EASYTUTORGUIDE

Practical tutorials, tools, courses, digital skills, and business promotion.

Free Learning
Google Translate — English / فارسی / العربية
EasyTutorGuide LogoLearn, Build, & Grow

Chapter 37: Populations, Samples, and Sampling

Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.

Grade 6Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
Estimated reading time0% read
Advertisement area — AdSense / Auto Ads

Chapter Overview

This chapter teaches Populations, Samples, and Sampling in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

  • Population (A population is the complete group being studied.)
  • Sample (A sample is a smaller group selected from a population.)
  • Sampling bias (Sampling bias is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Survey questions (Survey questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Biased questions (Biased questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Real-life sampling decisions (Real-life sampling decisions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)

How to Learn This Chapter

Read the explanation first, follow each worked example slowly, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.

37.1 Population

A population is the complete group being studied. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 2

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 3

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 4

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 5

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 6

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 7

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 8

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 9

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 10

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Practice Exercise

Create one new Grade 6 problem about Population. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

37.2 Sample

A sample is a smaller group selected from a population. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 2

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 3

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 4

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 5

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 6

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 7

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 8

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 9

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 10

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Practice Exercise

Create one new Grade 6 problem about Sample. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

37.3 Representative sample

A sample is a smaller group selected from a population. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 2

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 3

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 4

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 5

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 6

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 7

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 8

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 9

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 10

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Practice Exercise

Create one new Grade 6 problem about Representative sample. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

37.4 Random sample

A sample is a smaller group selected from a population. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 2

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 3

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 4

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 5

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 6

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 7

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 8

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 9

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 10

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Practice Exercise

Create one new Grade 6 problem about Random sample. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

37.5 Convenience sample

A sample is a smaller group selected from a population. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 2

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 3

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 4

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 5

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 6

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 7

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 8

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 9

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 10

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Practice Exercise

Create one new Grade 6 problem about Convenience sample. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

37.6 Sample size

A sample is a smaller group selected from a population. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 2

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 3

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 4

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 5

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 6

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 7

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 8

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 9

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 10

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Practice Exercise

Create one new Grade 6 problem about Sample size. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

37.7 Sampling bias

Sampling bias is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Sampling bias to analyze the values 20 and 11. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Sampling bias is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Sampling bias to analyze the values 19 and 10. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Sampling bias is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Sampling bias to analyze the values 17 and 16. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Sampling bias is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Sampling bias to analyze the values 22 and 7. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Sampling bias is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Sampling bias to analyze the values 10 and 7. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Sampling bias is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Sampling bias to analyze the values 17 and 20. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Sampling bias is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Sampling bias to analyze the values 5 and 17. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Sampling bias is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Sampling bias to analyze the values 14 and 13. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Sampling bias is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Sampling bias to analyze the values 16 and 16. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Sampling bias is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Sampling bias to analyze the values 15 and 16. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Sampling bias is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Sampling bias. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

37.8 Survey questions

Survey questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Survey questions to analyze the values 3 and 11. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Survey questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Survey questions to analyze the values 4 and 19. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Survey questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Survey questions to analyze the values 22 and 14. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Survey questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Survey questions to analyze the values 7 and 6. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Survey questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Survey questions to analyze the values 11 and 8. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Survey questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Survey questions to analyze the values 22 and 18. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Survey questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Survey questions to analyze the values 30 and 12. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Survey questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Survey questions to analyze the values 29 and 13. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Survey questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Survey questions to analyze the values 8 and 19. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Survey questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Survey questions to analyze the values 9 and 15. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Survey questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Survey questions. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

37.9 Biased questions

Biased questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Biased questions to analyze the values 19 and 16. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Biased questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Biased questions to analyze the values 12 and 11. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Biased questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Biased questions to analyze the values 17 and 13. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Biased questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Biased questions to analyze the values 14 and 8. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Biased questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Biased questions to analyze the values 12 and 13. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Biased questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Biased questions to analyze the values 18 and 2. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Biased questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Biased questions to analyze the values 14 and 15. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Biased questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Biased questions to analyze the values 11 and 3. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Biased questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Biased questions to analyze the values 12 and 6. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Biased questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Biased questions to analyze the values 10 and 14. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Biased questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Biased questions. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

37.10 Comparing samples

A sample is a smaller group selected from a population. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 2

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 3

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 4

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 5

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 6

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 7

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 8

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 9

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 10

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Practice Exercise

Create one new Grade 6 problem about Comparing samples. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

37.11 Drawing conclusions from samples

A sample is a smaller group selected from a population. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 2

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 3

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 4

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 5

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 6

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 7

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 8

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 9

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Worked Example 10

Problem: A school has 600 students. A survey asks 60 randomly selected students about lunch choices. Identify the population and sample.

