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Chapter 16: Mental Math and Powers of Ten

Learn Grade 4 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.

Grade 4Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
Estimated reading time0% read
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Chapter Overview

This chapter teaches Mental Math and Powers of Ten in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

16.1 Mental addition strategies

Addition combines quantities. Align place values, regroup when needed, and estimate first to predict a reasonable answer. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Calculate 2,658 + 2,358.

  1. Line up place values.
  2. Add from right to left.
  3. Regroup when needed.

Very beginner explanation: Place-value alignment keeps like places together.

Answer: 5,016

Worked Example 2

Problem: Calculate 3,915 + 2,692.

  1. Line up place values.
  2. Add from right to left.
  3. Regroup when needed.

Very beginner explanation: Place-value alignment keeps like places together.

Answer: 6,607

Worked Example 3

Problem: Calculate 791 + 2,382.

  1. Line up place values.
  2. Add from right to left.
  3. Regroup when needed.

Very beginner explanation: Place-value alignment keeps like places together.

Answer: 3,173

Worked Example 4

Problem: Calculate 3,686 + 2,479.

  1. Line up place values.
  2. Add from right to left.
  3. Regroup when needed.

Very beginner explanation: Place-value alignment keeps like places together.

Answer: 6,165

Worked Example 5

Problem: Calculate 251 + 2,976.

  1. Line up place values.
  2. Add from right to left.
  3. Regroup when needed.

Very beginner explanation: Place-value alignment keeps like places together.

Answer: 3,227

Worked Example 6

Problem: Calculate 3,956 + 1,393.

  1. Line up place values.
  2. Add from right to left.
  3. Regroup when needed.

Very beginner explanation: Place-value alignment keeps like places together.

Answer: 5,349

Worked Example 7

Problem: Calculate 641 + 777.

  1. Line up place values.
  2. Add from right to left.
  3. Regroup when needed.

Very beginner explanation: Place-value alignment keeps like places together.

Answer: 1,418

Worked Example 8

Problem: Calculate 227 + 1,652.

  1. Line up place values.
  2. Add from right to left.
  3. Regroup when needed.

Very beginner explanation: Place-value alignment keeps like places together.

Answer: 1,879

Worked Example 9

Problem: Calculate 3,602 + 2,286.

  1. Line up place values.
  2. Add from right to left.
  3. Regroup when needed.

Very beginner explanation: Place-value alignment keeps like places together.

Answer: 5,888

Worked Example 10

Problem: Calculate 2,894 + 837.

  1. Line up place values.
  2. Add from right to left.
  3. Regroup when needed.

Very beginner explanation: Place-value alignment keeps like places together.

Answer: 3,731

Practice Exercise

Create and solve one new example of Mental addition strategies. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

16.2 Mental subtraction strategies

Subtraction finds what remains or the difference between quantities. Addition is a useful way to check. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Calculate 4,036 − 1,241.

  1. Line up place values.
  2. Subtract from right to left.
  3. Regroup when needed.

Very beginner explanation: Addition can be used to check subtraction.

Answer: 2,795

Worked Example 2

Problem: Calculate 1,081 − 479.

  1. Line up place values.
  2. Subtract from right to left.
  3. Regroup when needed.

Very beginner explanation: Addition can be used to check subtraction.

Answer: 602

Worked Example 3

Problem: Calculate 4,180 − 2,316.

  1. Line up place values.
  2. Subtract from right to left.
  3. Regroup when needed.

Very beginner explanation: Addition can be used to check subtraction.

Answer: 1,864

Worked Example 4

Problem: Calculate 5,218 − 294.

  1. Line up place values.
  2. Subtract from right to left.
  3. Regroup when needed.

Very beginner explanation: Addition can be used to check subtraction.

Answer: 4,924

Worked Example 5

Problem: Calculate 5,059 − 852.

  1. Line up place values.
  2. Subtract from right to left.
  3. Regroup when needed.

Very beginner explanation: Addition can be used to check subtraction.

Answer: 4,207

Worked Example 6

Problem: Calculate 5,407 − 4,215.

  1. Line up place values.
  2. Subtract from right to left.
  3. Regroup when needed.

Very beginner explanation: Addition can be used to check subtraction.

Answer: 1,192

Worked Example 7

Problem: Calculate 3,282 − 1,604.

  1. Line up place values.
  2. Subtract from right to left.
  3. Regroup when needed.

Very beginner explanation: Addition can be used to check subtraction.

Answer: 1,678

Worked Example 8

Problem: Calculate 2,054 − 1,249.

