Chapter 22: Three-Digit by One-Digit Multiplication
Learn Grade 4 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Three-Digit by One-Digit Multiplication in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.
22.1 Breaking apart hundreds tens and ones
Breaking apart hundreds tens and ones is an important Grade 4 mathematics idea in Three-Digit by One-Digit Multiplication. 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 Breaking apart hundreds tens and ones using the numbers 4 and 13.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Breaking apart hundreds tens and ones.
Worked Example 2
Problem: Create a simple Grade 4 example about Breaking apart hundreds tens and ones using the numbers 10 and 17.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Breaking apart hundreds tens and ones.
Worked Example 3
Problem: Create a simple Grade 4 example about Breaking apart hundreds tens and ones using the numbers 18 and 19.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Breaking apart hundreds tens and ones.
Worked Example 4
Problem: Create a simple Grade 4 example about Breaking apart hundreds tens and ones using the numbers 10 and 14.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Breaking apart hundreds tens and ones.
Worked Example 5
Problem: Create a simple Grade 4 example about Breaking apart hundreds tens and ones using the numbers 14 and 18.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Breaking apart hundreds tens and ones.
Worked Example 6
Problem: Create a simple Grade 4 example about Breaking apart hundreds tens and ones using the numbers 18 and 18.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Breaking apart hundreds tens and ones.
Worked Example 7
Problem: Create a simple Grade 4 example about Breaking apart hundreds tens and ones using the numbers 14 and 20.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Breaking apart hundreds tens and ones.
Worked Example 8
Problem: Create a simple Grade 4 example about Breaking apart hundreds tens and ones using the numbers 5 and 19.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Breaking apart hundreds tens and ones.
Worked Example 9
Problem: Create a simple Grade 4 example about Breaking apart hundreds tens and ones using the numbers 6 and 10.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Breaking apart hundreds tens and ones.
Worked Example 10
Problem: Create a simple Grade 4 example about Breaking apart hundreds tens and ones using the numbers 11 and 9.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Breaking apart hundreds tens and ones.
Practice Exercise
Create and solve one new example of Breaking apart hundreds tens and ones. 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.
22.2 Area-model multiplication
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 × 2.
- Break 6 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 12
Worked Example 2
Problem: Calculate 12 × 6.
- Break 12 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 72
Worked Example 3
Problem: Calculate 8 × 6.
- Break 8 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 48
Worked Example 4
Problem: Calculate 9 × 8.
- Break 9 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 72
Worked Example 5
Problem: Calculate 9 × 2.
- Break 9 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 18
Worked Example 6
Problem: Calculate 3 × 2.
- Break 3 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 6
Worked Example 7
Problem: Calculate 9 × 5.
- Break 9 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 45
Worked Example 8
Problem: Calculate 4 × 3.
- Break 4 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 12
Worked Example 9
Problem: Calculate 12 × 9.
- Break 12 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 108
Worked Example 10
Problem: Calculate 4 × 8.
- Break 4 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 32
Practice Exercise
Create and solve one new example of Area-model multiplication. 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.
22.3 Partial 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 10 × 9.
- Break 10 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 90
Worked Example 2
Problem: Calculate 2 × 9.
- Break 2 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 18
Worked Example 3
Problem: Calculate 8 × 5.
- Break 8 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 40
Worked Example 4
Problem: Calculate 10 × 2.
- Break 10 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 20
Worked Example 5
Problem: Calculate 10 × 4.
- Break 10 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 40
Worked Example 6
Problem: Calculate 11 × 4.
- Break 11 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 44
Worked Example 7
Problem: Calculate 6 × 5.
- Break 6 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 30
Worked Example 8
Problem: Calculate 9 × 6.
- Break 9 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 54
Worked Example 9
Problem: Calculate 7 × 5.
- Break 7 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 35
Worked Example 10
Problem: Calculate 8 × 5.
- Break 8 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 40
Practice Exercise
Create and solve one new example of Partial 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.
22.4 Regrouping in multiplication
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 4 × 5.
