Chapter 29: Relations and Tables of Values
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Relations and Tables of Values with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Variable (a letter or symbol representing a number)
- Equation (a statement that two expressions are equal)
- Linear Relation (a relationship with a constant rate of change)
- Independent Events (events whose probabilities do not affect each other)
- Dependent Events (events where one outcome changes the probability of another)
- Estimate (a close approximation used to check whether an answer is reasonable)
- Solution (a value or result that satisfies the problem)
- Representation (a way to show mathematics using symbols, diagrams, tables, graphs, or words)
- Reasonableness (whether an answer makes sense in the context of the problem)
How to Learn This Chapter
Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
29.1 Relations
A relation pairs input values with output values. This topic focuses on Relations .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: For y=2x+(1), find y when x=3.
- Substitute x=3.
- y=2(3)+(1)=7.
Very beginner explanation: A relation pairs input values with output values. This topic focuses on Relations .
Answer: 7
Worked Example 2
Problem: For y=3x+(-2), find y when x=3.
- Substitute x=3.
- y=3(3)+(-2)=7.
Very beginner explanation: A relation pairs input values with output values. This topic focuses on Relations .
Answer: 7
Worked Example 3
Problem: For y=0.5x+(4), find y when x=3.
- Substitute x=3.
- y=0.5(3)+(4)=5.5.
Very beginner explanation: A relation pairs input values with output values. This topic focuses on Relations .
Answer: 5.5
Worked Example 4
Problem: For y=-1x+(5), find y when x=3.
- Substitute x=3.
- y=-1(3)+(5)=2.
Very beginner explanation: A relation pairs input values with output values. This topic focuses on Relations .
Answer: 2
Worked Example 5
Problem: For y=4x+(0), find y when x=3.
- Substitute x=3.
- y=4(3)+(0)=12.
Very beginner explanation: A relation pairs input values with output values. This topic focuses on Relations .
Answer: 12
Worked Example 6
Problem: For y = 2x + (1), find y when x = 3.
- Substitute x = 3.
- y = 2(3) + (1).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 7
Worked Example 7
Problem: For y = -1x + (4), find y when x = 3.
- Substitute x = 3.
- y = -1(3) + (4).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 1
Worked Example 8
Problem: For y = 0.5x + (-2), find y when x = 3.
- Substitute x = 3.
- y = 0.5(3) + (-2).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: -0.5
Worked Example 9
Problem: For y = 3x + (0), find y when x = 3.
- Substitute x = 3.
- y = 3(3) + (0).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 9
Worked Example 10
Problem: For y = -2x + (5), find y when x = 3.
- Substitute x = 3.
- y = -2(3) + (5).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: -1
Practice Exercise
Create one new question about Relations. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.2 Input
Input is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: For y=2x+(1), find y when x=3.
- Substitute x=3.
- y=2(3)+(1)=7.
Very beginner explanation: Input is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 7
Worked Example 2
Problem: For y=3x+(-2), find y when x=3.
- Substitute x=3.
- y=3(3)+(-2)=7.
Very beginner explanation: Input is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 7
Worked Example 3
Problem: For y=0.5x+(4), find y when x=3.
- Substitute x=3.
- y=0.5(3)+(4)=5.5.
Very beginner explanation: Input is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 5.5
Worked Example 4
Problem: For y=-1x+(5), find y when x=3.
- Substitute x=3.
- y=-1(3)+(5)=2.
Very beginner explanation: Input is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 2
Worked Example 5
Problem: For y=4x+(0), find y when x=3.
- Substitute x=3.
- y=4(3)+(0)=12.
Very beginner explanation: Input is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 12
Worked Example 6
Problem: For y = 2x + (1), find y when x = 3.
- Substitute x = 3.
- y = 2(3) + (1).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 7
Worked Example 7
Problem: For y = -1x + (4), find y when x = 3.
- Substitute x = 3.
- y = -1(3) + (4).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 1
Worked Example 8
Problem: For y = 0.5x + (-2), find y when x = 3.
- Substitute x = 3.
- y = 0.5(3) + (-2).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: -0.5
Worked Example 9
Problem: For y = 3x + (0), find y when x = 3.
- Substitute x = 3.
- y = 3(3) + (0).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 9
Worked Example 10
Problem: For y = -2x + (5), find y when x = 3.
- Substitute x = 3.
