Chapter 21: Two-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 Two-Digit by One-Digit Multiplication in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.
21.1 Using equal groups
Using equal groups is an important Grade 4 mathematics idea in Two-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 Using equal groups using the numbers 11 and 11.
- 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 Using equal groups.
Worked Example 2
Problem: Create a simple Grade 4 example about Using equal groups using the numbers 17 and 7.
- 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 Using equal groups.
Worked Example 3
Problem: Create a simple Grade 4 example about Using equal groups using the numbers 9 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 Using equal groups.
Worked Example 4
Problem: Create a simple Grade 4 example about Using equal groups using the numbers 12 and 11.
- 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 Using equal groups.
Worked Example 5
Problem: Create a simple Grade 4 example about Using equal groups using the numbers 17 and 8.
- 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 Using equal groups.
Worked Example 6
Problem: Create a simple Grade 4 example about Using equal groups using the numbers 6 and 7.
- 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 Using equal groups.
Worked Example 7
Problem: Create a simple Grade 4 example about Using equal groups using the numbers 20 and 8.
- 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 Using equal groups.
Worked Example 8
Problem: Create a simple Grade 4 example about Using equal groups using the numbers 15 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 Using equal groups.
Worked Example 9
Problem: Create a simple Grade 4 example about Using equal groups using the numbers 12 and 16.
- 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 Using equal groups.
Worked Example 10
Problem: Create a simple Grade 4 example about Using equal groups using the numbers 13 and 7.
- 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 Using equal groups.
Practice Exercise
Create and solve one new example of Using equal groups. 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.
21.2 Using arrays
Using arrays is an important Grade 4 mathematics idea in Two-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 Using arrays using the numbers 2 and 8.
- 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 Using arrays.
Worked Example 2
Problem: Create a simple Grade 4 example about Using arrays using the numbers 17 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 Using arrays.
Worked Example 3
Problem: Create a simple Grade 4 example about Using arrays using the numbers 2 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 Using arrays.
Worked Example 4
Problem: Create a simple Grade 4 example about Using arrays using the numbers 11 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 Using arrays.
Worked Example 5
Problem: Create a simple Grade 4 example about Using arrays using the numbers 20 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 Using arrays.
Worked Example 6
Problem: Create a simple Grade 4 example about Using arrays using the numbers 2 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 Using arrays.
Worked Example 7
Problem: Create a simple Grade 4 example about Using arrays using the numbers 16 and 15.
- 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 Using arrays.
Worked Example 8
Problem: Create a simple Grade 4 example about Using arrays using the numbers 8 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 Using arrays.
Worked Example 9
Problem: Create a simple Grade 4 example about Using arrays using the numbers 17 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 Using arrays.
Worked Example 10
Problem: Create a simple Grade 4 example about Using arrays 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 Using arrays.
Practice Exercise
Create and solve one new example of Using arrays. 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.
21.3 Using area models
Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows. 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: A data set is [10, 6, 11, 9, 4]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 11
Worked Example 2
Problem: A data set is [9, 9, 7, 8, 6]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 9
Worked Example 3
Problem: A data set is [14, 11, 4, 12, 4]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 4
Problem: A data set is [12, 15, 5, 4, 6]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 5
Problem: A data set is [8, 4, 15, 2, 14]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 15
Worked Example 6
Problem: A data set is [3, 14, 11, 5, 4]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 7
Problem: A data set is [6, 9, 11, 6, 2]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 11
Worked Example 8
Problem: A data set is [11, 14, 9, 4, 5]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Worked Example 9
Problem: A data set is [10, 10, 13, 13, 3]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 13
Worked Example 10
Problem: A data set is [10, 8, 9, 14, 9]. What is the greatest value?
- Read all the values.
- Choose the largest number.
Very beginner explanation: Data questions should be answered from the recorded values or display.
Answer: 14
Practice Exercise
Create and solve one new example of Using area models. 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.
21.4 Breaking apart the two-digit factor
Place value tells how much a digit is worth because of its position in the number. 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: In 2,666, what is the value of the digit 2?
- Find the digit's place.
- Multiply the digit by that place value.
Very beginner explanation: A digit's value depends on its location.
Answer: 2,000
Worked Example 2
Problem: In 5,767, what is the value of the digit 6?
- Find the digit's place.
- Multiply the digit by that place value.
Very beginner explanation: A digit's value depends on its location.
Answer: 60
Worked Example 3
Problem: In 5,692, what is the value of the digit 2?
- Find the digit's place.
- Multiply the digit by that place value.
Very beginner explanation: A digit's value depends on its location.
