inside a 2D shape.

Answer: 32 cm²

Worked Example 5

Problem: Find the area of a 10 cm by 6 cm rectangle.

Use area = length × width.
10 × 6 = 60.

Very beginner explanation: Area measures the surface inside a 2D shape.

Answer: 60 cm²

Worked Example 6

Problem: Find the area of a 12 cm by 8 cm rectangle.

Use area = length × width.
12 × 8 = 96.

Very beginner explanation: Area measures the surface inside a 2D shape.

Answer: 96 cm²

Worked Example 7

Problem: Find the area of a 10 cm by 5 cm rectangle.

Use area = length × width.
10 × 5 = 50.

Very beginner explanation: Area measures the surface inside a 2D shape.

Answer: 50 cm²

Worked Example 8

Problem: Find the area of a 5 cm by 3 cm rectangle.

Use area = length × width.
5 × 3 = 15.

Very beginner explanation: Area measures the surface inside a 2D shape.

Answer: 15 cm²

Worked Example 9

Problem: Find the area of a 7 cm by 6 cm rectangle.

Use area = length × width.
7 × 6 = 42.

Very beginner explanation: Area measures the surface inside a 2D shape.

Answer: 42 cm²

Worked Example 10

Problem: Find the area of a 12 cm by 3 cm rectangle.

Use area = length × width.
12 × 3 = 36.

Very beginner explanation: Area measures the surface inside a 2D shape.

Answer: 36 cm²

Practice Exercise

Create and solve one new example of Using rectangle area. 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.

41.6 Using a simple budget with whole dollars

Using a simple budget with whole dollars is an important Grade 4 mathematics idea in Mathematical Modelling Project: Designing a Schoolyard. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

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

10 Worked Examples with Answers

Worked Example 1

Problem: Create a simple Grade 4 example about Using a simple budget with whole dollars using the numbers 20 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 Using a simple budget with whole dollars.

Worked Example 2

Problem: Create a simple Grade 4 example about Using a simple budget with whole dollars using the numbers 7 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 Using a simple budget with whole dollars.

Worked Example 3

Problem: Create a simple Grade 4 example about Using a simple budget with whole dollars 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 Using a simple budget with whole dollars.

Worked Example 4

Problem: Create a simple Grade 4 example about Using a simple budget with whole dollars using the numbers 8 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 Using a simple budget with whole dollars.

Worked Example 5

Problem: Create a simple Grade 4 example about Using a simple budget with whole dollars using the numbers 5 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 Using a simple budget with whole dollars.

Worked Example 6

Problem: Create a simple Grade 4 example about Using a simple budget with whole dollars using the numbers 12 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 Using a simple budget with whole dollars.

Worked Example 7

Problem: Create a simple Grade 4 example about Using a simple budget with whole dollars using the numbers 13 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 Using a simple budget with whole dollars.

Worked Example 8

Problem: Create a simple Grade 4 example about Using a simple budget with whole dollars using the numbers 16 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 Using a simple budget with whole dollars.

Worked Example 9

Problem: Create a simple Grade 4 example about Using a simple budget with whole dollars using the numbers 13 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 Using a simple budget with whole dollars.

Worked Example 10

Problem: Create a simple Grade 4 example about Using a simple budget with whole dollars using the numbers 13 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 Using a simple budget with whole dollars.

Practice Exercise

Create and solve one new example of Using a simple budget with whole dollars. 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.

41.7 Collecting student-preference 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 [2, 2, 10, 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 2

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

Worked Example 3

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

Worked Example 4

Problem: A data set is [13, 10, 7, 3, 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: 13

Worked Example 5

Problem: A data set is [11, 8, 14, 10, 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 [10, 15, 12, 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: 15

Worked Example 7

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

Worked Example 8

Problem: A data set is [14, 12, 11, 4, 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: 14

Worked Example 9

Problem: A data set is [9, 6, 7, 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 10

Problem: A data set is [4, 15, 2, 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

Practice Exercise

Create and solve one new example of Collecting student-preference 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.

41.8 Comparing design choices

Comparing design choices is an important Grade 4 mathematics idea in Mathematical Modelling Project: Designing a Schoolyard. 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 Comparing design choices using the numbers 10 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 Comparing design choices.

Worked Example 2

Problem: Create a simple Grade 4 example about Comparing design choices using the numbers 4 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 Comparing design choices.

Worked Example 3

Problem: Create a simple Grade 4 example about Comparing design choices using the numbers 8 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 Comparing design choices.

Worked Example 4

Problem: Create a simple Grade 4 example about Comparing design choices using the numbers 10 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 Comparing design choices.

Worked Example 5

Problem: Create a simple Grade 4 example about Comparing design choices 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 Comparing design choices.