- Break 4 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 20
Worked Example 2
Problem: Calculate 3 × 2.
- Break 3 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 6
Worked Example 3
Problem: Calculate 5 × 8.
- Break 5 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 40
Worked Example 4
Problem: Calculate 4 × 5.
- Break 4 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 20
Worked Example 5
Problem: Calculate 10 × 5.
- Break 10 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 50
Worked Example 6
Problem: Calculate 9 × 3.
- Break 9 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 27
Worked Example 7
Problem: Calculate 10 × 9.
- Break 10 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 90
Worked Example 8
Problem: Calculate 5 × 9.
- Break 5 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 45
Worked Example 9
Problem: Calculate 5 × 9.
- Break 5 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 45
Worked Example 10
Problem: Calculate 8 × 2.
- Break 8 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 16
Practice Exercise
Create and solve one new example of Regrouping in multiplication. 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.
22.5 Standard multiplication algorithm
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.
- Break 5 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 35
Worked Example 2
Problem: Calculate 2 × 3.
- Break 2 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 6
Worked Example 3
Problem: Calculate 12 × 5.
- Break 12 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 60
Worked Example 4
Problem: Calculate 4 × 2.
- Break 4 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 8
Worked Example 5
Problem: Calculate 9 × 6.
- Break 9 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 54
Worked Example 6
Problem: Calculate 5 × 9.
- Break 5 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 45
Worked Example 7
Problem: Calculate 6 × 3.
- Break 6 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 18
Worked Example 8
Problem: Calculate 7 × 8.
- Break 7 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 56
Worked Example 9
Problem: Calculate 7 × 5.
- Break 7 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 35
Worked Example 10
Problem: Calculate 11 × 7.
- Break 11 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 77
Practice Exercise
Create and solve one new example of Standard multiplication algorithm. 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.
22.6 Multiplying with a zero digit
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 4 × 6.
- Break 4 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 24
Worked Example 2
Problem: Calculate 11 × 6.
- Break 11 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 66
Worked Example 3
Problem: Calculate 2 × 9.
- Break 2 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 18
Worked Example 4
Problem: Calculate 2 × 2.
- Break 2 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 4
Worked Example 5
Problem: Calculate 7 × 2.
- Break 7 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 14
Worked Example 6
Problem: Calculate 8 × 9.
- Break 8 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 72
Worked Example 7
Problem: Calculate 9 × 7.
- Break 9 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 63
Worked Example 8
Problem: Calculate 10 × 5.
- Break 10 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 50
Worked Example 9
Problem: Calculate 12 × 2.
- Break 12 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 24
Worked Example 10
Problem: Calculate 7 × 9.
- Break 7 apart if helpful.
- Multiply each part by the other factor.
- 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 with a zero digit. 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.
22.7 Estimating three-digit 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 11 × 8.
- Break 11 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 88
Worked Example 2
Problem: Calculate 2 × 3.
- Break 2 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 6
Worked Example 3
Problem: Calculate 4 × 9.
- Break 4 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 36
Worked Example 4
Problem: Calculate 6 × 3.
- Break 6 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 18
Worked Example 5
Problem: Calculate 8 × 9.
- Break 8 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 72
Worked Example 6
Problem: Calculate 3 × 5.
- Break 3 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 15
Worked Example 7
Problem: Calculate 6 × 4.
- Break 6 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 24
Worked Example 8
Problem: Calculate 7 × 4.
- Break 7 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 28
Worked Example 9
Problem: Calculate 3 × 5.
- Break 3 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 15
Worked Example 10
Problem: Calculate 8 × 7.
- Break 8 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 56
Practice Exercise
Create and solve one new example of Estimating three-digit 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.
22.8 Real-life quantity problems
Real-life quantity problems is an important Grade 4 mathematics idea in Three-Digit by One-Digit Multiplication. 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 Real-life quantity problems using the numbers 3 and 14.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Real-life quantity problems.
Worked Example 2
Problem: Create a simple Grade 4 example about Real-life quantity problems using the numbers 16 and 18.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Real-life quantity problems.
