Chapter 37: Organizing Data
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Organizing Data with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Variable (a letter or symbol representing a number)
- 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.
37.1 Tally tables
Tally tables is an important Grade 7 idea in Organizing Data. 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: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Tally tables is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Tally tables is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Tally tables is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Tally tables is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Tally tables is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Broaden the sample
Worked Example 6
Problem: Explain Tally tables in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Tally tables becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Tally tables and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Tally tables becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Tally tables using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Tally tables becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Tally tables problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Tally tables becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Tally tables could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Tally tables becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Tally tables. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
37.2 Frequency tables
Frequency is the number of times a value or category occurs. This topic focuses on Frequency tables .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Frequency is the number of times a value or category occurs. This topic focuses on Frequency tables .
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Frequency is the number of times a value or category occurs. This topic focuses on Frequency tables .
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Frequency is the number of times a value or category occurs. This topic focuses on Frequency tables .
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Frequency is the number of times a value or category occurs. This topic focuses on Frequency tables .
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Frequency is the number of times a value or category occurs. This topic focuses on Frequency tables .
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Frequency tables. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
37.3 Relative frequency
Frequency is the number of times a value or category occurs. This topic focuses on Relative frequency .
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: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Frequency is the number of times a value or category occurs. This topic focuses on Relative frequency .
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Frequency is the number of times a value or category occurs. This topic focuses on Relative frequency .
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Frequency is the number of times a value or category occurs. This topic focuses on Relative frequency .
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Frequency is the number of times a value or category occurs. This topic focuses on Relative frequency .
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Frequency is the number of times a value or category occurs. This topic focuses on Relative frequency .
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Relative frequency. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
37.4 Intervals
Intervals is an important Grade 7 idea in Organizing Data. 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: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Intervals is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Intervals is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Intervals is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Intervals is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Intervals is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Broaden the sample
Worked Example 6
Problem: Explain Intervals 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: Intervals 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 Intervals 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: Intervals 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 Intervals 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: Intervals 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 Intervals 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: Intervals 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 Intervals 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: Intervals 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 Intervals. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
37.5 Categories
Categories is an important Grade 7 idea in Organizing Data. 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: Categories: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Categories is an important Grade 7 idea in Organizing Data. 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: Categories: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Categories is an important Grade 7 idea in Organizing Data. 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: Categories: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Categories is an important Grade 7 idea in Organizing Data. 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: Categories: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Categories is an important Grade 7 idea in Organizing Data. 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: Categories: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Categories is an important Grade 7 idea in Organizing Data. 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 Categories 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: Categories 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 Categories 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: Categories 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 Categories 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: Categories 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 Categories 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: Categories 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 Categories 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: Categories 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 Categories. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
37.6 Sorting data
Data are observations, measurements, or categories collected to answer questions. This topic focuses on Sorting data .
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: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Sorting data .
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Sorting data .
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Sorting data .
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Sorting data .
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Sorting data .
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Sorting data. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
37.7 Grouping numerical data
Data are observations, measurements, or categories collected to answer questions. This topic focuses on Grouping numerical data .
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: List the factors of 18.
- Find all whole numbers that divide exactly.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Grouping numerical data .
Answer: 1, 2, 3, 6, 9, 18
Worked Example 2
Problem: List the factors of 24.
- Find all whole numbers that divide exactly.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Grouping numerical data .
Answer: 1, 2, 3, 4, 6, 8, 12, 24
Worked Example 3
Problem: List the factors of 36.
- Find all whole numbers that divide exactly.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Grouping numerical data .
Answer: 1, 2, 3, 4, 6, 9, 12, 18, 36
Worked Example 4
Problem: List the factors of 45.
- Find all whole numbers that divide exactly.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Grouping numerical data .
Answer: 1, 3, 5, 9, 15, 45
Worked Example 5
Problem: List the factors of 60.
- Find all whole numbers that divide exactly.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Grouping numerical data .
Answer: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Grouping numerical data. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
37.8 Two-variable tables introduction
A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Two-variable tables introduction .
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 Two-variable tables introduction .
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 Two-variable tables introduction .
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 Two-variable tables introduction .
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 Two-variable tables introduction .
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 Two-variable tables introduction .
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 Two-variable tables introduction. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
37.9 Organizing survey results
Organizing survey results is an important Grade 7 idea in Organizing Data. 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: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Organizing survey results is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Organizing survey results is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Organizing survey results is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Organizing survey results is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Organizing survey results is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Broaden the sample
Worked Example 6
Problem: Explain Organizing survey results 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: Organizing survey results 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 Organizing survey results 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: Organizing survey results 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 Organizing survey results 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: Organizing survey results 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 Organizing survey results 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: Organizing survey results 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 Organizing survey results 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: Organizing survey results 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 Organizing survey results. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
37.10 Spreadsheet-style tables
Spreadsheet-style tables is an important Grade 7 idea in Organizing Data. 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: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Spreadsheet-style tables is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Spreadsheet-style tables is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Spreadsheet-style tables is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Spreadsheet-style tables is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Spreadsheet-style tables is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Broaden the sample
Worked Example 6
Problem: Explain Spreadsheet-style tables in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Spreadsheet-style tables becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Spreadsheet-style tables and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Spreadsheet-style tables becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Spreadsheet-style tables using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Spreadsheet-style tables becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Spreadsheet-style tables problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Spreadsheet-style tables becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Spreadsheet-style tables could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Spreadsheet-style tables becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Spreadsheet-style tables. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
37.11 Choosing useful intervals
Choosing useful intervals is an important Grade 7 idea in Organizing Data. 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: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Choosing useful intervals is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Choosing useful intervals is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Choosing useful intervals is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Choosing useful intervals is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Choosing useful intervals is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Broaden the sample
Worked Example 6
Problem: Explain Choosing useful intervals 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: Choosing useful intervals 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 Choosing useful intervals 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: Choosing useful intervals 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 Choosing useful intervals 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: Choosing useful intervals 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 Choosing useful intervals 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: Choosing useful intervals 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 Choosing useful intervals 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: Choosing useful intervals 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 Choosing useful intervals. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
37.12 Checking data accuracy
Data are observations, measurements, or categories collected to answer questions. This topic focuses on Checking data accuracy .