Worked Example 6

Problem: Create a simple Grade 4 example about Comparing design choices using the numbers 18 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 Comparing design choices.

Worked Example 7

Problem: Create a simple Grade 4 example about Comparing design choices 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 Comparing design choices.

Worked Example 8

Problem: Create a simple Grade 4 example about Comparing design choices using the numbers 9 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 Comparing design choices.

Worked Example 9

Problem: Create a simple Grade 4 example about Comparing design choices using the numbers 3 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 Comparing design choices.

Worked Example 10

Problem: Create a simple Grade 4 example about Comparing design choices using the numbers 8 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 Comparing design choices.

Practice Exercise

Create and solve one new example of Comparing design choices. 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.

41.9 Building a mathematical plan

Building a mathematical plan is an important Grade 4 mathematics idea in Mathematical Modelling Project: Designing a Schoolyard. 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 Building a mathematical plan using the numbers 17 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 Building a mathematical plan.

Worked Example 2

Problem: Create a simple Grade 4 example about Building a mathematical plan using the numbers 17 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 Building a mathematical plan.

Worked Example 3

Problem: Create a simple Grade 4 example about Building a mathematical plan using the numbers 17 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 Building a mathematical plan.

Worked Example 4

Problem: Create a simple Grade 4 example about Building a mathematical plan using the numbers 18 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 Building a mathematical plan.

Worked Example 5

Problem: Create a simple Grade 4 example about Building a mathematical plan using the numbers 8 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 Building a mathematical plan.

Worked Example 6

Problem: Create a simple Grade 4 example about Building a mathematical plan using the numbers 14 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 Building a mathematical plan.

Worked Example 7

Problem: Create a simple Grade 4 example about Building a mathematical plan using the numbers 19 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 Building a mathematical plan.

Worked Example 8

Problem: Create a simple Grade 4 example about Building a mathematical plan 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 Building a mathematical plan.

Worked Example 9

Problem: Create a simple Grade 4 example about Building a mathematical plan using the numbers 20 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 Building a mathematical plan.

Worked Example 10

Problem: Create a simple Grade 4 example about Building a mathematical plan using the numbers 18 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 Building a mathematical plan.

Practice Exercise

Create and solve one new example of Building a mathematical plan. 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.

41.10 Testing the plan against constraints

Testing the plan against constraints is an important Grade 4 mathematics idea in Mathematical Modelling Project: Designing a Schoolyard. 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 Testing the plan against constraints using the numbers 11 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 Testing the plan against constraints.

Worked Example 2

Problem: Create a simple Grade 4 example about Testing the plan against constraints 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 Testing the plan against constraints.

Worked Example 3

Problem: Create a simple Grade 4 example about Testing the plan against constraints using the numbers 5 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 Testing the plan against constraints.

Worked Example 4

Problem: Create a simple Grade 4 example about Testing the plan against constraints using the numbers 7 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 Testing the plan against constraints.

Worked Example 5

Problem: Create a simple Grade 4 example about Testing the plan against constraints using the numbers 17 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 Testing the plan against constraints.

Worked Example 6

Problem: Create a simple Grade 4 example about Testing the plan against constraints using the numbers 8 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 Testing the plan against constraints.

Worked Example 7

Problem: Create a simple Grade 4 example about Testing the plan against constraints 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 Testing the plan against constraints.

Worked Example 8

Problem: Create a simple Grade 4 example about Testing the plan against constraints 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 Testing the plan against constraints.

Worked Example 9

Problem: Create a simple Grade 4 example about Testing the plan against constraints using the numbers 9 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 Testing the plan against constraints.

Worked Example 10

Problem: Create a simple Grade 4 example about Testing the plan against constraints using the numbers 4 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 Testing the plan against constraints.

Practice Exercise

Create and solve one new example of Testing the plan against constraints. 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.

41.11 Revising the design

Revising the design is an important Grade 4 mathematics idea in Mathematical Modelling Project: Designing a Schoolyard. 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 Revising the design using the numbers 5 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 Revising the design.

Worked Example 2

Problem: Create a simple Grade 4 example about Revising the design using the numbers 9 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 Revising the design.

Worked Example 3

Problem: Create a simple Grade 4 example about Revising the design using the numbers 8 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 Revising the design.

Worked Example 4

Problem: Create a simple Grade 4 example about Revising the design using the numbers 10 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 Revising the design.

Worked Example 5

Problem: Create a simple Grade 4 example about Revising the design using the numbers 18 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 Revising the design.

Worked Example 6

Problem: Create a simple Grade 4 example about Revising the design using the numbers 9 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 Revising the design.

Worked Example 7

Problem: Create a simple Grade 4 example about Revising the design using the numbers 10 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 Revising the design.

