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Chapter 1: Whole Numbers to One Million

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
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Chapter Overview

This chapter teaches Whole Numbers to One Million in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

  • Whole numbers to 1 million (Whole numbers to 1 million is a Grade 6 mathematics idea in Whole Numbers to One Million. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Place value (Place value is the value a digit has because of its position in a number.)
  • Reading six- and seven-digit numbers (Reading six- and seven-digit numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Writing numbers in standard form (Writing numbers in standard form is a Grade 6 mathematics idea in Whole Numbers to One Million. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Expanded form (Expanded form is a Grade 6 mathematics idea in Whole Numbers to One Million. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
  • Word form (Word form is a Grade 6 mathematics idea in Whole Numbers to One Million. 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.

1.1 Whole numbers to 1 million

Whole numbers to 1 million is a Grade 6 mathematics idea in Whole Numbers to One Million. 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: In 631,850, what is the value of the digit 1 in the 1,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 1,000

Worked Example 2

Problem: In 780,926, what is the value of the digit 7 in the 100,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 700,000

Worked Example 3

Problem: In 906,339, what is the value of the digit 9 in the 100,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 900,000

Worked Example 4

Problem: In 584,400, what is the value of the digit 4 in the 100 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 400

Worked Example 5

Problem: In 454,965, what is the value of the digit 6 in the 10 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 60

Worked Example 6

Problem: In 986,378, what is the value of the digit 8 in the 10,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 80,000

Worked Example 7

Problem: In 196,673, what is the value of the digit 6 in the 1,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 6,000

Worked Example 8

Problem: In 197,363, what is the value of the digit 9 in the 10,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 90,000

Worked Example 9

Problem: In 827,330, what is the value of the digit 2 in the 10,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 20,000

Worked Example 10

Problem: In 501,808, what is the value of the digit 0 in the 10 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 0

Practice Exercise

Create one new Grade 6 problem about Whole numbers to 1 million. 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.

1.2 Place value

Place value is the value a digit has because of its position in a number. 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: In 322,864, what is the value of the digit 2 in the 1,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 2,000

Worked Example 2

Problem: In 43,739, what is the value of the digit 3 in the 10 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 30

Worked Example 3

Problem: In 12,433, what is the value of the digit 0 in the 100,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 0

Worked Example 4

Problem: In 229,216, what is the value of the digit 1 in the 10 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 10

Worked Example 5

Problem: In 682,874, what is the value of the digit 8 in the 10,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 80,000

Worked Example 6

Problem: In 813,664, what is the value of the digit 6 in the 10 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 60

Worked Example 7

Problem: In 448,209, what is the value of the digit 0 in the 10 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 0

Worked Example 8

Problem: In 136,613, what is the value of the digit 1 in the 10 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 10

Worked Example 9

Problem: In 506,132, what is the value of the digit 5 in the 100,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 500,000

Worked Example 10

Problem: In 735,729, what is the value of the digit 7 in the 100 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 700

Practice Exercise

Create one new Grade 6 problem about Place value. 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.

1.3 Reading six- and seven-digit numbers

Reading six- and seven-digit numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 Reading six- and seven-digit numbers to analyze the values 25 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: Reading six- and seven-digit numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 Reading six- and seven-digit numbers to analyze the values 28 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: Reading six- and seven-digit numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 Reading six- and seven-digit numbers to analyze the values 8 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: Reading six- and seven-digit numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 Reading six- and seven-digit numbers 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: Reading six- and seven-digit numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 Reading six- and seven-digit numbers to analyze the values 10 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: Reading six- and seven-digit numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 Reading six- and seven-digit numbers to analyze the values 3 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: Reading six- and seven-digit numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 Reading six- and seven-digit numbers to analyze the values 30 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: Reading six- and seven-digit numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 Reading six- and seven-digit numbers to analyze the values 24 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: Reading six- and seven-digit numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 Reading six- and seven-digit numbers to analyze the values 7 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: Reading six- and seven-digit numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 Reading six- and seven-digit numbers to analyze the values 10 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: Reading six- and seven-digit numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 Reading six- and seven-digit numbers. 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.