Worked Example 3
Problem: Create a simple Grade 4 example about Real-life quantity problems using the numbers 12 and 13.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Real-life quantity problems.
Worked Example 4
Problem: Create a simple Grade 4 example about Real-life quantity problems using the numbers 9 and 20.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Real-life quantity problems.
Worked Example 5
Problem: Create a simple Grade 4 example about Real-life quantity problems using the numbers 5 and 4.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Real-life quantity problems.
Worked Example 6
Problem: Create a simple Grade 4 example about Real-life quantity problems using the numbers 3 and 2.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Real-life quantity problems.
Worked Example 7
Problem: Create a simple Grade 4 example about Real-life quantity problems using the numbers 19 and 20.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Real-life quantity problems.
Worked Example 8
Problem: Create a simple Grade 4 example about Real-life quantity problems using the numbers 12 and 6.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Real-life quantity problems.
Worked Example 9
Problem: Create a simple Grade 4 example about Real-life quantity problems using the numbers 5 and 20.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Real-life quantity problems.
Worked Example 10
Problem: Create a simple Grade 4 example about Real-life quantity problems using the numbers 15 and 18.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Real-life quantity problems.
Practice Exercise
Create and solve one new example of Real-life quantity problems. 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.
22.9 Checking multiplication
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 × 4.
- Break 6 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 24
Worked Example 2
Problem: Calculate 11 × 4.
- Break 11 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 44
Worked Example 3
Problem: Calculate 10 × 4.
- Break 10 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 40
Worked Example 4
Problem: Calculate 3 × 6.
- Break 3 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 18
Worked Example 5
Problem: Calculate 2 × 4.
- Break 2 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 8
Worked Example 6
Problem: Calculate 3 × 3.
- Break 3 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 9
Worked Example 7
Problem: Calculate 11 × 7.
- Break 11 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 77
Worked Example 8
Problem: Calculate 10 × 6.
- Break 10 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 60
Worked Example 9
Problem: Calculate 4 × 6.
- Break 4 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 24
Worked Example 10
Problem: Calculate 3 × 2.
- Break 3 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 6
Practice Exercise
Create and solve one new example of Checking multiplication. 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.
22.10 Reasonableness of 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 12 × 9.
- Break 12 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 108
Worked Example 2
Problem: Calculate 6 × 2.
- Break 6 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 12
Worked Example 3
Problem: Calculate 4 × 8.
- Break 4 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 32
Worked Example 4
Problem: Calculate 3 × 7.
- Break 3 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 21
Worked Example 5
Problem: Calculate 3 × 5.
- Break 3 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 15
Worked Example 6
Problem: Calculate 4 × 6.
- Break 4 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 24
Worked Example 7
Problem: Calculate 4 × 8.
- Break 4 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 32
Worked Example 8
Problem: Calculate 9 × 2.
- Break 9 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 18
Worked Example 9
Problem: Calculate 4 × 4.
- Break 4 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 16
Worked Example 10
Problem: Calculate 12 × 8.
- Break 12 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 96
Practice Exercise
Create and solve one new example of Reasonableness of 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.
22.11 Comparing two strategies
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 Comparing two strategies using the numbers 12 and 2.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Comparing two strategies.
Worked Example 2
Problem: Create a simple Grade 4 example about Comparing two strategies using the numbers 15 and 20.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Comparing two strategies.
Worked Example 3
Problem: Create a simple Grade 4 example about Comparing two strategies using the numbers 13 and 12.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Comparing two strategies.
Worked Example 4
Problem: Create a simple Grade 4 example about Comparing two strategies using the numbers 2 and 14.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Comparing two strategies.
Worked Example 5
Problem: Create a simple Grade 4 example about Comparing two strategies using the numbers 11 and 14.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Comparing two strategies.
Worked Example 6
Problem: Create a simple Grade 4 example about Comparing two strategies using the numbers 16 and 6.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Comparing two strategies.
Worked Example 7
Problem: Create a simple Grade 4 example about Comparing two strategies using the numbers 15 and 10.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Comparing two strategies.