  1. Line up place values.
  2. Subtract from right to left.
  3. Regroup when needed.

Very beginner explanation: Addition can be used to check subtraction.

Answer: 805

Worked Example 9

Problem: Calculate 5,861 − 4,665.

  1. Line up place values.
  2. Subtract from right to left.
  3. Regroup when needed.

Very beginner explanation: Addition can be used to check subtraction.

Answer: 1,196

Worked Example 10

Problem: Calculate 1,160 − 250.

  1. Line up place values.
  2. Subtract from right to left.
  3. Regroup when needed.

Very beginner explanation: Addition can be used to check subtraction.

Answer: 910

Practice Exercise

Create and solve one new example of Mental subtraction strategies. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

16.3 Doubling and halving

Doubling and halving is an important Grade 4 mathematics idea in Mental Math and Powers of Ten. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Create a simple Grade 4 example about Doubling and halving using the numbers 5 and 4.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Doubling and halving.

Worked Example 2

Problem: Create a simple Grade 4 example about Doubling and halving using the numbers 14 and 20.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Doubling and halving.

Worked Example 3

Problem: Create a simple Grade 4 example about Doubling and halving using the numbers 15 and 13.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Doubling and halving.

Worked Example 4

Problem: Create a simple Grade 4 example about Doubling and halving using the numbers 11 and 17.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Doubling and halving.

Worked Example 5

Problem: Create a simple Grade 4 example about Doubling and halving using the numbers 3 and 20.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Doubling and halving.

Worked Example 6

Problem: Create a simple Grade 4 example about Doubling and halving using the numbers 9 and 19.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Doubling and halving.

Worked Example 7

Problem: Create a simple Grade 4 example about Doubling and halving using the numbers 14 and 12.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Doubling and halving.

Worked Example 8

Problem: Create a simple Grade 4 example about Doubling and halving using the numbers 18 and 19.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Doubling and halving.

Worked Example 9

Problem: Create a simple Grade 4 example about Doubling and halving using the numbers 5 and 18.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Doubling and halving.

Worked Example 10

Problem: Create a simple Grade 4 example about Doubling and halving using the numbers 4 and 5.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Doubling and halving.

Practice Exercise

Create and solve one new example of Doubling and halving. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

16.4 Making tens and hundreds

Making tens and hundreds is an important Grade 4 mathematics idea in Mental Math and Powers of Ten. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Create a simple Grade 4 example about Making tens and hundreds using the numbers 14 and 7.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Making tens and hundreds.

Worked Example 2

Problem: Create a simple Grade 4 example about Making tens and hundreds using the numbers 19 and 15.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Making tens and hundreds.

Worked Example 3

Problem: Create a simple Grade 4 example about Making tens and hundreds using the numbers 9 and 3.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Making tens and hundreds.

Worked Example 4

Problem: Create a simple Grade 4 example about Making tens and hundreds using the numbers 15 and 19.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Making tens and hundreds.

Worked Example 5

Problem: Create a simple Grade 4 example about Making tens and hundreds using the numbers 11 and 19.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Making tens and hundreds.

Worked Example 6

Problem: Create a simple Grade 4 example about Making tens and hundreds using the numbers 18 and 7.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Making tens and hundreds.

Worked Example 7

Problem: Create a simple Grade 4 example about Making tens and hundreds using the numbers 17 and 5.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Making tens and hundreds.

Worked Example 8

Problem: Create a simple Grade 4 example about Making tens and hundreds using the numbers 14 and 12.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Making tens and hundreds.

Worked Example 9

Problem: Create a simple Grade 4 example about Making tens and hundreds using the numbers 13 and 13.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Making tens and hundreds.

Worked Example 10

Problem: Create a simple Grade 4 example about Making tens and hundreds using the numbers 17 and 18.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Making tens and hundreds.

Practice Exercise

Create and solve one new example of Making tens and hundreds. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

16.5 Multiplying by 10

Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Calculate 6 × 5.

  1. Break 6 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 30

Worked Example 2

Problem: Calculate 4 × 2.

  1. Break 4 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 8

Worked Example 3

Problem: Calculate 12 × 9.

  1. Break 12 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 108

Worked Example 4

Problem: Calculate 12 × 8.

  1. Break 12 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 96

Worked Example 5

Problem: Calculate 4 × 6.

  1. Break 4 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 24

Worked Example 6

Problem: Calculate 4 × 9.

  1. Break 4 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 36

Worked Example 7

Problem: Calculate 10 × 9.

