Chapter 57: Financial Goals, Budgets, and Savings Plans
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Financial Goals, Budgets, and Savings Plans with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Unit Rate (a rate per one unit)
- Variable (a letter or symbol representing a number)
- Exchange Rate (the value of one currency expressed in another currency)
- Interest Rate (percentage used to calculate interest)
- 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.
57.1 Financial goals
A financial goal is a money target with a purpose and usually a time frame. This topic focuses on Financial goals .
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: Monthly income $2000; spending $1500. Find savings and savings rate.
- Savings=2000-1500=500.
- Savings rate=500/2000×100%.
Very beginner explanation: A financial goal is a money target with a purpose and usually a time frame. This topic focuses on Financial goals .
Answer: $500; 25.0%
Worked Example 2
Problem: Monthly income $2500; spending $1850. Find savings and savings rate.
- Savings=2500-1850=650.
- Savings rate=650/2500×100%.
Very beginner explanation: A financial goal is a money target with a purpose and usually a time frame. This topic focuses on Financial goals .
Answer: $650; 26.0%
Worked Example 3
Problem: Monthly income $1800; spending $1400. Find savings and savings rate.
- Savings=1800-1400=400.
- Savings rate=400/1800×100%.
Very beginner explanation: A financial goal is a money target with a purpose and usually a time frame. This topic focuses on Financial goals .
Answer: $400; 22.2%
Worked Example 4
Problem: Monthly income $3200; spending $2600. Find savings and savings rate.
- Savings=3200-2600=600.
- Savings rate=600/3200×100%.
Very beginner explanation: A financial goal is a money target with a purpose and usually a time frame. This topic focuses on Financial goals .
Answer: $600; 18.8%
Worked Example 5
Problem: Monthly income $1500; spending $1275. Find savings and savings rate.
- Savings=1500-1275=225.
- Savings rate=225/1500×100%.
Very beginner explanation: A financial goal is a money target with a purpose and usually a time frame. This topic focuses on Financial goals .
Answer: $225; 15.0%
Worked Example 6
Problem: Monthly income is $1500 and spending is $1100. Find monthly savings.
- Savings = income - spending.
- 1500 - 1100 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 7
Problem: Monthly income is $2000 and spending is $1600. Find monthly savings.
- Savings = income - spending.
- 2000 - 1600 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 8
Problem: Monthly income is $1750 and spending is $1350. Find monthly savings.
- Savings = income - spending.
- 1750 - 1350 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 9
Problem: Monthly income is $2200 and spending is $1800. Find monthly savings.
- Savings = income - spending.
- 2200 - 1800 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 10
Problem: Monthly income is $3000 and spending is $2600. Find monthly savings.
- Savings = income - spending.
- 3000 - 2600 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Practice Exercise
Create one new question about Financial goals. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
57.2 Short-term goals
A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Short-term goals .
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 term is one part of an expression separated by addition or subtraction signs. This topic focuses on Short-term goals .
Answer: 5x
Worked Example 2
Problem: Simplify 4(a+3).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Short-term goals .
Answer: 4a+12
Worked Example 3
Problem: Simplify 7y-2y+5.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Short-term goals .
Answer: 5y+5
Worked Example 4
Problem: Simplify 2(3x-4).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Short-term goals .
Answer: 6x-8
Worked Example 5
Problem: Simplify 5m+3-2m.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Short-term goals .
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 Short-term goals. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
57.3 Long-term goals
A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Long-term goals .
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 term is one part of an expression separated by addition or subtraction signs. This topic focuses on Long-term goals .
Answer: 5x
Worked Example 2
Problem: Simplify 4(a+3).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Long-term goals .
Answer: 4a+12
Worked Example 3
Problem: Simplify 7y-2y+5.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Long-term goals .
Answer: 5y+5
Worked Example 4
Problem: Simplify 2(3x-4).
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Long-term goals .
Answer: 6x-8
Worked Example 5
Problem: Simplify 5m+3-2m.
- Identify like terms or use distribution.
- Combine carefully.