- y = -2(3) + (5).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: -1
Practice Exercise
Create one new question about Input. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.3 Output
Output is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: For y=2x+(1), find y when x=3.
- Substitute x=3.
- y=2(3)+(1)=7.
Very beginner explanation: Output is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 7
Worked Example 2
Problem: For y=3x+(-2), find y when x=3.
- Substitute x=3.
- y=3(3)+(-2)=7.
Very beginner explanation: Output is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 7
Worked Example 3
Problem: For y=0.5x+(4), find y when x=3.
- Substitute x=3.
- y=0.5(3)+(4)=5.5.
Very beginner explanation: Output is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 5.5
Worked Example 4
Problem: For y=-1x+(5), find y when x=3.
- Substitute x=3.
- y=-1(3)+(5)=2.
Very beginner explanation: Output is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 2
Worked Example 5
Problem: For y=4x+(0), find y when x=3.
- Substitute x=3.
- y=4(3)+(0)=12.
Very beginner explanation: Output is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 12
Worked Example 6
Problem: For y = 2x + (1), find y when x = 3.
- Substitute x = 3.
- y = 2(3) + (1).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 7
Worked Example 7
Problem: For y = -1x + (4), find y when x = 3.
- Substitute x = 3.
- y = -1(3) + (4).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 1
Worked Example 8
Problem: For y = 0.5x + (-2), find y when x = 3.
- Substitute x = 3.
- y = 0.5(3) + (-2).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: -0.5
Worked Example 9
Problem: For y = 3x + (0), find y when x = 3.
- Substitute x = 3.
- y = 3(3) + (0).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 9
Worked Example 10
Problem: For y = -2x + (5), find y when x = 3.
- Substitute x = 3.
- y = -2(3) + (5).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: -1
Practice Exercise
Create one new question about Output. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.4 Independent variable
A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Independent variable .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Simplify 3x+2x.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Independent variable .
Answer: 5x
Worked Example 2
Problem: Simplify 4(a+3).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Independent variable .
Answer: 4a+12
Worked Example 3
Problem: Simplify 7y-2y+5.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Independent variable .
Answer: 5y+5
Worked Example 4
Problem: Simplify 2(3x-4).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Independent variable .
Answer: 6x-8
Worked Example 5
Problem: Simplify 5m+3-2m.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Independent variable .
Answer: 3m+3
Worked Example 6
Problem: Simplify 3x + 4x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x
Worked Example 7
Problem: Simplify 8y - 3y + 2.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 5y + 2
Worked Example 8
Problem: Simplify 4(a + 2).
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4a + 8
Worked Example 9
Problem: Simplify 2(3x - 5) + x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x - 10
Worked Example 10
Problem: Simplify 6m + 7 - 2m - 3.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4m + 4
Practice Exercise
Create one new question about Independent variable. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.5 Dependent variable
A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Dependent variable .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Simplify 3x+2x.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Dependent variable .
Answer: 5x
Worked Example 2
Problem: Simplify 4(a+3).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Dependent variable .
Answer: 4a+12
Worked Example 3
Problem: Simplify 7y-2y+5.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Dependent variable .
Answer: 5y+5
Worked Example 4
Problem: Simplify 2(3x-4).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Dependent variable .
Answer: 6x-8
Worked Example 5
Problem: Simplify 5m+3-2m.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Dependent variable .
Answer: 3m+3
Worked Example 6
Problem: Simplify 3x + 4x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x
Worked Example 7
Problem: Simplify 8y - 3y + 2.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 5y + 2
Worked Example 8
Problem: Simplify 4(a + 2).
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4a + 8
Worked Example 9
Problem: Simplify 2(3x - 5) + x.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 7x - 10
Worked Example 10
Problem: Simplify 6m + 7 - 2m - 3.
- Identify like terms or distribute first if parentheses are present.
- Combine coefficients carefully.
Very beginner explanation: Like terms have the same variable part. The distributive property multiplies every term inside parentheses.
Answer: 4m + 4
Practice Exercise
Create one new question about Dependent variable. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.6 Input-output tables
Input-output tables is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: For y=2x+(1), find y when x=3.
- Substitute x=3.
- y=2(3)+(1)=7.
Very beginner explanation: Input-output tables is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 7
Worked Example 2
Problem: For y=3x+(-2), find y when x=3.