  1. Break 10 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 90

Worked Example 8

Problem: Calculate 11 × 9.

  1. Break 11 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 99

Worked Example 9

Problem: Calculate 3 × 3.

  1. Break 3 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 9

Worked Example 10

Problem: Calculate 2 × 6.

  1. Break 2 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 12

Practice Exercise

Create and solve one new example of Multiplying by 10. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

16.6 Multiplying by 100

Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Calculate 3 × 7.

  1. Break 3 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 21

Worked Example 2

Problem: Calculate 7 × 4.

  1. Break 7 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 28

Worked Example 3

Problem: Calculate 3 × 4.

  1. Break 3 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 12

Worked Example 4

Problem: Calculate 5 × 7.

  1. Break 5 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 35

Worked Example 5

Problem: Calculate 3 × 6.

  1. Break 3 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 18

Worked Example 6

Problem: Calculate 2 × 6.

  1. Break 2 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 12

Worked Example 7

Problem: Calculate 4 × 6.

  1. Break 4 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 24

Worked Example 8

Problem: Calculate 2 × 7.

  1. Break 2 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 14

Worked Example 9

Problem: Calculate 4 × 7.

  1. Break 4 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 28

Worked Example 10

Problem: Calculate 3 × 6.

  1. Break 3 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 18

Practice Exercise

Create and solve one new example of Multiplying by 100. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

16.7 Multiplying by 1,000

Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Calculate 12 × 3.

  1. Break 12 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 36

Worked Example 2

Problem: Calculate 3 × 7.

  1. Break 3 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 21

Worked Example 3

Problem: Calculate 10 × 5.

  1. Break 10 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 50

Worked Example 4

Problem: Calculate 10 × 6.

  1. Break 10 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 60

Worked Example 5

Problem: Calculate 3 × 7.

  1. Break 3 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 21

Worked Example 6

Problem: Calculate 7 × 6.

  1. Break 7 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 42

Worked Example 7

Problem: Calculate 9 × 3.

  1. Break 9 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 27

Worked Example 8

Problem: Calculate 5 × 8.

  1. Break 5 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 40

Worked Example 9

Problem: Calculate 2 × 2.

  1. Break 2 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 4

Worked Example 10

Problem: Calculate 9 × 7.

  1. Break 9 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 63

Practice Exercise

Create and solve one new example of Multiplying by 1,000. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

16.8 Dividing by 10 in simple whole-number cases

Dividing by 10 in simple whole-number cases is an important Grade 4 mathematics idea in Mental Math and Powers of Ten. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Create a simple Grade 4 example about Dividing by 10 in simple whole-number cases using the numbers 5 and 2.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Dividing by 10 in simple whole-number cases.

Worked Example 2

Problem: Create a simple Grade 4 example about Dividing by 10 in simple whole-number cases using the numbers 19 and 19.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Dividing by 10 in simple whole-number cases.

Worked Example 3

Problem: Create a simple Grade 4 example about Dividing by 10 in simple whole-number cases using the numbers 12 and 8.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Dividing by 10 in simple whole-number cases.

Worked Example 4

Problem: Create a simple Grade 4 example about Dividing by 10 in simple whole-number cases using the numbers 2 and 4.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Dividing by 10 in simple whole-number cases.

Worked Example 5

Problem: Create a simple Grade 4 example about Dividing by 10 in simple whole-number cases using the numbers 15 and 7.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Dividing by 10 in simple whole-number cases.

Worked Example 6

Problem: Create a simple Grade 4 example about Dividing by 10 in simple whole-number cases using the numbers 8 and 10.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Dividing by 10 in simple whole-number cases.

Worked Example 7

Problem: Create a simple Grade 4 example about Dividing by 10 in simple whole-number cases using the numbers 13 and 7.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Dividing by 10 in simple whole-number cases.

Worked Example 8

Problem: Create a simple Grade 4 example about Dividing by 10 in simple whole-number cases using the numbers 5 and 8.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Dividing by 10 in simple whole-number cases.

Worked Example 9

Problem: Create a simple Grade 4 example about Dividing by 10 in simple whole-number cases using the numbers 9 and 3.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Dividing by 10 in simple whole-number cases.

Worked Example 10

Problem: Create a simple Grade 4 example about Dividing by 10 in simple whole-number cases using the numbers 14 and 19.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Dividing by 10 in simple whole-number cases.

