Grade 6 Math Chapter 3: Comparing, Ordering, and Rounding Whole Numbers

Chapter Overview

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

Key Technical Terms

Comparing by greatest place (Comparing by greatest place is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Using greater-than and less-than symbols (Using greater-than and less-than symbols is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Ordering from least to greatest (Ordering from least to greatest is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Ordering from greatest to least (Ordering from greatest to least is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Rounding to the nearest 10 (Rounding to the nearest 10 is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
Rounding to the nearest 100 (Rounding to the nearest 100 is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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.

3.1 Comparing by greatest place

Comparing by greatest place is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Comparing by greatest place to analyze the values 3 and 14. What should be checked first?

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

Very beginner explanation: Comparing by greatest place is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Comparing by greatest place to analyze the values 27 and 18. What should be checked first?

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

Very beginner explanation: Comparing by greatest place is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Comparing by greatest place to analyze the values 8 and 11. What should be checked first?

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

Very beginner explanation: Comparing by greatest place is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Comparing by greatest place to analyze the values 13 and 15. What should be checked first?

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

Very beginner explanation: Comparing by greatest place is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Comparing by greatest place to analyze the values 18 and 9. What should be checked first?

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

Very beginner explanation: Comparing by greatest place is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Comparing by greatest place to analyze the values 9 and 8. What should be checked first?

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

Very beginner explanation: Comparing by greatest place is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Comparing by greatest place to analyze the values 22 and 11. What should be checked first?

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

Very beginner explanation: Comparing by greatest place is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Comparing by greatest place to analyze the values 26 and 18. What should be checked first?

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

Very beginner explanation: Comparing by greatest place is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Comparing by greatest place to analyze the values 6 and 20. What should be checked first?

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

Very beginner explanation: Comparing by greatest place is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Comparing by greatest place to analyze the values 19 and 14. What should be checked first?

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

Very beginner explanation: Comparing by greatest place is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Comparing by greatest place. 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.

3.2 Using greater-than and less-than symbols

Using greater-than and less-than symbols is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Using greater-than and less-than symbols to analyze the values 13 and 7. What should be checked first?

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

Very beginner explanation: Using greater-than and less-than symbols is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Using greater-than and less-than symbols to analyze the values 15 and 10. What should be checked first?

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

Very beginner explanation: Using greater-than and less-than symbols is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Using greater-than and less-than symbols to analyze the values 19 and 20. What should be checked first?

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

Very beginner explanation: Using greater-than and less-than symbols is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Using greater-than and less-than symbols to analyze the values 26 and 20. What should be checked first?

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

Very beginner explanation: Using greater-than and less-than symbols is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Using greater-than and less-than symbols to analyze the values 10 and 10. What should be checked first?

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

Very beginner explanation: Using greater-than and less-than symbols is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Using greater-than and less-than symbols to analyze the values 25 and 13. What should be checked first?

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

Very beginner explanation: Using greater-than and less-than symbols is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Using greater-than and less-than symbols to analyze the values 11 and 13. What should be checked first?

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

Very beginner explanation: Using greater-than and less-than symbols is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Using greater-than and less-than symbols to analyze the values 25 and 20. What should be checked first?

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

Very beginner explanation: Using greater-than and less-than symbols is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Using greater-than and less-than symbols to analyze the values 18 and 13. What should be checked first?

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

Very beginner explanation: Using greater-than and less-than symbols is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Using greater-than and less-than symbols to analyze the values 2 and 3. What should be checked first?

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

Very beginner explanation: Using greater-than and less-than symbols is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Using greater-than and less-than symbols. 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.

3.3 Ordering from least to greatest

Ordering from least to greatest is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from least to greatest to analyze the values 29 and 19. What should be checked first?

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

Very beginner explanation: Ordering from least to greatest is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from least to greatest to analyze the values 17 and 11. What should be checked first?

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

Very beginner explanation: Ordering from least to greatest is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from least to greatest to analyze the values 8 and 20. What should be checked first?

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

Very beginner explanation: Ordering from least to greatest is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from least to greatest to analyze the values 23 and 2. What should be checked first?

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

Very beginner explanation: Ordering from least to greatest is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from least to greatest to analyze the values 21 and 7. What should be checked first?

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

Very beginner explanation: Ordering from least to greatest is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from least to greatest to analyze the values 28 and 18. What should be checked first?

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

Very beginner explanation: Ordering from least to greatest is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from least to greatest to analyze the values 16 and 2. What should be checked first?

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

Very beginner explanation: Ordering from least to greatest is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from least to greatest to analyze the values 17 and 10. What should be checked first?

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

Very beginner explanation: Ordering from least to greatest is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from least to greatest to analyze the values 2 and 15. What should be checked first?

