Chapter 59: Budgets, Credit, Debt, and Best Value
Learn Grade 5 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Budgets, Credit, Debt, and Best Value with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Income and earnings (a Grade 5 idea used in this chapter)
- Expenses and spending (a Grade 5 idea used in this chapter)
- Needs and wants (a Grade 5 idea used in this chapter)
- Creating a basic budget (a Grade 5 idea used in this chapter)
- Balancing and adjusting a budget (a Grade 5 idea used in this chapter)
- Meaning of credit (a Grade 5 idea used in this chapter)
- Meaning of debt (a Grade 5 idea used in this chapter)
- How credit and debt affect decisions (a Grade 5 idea used in this chapter)
- Unit rates for goods and services (a Grade 5 idea used in this chapter)
- Comparing options for best value (a Grade 5 idea used in this chapter)
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.
59.1 Income and earnings
Income and earnings is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Income and earnings?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Income and earnings is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Income and earnings is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Income and earnings?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Income and earnings is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Income and earnings.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Income and earnings is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Income and earnings problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Income and earnings is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Income and earnings.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Income and earnings is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Income and earnings can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
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 and earnings. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
59.2 Expenses and spending
Expenses and spending is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Expenses and spending?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Expenses and spending is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Expenses and spending is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Expenses and spending?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Expenses and spending is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Expenses and spending.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Expenses and spending is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Expenses and spending problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Expenses and spending is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Expenses and spending.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Expenses and spending is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Expenses and spending can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
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 Expenses and spending. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
59.3 Needs and wants
Needs and wants is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Needs and wants?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Needs and wants is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Needs and wants is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Needs and wants?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Needs and wants is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Needs and wants.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Needs and wants is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Needs and wants problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Needs and wants is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Needs and wants.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Needs and wants is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Needs and wants can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
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.
59.4 Creating a basic budget
Creating a basic budget builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Creating a basic budget?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Creating a basic budget builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: Creating a basic budget builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Worked Example 2
Problem: What should you identify first before solving a problem about Creating a basic budget?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Creating a basic budget builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Creating a basic budget.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Creating a basic budget builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Creating a basic budget problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Creating a basic budget builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Creating a basic budget.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Creating a basic budget builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: Creating a basic budget can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
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 basic budget. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
59.5 Balancing and adjusting a budget
Balancing and adjusting a budget builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Balancing and adjusting a budget?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Balancing and adjusting a budget builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: Balancing and adjusting a budget builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Worked Example 2
Problem: What should you identify first before solving a problem about Balancing and adjusting a budget?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Balancing and adjusting a budget builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Balancing and adjusting a budget.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Balancing and adjusting a budget builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Balancing and adjusting a budget problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Balancing and adjusting a budget builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Balancing and adjusting a budget.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Balancing and adjusting a budget builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: Balancing and adjusting a budget can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
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 Balancing and adjusting a budget. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
59.6 Meaning of credit
Meaning of credit helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Meaning of credit?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Meaning of credit helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: Meaning of credit helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Worked Example 2
Problem: What should you identify first before solving a problem about Meaning of credit?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Meaning of credit helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Meaning of credit.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Meaning of credit helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Meaning of credit problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Meaning of credit helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Meaning of credit.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Meaning of credit helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: Meaning of credit can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Find the mean of [4, 6, 8].
- Add the values: 18.
- Divide by 3.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 6
Worked Example 7
Problem: Find the mean of [5, 9, 10, 12].
- Add the values: 36.
- Divide by 4.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 9
Worked Example 8
Problem: Find the mean of [3, 7, 7, 11].
- Add the values: 28.
- Divide by 4.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 7
Worked Example 9
Problem: Find the mean of [20, 25, 30].
- Add the values: 75.
- Divide by 3.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 25
Worked Example 10
Problem: Find the mean of [6, 8, 9, 12, 15].
- Add the values: 50.
- Divide by 5.
Very beginner explanation: The mean is the total shared equally among all values.
Answer: 10
Practice Exercise
Create one new question about Meaning of credit. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
59.7 Meaning of debt
Meaning of debt helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Meaning of debt?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Meaning of debt helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: Meaning of debt helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Worked Example 2
Problem: What should you identify first before solving a problem about Meaning of debt?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Meaning of debt helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Meaning of debt.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Meaning of debt helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Meaning of debt problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Meaning of debt helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Meaning of debt.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Meaning of debt helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Answer: Meaning of debt can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Calculate -8 + (5).
- Use a number line or sign rules.