1.4 Writing numbers in standard form

Writing numbers in standard form is a Grade 6 mathematics idea in Whole Numbers to One Million. 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: In 168,134, what is the value of the digit 6 in the 10,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 60,000

Worked Example 2

Problem: In 137,687, what is the value of the digit 6 in the 100 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 600

Worked Example 3

Problem: In 526,746, what is the value of the digit 2 in the 10,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 20,000

Worked Example 4

Problem: In 758,425, what is the value of the digit 2 in the 10 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 20

Worked Example 5

Problem: In 996,893, what is the value of the digit 9 in the 10 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 90

Worked Example 6

Problem: In 321,312, what is the value of the digit 2 in the 10,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 20,000

Worked Example 7

Problem: In 212,630, what is the value of the digit 1 in the 10,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 10,000

Worked Example 8

Problem: In 165,359, what is the value of the digit 5 in the 10 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 50

Worked Example 9

Problem: In 483,811, what is the value of the digit 1 in the 10 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 10

Worked Example 10

Problem: In 995,000, what is the value of the digit 0 in the 100 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 0

Practice Exercise

Create one new Grade 6 problem about Writing numbers in standard form. 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.

1.5 Expanded form

Expanded form is a Grade 6 mathematics idea in Whole Numbers to One Million. 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: Write 959,150 in expanded form.

  1. Read each digit by place value.
  2. Write the value of every non-zero digit.
  3. Join the values with plus signs.

Very beginner explanation: Expanded form shows the value contributed by each digit.

Answer: 900,000 + 50,000 + 9,000 + 100 + 50

Worked Example 2

Problem: Write 925,138 in expanded form.

  1. Read each digit by place value.
  2. Write the value of every non-zero digit.
  3. Join the values with plus signs.

Very beginner explanation: Expanded form shows the value contributed by each digit.

Answer: 900,000 + 20,000 + 5,000 + 100 + 30 + 8

Worked Example 3

Problem: Write 397,503 in expanded form.

  1. Read each digit by place value.
  2. Write the value of every non-zero digit.
  3. Join the values with plus signs.

Very beginner explanation: Expanded form shows the value contributed by each digit.

Answer: 300,000 + 90,000 + 7,000 + 500 + 3

Worked Example 4

Problem: Write 795,562 in expanded form.

  1. Read each digit by place value.
  2. Write the value of every non-zero digit.
  3. Join the values with plus signs.

Very beginner explanation: Expanded form shows the value contributed by each digit.

Answer: 700,000 + 90,000 + 5,000 + 500 + 60 + 2

Worked Example 5

Problem: Write 708,828 in expanded form.

  1. Read each digit by place value.
  2. Write the value of every non-zero digit.
  3. Join the values with plus signs.

Very beginner explanation: Expanded form shows the value contributed by each digit.

Answer: 700,000 + 8,000 + 800 + 20 + 8

Worked Example 6

Problem: Write 299,056 in expanded form.

  1. Read each digit by place value.
  2. Write the value of every non-zero digit.
  3. Join the values with plus signs.

Very beginner explanation: Expanded form shows the value contributed by each digit.

Answer: 200,000 + 90,000 + 9,000 + 50 + 6

Worked Example 7

Problem: Write 110,810 in expanded form.

  1. Read each digit by place value.
  2. Write the value of every non-zero digit.
  3. Join the values with plus signs.

Very beginner explanation: Expanded form shows the value contributed by each digit.

Answer: 100,000 + 10,000 + 800 + 10

Worked Example 8

Problem: Write 806,952 in expanded form.

  1. Read each digit by place value.
  2. Write the value of every non-zero digit.
  3. Join the values with plus signs.

Very beginner explanation: Expanded form shows the value contributed by each digit.

Answer: 800,000 + 6,000 + 900 + 50 + 2

Worked Example 9

Problem: Write 525,284 in expanded form.