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

Very beginner explanation: Ordering from least to greatest is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from least to greatest to analyze the values 14 and 7. What should be checked first?

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

Very beginner explanation: Ordering from least to greatest is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from least to greatest. 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.

3.4 Ordering from greatest to least

Ordering from greatest to least is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from greatest to least to analyze the values 5 and 15. What should be checked first?

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

Very beginner explanation: Ordering from greatest to least is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from greatest to least to analyze the values 24 and 8. What should be checked first?

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

Very beginner explanation: Ordering from greatest to least is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from greatest to least to analyze the values 30 and 10. What should be checked first?

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

Very beginner explanation: Ordering from greatest to least is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from greatest to least to analyze the values 19 and 19. What should be checked first?

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

Very beginner explanation: Ordering from greatest to least is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from greatest to least to analyze the values 30 and 15. What should be checked first?

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

Very beginner explanation: Ordering from greatest to least is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from greatest to least to analyze the values 30 and 16. What should be checked first?

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

Very beginner explanation: Ordering from greatest to least is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from greatest to least to analyze the values 10 and 16. What should be checked first?

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

Very beginner explanation: Ordering from greatest to least is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from greatest to least to analyze the values 25 and 18. What should be checked first?

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

Very beginner explanation: Ordering from greatest to least is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from greatest to least to analyze the values 26 and 2. What should be checked first?

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

Very beginner explanation: Ordering from greatest to least is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from greatest to least to analyze the values 19 and 9. What should be checked first?

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

Very beginner explanation: Ordering from greatest to least is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from greatest to least. 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.

3.5 Rounding to the nearest 10

Rounding to the nearest 10 is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 284,855 to the nearest 10.

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

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

Answer: 284,860

Worked Example 2

Problem: Round 632,198 to the nearest 100.

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

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

Answer: 632,200

Worked Example 3

Problem: Round 638,451 to the nearest 1,000.

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

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

Answer: 638,000

Worked Example 4

Problem: Round 506,685 to the nearest 10,000.

Find the 10,000 place.
Look at the digit one place to the right.
0–4 means keep the target digit; 5–9 means increase it by 1.
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 5

Problem: Round 970,580 to the nearest 100,000.

Find the 100,000 place.
Look at the digit one place to the right.
0–4 means keep the target digit; 5–9 means increase it by 1.
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

Worked Example 6

Problem: Round 299,633 to the nearest 10.

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

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

Answer: 299,630

Worked Example 7

Problem: Round 963,802 to the nearest 100.

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

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

Answer: 963,800

Worked Example 8

Problem: Round 817,669 to the nearest 1,000.

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

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

Answer: 818,000

Worked Example 9

Problem: Round 151,264 to the nearest 10,000.

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

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

Answer: 150,000

Worked Example 10

Problem: Round 394,444 to the nearest 100,000.

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

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

Answer: 400,000

Practice Exercise

Create one new Grade 6 problem about Rounding to the nearest 10. 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.

3.6 Rounding to the nearest 100

Rounding to the nearest 100 is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 778,220 to the nearest 10.

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

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

Answer: 778,220

Worked Example 2

Problem: Round 771,995 to the nearest 100.

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

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

Answer: 772,000

Worked Example 3

Problem: Round 509,572 to the nearest 1,000.

Find the 1,000 place.
Look at the digit one place to the right.
0–4 means keep the target digit; 5–9 means increase it by 1.
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 931,583 to the nearest 10,000.

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

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

Answer: 930,000

Worked Example 5

Problem: Round 145,098 to the nearest 100,000.

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

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

Answer: 100,000

Worked Example 6

Problem: Round 412,916 to the nearest 10.

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

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

Answer: 412,920

Worked Example 7

Problem: Round 610,051 to the nearest 100.

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

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

Answer: 610,100

Worked Example 8

Problem: Round 549,252 to the nearest 1,000.

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

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

Answer: 549,000

Worked Example 9

Problem: Round 302,016 to the nearest 10,000.

Find the 10,000 place.
Look at the digit one place to the right.
0–4 means keep the target digit; 5–9 means increase it by 1.
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

Worked Example 10

Problem: Round 810,595 to the nearest 100,000.

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

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

Answer: 800,000

Practice Exercise

Create one new Grade 6 problem about Rounding to the nearest 100. 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.

3.7 Rounding to the nearest 1,000

Rounding to the nearest 1,000 is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 352,115 to the nearest 10.

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

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

Answer: 352,120

Worked Example 2

Problem: Round 362,235 to the nearest 100.

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

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

Answer: 362,200

Worked Example 3

Problem: Round 297,641 to the nearest 1,000.

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

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

Answer: 298,000

Worked Example 4

Problem: Round 836,724 to the nearest 10,000.

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

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

Answer: 840,000

Worked Example 5

Problem: Round 813,485 to the nearest 100,000.