- If signs differ, subtract absolute values and keep the sign of the larger absolute value.
Very beginner explanation: Integer addition can be understood as movement left and right on a number line.
Answer: -3
Worked Example 7
Problem: Calculate 7 + (-12).
- Use a number line or sign rules.
- If signs differ, subtract absolute values and keep the sign of the larger absolute value.
Very beginner explanation: Integer addition can be understood as movement left and right on a number line.
Answer: -5
Worked Example 8
Problem: Calculate -4 + (-9).
- Use a number line or sign rules.
- If signs differ, subtract absolute values and keep the sign of the larger absolute value.
Very beginner explanation: Integer addition can be understood as movement left and right on a number line.
Answer: -13
Worked Example 9
Problem: Calculate 15 + (-6).
- Use a number line or sign rules.
- If signs differ, subtract absolute values and keep the sign of the larger absolute value.
Very beginner explanation: Integer addition can be understood as movement left and right on a number line.
Answer: 9
Worked Example 10
Problem: Calculate -20 + (13).
- Use a number line or sign rules.
- If signs differ, subtract absolute values and keep the sign of the larger absolute value.
Very beginner explanation: Integer addition can be understood as movement left and right on a number line.
Answer: -7
Practice Exercise
Create one new question about Meaning of debt. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
59.8 How credit and debt affect decisions
How credit and debt affect decisions builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of How credit and debt affect decisions?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: How credit and debt affect decisions builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: How credit and debt affect decisions builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Worked Example 2
Problem: What should you identify first before solving a problem about How credit and debt affect decisions?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: How credit and debt affect decisions builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for How credit and debt affect decisions.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: How credit and debt affect decisions builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a How credit and debt affect decisions problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: How credit and debt affect decisions builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for How credit and debt affect decisions.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: How credit and debt affect decisions builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: How credit and debt affect decisions can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Calculate -8 + (5).
- Use a number line or sign rules.
- If signs differ, subtract absolute values and keep the sign of the larger absolute value.
Very beginner explanation: Integer addition can be understood as movement left and right on a number line.
Answer: -3
Worked Example 7
Problem: Calculate 7 + (-12).
- Use a number line or sign rules.
- If signs differ, subtract absolute values and keep the sign of the larger absolute value.
Very beginner explanation: Integer addition can be understood as movement left and right on a number line.
Answer: -5
Worked Example 8
Problem: Calculate -4 + (-9).
- Use a number line or sign rules.
- If signs differ, subtract absolute values and keep the sign of the larger absolute value.
Very beginner explanation: Integer addition can be understood as movement left and right on a number line.
Answer: -13
Worked Example 9
Problem: Calculate 15 + (-6).
- Use a number line or sign rules.
- If signs differ, subtract absolute values and keep the sign of the larger absolute value.
Very beginner explanation: Integer addition can be understood as movement left and right on a number line.
Answer: 9
Worked Example 10
Problem: Calculate -20 + (13).
- Use a number line or sign rules.
- If signs differ, subtract absolute values and keep the sign of the larger absolute value.
Very beginner explanation: Integer addition can be understood as movement left and right on a number line.
Answer: -7
Practice Exercise
Create one new question about How credit and debt affect decisions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
59.9 Unit rates for goods and services
Unit rates for goods and services compares quantities. Equivalent ratios and unit rates help learners scale situations and compare choices fairly.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Unit rates for goods and services?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Unit rates for goods and services compares quantities. Equivalent ratios and unit rates help learners scale situations and compare choices fairly.
Answer: Unit rates for goods and services compares quantities. Equivalent ratios and unit rates help learners scale situations and compare choices fairly.
Worked Example 2
Problem: What should you identify first before solving a problem about Unit rates for goods and services?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Unit rates for goods and services compares quantities. Equivalent ratios and unit rates help learners scale situations and compare choices fairly.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Unit rates for goods and services.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Unit rates for goods and services compares quantities. Equivalent ratios and unit rates help learners scale situations and compare choices fairly.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Unit rates for goods and services problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Unit rates for goods and services compares quantities. Equivalent ratios and unit rates help learners scale situations and compare choices fairly.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Unit rates for goods and services.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Unit rates for goods and services compares quantities. Equivalent ratios and unit rates help learners scale situations and compare choices fairly.