Very beginner explanation: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Long-term goals .
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 Long-term goals. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
57.4 Income
Income is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. 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: Monthly income $2000; spending $1500. Find savings and savings rate.
- Savings=2000-1500=500.
- Savings rate=500/2000×100%.
Very beginner explanation: Income is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $500; 25.0%
Worked Example 2
Problem: Monthly income $2500; spending $1850. Find savings and savings rate.
- Savings=2500-1850=650.
- Savings rate=650/2500×100%.
Very beginner explanation: Income is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $650; 26.0%
Worked Example 3
Problem: Monthly income $1800; spending $1400. Find savings and savings rate.
- Savings=1800-1400=400.
- Savings rate=400/1800×100%.
Very beginner explanation: Income is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $400; 22.2%
Worked Example 4
Problem: Monthly income $3200; spending $2600. Find savings and savings rate.
- Savings=3200-2600=600.
- Savings rate=600/3200×100%.
Very beginner explanation: Income is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $600; 18.8%
Worked Example 5
Problem: Monthly income $1500; spending $1275. Find savings and savings rate.
- Savings=1500-1275=225.
- Savings rate=225/1500×100%.
Very beginner explanation: Income is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $225; 15.0%
Worked Example 6
Problem: Monthly income is $1500 and spending is $1100. Find monthly savings.
- Savings = income - spending.
- 1500 - 1100 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 7
Problem: Monthly income is $2000 and spending is $1600. Find monthly savings.
- Savings = income - spending.
- 2000 - 1600 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 8
Problem: Monthly income is $1750 and spending is $1350. Find monthly savings.
- Savings = income - spending.
- 1750 - 1350 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 9
Problem: Monthly income is $2200 and spending is $1800. Find monthly savings.
- Savings = income - spending.
- 2200 - 1800 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 10
Problem: Monthly income is $3000 and spending is $2600. Find monthly savings.
- Savings = income - spending.
- 3000 - 2600 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Practice Exercise
Create one new question about Income. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
57.5 Fixed expenses
Fixed expenses is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. 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: Monthly income $2000; spending $1500. Find savings and savings rate.
- Savings=2000-1500=500.
- Savings rate=500/2000×100%.
Very beginner explanation: Fixed expenses is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $500; 25.0%
Worked Example 2
Problem: Monthly income $2500; spending $1850. Find savings and savings rate.
- Savings=2500-1850=650.
- Savings rate=650/2500×100%.
Very beginner explanation: Fixed expenses is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $650; 26.0%
Worked Example 3
Problem: Monthly income $1800; spending $1400. Find savings and savings rate.
- Savings=1800-1400=400.
- Savings rate=400/1800×100%.
Very beginner explanation: Fixed expenses is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $400; 22.2%
Worked Example 4
Problem: Monthly income $3200; spending $2600. Find savings and savings rate.
- Savings=3200-2600=600.
- Savings rate=600/3200×100%.
Very beginner explanation: Fixed expenses is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $600; 18.8%
Worked Example 5
Problem: Monthly income $1500; spending $1275. Find savings and savings rate.
- Savings=1500-1275=225.
- Savings rate=225/1500×100%.
Very beginner explanation: Fixed expenses is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $225; 15.0%
Worked Example 6
Problem: Monthly income is $1500 and spending is $1100. Find monthly savings.
- Savings = income - spending.
- 1500 - 1100 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 7
Problem: Monthly income is $2000 and spending is $1600. Find monthly savings.
- Savings = income - spending.
- 2000 - 1600 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 8
Problem: Monthly income is $1750 and spending is $1350. Find monthly savings.
- Savings = income - spending.
- 1750 - 1350 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 9
Problem: Monthly income is $2200 and spending is $1800. Find monthly savings.
- Savings = income - spending.
- 2200 - 1800 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 10
Problem: Monthly income is $3000 and spending is $2600. Find monthly savings.
- Savings = income - spending.
- 3000 - 2600 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Practice Exercise
Create one new question about Fixed expenses. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
57.6 Variable expenses
A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Variable expenses .