  1. Read each digit by place value.
  2. Write the value of every non-zero digit.
  3. Join the values with plus signs.

Very beginner explanation: Expanded form shows the value contributed by each digit.

Answer: 500,000 + 20,000 + 5,000 + 200 + 80 + 4

Worked Example 10

Problem: Write 659,681 in expanded form.

  1. Read each digit by place value.
  2. Write the value of every non-zero digit.
  3. Join the values with plus signs.

Very beginner explanation: Expanded form shows the value contributed by each digit.

Answer: 600,000 + 50,000 + 9,000 + 600 + 80 + 1

Practice Exercise

Create one new Grade 6 problem about Expanded form. 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.

1.6 Word form

Word form is a Grade 6 mathematics idea in Whole Numbers to One Million. 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: In 215,626, what is the value of the digit 1 in the 10,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 10,000

Worked Example 2

Problem: In 402,141, what is the value of the digit 1 in the 100 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 100

Worked Example 3

Problem: In 322,646, what is the value of the digit 4 in the 10 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 40

Worked Example 4

Problem: In 737,301, what is the value of the digit 0 in the 10 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 0

Worked Example 5

Problem: In 340,331, what is the value of the digit 3 in the 10 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 30

Worked Example 6

Problem: In 630,201, what is the value of the digit 0 in the 10 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 0

Worked Example 7

Problem: In 28,981, what is the value of the digit 8 in the 1,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 8,000

Worked Example 8

Problem: In 179,530, what is the value of the digit 7 in the 10,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 70,000

Worked Example 9

Problem: In 568,492, what is the value of the digit 8 in the 1,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 8,000

Worked Example 10

Problem: In 174,904, what is the value of the digit 0 in the 10 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 0

Practice Exercise

Create one new Grade 6 problem about Word form. 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.

1.7 Composing and decomposing numbers

Composing and decomposing numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. 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: Write 441,343 in expanded form.

  1. Read each digit by place value.
  2. Write the value of every non-zero digit.
  3. Join the values with plus signs.

Very beginner explanation: Expanded form shows the value contributed by each digit.

Answer: 400,000 + 40,000 + 1,000 + 300 + 40 + 3

Worked Example 2

Problem: Write 931,832 in expanded form.

  1. Read each digit by place value.
  2. Write the value of every non-zero digit.
  3. Join the values with plus signs.

Very beginner explanation: Expanded form shows the value contributed by each digit.

Answer: 900,000 + 30,000 + 1,000 + 800 + 30 + 2

Worked Example 3

Problem: Write 917,278 in expanded form.

  1. Read each digit by place value.
  2. Write the value of every non-zero digit.
  3. Join the values with plus signs.

Very beginner explanation: Expanded form shows the value contributed by each digit.

Answer: 900,000 + 10,000 + 7,000 + 200 + 70 + 8

Worked Example 4

Problem: Write 202,934 in expanded form.

  1. Read each digit by place value.
  2. Write the value of every non-zero digit.
  3. Join the values with plus signs.

Very beginner explanation: Expanded form shows the value contributed by each digit.

Answer: 200,000 + 2,000 + 900 + 30 + 4

Worked Example 5

Problem: Write 556,582 in expanded form.

  1. Read each digit by place value.
  2. Write the value of every non-zero digit.
  3. Join the values with plus signs.

Very beginner explanation: Expanded form shows the value contributed by each digit.

Answer: 500,000 + 50,000 + 6,000 + 500 + 80 + 2

Worked Example 6

Problem: Write 633,514 in expanded form.

  1. Read each digit by place value.
  2. Write the value of every non-zero digit.
  3. Join the values with plus signs.

Very beginner explanation: Expanded form shows the value contributed by each digit.

Answer: 600,000 + 30,000 + 3,000 + 500 + 10 + 4

Worked Example 7

Problem: Write 23,592 in expanded form.

  1. Read each digit by place value.
  2. Write the value of every non-zero digit.
  3. Join the values with plus signs.

Very beginner explanation: Expanded form shows the value contributed by each digit.