Answer: Unit rates for goods and services can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
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 Unit rates for goods and services. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
59.10 Comparing options for best value
Comparing options for best value builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Comparing options for best value?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Comparing options for best value builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: Comparing options for best value builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Worked Example 2
Problem: What should you identify first before solving a problem about Comparing options for best value?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Comparing options for best value builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Comparing options for best value.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Comparing options for best value builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Comparing options for best value problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Comparing options for best value builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Comparing options for best value.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Comparing options for best value builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Answer: Comparing options for best value can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Comparing options for best value 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: Comparing options for best value 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 Comparing options for best value 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: Comparing options for best value 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 Comparing options for best value 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: Comparing options for best value 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 Comparing options for best value 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: Comparing options for best value 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 Comparing options for best value 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: Comparing options for best value 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 Comparing options for best value. 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 question before calculating.
- Represent the mathematics with a model, table, graph, diagram, number line, or equation when useful.
- Show the reasoning and check the final answer with a second method when possible.
Extra Practice
- Create and solve one original problem about Income and earnings.
- Create and solve one original problem about Expenses and spending.
- Create and solve one original problem about Needs and wants.
- Create and solve one original problem about Creating a basic budget.
- Create and solve one original problem about Balancing and adjusting a budget.
- Create and solve one original problem about Meaning of credit.
Common Mistakes
- Skipping the meaning and trying to memorize a rule only.
- Using the wrong operation because the question was not read completely.
- Ignoring units, labels, place values, or the context of the problem.
- Not estimating or checking whether the final answer is reasonable.
30 Review Questions and Answers
Q1. What is the key idea in Income and earnings?
Answer: Income and earnings is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q2. What is the key idea in Expenses and spending?
Answer: Expenses and spending is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q3. What is the key idea in Needs and wants?
Answer: Needs and wants is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q4. What is the key idea in Creating a basic budget?
Answer: Creating a basic budget builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Q5. What is the key idea in Balancing and adjusting a budget?
Answer: Balancing and adjusting a budget builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Q6. What is the key idea in Meaning of credit?
Answer: Meaning of credit helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Q7. What is the key idea in Meaning of debt?
Answer: Meaning of debt helps learners collect, organize, display, and interpret information carefully so conclusions are supported by evidence.
Q8. What is the key idea in How credit and debt affect decisions?
Answer: How credit and debt affect decisions builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Q9. What is the key idea in Unit rates for goods and services?
Answer: Unit rates for goods and services compares quantities. Equivalent ratios and unit rates help learners scale situations and compare choices fairly.
Q10. What is the key idea in Comparing options for best value?
Answer: Comparing options for best value builds practical financial literacy by using arithmetic, unit rates, and careful comparison to make informed money decisions.
Q11. Why should you estimate before or after a calculation?
Answer: Estimation gives a reasonable range and can reveal place-value or operation mistakes.
Q12. Why are labels and units important?
Answer: They show what a number represents and help prevent mixing unlike quantities.
Q13. How can a diagram help solve a problem?
Answer: A diagram makes quantities and relationships visible before calculation.
Q14. How can inverse operations check an answer?
Answer: An inverse operation reverses the original operation and should recover the starting value when the work is correct.
Q15. Why should you show steps?
Answer: Showing steps makes reasoning clear and helps find where an error happened.
Q16. What should you do after making a mistake?
Answer: Find the step where the reasoning changed, correct it, and try a similar problem again.
Q17. How can a number line support reasoning?
Answer: It shows order, distance, relative size, fractions, decimals, and inequality solutions visually.
Q18. When is a table useful?
Answer: A table organizes related values so patterns and comparisons are easier to see.
Q19. When is a graph useful?
Answer: A graph makes trends, comparisons, locations, or data patterns visible.
Q20. How do you decide which operation to use?
Answer: Use the meaning of the situation: combine, compare, find a difference, form equal groups, or find how many groups fit.
Q21. Why should you check place value?
Answer: A digit or decimal has a different value depending on its position.
Q22. What makes an answer reasonable?
Answer: It fits the context, has the expected size and units, and agrees with an estimate or second method.
Q23. How can you explain mathematical reasoning clearly?
Answer: Name the information, the rule or operation, the steps, and why the final answer fits the problem.
Q24. Why can more than one strategy be correct?
Answer: Different valid strategies can represent the same mathematical relationship and lead to the same result.
Q25. How should you approach a difficult Grade 5 problem?
Answer: Break it into smaller parts, solve one part at a time, and check each result before continuing.
Q26. How can you practise Budgets, Credit, Debt, and Best Value effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q27. How can you practise Budgets, Credit, Debt, and Best Value effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q28. How can you practise Budgets, Credit, Debt, and Best Value effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q29. How can you practise Budgets, Credit, Debt, and Best Value effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q30. How can you practise Budgets, Credit, Debt, and Best Value effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.