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 Variable expenses .
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 Variable expenses .
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 Variable expenses .
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 Variable expenses .
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 Variable expenses .
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 Variable expenses. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
57.7 Needs and wants
Needs and wants is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. 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: Monthly income $2000; spending $1500. Find savings and savings rate.
- Savings=2000-1500=500.
- Savings rate=500/2000×100%.
Very beginner explanation: Needs and wants is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $500; 25.0%
Worked Example 2
Problem: Monthly income $2500; spending $1850. Find savings and savings rate.
- Savings=2500-1850=650.
- Savings rate=650/2500×100%.
Very beginner explanation: Needs and wants is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $650; 26.0%
Worked Example 3
Problem: Monthly income $1800; spending $1400. Find savings and savings rate.
- Savings=1800-1400=400.
- Savings rate=400/1800×100%.
Very beginner explanation: Needs and wants is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $400; 22.2%
Worked Example 4
Problem: Monthly income $3200; spending $2600. Find savings and savings rate.
- Savings=3200-2600=600.
- Savings rate=600/3200×100%.
Very beginner explanation: Needs and wants is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $600; 18.8%
Worked Example 5
Problem: Monthly income $1500; spending $1275. Find savings and savings rate.
- Savings=1500-1275=225.
- Savings rate=225/1500×100%.
Very beginner explanation: Needs and wants is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $225; 15.0%
Worked Example 6
Problem: Explain Needs and wants 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: Needs and wants 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 Needs and wants 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: Needs and wants 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 Needs and wants 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: Needs and wants 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 Needs and wants 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: Needs and wants 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 Needs and wants 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: Needs and wants 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 Needs and wants. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
57.8 Creating a budget
A budget is a plan that compares income, spending, and saving. This topic focuses on Creating a budget .
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: Paint a room
- Model wall area and paint coverage
- State assumptions.
- Calculate using the model.
- Check whether the result is realistic.
- Revise if needed.
Very beginner explanation: A budget is a plan that compares income, spending, and saving. This topic focuses on Creating a budget .
Answer: Estimate litres and cost
Worked Example 2
Problem: Tile a floor
- Model floor area and tile area
- State assumptions.
- Calculate using the model.
- Check whether the result is realistic.
- Revise if needed.
Very beginner explanation: A budget is a plan that compares income, spending, and saving. This topic focuses on Creating a budget .
Answer: Estimate tile count plus waste
Worked Example 3
Problem: Plan a school event
- Model attendance and cost per person
- State assumptions.
- Calculate using the model.
- Check whether the result is realistic.
- Revise if needed.
Very beginner explanation: A budget is a plan that compares income, spending, and saving. This topic focuses on Creating a budget .
Answer: Estimate total cost
Worked Example 4
Problem: Compare transportation
- Model fixed and per-kilometre costs
- State assumptions.
- Calculate using the model.
- Check whether the result is realistic.
- Revise if needed.
Very beginner explanation: A budget is a plan that compares income, spending, and saving. This topic focuses on Creating a budget .
Answer: Find a break-even distance
Worked Example 5
Problem: Plan monthly savings
- Model starting savings plus monthly deposits
- State assumptions.
- Calculate using the model.
- Check whether the result is realistic.
- Revise if needed.
Very beginner explanation: A budget is a plan that compares income, spending, and saving. This topic focuses on Creating a budget .
Answer: Predict when a goal is reached
Worked Example 6
Problem: Tile a floor
- Write a simple rule: area = length × width.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Estimate tile quantity and include a small waste allowance.
Worked Example 7
Problem: Plan monthly savings
- Write a simple rule: total = starting amount + monthly deposit × months.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Predict when the savings goal is reached.
Worked Example 8
Problem: Simulate a die
- Write a simple rule: generate a random whole number from 1 to 6.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Repeat many times and compare frequencies.
Worked Example 9
Problem: Translate a point
- Write a simple rule: new x = x + 3; new y = y - 2.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Apply the same rule to every point.