Answer: 20,000 + 3,000 + 500 + 90 + 2

Worked Example 8

Problem: Write 575,983 in expanded form.

  1. Read each digit by place value.
  2. Write the value of every non-zero digit.
  3. Join the values with plus signs.

Very beginner explanation: Expanded form shows the value contributed by each digit.

Answer: 500,000 + 70,000 + 5,000 + 900 + 80 + 3

Worked Example 9

Problem: Write 336,612 in expanded form.

  1. Read each digit by place value.
  2. Write the value of every non-zero digit.
  3. Join the values with plus signs.

Very beginner explanation: Expanded form shows the value contributed by each digit.

Answer: 300,000 + 30,000 + 6,000 + 600 + 10 + 2

Worked Example 10

Problem: Write 930,064 in expanded form.

  1. Read each digit by place value.
  2. Write the value of every non-zero digit.
  3. Join the values with plus signs.

Very beginner explanation: Expanded form shows the value contributed by each digit.

Answer: 900,000 + 30,000 + 60 + 4

Practice Exercise

Create one new Grade 6 problem about Composing and decomposing numbers. 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.

1.8 Comparing whole numbers

Comparing whole numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. 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: Compare 794,626 and 793,882.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 794,626 > 793,882

Worked Example 2

Problem: Compare 666,699 and 671,115.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 666,699 < 671,115

Worked Example 3

Problem: Compare 334,813 and 335,355.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 334,813 < 335,355

Worked Example 4

Problem: Compare 704,726 and 707,375.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 704,726 < 707,375

Worked Example 5

Problem: Compare 669,616 and 673,618.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 669,616 < 673,618

Worked Example 6

Problem: Compare 150,412 and 154,670.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 150,412 < 154,670

Worked Example 7

Problem: Compare 83,883 and 87,576.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 83,883 < 87,576

Worked Example 8

Problem: Compare 903,582 and 899,083.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 903,582 > 899,083

Worked Example 9

Problem: Compare 608,619 and 608,313.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 608,619 > 608,313

Worked Example 10

Problem: Compare 110,075 and 107,960.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 110,075 > 107,960

Practice Exercise

Create one new Grade 6 problem about Comparing whole numbers. 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.

1.9 Ordering whole numbers

Ordering whole numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. 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: Compare 494,321 and 496,877.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 494,321 < 496,877

Worked Example 2

Problem: Compare 863,135 and 863,604.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 863,135 < 863,604

Worked Example 3

Problem: Compare 299,472 and 296,808.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 299,472 > 296,808

Worked Example 4

Problem: Compare 646,785 and 642,997.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 646,785 > 642,997

Worked Example 5

Problem: Compare 99,971 and 100,747.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 99,971 < 100,747

Worked Example 6

Problem: Compare 668,057 and 668,935.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 668,057 < 668,935

Worked Example 7

Problem: Compare 338,584 and 337,762.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 338,584 > 337,762

Worked Example 8

Problem: Compare 18,750 and 18,939.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 18,750 < 18,939

Worked Example 9

Problem: Compare 57,169 and 54,716.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 57,169 > 54,716

Worked Example 10

Problem: Compare 396,600 and 392,234.

  1. Compare the greatest place values first.
  2. If they match, move right until the digits differ.

Very beginner explanation: For positive whole numbers, the first different digit from the left decides which number is greater.

Answer: 396,600 > 392,234

Practice Exercise

Create one new Grade 6 problem about Ordering whole numbers. 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.