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

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

Answer: 800,000

Worked Example 6

Problem: Round 33,359 to the nearest 10.

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

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

Answer: 33,360

Worked Example 7

Problem: Round 495,993 to the nearest 100.

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

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

Answer: 496,000

Worked Example 8

Problem: Round 168,662 to the nearest 1,000.

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

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

Answer: 169,000

Worked Example 9

Problem: Round 834,568 to the nearest 10,000.

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

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

Answer: 830,000

Worked Example 10

Problem: Round 313,760 to the nearest 100,000.

Find the 100,000 place.
Look at the digit one place to the right.
0–4 means keep the target digit; 5–9 means increase it by 1.
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 Rounding to the nearest 1,000. 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.

3.8 Rounding to the nearest 10,000

Rounding to the nearest 10,000 is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 188,012 to the nearest 10.

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

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

Answer: 188,010

Worked Example 2

Problem: Round 248,753 to the nearest 100.

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

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

Answer: 248,800

Worked Example 3

Problem: Round 258,033 to the nearest 1,000.

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

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

Answer: 258,000

Worked Example 4

Problem: Round 167,423 to the nearest 10,000.

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

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

Answer: 170,000

Worked Example 5

Problem: Round 262,431 to the nearest 100,000.

Find the 100,000 place.
Look at the digit one place to the right.
0–4 means keep the target digit; 5–9 means increase it by 1.
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

Worked Example 6

Problem: Round 744,888 to the nearest 10.

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

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

Answer: 744,890

Worked Example 7

Problem: Round 833,503 to the nearest 100.

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

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

Answer: 833,500

Worked Example 8

Problem: Round 247,516 to the nearest 1,000.

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

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

Answer: 248,000

Worked Example 9

Problem: Round 422,361 to the nearest 10,000.

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

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

Answer: 420,000

Worked Example 10

Problem: Round 774,705 to the nearest 100,000.

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

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

Answer: 800,000

Practice Exercise

Create one new Grade 6 problem about Rounding to the nearest 10,000. 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.

3.9 Rounding to the nearest 100,000

Rounding to the nearest 100,000 is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 536,078 to the nearest 10.

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

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

Answer: 536,080

Worked Example 2

Problem: Round 231,831 to the nearest 100.

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

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

Answer: 231,800

Worked Example 3

Problem: Round 562,585 to the nearest 1,000.

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

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

Answer: 563,000

Worked Example 4

Problem: Round 637,275 to the nearest 10,000.

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

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

Answer: 640,000

Worked Example 5

Problem: Round 947,983 to the nearest 100,000.

Find the 100,000 place.
Look at the digit one place to the right.
0–4 means keep the target digit; 5–9 means increase it by 1.
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 656,092 to the nearest 10.

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

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

Answer: 656,090

Worked Example 7

Problem: Round 987,560 to the nearest 100.

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

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

Answer: 987,600

Worked Example 8

Problem: Round 199,658 to the nearest 1,000.

Find the 1,000 place.
Look at the digit one place to the right.
0–4 means keep the target digit; 5–9 means increase it by 1.
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 9

Problem: Round 375,080 to the nearest 10,000.

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

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

Answer: 380,000

Worked Example 10

Problem: Round 612,682 to the nearest 100,000.

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

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

Answer: 600,000

Practice Exercise

Create one new Grade 6 problem about Rounding to the nearest 100,000. 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.

3.10 Estimating sums

Estimating sums is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating sums to analyze the values 2 and 12. What should be checked first?

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

Very beginner explanation: Estimating sums is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating sums to analyze the values 10 and 15. What should be checked first?

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

Very beginner explanation: Estimating sums is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating sums to analyze the values 28 and 16. What should be checked first?

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

Very beginner explanation: Estimating sums is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating sums to analyze the values 23 and 17. What should be checked first?

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

Very beginner explanation: Estimating sums is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating sums to analyze the values 27 and 3. What should be checked first?

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

Very beginner explanation: Estimating sums is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating sums to analyze the values 18 and 16. What should be checked first?

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

Very beginner explanation: Estimating sums is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating sums to analyze the values 27 and 8. What should be checked first?

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

Very beginner explanation: Estimating sums is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating sums to analyze the values 23 and 18. What should be checked first?

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

Very beginner explanation: Estimating sums is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating sums to analyze the values 9 and 14. What should be checked first?

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

Very beginner explanation: Estimating sums is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating sums to analyze the values 12 and 13. What should be checked first?

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

Very beginner explanation: Estimating sums is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating sums. 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.

3.11 Estimating differences

Estimating differences is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating differences to analyze the values 28 and 18. What should be checked first?

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

Very beginner explanation: Estimating differences is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating differences to analyze the values 16 and 17. What should be checked first?