Worked Example 10
Problem: Estimate paint needed
- Write a simple rule: paint = wall area ÷ coverage per can.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Round up because a partial can may not be enough.
Practice Exercise
Create one new question about Creating a budget. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
57.9 Balanced budget
A budget is a plan that compares income, spending, and saving. This topic focuses on Balanced budget .
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: Paint a room
- Model wall area and paint coverage
- State assumptions.
- Calculate using the model.
- Check whether the result is realistic.
- Revise if needed.
Very beginner explanation: A budget is a plan that compares income, spending, and saving. This topic focuses on Balanced budget .
Answer: Estimate litres and cost
Worked Example 2
Problem: Tile a floor
- Model floor area and tile area
- State assumptions.
- Calculate using the model.
- Check whether the result is realistic.
- Revise if needed.
Very beginner explanation: A budget is a plan that compares income, spending, and saving. This topic focuses on Balanced budget .
Answer: Estimate tile count plus waste
Worked Example 3
Problem: Plan a school event
- Model attendance and cost per person
- State assumptions.
- Calculate using the model.
- Check whether the result is realistic.
- Revise if needed.
Very beginner explanation: A budget is a plan that compares income, spending, and saving. This topic focuses on Balanced budget .
Answer: Estimate total cost
Worked Example 4
Problem: Compare transportation
- Model fixed and per-kilometre costs
- State assumptions.
- Calculate using the model.
- Check whether the result is realistic.
- Revise if needed.
Very beginner explanation: A budget is a plan that compares income, spending, and saving. This topic focuses on Balanced budget .
Answer: Find a break-even distance
Worked Example 5
Problem: Plan monthly savings
- Model starting savings plus monthly deposits
- State assumptions.
- Calculate using the model.
- Check whether the result is realistic.
- Revise if needed.
Very beginner explanation: A budget is a plan that compares income, spending, and saving. This topic focuses on Balanced budget .
Answer: Predict when a goal is reached
Worked Example 6
Problem: Tile a floor
- Write a simple rule: area = length × width.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Estimate tile quantity and include a small waste allowance.
Worked Example 7
Problem: Plan monthly savings
- Write a simple rule: total = starting amount + monthly deposit × months.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Predict when the savings goal is reached.
Worked Example 8
Problem: Simulate a die
- Write a simple rule: generate a random whole number from 1 to 6.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Repeat many times and compare frequencies.
Worked Example 9
Problem: Translate a point
- Write a simple rule: new x = x + 3; new y = y - 2.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Apply the same rule to every point.
Worked Example 10
Problem: Estimate paint needed
- Write a simple rule: paint = wall area ÷ coverage per can.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Round up because a partial can may not be enough.
Practice Exercise
Create one new question about Balanced budget. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
57.10 Savings amount
Savings amount is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. 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: Monthly income $2000; spending $1500. Find savings and savings rate.
- Savings=2000-1500=500.
- Savings rate=500/2000×100%.
Very beginner explanation: Savings amount is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $500; 25.0%
Worked Example 2
Problem: Monthly income $2500; spending $1850. Find savings and savings rate.
- Savings=2500-1850=650.
- Savings rate=650/2500×100%.
Very beginner explanation: Savings amount is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $650; 26.0%
Worked Example 3
Problem: Monthly income $1800; spending $1400. Find savings and savings rate.
- Savings=1800-1400=400.
- Savings rate=400/1800×100%.
Very beginner explanation: Savings amount is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $400; 22.2%
Worked Example 4
Problem: Monthly income $3200; spending $2600. Find savings and savings rate.
- Savings=3200-2600=600.
- Savings rate=600/3200×100%.
Very beginner explanation: Savings amount is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $600; 18.8%
Worked Example 5
Problem: Monthly income $1500; spending $1275. Find savings and savings rate.
- Savings=1500-1275=225.
- Savings rate=225/1500×100%.
Very beginner explanation: Savings amount is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $225; 15.0%
Worked Example 6
Problem: Monthly income is $1500 and spending is $1100. Find monthly savings.