1.10 Whole numbers on number lines

Whole numbers on number lines is a Grade 6 mathematics idea in Whole Numbers to One Million. 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: In 231,763, what is the value of the digit 1 in the 1,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 1,000

Worked Example 2

Problem: In 646,747, what is the value of the digit 6 in the 100,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 600,000

Worked Example 3

Problem: In 636,918, what is the value of the digit 6 in the 1,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 6,000

Worked Example 4

Problem: In 296,889, what is the value of the digit 9 in the 10,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 90,000

Worked Example 5

Problem: In 962,407, what is the value of the digit 2 in the 1,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 2,000

Worked Example 6

Problem: In 12,110, what is the value of the digit 1 in the 10,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 10,000

Worked Example 7

Problem: In 482,427, what is the value of the digit 8 in the 10,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 80,000

Worked Example 8

Problem: In 828,849, what is the value of the digit 2 in the 10,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 20,000

Worked Example 9

Problem: In 547,607, what is the value of the digit 4 in the 10,000 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 40,000

Worked Example 10

Problem: In 608,635, what is the value of the digit 3 in the 10 place?

  1. Locate the requested place.
  2. Multiply the digit by the place value.

Very beginner explanation: A digit can have different values depending on its position.

Answer: 30

Practice Exercise

Create one new Grade 6 problem about Whole numbers on number lines. 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.

1.11 Rounding whole numbers

Rounding whole numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. 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: Round 618,732 to the nearest 10.

  1. Find the 10 place.
  2. Look at the digit one place to the right.
  3. 0–4 means keep the target digit; 5–9 means increase it by 1.
  4. Replace smaller places with zeros.

Very beginner explanation: Rounding keeps the number close to its original value while making it easier to use.

Answer: 618,730

Worked Example 2

Problem: Round 486,778 to the nearest 100.

  1. Find the 100 place.
  2. Look at the digit one place to the right.
  3. 0–4 means keep the target digit; 5–9 means increase it by 1.
  4. Replace smaller places with zeros.

Very beginner explanation: Rounding keeps the number close to its original value while making it easier to use.

Answer: 486,800

Worked Example 3

Problem: Round 509,609 to the nearest 1,000.

  1. Find the 1,000 place.
  2. Look at the digit one place to the right.
  3. 0–4 means keep the target digit; 5–9 means increase it by 1.
  4. Replace smaller places with zeros.

Very beginner explanation: Rounding keeps the number close to its original value while making it easier to use.

Answer: 510,000

Worked Example 4

Problem: Round 959,738 to the nearest 10,000.

  1. Find the 10,000 place.
  2. Look at the digit one place to the right.
  3. 0–4 means keep the target digit; 5–9 means increase it by 1.
  4. Replace smaller places with zeros.

Very beginner explanation: Rounding keeps the number close to its original value while making it easier to use.

Answer: 960,000

Worked Example 5

Problem: Round 941,116 to the nearest 100,000.

  1. Find the 100,000 place.
  2. Look at the digit one place to the right.
  3. 0–4 means keep the target digit; 5–9 means increase it by 1.
  4. Replace smaller places with zeros.

Very beginner explanation: Rounding keeps the number close to its original value while making it easier to use.

Answer: 900,000

Worked Example 6

Problem: Round 636,825 to the nearest 10.

  1. Find the 10 place.
  2. Look at the digit one place to the right.
  3. 0–4 means keep the target digit; 5–9 means increase it by 1.
  4. Replace smaller places with zeros.

Very beginner explanation: Rounding keeps the number close to its original value while making it easier to use.

Answer: 636,820

Worked Example 7

Problem: Round 366,532 to the nearest 100.

  1. Find the 100 place.
  2. Look at the digit one place to the right.
  3. 0–4 means keep the target digit; 5–9 means increase it by 1.
  4. Replace smaller places with zeros.

Very beginner explanation: Rounding keeps the number close to its original value while making it easier to use.

Answer: 366,500

Worked Example 8

Problem: Round 401,231 to the nearest 1,000.

  1. Find the 1,000 place.
  2. Look at the digit one place to the right.
  3. 0–4 means keep the target digit; 5–9 means increase it by 1.
  4. Replace smaller places with zeros.

Very beginner explanation: Rounding keeps the number close to its original value while making it easier to use.

Answer: 401,000

Worked Example 9

Problem: Round 710,718 to the nearest 10,000.

  1. Find the 10,000 place.
  2. Look at the digit one place to the right.
  3. 0–4 means keep the target digit; 5–9 means increase it by 1.
  4. Replace smaller places with zeros.