- Substitute x=3.
- y=3(3)+(-2)=7.
Very beginner explanation: Input-output tables is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 7
Worked Example 3
Problem: For y=0.5x+(4), find y when x=3.
- Substitute x=3.
- y=0.5(3)+(4)=5.5.
Very beginner explanation: Input-output tables is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 5.5
Worked Example 4
Problem: For y=-1x+(5), find y when x=3.
- Substitute x=3.
- y=-1(3)+(5)=2.
Very beginner explanation: Input-output tables is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 2
Worked Example 5
Problem: For y=4x+(0), find y when x=3.
- Substitute x=3.
- y=4(3)+(0)=12.
Very beginner explanation: Input-output tables is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 12
Worked Example 6
Problem: For y = 2x + (1), find y when x = 3.
- Substitute x = 3.
- y = 2(3) + (1).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 7
Worked Example 7
Problem: For y = -1x + (4), find y when x = 3.
- Substitute x = 3.
- y = -1(3) + (4).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 1
Worked Example 8
Problem: For y = 0.5x + (-2), find y when x = 3.
- Substitute x = 3.
- y = 0.5(3) + (-2).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: -0.5
Worked Example 9
Problem: For y = 3x + (0), find y when x = 3.
- Substitute x = 3.
- y = 3(3) + (0).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 9
Worked Example 10
Problem: For y = -2x + (5), find y when x = 3.
- Substitute x = 3.
- y = -2(3) + (5).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: -1
Practice Exercise
Create one new question about Input-output tables. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.7 Finding a rule from a table
Finding a rule from a table is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Finding a rule from a table: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Finding a rule from a table is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Finding a rule from a table: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Finding a rule from a table is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Finding a rule from a table: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Finding a rule from a table is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Finding a rule from a table: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Finding a rule from a table is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Finding a rule from a table: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Finding a rule from a table is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Explain Finding a rule from a table in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Finding a rule from a table becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Finding a rule from a table and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Finding a rule from a table becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Finding a rule from a table using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Finding a rule from a table becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Finding a rule from a table problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Finding a rule from a table becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Finding a rule from a table could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Finding a rule from a table becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Finding a rule from a table. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.8 Writing equations from tables
An equation says that two expressions are equal. This topic focuses on Writing equations from tables .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Solve 2x+5=3x-1.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Writing equations from tables .
Answer: x=6
Worked Example 2
Problem: Solve 4x-7=13.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Writing equations from tables .
Answer: x=5
Worked Example 3
Problem: Solve 3x+2=2x+9.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Writing equations from tables .
Answer: x=7
Worked Example 4
Problem: Solve 5x+4=2x+19.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Writing equations from tables .
Answer: x=5
Worked Example 5
Problem: Solve 2(x+3)=18.
- Simplify each side if needed.
- Collect variable terms on one side.
- Collect constants on the other side.
- Divide to isolate the variable.
- Check by substitution.
Very beginner explanation: An equation says that two expressions are equal. This topic focuses on Writing equations from tables .
Answer: x=6
Worked Example 6
Problem: Solve 2x + 5 = 17.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 6
Worked Example 7
Problem: Solve 3x - 4 = 11.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Worked Example 8
Problem: Solve 5x + 7 = 2x + 22.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Worked Example 9
Problem: Solve 4(x + 2) = 24.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 4
Worked Example 10
Problem: Solve 7x - 3 = 4x + 12.
- Simplify each side if needed.
- Use inverse operations to collect variable terms and constants.
- Keep both sides balanced.
- Check by substitution.
Very beginner explanation: An equation stays balanced when equivalent operations are applied correctly.
Answer: x = 5
Practice Exercise
Create one new question about Writing equations from tables. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.9 Completing tables
Completing tables is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Completing tables: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Completing tables is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Completing tables: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Completing tables is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Completing tables: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Completing tables is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Completing tables: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Completing tables is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Completing tables: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Completing tables is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Explain Completing tables in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Completing tables becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Completing tables and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Completing tables becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Completing tables using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Completing tables becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Completing tables problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Completing tables becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Completing tables could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Completing tables becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Completing tables. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.10 Comparing relations
A relation pairs input values with output values. This topic focuses on Comparing relations .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: For y=2x+(1), find y when x=3.
- Substitute x=3.
- y=2(3)+(1)=7.