Practice Exercise

Create and solve one new example of Dividing by 10 in simple whole-number cases. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

16.9 Place-value shifts

Financial literacy helps compare choices, understand payments, protect information, and judge whether a purchase gives reasonable value. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Option A costs $12 for 5 items. Option B costs $6 for 1 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option A

Worked Example 2

Problem: Option A costs $8 for 1 items. Option B costs $12 for 5 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option B

Worked Example 3

Problem: Option A costs $4 for 2 items. Option B costs $6 for 2 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option A

Worked Example 4

Problem: Option A costs $12 for 2 items. Option B costs $11 for 2 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option B

Worked Example 5

Problem: Option A costs $8 for 3 items. Option B costs $12 for 2 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option A

Worked Example 6

Problem: Option A costs $7 for 5 items. Option B costs $3 for 1 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option A

Worked Example 7

Problem: Option A costs $7 for 1 items. Option B costs $3 for 4 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option B

Worked Example 8

Problem: Option A costs $9 for 5 items. Option B costs $2 for 4 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option B

Worked Example 9

Problem: Option A costs $11 for 3 items. Option B costs $10 for 2 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option A

Worked Example 10

Problem: Option A costs $11 for 2 items. Option B costs $11 for 2 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Same value

Practice Exercise

Create and solve one new example of Place-value shifts. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

16.10 Estimating products

Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Calculate 5 × 7.

  1. Break 5 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 35

Worked Example 2

Problem: Calculate 7 × 9.

  1. Break 7 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 63

Worked Example 3

Problem: Calculate 9 × 9.

  1. Break 9 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 81

Worked Example 4

Problem: Calculate 6 × 7.

  1. Break 6 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 42

Worked Example 5

Problem: Calculate 4 × 5.

  1. Break 4 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 20

Worked Example 6

Problem: Calculate 12 × 4.

  1. Break 12 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 48

Worked Example 7

Problem: Calculate 5 × 3.

  1. Break 5 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 15

Worked Example 8

Problem: Calculate 2 × 6.

  1. Break 2 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 12

Worked Example 9

Problem: Calculate 6 × 3.

  1. Break 6 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 18

Worked Example 10

Problem: Calculate 12 × 9.

  1. Break 12 apart if helpful.
  2. Multiply each part by the other factor.
  3. Combine the partial products.

Very beginner explanation: Multiplication finds a total made from equal groups.

Answer: 108

Practice Exercise

Create and solve one new example of Estimating products. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

16.11 Estimating quotients

Division means sharing equally or finding equal groups. Multiplication can be used to check the result. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Calculate 135 ÷ 9.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 15

Worked Example 2

Problem: Calculate 57 ÷ 4.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 14 remainder 1

Worked Example 3

Problem: Calculate 30 ÷ 8.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 3 remainder 6

Worked Example 4

Problem: Calculate 28 ÷ 2.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 14

Worked Example 5

Problem: Calculate 81 ÷ 7.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 11 remainder 4

Worked Example 6

Problem: Calculate 54 ÷ 6.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 9

Worked Example 7

Problem: Calculate 60 ÷ 4.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 15

Worked Example 8

Problem: Calculate 28 ÷ 4.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 7

Worked Example 9

Problem: Calculate 37 ÷ 4.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 9 remainder 1

Worked Example 10

Problem: Calculate 109 ÷ 9.

  1. Use multiplication facts to find the largest equal group.
  2. Find any amount left over.
  3. Check with divisor × quotient + remainder.

Very beginner explanation: The remainder must be smaller than the divisor.

Answer: 12 remainder 1

Practice Exercise

Create and solve one new example of Estimating quotients. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

16.12 Choosing an efficient mental strategy

A rate compares two quantities with different units, such as pages per day or items per box. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Create a simple Grade 4 example about Choosing an efficient mental strategy using the numbers 20 and 14.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Choosing an efficient mental strategy.

Worked Example 2

Problem: Create a simple Grade 4 example about Choosing an efficient mental strategy using the numbers 14 and 6.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Choosing an efficient mental strategy.

Worked Example 3

Problem: Create a simple Grade 4 example about Choosing an efficient mental strategy using the numbers 18 and 18.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Choosing an efficient mental strategy.

Worked Example 4

Problem: Create a simple Grade 4 example about Choosing an efficient mental strategy using the numbers 3 and 2.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Choosing an efficient mental strategy.

Worked Example 5

Problem: Create a simple Grade 4 example about Choosing an efficient mental strategy using the numbers 7 and 17.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Choosing an efficient mental strategy.