Very beginner explanation: Rounding keeps the number close to its original value while making it easier to use.

Answer: 710,000

Worked Example 10

Problem: Round 968,373 to the nearest 100,000.

  1. Find the 100,000 place.
  2. Look at the digit one place to the right.
  3. 0–4 means keep the target digit; 5–9 means increase it by 1.
  4. Replace smaller places with zeros.

Very beginner explanation: Rounding keeps the number close to its original value while making it easier to use.

Answer: 1,000,000

Practice Exercise

Create one new Grade 6 problem about Rounding whole numbers. 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.

1.12 Estimating large quantities

Estimating large quantities is a Grade 6 mathematics idea in Whole Numbers to One Million. 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: Round 425,540 to the nearest 10.

  1. Find the 10 place.
  2. Look at the digit one place to the right.
  3. 0–4 means keep the target digit; 5–9 means increase it by 1.
  4. Replace smaller places with zeros.

Very beginner explanation: Rounding keeps the number close to its original value while making it easier to use.

Answer: 425,540

Worked Example 2

Problem: Round 313,419 to the nearest 100.

  1. Find the 100 place.
  2. Look at the digit one place to the right.
  3. 0–4 means keep the target digit; 5–9 means increase it by 1.
  4. Replace smaller places with zeros.

Very beginner explanation: Rounding keeps the number close to its original value while making it easier to use.

Answer: 313,400

Worked Example 3

Problem: Round 154,739 to the nearest 1,000.

  1. Find the 1,000 place.
  2. Look at the digit one place to the right.
  3. 0–4 means keep the target digit; 5–9 means increase it by 1.
  4. Replace smaller places with zeros.

Very beginner explanation: Rounding keeps the number close to its original value while making it easier to use.

Answer: 155,000

Worked Example 4

Problem: Round 464,519 to the nearest 10,000.

  1. Find the 10,000 place.
  2. Look at the digit one place to the right.
  3. 0–4 means keep the target digit; 5–9 means increase it by 1.
  4. Replace smaller places with zeros.

Very beginner explanation: Rounding keeps the number close to its original value while making it easier to use.

Answer: 460,000

Worked Example 5

Problem: Round 238,348 to the nearest 100,000.

  1. Find the 100,000 place.
  2. Look at the digit one place to the right.
  3. 0–4 means keep the target digit; 5–9 means increase it by 1.
  4. Replace smaller places with zeros.

Very beginner explanation: Rounding keeps the number close to its original value while making it easier to use.

Answer: 200,000

Worked Example 6

Problem: Round 821,216 to the nearest 10.

  1. Find the 10 place.
  2. Look at the digit one place to the right.
  3. 0–4 means keep the target digit; 5–9 means increase it by 1.
  4. Replace smaller places with zeros.

Very beginner explanation: Rounding keeps the number close to its original value while making it easier to use.

Answer: 821,220

Worked Example 7

Problem: Round 965,349 to the nearest 100.

  1. Find the 100 place.
  2. Look at the digit one place to the right.
  3. 0–4 means keep the target digit; 5–9 means increase it by 1.
  4. Replace smaller places with zeros.

Very beginner explanation: Rounding keeps the number close to its original value while making it easier to use.

Answer: 965,300

Worked Example 8

Problem: Round 942,093 to the nearest 1,000.

  1. Find the 1,000 place.
  2. Look at the digit one place to the right.
  3. 0–4 means keep the target digit; 5–9 means increase it by 1.
  4. Replace smaller places with zeros.

Very beginner explanation: Rounding keeps the number close to its original value while making it easier to use.

Answer: 942,000

Worked Example 9

Problem: Round 32,340 to the nearest 10,000.

  1. Find the 10,000 place.
  2. Look at the digit one place to the right.
  3. 0–4 means keep the target digit; 5–9 means increase it by 1.
  4. Replace smaller places with zeros.

Very beginner explanation: Rounding keeps the number close to its original value while making it easier to use.