  1. The population is the full group of interest.
  2. The sample is the smaller group actually surveyed.

Very beginner explanation: A good sample should represent the population fairly.

Answer: Population: 600 students; Sample: 60 surveyed students

Practice Exercise

Create one new Grade 6 problem about Drawing conclusions from samples. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

37.12 Real-life sampling decisions

Real-life sampling decisions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.

Beginner Note

Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Use Real-life sampling decisions to analyze the values 8 and 10. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Real-life sampling decisions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 2

Problem: Use Real-life sampling decisions to analyze the values 24 and 16. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Real-life sampling decisions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 3

Problem: Use Real-life sampling decisions to analyze the values 9 and 5. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Real-life sampling decisions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 4

Problem: Use Real-life sampling decisions to analyze the values 7 and 19. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Real-life sampling decisions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 5

Problem: Use Real-life sampling decisions to analyze the values 18 and 19. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Real-life sampling decisions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 6

Problem: Use Real-life sampling decisions to analyze the values 20 and 18. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Real-life sampling decisions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 7

Problem: Use Real-life sampling decisions to analyze the values 18 and 9. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Real-life sampling decisions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 8

Problem: Use Real-life sampling decisions to analyze the values 27 and 3. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Real-life sampling decisions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 9

Problem: Use Real-life sampling decisions to analyze the values 13 and 10. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Real-life sampling decisions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Worked Example 10

Problem: Use Real-life sampling decisions to analyze the values 7 and 4. What should be checked first?

  1. Identify what each value represents.
  2. Choose the rule, representation, or comparison that matches the topic.
  3. Show the reasoning before accepting the result.

Very beginner explanation: Real-life sampling decisions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Answer: Check the meaning of the values and the rule required by the problem.

Practice Exercise

Create one new Grade 6 problem about Real-life sampling decisions. Solve it step by step, label any units, and explain how you checked your answer.

Common Mistake

A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.

Advertisement area — AdSense / Auto Ads

30 Review Questions and Answers

Q1. What is important to understand about Population?

Answer: A population is the complete group being studied.

Q2. What is important to understand about Sample?

Answer: A sample is a smaller group selected from a population.

Q3. What is important to understand about Representative sample?

Answer: A sample is a smaller group selected from a population.

Q4. What is important to understand about Random sample?

Answer: A sample is a smaller group selected from a population.

Q5. What is important to understand about Convenience sample?

Answer: A sample is a smaller group selected from a population.

Q6. What is important to understand about Sample size?

Answer: A sample is a smaller group selected from a population.

Q7. What is important to understand about Sampling bias?

Answer: Sampling bias is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q8. What is important to understand about Survey questions?

Answer: Survey questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q9. What is important to understand about Biased questions?

Answer: Biased questions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q10. What is important to understand about Comparing samples?

Answer: A sample is a smaller group selected from a population.

Q11. What is important to understand about Drawing conclusions from samples?

Answer: A sample is a smaller group selected from a population.

Q12. What is important to understand about Real-life sampling decisions?

Answer: Real-life sampling decisions is a Grade 6 mathematics idea in Populations, Samples, and Sampling. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

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 help prevent incompatible quantities from being mixed.

Q16. When should you round?

Answer: Usually round near the end unless the question specifically asks for earlier rounding.

Q17. How can you check an answer?

Answer: Use an inverse operation, substitution, estimation, a graph, a table, 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 and check copied values, operations, signs, units, rules, and calculations.

Q21. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships that are harder to see in words alone.

Q22. Why are tables useful?

Answer: Tables organize values so patterns, rates, comparisons, and missing information are easier to see.

Q23. Why are graphs useful?

Answer: Graphs make relationships, changes, trends, and comparisons visible.

Q24. Why should you explain your reasoning?

Answer: An explanation shows why a method works instead of only giving a final number.

Q25. Why can more than one strategy be correct?

Answer: Different correct strategies can represent the same mathematics in different but equivalent ways.

Q26. What should you do before using a formula or rule?

Answer: Check what each quantity means and whether the rule matches the situation.

Q27. How does practice help in mathematics?

Answer: Practice builds accuracy and fluency while helping you recognize which strategies fit different problems.

Q28. What is a good way to learn from a mistake?

Answer: Find the exact step where the reasoning changed from correct to incorrect, then solve a similar problem again.

Q29. Why should you compare an exact answer with an estimate?

Answer: The estimate gives a quick reasonableness check for the exact calculation.

Q30. What does representing mathematics mean?

Answer: It means showing an idea with numbers, symbols, words, diagrams, tables, graphs, or models.