Very beginner explanation: A relation pairs input values with output values. This topic focuses on Comparing relations .
Answer: 7
Worked Example 2
Problem: For y=3x+(-2), find y when x=3.
- Substitute x=3.
- y=3(3)+(-2)=7.
Very beginner explanation: A relation pairs input values with output values. This topic focuses on Comparing relations .
Answer: 7
Worked Example 3
Problem: For y=0.5x+(4), find y when x=3.
- Substitute x=3.
- y=0.5(3)+(4)=5.5.
Very beginner explanation: A relation pairs input values with output values. This topic focuses on Comparing relations .
Answer: 5.5
Worked Example 4
Problem: For y=-1x+(5), find y when x=3.
- Substitute x=3.
- y=-1(3)+(5)=2.
Very beginner explanation: A relation pairs input values with output values. This topic focuses on Comparing relations .
Answer: 2
Worked Example 5
Problem: For y=4x+(0), find y when x=3.
- Substitute x=3.
- y=4(3)+(0)=12.
Very beginner explanation: A relation pairs input values with output values. This topic focuses on Comparing relations .
Answer: 12
Worked Example 6
Problem: For y = 2x + (1), find y when x = 3.
- Substitute x = 3.
- y = 2(3) + (1).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 7
Worked Example 7
Problem: For y = -1x + (4), find y when x = 3.
- Substitute x = 3.
- y = -1(3) + (4).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 1
Worked Example 8
Problem: For y = 0.5x + (-2), find y when x = 3.
- Substitute x = 3.
- y = 0.5(3) + (-2).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: -0.5
Worked Example 9
Problem: For y = 3x + (0), find y when x = 3.
- Substitute x = 3.
- y = 3(3) + (0).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 9
Worked Example 10
Problem: For y = -2x + (5), find y when x = 3.
- Substitute x = 3.
- y = -2(3) + (5).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: -1
Practice Exercise
Create one new question about Comparing relations. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.11 Equivalent representations
Equivalent representations is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Equivalent representations: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Equivalent representations is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Equivalent representations: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Equivalent representations is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Equivalent representations: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Equivalent representations is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Equivalent representations: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Equivalent representations is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Equivalent representations: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Equivalent representations is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Explain Equivalent representations in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Equivalent representations becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Equivalent representations and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Equivalent representations becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Equivalent representations using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Equivalent representations becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Equivalent representations problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Equivalent representations becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Equivalent representations could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Equivalent representations becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Equivalent representations. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.12 Real-life relations
A relation pairs input values with output values. This topic focuses on Real-life relations .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: For y=2x+(1), find y when x=3.
- Substitute x=3.
- y=2(3)+(1)=7.
Very beginner explanation: A relation pairs input values with output values. This topic focuses on Real-life relations .
Answer: 7
Worked Example 2
Problem: For y=3x+(-2), find y when x=3.
- Substitute x=3.
- y=3(3)+(-2)=7.
Very beginner explanation: A relation pairs input values with output values. This topic focuses on Real-life relations .
Answer: 7
Worked Example 3
Problem: For y=0.5x+(4), find y when x=3.
- Substitute x=3.
- y=0.5(3)+(4)=5.5.
Very beginner explanation: A relation pairs input values with output values. This topic focuses on Real-life relations .
Answer: 5.5
Worked Example 4
Problem: For y=-1x+(5), find y when x=3.
- Substitute x=3.
- y=-1(3)+(5)=2.
Very beginner explanation: A relation pairs input values with output values. This topic focuses on Real-life relations .
Answer: 2
Worked Example 5
Problem: For y=4x+(0), find y when x=3.
- Substitute x=3.
- y=4(3)+(0)=12.
Very beginner explanation: A relation pairs input values with output values. This topic focuses on Real-life relations .
Answer: 12
Worked Example 6
Problem: For y = 2x + (1), find y when x = 3.
- Substitute x = 3.
- y = 2(3) + (1).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 7
Worked Example 7
Problem: For y = -1x + (4), find y when x = 3.
- Substitute x = 3.
- y = -1(3) + (4).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 1
Worked Example 8
Problem: For y = 0.5x + (-2), find y when x = 3.
- Substitute x = 3.
- y = 0.5(3) + (-2).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: -0.5
Worked Example 9
Problem: For y = 3x + (0), find y when x = 3.