Answer: 30,000

Worked Example 10

Problem: Round 304,466 to the nearest 100,000.

  1. Find the 100,000 place.
  2. Look at the digit one place to the right.
  3. 0–4 means keep the target digit; 5–9 means increase it by 1.
  4. Replace smaller places with zeros.

Very beginner explanation: Rounding keeps the number close to its original value while making it easier to use.

Answer: 300,000

Practice Exercise

Create one new Grade 6 problem about Estimating large quantities. 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.

1.13 Real-life whole-number problems

Real-life whole-number problems is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 whole-number problems 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: Real-life whole-number problems is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 whole-number problems to analyze the values 4 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: Real-life whole-number problems is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 whole-number problems to analyze the values 29 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: Real-life whole-number problems is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 whole-number problems to analyze the values 11 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 whole-number problems is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 whole-number problems to analyze the values 13 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 whole-number problems is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 whole-number problems to analyze the values 4 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: Real-life whole-number problems is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 whole-number problems to analyze the values 22 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: Real-life whole-number problems is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 whole-number problems to analyze the values 24 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 whole-number problems is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 whole-number problems to analyze the values 21 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 whole-number problems is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 whole-number problems to analyze the values 29 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: Real-life whole-number problems is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 whole-number problems. 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.

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30 Review Questions and Answers

Q1. What is important to understand about Whole numbers to 1 million?

Answer: Whole numbers to 1 million is a Grade 6 mathematics idea in Whole Numbers to One Million. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q2. What is important to understand about Place value?

Answer: Place value is the value a digit has because of its position in a number.

Q3. What is important to understand about Reading six- and seven-digit numbers?

Answer: Reading six- and seven-digit numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q4. What is important to understand about Writing numbers in standard form?

Answer: Writing numbers in standard form is a Grade 6 mathematics idea in Whole Numbers to One Million. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q5. What is important to understand about Expanded form?

Answer: Expanded form is a Grade 6 mathematics idea in Whole Numbers to One Million. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q6. What is important to understand about Word form?

Answer: Word form is a Grade 6 mathematics idea in Whole Numbers to One Million. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q7. What is important to understand about Composing and decomposing numbers?

Answer: Composing and decomposing numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 Comparing whole numbers?

Answer: Comparing whole numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 Ordering whole numbers?

Answer: Ordering whole numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. 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 Whole numbers on number lines?

Answer: Whole numbers on number lines is a Grade 6 mathematics idea in Whole Numbers to One Million. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q11. What is important to understand about Rounding whole numbers?

Answer: Rounding whole numbers is a Grade 6 mathematics idea in Whole Numbers to One Million. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q12. What is important to understand about Estimating large quantities?

Answer: Estimating large quantities is a Grade 6 mathematics idea in Whole Numbers to One Million. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q13. What is important to understand about Real-life whole-number problems?

Answer: Real-life whole-number problems is a Grade 6 mathematics idea in Whole Numbers to One Million. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q14. Why should you show your steps?

Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.

Q15. Why is estimation useful?

Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.

Q16. Why do units matter?

Answer: Units tell what a value measures and help prevent incompatible quantities from being mixed.

Q17. When should you round?

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

Q18. How can you check an answer?

Answer: Use an inverse operation, substitution, estimation, a graph, a table, or a second method.

Q19. What should you identify first in a word problem?

Answer: Identify what is known, what is unknown, and the relationship connecting them.

Q20. What makes a final answer complete?

Answer: Give the value, correct units when needed, and a brief interpretation in context.

Q21. What should you do if an answer seems unreasonable?

Answer: Re-read the question and check copied values, operations, signs, units, rules, and calculations.

Q22. Why are diagrams useful?

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

Q23. Why are tables useful?

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

Q24. Why are graphs useful?

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

Q25. Why should you explain your reasoning?

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

Q26. Why can more than one strategy be correct?

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

Q27. What should you do before using a formula or rule?

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

Q28. How does practice help in mathematics?

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

Q29. 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.

Q30. Why should you compare an exact answer with an estimate?

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