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

Very beginner explanation: Estimating differences is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating differences to analyze the values 2 and 12. What should be checked first?

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

Very beginner explanation: Estimating differences is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating differences to analyze the values 19 and 17. What should be checked first?

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

Very beginner explanation: Estimating differences is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating differences to analyze the values 22 and 15. What should be checked first?

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

Very beginner explanation: Estimating differences is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating differences to analyze the values 17 and 6. What should be checked first?

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

Very beginner explanation: Estimating differences is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating differences to analyze the values 11 and 19. What should be checked first?

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

Very beginner explanation: Estimating differences is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating differences to analyze the values 29 and 10. What should be checked first?

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

Very beginner explanation: Estimating differences is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating differences to analyze the values 19 and 12. What should be checked first?

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

Very beginner explanation: Estimating differences is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating differences to analyze the values 22 and 5. What should be checked first?

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

Very beginner explanation: Estimating differences is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating differences. 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.

3.12 Checking reasonableness

Checking reasonableness is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Checking reasonableness to analyze the values 23 and 6. What should be checked first?

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

Very beginner explanation: Checking reasonableness is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Checking reasonableness to analyze the values 4 and 17. What should be checked first?

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

Very beginner explanation: Checking reasonableness is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Checking reasonableness to analyze the values 28 and 15. What should be checked first?

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

Very beginner explanation: Checking reasonableness is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Checking reasonableness to analyze the values 21 and 16. What should be checked first?

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

Very beginner explanation: Checking reasonableness is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Checking reasonableness to analyze the values 11 and 14. What should be checked first?

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

Very beginner explanation: Checking reasonableness is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Checking reasonableness to analyze the values 28 and 19. What should be checked first?

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

Very beginner explanation: Checking reasonableness is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Checking reasonableness to analyze the values 11 and 20. What should be checked first?

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

Very beginner explanation: Checking reasonableness is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Checking reasonableness to analyze the values 27 and 18. What should be checked first?

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

Very beginner explanation: Checking reasonableness is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Checking reasonableness to analyze the values 7 and 20. What should be checked first?

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

Very beginner explanation: Checking reasonableness is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Checking reasonableness to analyze the values 8 and 16. What should be checked first?

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

Very beginner explanation: Checking reasonableness is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Checking reasonableness. 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.

3.13 Whole-number word problems

Whole-number word problems is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Whole-number word problems to analyze the values 26 and 8. What should be checked first?

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

Very beginner explanation: Whole-number word problems is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Whole-number word problems to analyze the values 5 and 17. What should be checked first?

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

Very beginner explanation: Whole-number word problems is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Whole-number word problems to analyze the values 29 and 18. What should be checked first?

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

Very beginner explanation: Whole-number word problems is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Whole-number word problems to analyze the values 26 and 6. What should be checked first?

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

Very beginner explanation: Whole-number word problems is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Whole-number word problems to analyze the values 18 and 6. What should be checked first?

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

Very beginner explanation: Whole-number word problems is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Whole-number word problems to analyze the values 19 and 10. What should be checked first?

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

Very beginner explanation: Whole-number word problems is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Whole-number word problems to analyze the values 15 and 2. What should be checked first?

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

Very beginner explanation: Whole-number word problems is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Whole-number word problems to analyze the values 26 and 13. What should be checked first?

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

Very beginner explanation: Whole-number word problems is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Whole-number word problems to analyze the values 3 and 20. What should be checked first?

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

Very beginner explanation: Whole-number word problems is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Whole-number word problems to analyze the values 6 and 5. What should be checked first?

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

Very beginner explanation: Whole-number word problems is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Whole-number word 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.

30 Review Questions and Answers

Q1. What is important to understand about Comparing by greatest place?

Answer: Comparing by greatest place is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Using greater-than and less-than symbols?

Answer: Using greater-than and less-than symbols is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q3. What is important to understand about Ordering from least to greatest?

Answer: Ordering from least to greatest is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Ordering from greatest to least?

Answer: Ordering from greatest to least is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Rounding to the nearest 10?

Answer: Rounding to the nearest 10 is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Rounding to the nearest 100?

Answer: Rounding to the nearest 100 is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Rounding to the nearest 1,000?

Answer: Rounding to the nearest 1,000 is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Rounding to the nearest 10,000?

Answer: Rounding to the nearest 10,000 is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Rounding to the nearest 100,000?

Answer: Rounding to the nearest 100,000 is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating sums?

Answer: Estimating sums is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Estimating differences?

Answer: Estimating differences is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Checking reasonableness?

Answer: Checking reasonableness is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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 Whole-number word problems?

Answer: Whole-number word problems is a Grade 6 mathematics idea in Comparing, Ordering, and Rounding Whole Numbers. 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.