- Substitute x = 3.
- y = 3(3) + (0).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: 9
Worked Example 10
Problem: For y = -2x + (5), find y when x = 3.
- Substitute x = 3.
- y = -2(3) + (5).
- Multiply first, then add.
Very beginner explanation: A relation pairs inputs with outputs. In a linear relation, the rate of change is constant.
Answer: -1
Practice Exercise
Create one new question about Real-life relations. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
29.13 Word problems
Word problems is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Word problems: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Word problems is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: Word problems: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Word problems is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: Word problems: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Word problems is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: Word problems: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Word problems is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: Word problems: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Word problems is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Explain Word problems in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Word problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Word problems and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Word problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Word problems using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Word problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Word problems problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Word problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Word problems could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Word problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Word problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
Chapter Notes, Practice, and Common Mistakes
Chapter Notes
- Read the complete question before choosing an operation, formula, graph, or model.
- Write technical words together with their meaning until you are comfortable using them.
- Show all important steps so another student can follow your reasoning.
- Keep units, labels, signs, axes, variables, and mathematical symbols clear.
- Estimate before or after calculating when an estimate can help check reasonableness.
- For real-life problems, explain what the final number means in the situation.
Extra Practice
- Create and solve a new question about Relations . Show your reasoning and check your answer.
- Create and solve a new question about Input . Show your reasoning and check your answer.
- Create and solve a new question about Output . Show your reasoning and check your answer.
- Create and solve a new question about Independent variable . Show your reasoning and check your answer.
- Create and solve a new question about Dependent variable . Show your reasoning and check your answer.
- Create and solve a new question about Input-output tables . Show your reasoning and check your answer.
- Create and solve a new question about Finding a rule from a table . Show your reasoning and check your answer.
- Create and solve a new question about Writing equations from tables . Show your reasoning and check your answer.
- Create and solve a new question about Completing tables . Show your reasoning and check your answer.
- Create and solve a new question about Comparing relations . Show your reasoning and check your answer.
- Create and solve a new question about Equivalent representations . Show your reasoning and check your answer.
- Create and solve a new question about Real-life relations . Show your reasoning and check your answer.
Common Mistakes
- Combining unlike terms.
- Changing only one side of an equation.
- Forgetting to distribute to every term.
- Using a pattern rule that works only for the first few terms.
- Writing code without tracing variable values.
- Using a mathematical model without stating assumptions.
30 Review Questions and Answers
Q1. What is important to remember about Relations?
Answer: A relation pairs input values with output values. This topic focuses on Relations.
Q2. What is important to remember about Input?
Answer: Input is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q3. What is important to remember about Output?
Answer: Output is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q4. What is important to remember about Independent variable?
Answer: A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Independent variable.
Q5. What is important to remember about Dependent variable?
Answer: A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Dependent variable.
Q6. What is important to remember about Input-output tables?
Answer: Input-output tables is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q7. What is important to remember about Finding a rule from a table?
Answer: Finding a rule from a table is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q8. What is important to remember about Writing equations from tables?
Answer: An equation says that two expressions are equal. This topic focuses on Writing equations from tables.
Q9. What is important to remember about Completing tables?
Answer: Completing tables is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q10. What is important to remember about Comparing relations?
Answer: A relation pairs input values with output values. This topic focuses on Comparing relations.
Q11. What is important to remember about Equivalent representations?
Answer: Equivalent representations is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q12. What is important to remember about Real-life relations?
Answer: A relation pairs input values with output values. This topic focuses on Real-life relations.
Q13. What is important to remember about Word problems?
Answer: Word problems is an important Grade 7 idea in Relations and Tables of Values. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q14. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q15. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q16. Why do units matter?
Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.
Q17. When should you round?
Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.
Q18. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.
Q19. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q20. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q21. What should you do if an answer seems unreasonable?
Answer: Re-read the question, check copied values, signs, units, formulas, and calculations.
Q22. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q23. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q24. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q25. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q26. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q27. When is a calculator useful?
Answer: A calculator is useful for lengthy arithmetic after you understand the mathematical setup and can estimate the expected size of the answer.
Q28. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.
Q29. What is a mathematical model?
Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.
Q30. Why should assumptions be stated?
Answer: Assumptions show what conditions the solution depends on and help readers judge whether the model is reasonable.