Worked Example 8

Problem: Create a simple Grade 4 example about Revising the design using the numbers 14 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 Revising the design.

Worked Example 9

Problem: Create a simple Grade 4 example about Revising the design using the numbers 2 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 Revising the design.

Worked Example 10

Problem: Create a simple Grade 4 example about Revising the design using the numbers 7 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 Revising the design.

Practice Exercise

Create and solve one new example of Revising the design. 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.

41.12 Presenting a final recommendation

Presenting a final recommendation is an important Grade 4 mathematics idea in Mathematical Modelling Project: Designing a Schoolyard. 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 Presenting a final recommendation using the numbers 19 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 Presenting a final recommendation.

Worked Example 2

Problem: Create a simple Grade 4 example about Presenting a final recommendation using the numbers 10 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 Presenting a final recommendation.

Worked Example 3

Problem: Create a simple Grade 4 example about Presenting a final recommendation using the numbers 14 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 Presenting a final recommendation.

Worked Example 4

Problem: Create a simple Grade 4 example about Presenting a final recommendation 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 Presenting a final recommendation.

Worked Example 5

Problem: Create a simple Grade 4 example about Presenting a final recommendation using the numbers 19 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 Presenting a final recommendation.

Worked Example 6

Problem: Create a simple Grade 4 example about Presenting a final recommendation 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 Presenting a final recommendation.

Worked Example 7

Problem: Create a simple Grade 4 example about Presenting a final recommendation using the numbers 2 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 Presenting a final recommendation.

Worked Example 8

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

Worked Example 9

Problem: Create a simple Grade 4 example about Presenting a final recommendation 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 Presenting a final recommendation.

Worked Example 10

Problem: Create a simple Grade 4 example about Presenting a final recommendation 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 Presenting a final recommendation.

Practice Exercise

Create and solve one new example of Presenting a final 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.

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30 Review Questions and Answers

Q1. What is important to understand about Defining the design problem?

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

Q2. What is important to understand about Listing needs and constraints?

Answer: Listing needs and constraints is an important Grade 4 mathematics idea in Mathematical Modelling Project: Designing a Schoolyard. 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 Measuring available space?

Answer: Measuring available space is an important Grade 4 mathematics idea in Mathematical Modelling Project: Designing a Schoolyard. 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 Using whole numbers in a plan?

Answer: Using whole numbers in a plan is an important Grade 4 mathematics idea in Mathematical Modelling Project: Designing a Schoolyard. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q5. What is important to understand about Using rectangle area?

Answer: Spatial reasoning uses shape, position, movement, and measurement. Diagrams, coordinates, and measurements make relationships easier to see.

Q6. What is important to understand about Using a simple budget with whole dollars?

Answer: Using a simple budget with whole dollars is an important Grade 4 mathematics idea in Mathematical Modelling Project: Designing a Schoolyard. 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 Collecting student-preference data?

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 Comparing design choices?

Answer: Comparing design choices is an important Grade 4 mathematics idea in Mathematical Modelling Project: Designing a Schoolyard. 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 Building a mathematical plan?

Answer: Building a mathematical plan is an important Grade 4 mathematics idea in Mathematical Modelling Project: Designing a Schoolyard. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q10. What is important to understand about Testing the plan against constraints?

Answer: Testing the plan against constraints is an important Grade 4 mathematics idea in Mathematical Modelling Project: Designing a Schoolyard. 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 Revising the design?

Answer: Revising the design is an important Grade 4 mathematics idea in Mathematical Modelling Project: Designing a Schoolyard. 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 Presenting a final recommendation?

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

Q13. How would you explain Defining the design problem?

Q14. How would you explain Listing needs and constraints?

Q15. How would you explain Measuring available space?

Q16. How would you explain Using whole numbers in a plan?

Q17. How would you explain Using rectangle area?

Answer: Spatial reasoning uses shape, position, movement, and measurement. Diagrams, coordinates, and measurements make relationships easier to see.

Q18. How would you explain Using a simple budget with whole dollars?

Q19. How would you explain Collecting student-preference data?

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 Comparing design choices?

Q21. How would you explain Building a mathematical plan?

Q22. How would you explain Testing the plan against constraints?

Q23. How would you explain Revising the design?

Q24. How would you explain Presenting a final recommendation?

Q25. What should a beginner check when working with Defining the design problem?

Q26. What should a beginner check when working with Listing needs and constraints?

Q27. What should a beginner check when working with Measuring available space?

Q28. What should a beginner check when working with Using whole numbers in a plan?

Q29. What should a beginner check when working with Using rectangle area?

Answer: Spatial reasoning uses shape, position, movement, and measurement. Diagrams, coordinates, and measurements make relationships easier to see.