- Savings = income - spending.
- 1500 - 1100 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 7
Problem: Monthly income is $2000 and spending is $1600. Find monthly savings.
- Savings = income - spending.
- 2000 - 1600 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 8
Problem: Monthly income is $1750 and spending is $1350. Find monthly savings.
- Savings = income - spending.
- 1750 - 1350 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 9
Problem: Monthly income is $2200 and spending is $1800. Find monthly savings.
- Savings = income - spending.
- 2200 - 1800 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 10
Problem: Monthly income is $3000 and spending is $2600. Find monthly savings.
- Savings = income - spending.
- 3000 - 2600 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Practice Exercise
Create one new question about Savings amount. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
57.11 Savings rate
A rate compares two quantities measured in different units. This topic focuses on Savings rate .
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: 120 km in 2 h. Find the unit rate.
- Use rate = distance ÷ time.
- 120÷2=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Savings rate .
Answer: 60 km/h
Worked Example 2
Problem: 180 km in 3 h. Find the unit rate.
- Use rate = distance ÷ time.
- 180÷3=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Savings rate .
Answer: 60 km/h
Worked Example 3
Problem: 250 km in 5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 250÷5=50.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Savings rate .
Answer: 50 km/h
Worked Example 4
Problem: 72 km in 1.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 72÷1.5=48.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Savings rate .
Answer: 48 km/h
Worked Example 5
Problem: 315 km in 4.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 315÷4.5=70.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Savings rate .
Answer: 70 km/h
Worked Example 6
Problem: 120 km are travelled in 2 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 120 ÷ 2 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 7
Problem: 180 km are travelled in 3 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 180 ÷ 3 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 8
Problem: 240 km are travelled in 4 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 240 ÷ 4 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 9
Problem: 300 km are travelled in 5 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 300 ÷ 5 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 10
Problem: 360 km are travelled in 6 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 360 ÷ 6 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Practice Exercise
Create one new question about Savings rate. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
57.12 Planning monthly savings
Planning monthly savings is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. 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: Monthly income $2000; spending $1500. Find savings and savings rate.
- Savings=2000-1500=500.
- Savings rate=500/2000×100%.
Very beginner explanation: Planning monthly savings is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $500; 25.0%
Worked Example 2
Problem: Monthly income $2500; spending $1850. Find savings and savings rate.
- Savings=2500-1850=650.
- Savings rate=650/2500×100%.
Very beginner explanation: Planning monthly savings is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $650; 26.0%
Worked Example 3
Problem: Monthly income $1800; spending $1400. Find savings and savings rate.
- Savings=1800-1400=400.
- Savings rate=400/1800×100%.
Very beginner explanation: Planning monthly savings is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $400; 22.2%
Worked Example 4
Problem: Monthly income $3200; spending $2600. Find savings and savings rate.
- Savings=3200-2600=600.
- Savings rate=600/3200×100%.
Very beginner explanation: Planning monthly savings is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $600; 18.8%
Worked Example 5
Problem: Monthly income $1500; spending $1275. Find savings and savings rate.
- Savings=1500-1275=225.
- Savings rate=225/1500×100%.
Very beginner explanation: Planning monthly savings is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $225; 15.0%
Worked Example 6
Problem: Monthly income is $1500 and spending is $1100. Find monthly savings.
- Savings = income - spending.
- 1500 - 1100 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 7
Problem: Monthly income is $2000 and spending is $1600. Find monthly savings.
- Savings = income - spending.
- 2000 - 1600 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 8
Problem: Monthly income is $1750 and spending is $1350. Find monthly savings.
- Savings = income - spending.
- 1750 - 1350 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 9
Problem: Monthly income is $2200 and spending is $1800. Find monthly savings.
- Savings = income - spending.
- 2200 - 1800 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Worked Example 10
Problem: Monthly income is $3000 and spending is $2600. Find monthly savings.
- Savings = income - spending.
- 3000 - 2600 = 400.
Very beginner explanation: A budget compares money coming in with money going out and can show how much remains for saving.