Answer: 2
Worked Example 4
Problem: In 6,381, what is the value of the digit 1?
- Find the digit's place.
- Multiply the digit by that place value.
Very beginner explanation: A digit's value depends on its location.
Answer: 1
Worked Example 5
Problem: In 4,699, what is the value of the digit 4?
- Find the digit's place.
- Multiply the digit by that place value.
Very beginner explanation: A digit's value depends on its location.
Answer: 4,000
Worked Example 6
Problem: In 4,782, what is the value of the digit 2?
- Find the digit's place.
- Multiply the digit by that place value.
Very beginner explanation: A digit's value depends on its location.
Answer: 2
Worked Example 7
Problem: In 2,189, what is the value of the digit 2?
- Find the digit's place.
- Multiply the digit by that place value.
Very beginner explanation: A digit's value depends on its location.
Answer: 2,000
Worked Example 8
Problem: In 4,269, what is the value of the digit 2?
- Find the digit's place.
- Multiply the digit by that place value.
Very beginner explanation: A digit's value depends on its location.
Answer: 200
Worked Example 9
Problem: In 3,497, what is the value of the digit 4?
- Find the digit's place.
- Multiply the digit by that place value.
Very beginner explanation: A digit's value depends on its location.
Answer: 400
Worked Example 10
Problem: In 3,744, what is the value of the digit 4?
- Find the digit's place.
- Multiply the digit by that place value.
Very beginner explanation: A digit's value depends on its location.
Answer: 40
Practice Exercise
Create and solve one new example of Breaking apart the two-digit factor. 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.
21.5 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 11 × 2.
- 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: 22
Worked Example 2
Problem: Calculate 3 × 9.
- 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: 27
Worked Example 3
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 4
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 5
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 6
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 7
Problem: Calculate 11 × 2.
- 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: 22
Worked Example 8
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 9
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 10
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
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.
21.6 Distributive 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 Distributive strategy using the numbers 18 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 Distributive strategy.
Worked Example 2
Problem: Create a simple Grade 4 example about Distributive strategy using the numbers 4 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 Distributive strategy.
Worked Example 3
Problem: Create a simple Grade 4 example about Distributive strategy using the numbers 12 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 Distributive strategy.
Worked Example 4
Problem: Create a simple Grade 4 example about Distributive strategy using the numbers 12 and 11.
- 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 Distributive strategy.
Worked Example 5
Problem: Create a simple Grade 4 example about Distributive strategy using the numbers 15 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 Distributive strategy.
Worked Example 6
Problem: Create a simple Grade 4 example about Distributive strategy using the numbers 18 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 Distributive strategy.
Worked Example 7
Problem: Create a simple Grade 4 example about Distributive strategy using the numbers 14 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 Distributive strategy.
Worked Example 8
Problem: Create a simple Grade 4 example about Distributive strategy 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 Distributive strategy.
Worked Example 9
Problem: Create a simple Grade 4 example about Distributive strategy using the numbers 9 and 16.
- 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 Distributive strategy.
Worked Example 10
Problem: Create a simple Grade 4 example about Distributive strategy using the numbers 6 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 Distributive strategy.
Practice Exercise
Create and solve one new example of Distributive 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.
21.7 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 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 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 3
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 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 6 × 6.
- 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: 36
Worked Example 6
Problem: Calculate 12 × 7.
- 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: 84
Worked Example 7
Problem: Calculate 3 × 4.
- 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: 12
Worked Example 8
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 9
Problem: Calculate 4 × 7.
- 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: 28
Worked Example 10
Problem: Calculate 2 × 8.
- 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: 16
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.
21.8 Estimating a product
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 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 2
Problem: Calculate 5 × 4.
- 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: 20
Worked Example 3
Problem: Calculate 8 × 4.
- 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: 32
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 2 × 5.
- 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: 10
Worked Example 6
Problem: Calculate 3 × 8.
- 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: 24
Worked Example 7
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 8
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
Worked Example 9
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 10
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
Practice Exercise
Create and solve one new example of Estimating a product. 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.
21.9 Word problems
Word problems is an important Grade 4 mathematics idea in Two-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 Word problems using the numbers 18 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 Word problems.
Worked Example 2
Problem: Create a simple Grade 4 example about Word problems using the numbers 19 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 Word problems.
Worked Example 3
Problem: Create a simple Grade 4 example about Word problems using the numbers 16 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 Word problems.
Worked Example 4
Problem: Create a simple Grade 4 example about Word problems 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 Word problems.
Worked Example 5
Problem: Create a simple Grade 4 example about Word problems using the numbers 8 and 11.