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: Favourite school subject
- Classify it as categorical/qualitative data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Checking data accuracy .
Answer: Use a frequency table
Worked Example 2
Problem: Student heights
- Classify it as quantitative continuous data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Checking data accuracy .
Answer: Measure in centimetres
Worked Example 3
Problem: Number of siblings
- Classify it as quantitative discrete data.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Checking data accuracy .
Answer: Count whole numbers
Worked Example 4
Problem: Survey every 10th student
- Classify it as systematic sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Checking data accuracy .
Answer: Check that the list order does not create bias
Worked Example 5
Problem: Survey only basketball team members about school sports
- Classify it as biased sample.
- Choose an appropriate collection/organization method.
Very beginner explanation: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Checking data accuracy .
Answer: Broaden the sample
Worked Example 6
Problem: Classify the data [4, 6, 8].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 7
Problem: Classify the data [5, 9, 10, 12].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 8
Problem: Classify the data [3, 7, 7, 11].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 9
Problem: Classify the data [20, 25, 30].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Worked Example 10
Problem: Classify the data [6, 8, 9, 12, 15].
- These values are numerical.
- Decide whether they represent counts or measurements.
Very beginner explanation: Quantitative data are numerical values used for calculations or comparisons.
Answer: Quantitative data
Practice Exercise
Create one new question about Checking data accuracy. 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 Tally tables . Show your reasoning and check your answer.
- Create and solve a new question about Frequency tables . Show your reasoning and check your answer.
- Create and solve a new question about Relative frequency . Show your reasoning and check your answer.
- Create and solve a new question about Intervals . Show your reasoning and check your answer.
- Create and solve a new question about Categories . Show your reasoning and check your answer.
- Create and solve a new question about Sorting data . Show your reasoning and check your answer.
- Create and solve a new question about Grouping numerical data . Show your reasoning and check your answer.
- Create and solve a new question about Two-variable tables introduction . Show your reasoning and check your answer.
- Create and solve a new question about Organizing survey results . Show your reasoning and check your answer.
- Create and solve a new question about Spreadsheet-style tables . Show your reasoning and check your answer.
- Create and solve a new question about Choosing useful intervals . Show your reasoning and check your answer.
- Create and solve a new question about Checking data accuracy . Show your reasoning and check your answer.
Common Mistakes
- Using a biased or unrepresentative sample.
- Reading graph scales incorrectly.
- Treating a misleading graph as trustworthy without checking the axes.
- Assuming dependent events are independent.
- Using percentages in a circle graph that do not total 100%.
30 Review Questions and Answers
Q1. What is important to remember about Tally tables?
Answer: Tally tables is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q2. What is important to remember about Frequency tables?
Answer: Frequency is the number of times a value or category occurs. This topic focuses on Frequency tables.
Q3. What is important to remember about Relative frequency?
Answer: Frequency is the number of times a value or category occurs. This topic focuses on Relative frequency.
Q4. What is important to remember about Intervals?
Answer: Intervals is an important Grade 7 idea in Organizing Data. 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 Categories?
Answer: Categories is an important Grade 7 idea in Organizing Data. 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 Sorting data?
Answer: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Sorting data.
Q7. What is important to remember about Grouping numerical data?
Answer: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Grouping numerical data.
Q8. What is important to remember about Two-variable tables introduction?
Answer: A variable is a letter or symbol representing a number that can change or may be unknown. This topic focuses on Two-variable tables introduction.
Q9. What is important to remember about Organizing survey results?
Answer: Organizing survey results is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q10. What is important to remember about Spreadsheet-style tables?
Answer: Spreadsheet-style tables is an important Grade 7 idea in Organizing Data. 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 Choosing useful intervals?
Answer: Choosing useful intervals is an important Grade 7 idea in Organizing Data. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q12. What is important to remember about Checking data accuracy?
Answer: Data are observations, measurements, or categories collected to answer questions. This topic focuses on Checking data accuracy.
Q13. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q14. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q15. Why do units matter?
Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.
Q16. When should you round?
Answer: Usually round near the end of a calculation unless the question specifically asks for earlier rounding.
Q17. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.
Q18. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q19. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q20. What should you do if an answer seems unreasonable?
Answer: Re-read the question, check copied values, signs, units, formulas, and calculations.
Q21. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q22. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q23. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q24. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q25. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q26. 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.
Q27. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.
Q28. What is a mathematical model?
Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.
Q29. Why should assumptions be stated?
Answer: Assumptions show what conditions the solution depends on and help readers judge whether the model is reasonable.
Q30. Why should sources be checked in data problems?
Answer: Reliable sources and fair collection methods make conclusions more trustworthy.