Answer: $400
Practice Exercise
Create one new question about Planning monthly savings. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
57.13 Adjusting a budget
A budget is a plan that compares income, spending, and saving. This topic focuses on Adjusting a budget .
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: Paint a room
- Model wall area and paint coverage
- State assumptions.
- Calculate using the model.
- Check whether the result is realistic.
- Revise if needed.
Very beginner explanation: A budget is a plan that compares income, spending, and saving. This topic focuses on Adjusting a budget .
Answer: Estimate litres and cost
Worked Example 2
Problem: Tile a floor
- Model floor area and tile area
- State assumptions.
- Calculate using the model.
- Check whether the result is realistic.
- Revise if needed.
Very beginner explanation: A budget is a plan that compares income, spending, and saving. This topic focuses on Adjusting a budget .
Answer: Estimate tile count plus waste
Worked Example 3
Problem: Plan a school event
- Model attendance and cost per person
- State assumptions.
- Calculate using the model.
- Check whether the result is realistic.
- Revise if needed.
Very beginner explanation: A budget is a plan that compares income, spending, and saving. This topic focuses on Adjusting a budget .
Answer: Estimate total cost
Worked Example 4
Problem: Compare transportation
- Model fixed and per-kilometre costs
- State assumptions.
- Calculate using the model.
- Check whether the result is realistic.
- Revise if needed.
Very beginner explanation: A budget is a plan that compares income, spending, and saving. This topic focuses on Adjusting a budget .
Answer: Find a break-even distance
Worked Example 5
Problem: Plan monthly savings
- Model starting savings plus monthly deposits
- State assumptions.
- Calculate using the model.
- Check whether the result is realistic.
- Revise if needed.
Very beginner explanation: A budget is a plan that compares income, spending, and saving. This topic focuses on Adjusting a budget .
Answer: Predict when a goal is reached
Worked Example 6
Problem: Tile a floor
- Write a simple rule: area = length × width.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Estimate tile quantity and include a small waste allowance.
Worked Example 7
Problem: Plan monthly savings
- Write a simple rule: total = starting amount + monthly deposit × months.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Predict when the savings goal is reached.
Worked Example 8
Problem: Simulate a die
- Write a simple rule: generate a random whole number from 1 to 6.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Repeat many times and compare frequencies.
Worked Example 9
Problem: Translate a point
- Write a simple rule: new x = x + 3; new y = y - 2.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Apply the same rule to every point.
Worked Example 10
Problem: Estimate paint needed
- Write a simple rule: paint = wall area ÷ coverage per can.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Round up because a partial can may not be enough.
Practice Exercise
Create one new question about Adjusting a budget. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
57.14 Tracking progress
Tracking progress is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. 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: Monthly income $2000; spending $1500. Find savings and savings rate.
- Savings=2000-1500=500.
- Savings rate=500/2000×100%.
Very beginner explanation: Tracking progress is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $500; 25.0%
Worked Example 2
Problem: Monthly income $2500; spending $1850. Find savings and savings rate.
- Savings=2500-1850=650.
- Savings rate=650/2500×100%.
Very beginner explanation: Tracking progress is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $650; 26.0%
Worked Example 3
Problem: Monthly income $1800; spending $1400. Find savings and savings rate.
- Savings=1800-1400=400.
- Savings rate=400/1800×100%.
Very beginner explanation: Tracking progress is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $400; 22.2%
Worked Example 4
Problem: Monthly income $3200; spending $2600. Find savings and savings rate.
- Savings=3200-2600=600.
- Savings rate=600/3200×100%.
Very beginner explanation: Tracking progress is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $600; 18.8%
Worked Example 5
Problem: Monthly income $1500; spending $1275. Find savings and savings rate.
- Savings=1500-1275=225.
- Savings rate=225/1500×100%.