- 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 Word problems.
Worked Example 6
Problem: Create a simple Grade 4 example about Word problems using the numbers 19 and 15.
- 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 Word problems.
Worked Example 7
Problem: Create a simple Grade 4 example about Word problems using the numbers 17 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 Word problems.
Worked Example 8
Problem: Create a simple Grade 4 example about Word problems using the numbers 19 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 Word problems.
Worked Example 9
Problem: Create a simple Grade 4 example about Word problems using the numbers 20 and 15.
- 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 Word problems.
Worked Example 10
Problem: Create a simple Grade 4 example about Word problems 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 Word problems.
Practice Exercise
Create and solve one new example of Word 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.
21.10 Measurement contexts
Measurement contexts is an important Grade 4 mathematics idea in Two-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 Measurement contexts using the numbers 4 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 Measurement contexts.
Worked Example 2
Problem: Create a simple Grade 4 example about Measurement contexts using the numbers 12 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 Measurement contexts.
Worked Example 3
Problem: Create a simple Grade 4 example about Measurement contexts using the numbers 19 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 Measurement contexts.
Worked Example 4
Problem: Create a simple Grade 4 example about Measurement contexts using the numbers 2 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 Measurement contexts.
Worked Example 5
Problem: Create a simple Grade 4 example about Measurement contexts 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 Measurement contexts.
Worked Example 6
Problem: Create a simple Grade 4 example about Measurement contexts using the numbers 17 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 Measurement contexts.
Worked Example 7
Problem: Create a simple Grade 4 example about Measurement contexts using the numbers 2 and 3.
- 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 Measurement contexts.
Worked Example 8
Problem: Create a simple Grade 4 example about Measurement contexts using the numbers 20 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 Measurement contexts.
Worked Example 9
Problem: Create a simple Grade 4 example about Measurement contexts using the numbers 5 and 16.
- 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 Measurement contexts.
Worked Example 10
Problem: Create a simple Grade 4 example about Measurement contexts using the numbers 2 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 Measurement contexts.
Practice Exercise
Create and solve one new example of Measurement contexts. 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.
21.11 Checking with division
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 78 ÷ 8.
- Use multiplication facts to find the largest equal group.
- Find any amount left over.
- Check with divisor × quotient + remainder.
Very beginner explanation: The remainder must be smaller than the divisor.
Answer: 9 remainder 6
Worked Example 2
Problem: Calculate 43 ÷ 3.
- Use multiplication facts to find the largest equal group.
- Find any amount left over.
- 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 44 ÷ 3.
- Use multiplication facts to find the largest equal group.
- Find any amount left over.
- Check with divisor × quotient + remainder.
Very beginner explanation: The remainder must be smaller than the divisor.
Answer: 14 remainder 2
Worked Example 4
Problem: Calculate 42 ÷ 8.
- Use multiplication facts to find the largest equal group.
- Find any amount left over.
- Check with divisor × quotient + remainder.
Very beginner explanation: The remainder must be smaller than the divisor.
Answer: 5 remainder 2
Worked Example 5
Problem: Calculate 44 ÷ 8.
- Use multiplication facts to find the largest equal group.
- Find any amount left over.
- Check with divisor × quotient + remainder.
Very beginner explanation: The remainder must be smaller than the divisor.
Answer: 5 remainder 4
Worked Example 6
Problem: Calculate 39 ÷ 2.
- Use multiplication facts to find the largest equal group.
- Find any amount left over.
- Check with divisor × quotient + remainder.
Very beginner explanation: The remainder must be smaller than the divisor.
Answer: 19 remainder 1
Worked Example 7
Problem: Calculate 77 ÷ 4.
- Use multiplication facts to find the largest equal group.
- Find any amount left over.
- Check with divisor × quotient + remainder.
Very beginner explanation: The remainder must be smaller than the divisor.
Answer: 19 remainder 1
Worked Example 8
Problem: Calculate 58 ÷ 7.
- Use multiplication facts to find the largest equal group.
- Find any amount left over.
- Check with divisor × quotient + remainder.
Very beginner explanation: The remainder must be smaller than the divisor.
Answer: 8 remainder 2
Worked Example 9
Problem: Calculate 126 ÷ 7.
- Use multiplication facts to find the largest equal group.
- Find any amount left over.
- Check with divisor × quotient + remainder.
Very beginner explanation: The remainder must be smaller than the divisor.
Answer: 18
Worked Example 10
Problem: Calculate 118 ÷ 8.
- Use multiplication facts to find the largest equal group.