Worked Example 6

Problem: Create a simple Grade 4 example about Choosing an efficient mental strategy using the numbers 20 and 13.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Choosing an efficient mental strategy.

Worked Example 7

Problem: Create a simple Grade 4 example about Choosing an efficient mental strategy using the numbers 6 and 17.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Choosing an efficient mental strategy.

Worked Example 8

Problem: Create a simple Grade 4 example about Choosing an efficient mental strategy using the numbers 19 and 11.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Choosing an efficient mental strategy.

Worked Example 9

Problem: Create a simple Grade 4 example about Choosing an efficient mental strategy using the numbers 4 and 11.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Choosing an efficient mental strategy.

Worked Example 10

Problem: Create a simple Grade 4 example about Choosing an efficient mental strategy using the numbers 9 and 14.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Choosing an efficient mental strategy.

Practice Exercise

Create and solve one new example of Choosing an efficient mental strategy. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

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30 Review Questions and Answers

Q1. What is important to understand about Mental addition strategies?

Answer: Addition combines quantities. Align place values, regroup when needed, and estimate first to predict a reasonable answer.

Q2. What is important to understand about Mental subtraction strategies?

Answer: Subtraction finds what remains or the difference between quantities. Addition is a useful way to check.

Q3. What is important to understand about Doubling and halving?

Answer: Doubling and halving is an important Grade 4 mathematics idea in Mental Math and Powers of Ten. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q4. What is important to understand about Making tens and hundreds?

Answer: Making tens and hundreds is an important Grade 4 mathematics idea in Mental Math and Powers of Ten. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q5. What is important to understand about Multiplying by 10?

Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.

Q6. What is important to understand about Multiplying by 100?

Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.

Q7. What is important to understand about Multiplying by 1,000?

Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.

Q8. What is important to understand about Dividing by 10 in simple whole-number cases?

Answer: Dividing by 10 in simple whole-number cases is an important Grade 4 mathematics idea in Mental Math and Powers of Ten. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q9. What is important to understand about Place-value shifts?

Answer: Financial literacy helps compare choices, understand payments, protect information, and judge whether a purchase gives reasonable value.

Q10. What is important to understand about Estimating products?

Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.

Q11. What is important to understand about Estimating quotients?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q12. What is important to understand about Choosing an efficient mental strategy?

Answer: A rate compares two quantities with different units, such as pages per day or items per box.

Q13. How would you explain Mental addition strategies?

Answer: Addition combines quantities. Align place values, regroup when needed, and estimate first to predict a reasonable answer.

Q14. How would you explain Mental subtraction strategies?

Answer: Subtraction finds what remains or the difference between quantities. Addition is a useful way to check.

Q15. How would you explain Doubling and halving?

Answer: Doubling and halving is an important Grade 4 mathematics idea in Mental Math and Powers of Ten. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q16. How would you explain Making tens and hundreds?

Answer: Making tens and hundreds is an important Grade 4 mathematics idea in Mental Math and Powers of Ten. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q17. How would you explain Multiplying by 10?

Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.

Q18. How would you explain Multiplying by 100?

Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.

Q19. How would you explain Multiplying by 1,000?

Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.

Q20. How would you explain Dividing by 10 in simple whole-number cases?

Answer: Dividing by 10 in simple whole-number cases is an important Grade 4 mathematics idea in Mental Math and Powers of Ten. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q21. How would you explain Place-value shifts?

Answer: Financial literacy helps compare choices, understand payments, protect information, and judge whether a purchase gives reasonable value.

Q22. How would you explain Estimating products?

Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.

Q23. How would you explain Estimating quotients?

Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.

Q24. How would you explain Choosing an efficient mental strategy?

Answer: A rate compares two quantities with different units, such as pages per day or items per box.

Q25. What should a beginner check when working with Mental addition strategies?

Answer: Addition combines quantities. Align place values, regroup when needed, and estimate first to predict a reasonable answer.

Q26. What should a beginner check when working with Mental subtraction strategies?

Answer: Subtraction finds what remains or the difference between quantities. Addition is a useful way to check.

Q27. What should a beginner check when working with Doubling and halving?

Answer: Doubling and halving is an important Grade 4 mathematics idea in Mental Math and Powers of Ten. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q28. What should a beginner check when working with Making tens and hundreds?

Answer: Making tens and hundreds is an important Grade 4 mathematics idea in Mental Math and Powers of Ten. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q29. What should a beginner check when working with Multiplying by 10?

Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.

Q30. What should a beginner check when working with Multiplying by 100?

Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.