Very beginner explanation: Tracking progress is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $225; 15.0%
Worked Example 6
Problem: Explain Tracking progress 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: Tracking progress 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 Tracking progress 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: Tracking progress 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 Tracking progress 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: Tracking progress 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 Tracking progress 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: Tracking progress 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 Tracking progress 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: Tracking progress 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 Tracking progress. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
57.15 Real-life financial decisions
Real-life financial decisions is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. 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: Real-life financial decisions: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Real-life financial decisions is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. 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: Real-life financial decisions: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Real-life financial decisions is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. 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: Real-life financial decisions: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Real-life financial decisions is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. 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: Real-life financial decisions: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Real-life financial decisions is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. 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: Real-life financial decisions: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Real-life financial decisions is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. 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 Real-life financial decisions 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: Real-life financial decisions 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 Real-life financial decisions 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: Real-life financial decisions 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 Real-life financial decisions 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: Real-life financial decisions 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 Real-life financial decisions 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: Real-life financial decisions 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 Real-life financial decisions 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: Real-life financial decisions 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 Real-life financial decisions. 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 Financial goals . Show your reasoning and check your answer.
- Create and solve a new question about Short-term goals . Show your reasoning and check your answer.
- Create and solve a new question about Long-term goals . Show your reasoning and check your answer.
- Create and solve a new question about Income . Show your reasoning and check your answer.
- Create and solve a new question about Fixed expenses . Show your reasoning and check your answer.
- Create and solve a new question about Variable expenses . Show your reasoning and check your answer.
- Create and solve a new question about Needs and wants . Show your reasoning and check your answer.
- Create and solve a new question about Creating a budget . Show your reasoning and check your answer.
- Create and solve a new question about Balanced budget . Show your reasoning and check your answer.
- Create and solve a new question about Savings amount . Show your reasoning and check your answer.
- Create and solve a new question about Savings rate . Show your reasoning and check your answer.
- Create and solve a new question about Planning monthly savings . Show your reasoning and check your answer.
Common Mistakes
- Reversing an exchange-rate calculation.
- Comparing financial options without including fees.
- Treating interest rate as a whole number instead of a decimal in calculations.
- Ignoring time when comparing savings or borrowing.
- Giving a number without explaining what it means.
30 Review Questions and Answers
Q1. What is important to remember about Financial goals?
Answer: A financial goal is a money target with a purpose and usually a time frame. This topic focuses on Financial goals.
Q2. What is important to remember about Short-term goals?
Answer: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Short-term goals.
Q3. What is important to remember about Long-term goals?
Answer: A term is one part of an expression separated by addition or subtraction signs. This topic focuses on Long-term goals.
Q4. What is important to remember about Income?
Answer: Income is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q5. What is important to remember about Fixed expenses?
Answer: Fixed expenses is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q6. What is important to remember about Variable expenses?
Answer: A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Variable expenses.
Q7. What is important to remember about Needs and wants?
Answer: Needs and wants is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. 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 Creating a budget?
Answer: A budget is a plan that compares income, spending, and saving. This topic focuses on Creating a budget.
Q9. What is important to remember about Balanced budget?
Answer: A budget is a plan that compares income, spending, and saving. This topic focuses on Balanced budget.
Q10. What is important to remember about Savings amount?
Answer: Savings amount is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q11. What is important to remember about Savings rate?
Answer: A rate compares two quantities measured in different units. This topic focuses on Savings rate.
Q12. What is important to remember about Planning monthly savings?
Answer: Planning monthly savings is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q13. What is important to remember about Adjusting a budget?
Answer: A budget is a plan that compares income, spending, and saving. This topic focuses on Adjusting a budget.
Q14. What is important to remember about Tracking progress?
Answer: Tracking progress is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q15. What is important to remember about Real-life financial decisions?
Answer: Real-life financial decisions is an important Grade 7 idea in Financial Goals, Budgets, and Savings Plans. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q16. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q17. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q18. Why do units matter?
Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.
Q19. When should you round?
Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.
Q20. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.
Q21. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q22. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q23. What should you do if an answer seems unreasonable?
Answer: Re-read the question, check copied values, signs, units, formulas, and calculations.
Q24. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q25. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q26. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q27. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q28. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q29. 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.
Q30. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.