- Find any amount left over.
- Check with divisor × quotient + remainder.
Very beginner explanation: The remainder must be smaller than the divisor.
Answer: 14 remainder 6
Practice Exercise
Create and solve one new example of Checking with division. 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.
21.12 Choosing an efficient 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 strategy using the numbers 19 and 3.
- 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 Choosing an efficient strategy.
Worked Example 2
Problem: Create a simple Grade 4 example about Choosing an efficient strategy using the numbers 18 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 Choosing an efficient strategy.
Worked Example 3
Problem: Create a simple Grade 4 example about Choosing an efficient strategy using the numbers 2 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 Choosing an efficient strategy.
Worked Example 4
Problem: Create a simple Grade 4 example about Choosing an efficient strategy using the numbers 19 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 Choosing an efficient strategy.
Worked Example 5
Problem: Create a simple Grade 4 example about Choosing an efficient strategy using the numbers 5 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 Choosing an efficient strategy.
Worked Example 6
Problem: Create a simple Grade 4 example about Choosing an efficient strategy using the numbers 13 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 Choosing an efficient strategy.
Worked Example 7
Problem: Create a simple Grade 4 example about Choosing an efficient strategy using the numbers 9 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 Choosing an efficient strategy.
Worked Example 8
Problem: Create a simple Grade 4 example about Choosing an efficient strategy using the numbers 18 and 16.
- 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 Choosing an efficient strategy.
Worked Example 9
Problem: Create a simple Grade 4 example about Choosing an efficient strategy using the numbers 18 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 Choosing an efficient strategy.
Worked Example 10
Problem: Create a simple Grade 4 example about Choosing an efficient strategy using the numbers 20 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 Choosing an efficient strategy.
Practice Exercise
Create and solve one new example of Choosing an efficient 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.
30 Review Questions and Answers
Q1. What is important to understand about Using equal groups?
Answer: Using equal groups is an important Grade 4 mathematics idea in Two-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 Using arrays?
Answer: Using arrays is an important Grade 4 mathematics idea in Two-Digit by One-Digit Multiplication. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q3. What is important to understand about Using area models?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q4. What is important to understand about Breaking apart the two-digit factor?
Answer: Place value tells how much a digit is worth because of its position in the number.
Q5. 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.
Q6. What is important to understand about Distributive strategy?
Answer: A rate compares two quantities with different units, such as pages per day or items per box.
Q7. 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.
Q8. What is important to understand about Estimating a product?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q9. What is important to understand about Word problems?
Answer: Word problems is an important Grade 4 mathematics idea in Two-Digit by One-Digit Multiplication. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q10. What is important to understand about Measurement contexts?
Answer: Measurement contexts is an important Grade 4 mathematics idea in Two-Digit by One-Digit Multiplication. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q11. What is important to understand about Checking with division?
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 strategy?
Answer: A rate compares two quantities with different units, such as pages per day or items per box.
Q13. How would you explain Using equal groups?
Answer: Using equal groups is an important Grade 4 mathematics idea in Two-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 Using arrays?
Answer: Using arrays is an important Grade 4 mathematics idea in Two-Digit by One-Digit Multiplication. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q15. How would you explain Using area models?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q16. How would you explain Breaking apart the two-digit factor?
Answer: Place value tells how much a digit is worth because of its position in the number.
Q17. How would you explain Partial products?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q18. How would you explain Distributive strategy?
Answer: A rate compares two quantities with different units, such as pages per day or items per box.
Q19. How would you explain Standard multiplication algorithm?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q20. How would you explain Estimating a product?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q21. How would you explain Word problems?
Answer: Word problems is an important Grade 4 mathematics idea in Two-Digit by One-Digit Multiplication. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q22. How would you explain Measurement contexts?
Answer: Measurement contexts is an important Grade 4 mathematics idea in Two-Digit by One-Digit Multiplication. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q23. How would you explain Checking with division?
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 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 Using equal groups?
Answer: Using equal groups is an important Grade 4 mathematics idea in Two-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 Using arrays?
Answer: Using arrays is an important Grade 4 mathematics idea in Two-Digit by One-Digit Multiplication. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q27. What should a beginner check when working with Using area models?
Answer: Data are collected to answer questions. Organize them clearly, choose a suitable display, and explain what the evidence shows.
Q28. What should a beginner check when working with Breaking apart the two-digit factor?
Answer: Place value tells how much a digit is worth because of its position in the number.
Q29. 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.
Q30. What should a beginner check when working with Distributive strategy?
Answer: A rate compares two quantities with different units, such as pages per day or items per box.