Worked Example 8
Problem: Create a simple Grade 4 example about Comparing two strategies using the numbers 20 and 6.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Comparing two strategies.
Worked Example 9
Problem: Create a simple Grade 4 example about Comparing two strategies using the numbers 10 and 4.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Comparing two strategies.
Worked Example 10
Problem: Create a simple Grade 4 example about Comparing two strategies using the numbers 3 and 5.
- Identify what the topic means.
- Use the numbers in a way that follows the rule.
- 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 Comparing two strategies.
Practice Exercise
Create and solve one new example of Comparing two 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.
22.12 Mixed multiplication practice
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 10 × 5.
- Break 10 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 50
Worked Example 2
Problem: Calculate 5 × 7.
- Break 5 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 35
Worked Example 3
Problem: Calculate 4 × 9.
- Break 4 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 36
Worked Example 4
Problem: Calculate 9 × 4.
- Break 9 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 36
Worked Example 5
Problem: Calculate 9 × 5.
- Break 9 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 45
Worked Example 6
Problem: Calculate 12 × 6.
- Break 12 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 72
Worked Example 7
Problem: Calculate 2 × 4.
- Break 2 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 8
Worked Example 8
Problem: Calculate 9 × 4.
- Break 9 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 36
Worked Example 9
Problem: Calculate 2 × 3.
- Break 2 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 6
Worked Example 10
Problem: Calculate 5 × 7.
- Break 5 apart if helpful.
- Multiply each part by the other factor.
- Combine the partial products.
Very beginner explanation: Multiplication finds a total made from equal groups.
Answer: 35
Practice Exercise
Create and solve one new example of Mixed multiplication practice. 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.
30 Review Questions and Answers
Q1. What is important to understand about Breaking apart hundreds tens and ones?
Answer: Breaking apart hundreds tens and ones is an important Grade 4 mathematics idea in Three-Digit by One-Digit Multiplication. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q2. What is important to understand about Area-model multiplication?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q3. What is important to understand about Partial products?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q4. What is important to understand about Regrouping in multiplication?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q5. What is important to understand about Standard multiplication algorithm?
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 with a zero digit?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q7. What is important to understand about Estimating three-digit products?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q8. What is important to understand about Real-life quantity problems?
Answer: Real-life quantity problems is an important Grade 4 mathematics idea in Three-Digit by One-Digit Multiplication. 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 Checking multiplication?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q10. What is important to understand about Reasonableness of 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 Comparing two strategies?
Answer: A rate compares two quantities with different units, such as pages per day or items per box.
Q12. What is important to understand about Mixed multiplication practice?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q13. How would you explain Breaking apart hundreds tens and ones?
Answer: Breaking apart hundreds tens and ones is an important Grade 4 mathematics idea in Three-Digit by One-Digit Multiplication. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q14. How would you explain Area-model multiplication?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q15. How would you explain Partial products?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q16. How would you explain Regrouping in multiplication?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q17. How would you explain Standard multiplication algorithm?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q18. How would you explain Multiplying with a zero digit?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q19. How would you explain Estimating three-digit products?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q20. How would you explain Real-life quantity problems?
Answer: Real-life quantity problems is an important Grade 4 mathematics idea in Three-Digit by One-Digit Multiplication. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q21. How would you explain Checking multiplication?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q22. How would you explain Reasonableness of products?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q23. How would you explain Comparing two strategies?
Answer: A rate compares two quantities with different units, such as pages per day or items per box.
Q24. How would you explain Mixed multiplication practice?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q25. What should a beginner check when working with Breaking apart hundreds tens and ones?
Answer: Breaking apart hundreds tens and ones is an important Grade 4 mathematics idea in Three-Digit by One-Digit Multiplication. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q26. What should a beginner check when working with Area-model multiplication?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q27. What should a beginner check when working with Partial products?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q28. What should a beginner check when working with Regrouping in multiplication?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q29. What should a beginner check when working with Standard multiplication algorithm?
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 with a zero digit?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.