Chapter 35: Solving Equations with Whole Numbers to 50
Learn Grade 4 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Solving Equations with Whole Numbers to 50 in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.
35.1 Addition equations
Addition combines quantities. Align place values, regroup when needed, and estimate first to predict a reasonable answer. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: Solve n + 2 = 5.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 3
Worked Example 2
Problem: Solve n + 4 = 17.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 13
Worked Example 3
Problem: Solve n + 4 = 6.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 2
Worked Example 4
Problem: Solve n + 1 = 4.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 3
Worked Example 5
Problem: Solve n + 3 = 13.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 10
Worked Example 6
Problem: Solve n + 5 = 18.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 13
Worked Example 7
Problem: Solve n + 9 = 21.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 12
Worked Example 8
Problem: Solve n + 10 = 21.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 11
Worked Example 9
Problem: Solve n + 3 = 7.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 4
Worked Example 10
Problem: Solve n + 3 = 5.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 2
Practice Exercise
Create and solve one new example of Addition equations. 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.
35.2 Subtraction equations
Subtraction finds what remains or the difference between quantities. Addition is a useful way to check. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.
Beginner Explanation
First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.
10 Worked Examples with Answers
Worked Example 1
Problem: Solve n + 3 = 5.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 2
Worked Example 2
Problem: Solve n + 2 = 5.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 3
Worked Example 3
Problem: Solve n + 9 = 20.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 11
Worked Example 4
Problem: Solve n + 6 = 11.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 5
Worked Example 5
Problem: Solve n + 4 = 19.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 15
Worked Example 6
Problem: Solve n + 10 = 12.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 2
Worked Example 7
Problem: Solve n + 6 = 14.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 8
Worked Example 8
Problem: Solve n + 4 = 18.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 14
Worked Example 9
Problem: Solve n + 6 = 8.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 2
Worked Example 10
Problem: Solve n + 8 = 13.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 5
Practice Exercise
Create and solve one new example of Subtraction equations. 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.
35.3 Multiplication equations
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 × 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 2
Problem: Calculate 11 × 9.
- 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: 99
Worked Example 3
Problem: Calculate 2 × 7.
- 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: 14
Worked Example 4
Problem: Calculate 11 × 9.
- 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: 99
Worked Example 5
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 6
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 7
Problem: Calculate 7 × 3.
- 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: 21
Worked Example 8
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 9
Problem: Calculate 6 × 9.
- 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: 54
Worked Example 10
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
Practice Exercise
Create and solve one new example of Multiplication equations. 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.
35.4 Division equations
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 28 ÷ 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: 7
Worked Example 2
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 3
Problem: Calculate 40 ÷ 9.
- 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: 4 remainder 4
Worked Example 4
Problem: Calculate 6 ÷ 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: 3
Worked Example 5
Problem: Calculate 26 ÷ 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: 8 remainder 2
Worked Example 6
Problem: Calculate 16 ÷ 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: 5 remainder 1
Worked Example 7
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 8
Problem: Calculate 14 ÷ 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: 7
Worked Example 9
Problem: Calculate 54 ÷ 5.
- 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: 10 remainder 4
Worked Example 10
Problem: Calculate 38 ÷ 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
Practice Exercise
Create and solve one new example of Division equations. 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.
35.5 Unknown on the left side
Unknown on the left side is an important Grade 4 mathematics idea in Solving Equations with Whole Numbers to 50. 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 Unknown on the left side using the numbers 6 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 Unknown on the left side.
Worked Example 2
Problem: Create a simple Grade 4 example about Unknown on the left side using the numbers 13 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 Unknown on the left side.
Worked Example 3
Problem: Create a simple Grade 4 example about Unknown on the left side using the numbers 12 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 Unknown on the left side.
Worked Example 4
Problem: Create a simple Grade 4 example about Unknown on the left side using the numbers 10 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 Unknown on the left side.
Worked Example 5
Problem: Create a simple Grade 4 example about Unknown on the left side using the numbers 14 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 Unknown on the left side.
Worked Example 6
Problem: Create a simple Grade 4 example about Unknown on the left side using the numbers 13 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 Unknown on the left side.
Worked Example 7
Problem: Create a simple Grade 4 example about Unknown on the left side using the numbers 10 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 Unknown on the left side.
Worked Example 8
Problem: Create a simple Grade 4 example about Unknown on the left side using the numbers 7 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 Unknown on the left side.
Worked Example 9
Problem: Create a simple Grade 4 example about Unknown on the left side 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 Unknown on the left side.
Worked Example 10
Problem: Create a simple Grade 4 example about Unknown on the left side using the numbers 14 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 Unknown on the left side.
Practice Exercise
Create and solve one new example of Unknown on the left side. 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.
35.6 Unknown on the right side
Unknown on the right side is an important Grade 4 mathematics idea in Solving Equations with Whole Numbers to 50. 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 Unknown on the right side using the numbers 10 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 Unknown on the right side.
Worked Example 2
Problem: Create a simple Grade 4 example about Unknown on the right side 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 Unknown on the right side.
Worked Example 3
Problem: Create a simple Grade 4 example about Unknown on the right side using the numbers 9 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 Unknown on the right side.
Worked Example 4
Problem: Create a simple Grade 4 example about Unknown on the right side using the numbers 17 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 Unknown on the right side.
Worked Example 5
Problem: Create a simple Grade 4 example about Unknown on the right side using the numbers 7 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 Unknown on the right side.
Worked Example 6
Problem: Create a simple Grade 4 example about Unknown on the right side using the numbers 9 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 Unknown on the right side.
Worked Example 7
Problem: Create a simple Grade 4 example about Unknown on the right side 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 Unknown on the right side.
Worked Example 8
Problem: Create a simple Grade 4 example about Unknown on the right side using the numbers 7 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 Unknown on the right side.
Worked Example 9
Problem: Create a simple Grade 4 example about Unknown on the right side 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 Unknown on the right side.
Worked Example 10
Problem: Create a simple Grade 4 example about Unknown on the right side using the numbers 7 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 Unknown on the right side.
Practice Exercise
Create and solve one new example of Unknown on the right side. 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.
35.7 Using inverse operations
Using inverse operations is an important Grade 4 mathematics idea in Solving Equations with Whole Numbers to 50. 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 inverse operations using the numbers 11 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 inverse operations.
Worked Example 2
Problem: Create a simple Grade 4 example about Using inverse operations using the numbers 6 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 Using inverse operations.
Worked Example 3
Problem: Create a simple Grade 4 example about Using inverse operations using the numbers 3 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 inverse operations.
Worked Example 4
Problem: Create a simple Grade 4 example about Using inverse operations using the numbers 6 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 inverse operations.
Worked Example 5
Problem: Create a simple Grade 4 example about Using inverse operations using the numbers 6 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 inverse operations.
Worked Example 6
Problem: Create a simple Grade 4 example about Using inverse operations 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 Using inverse operations.
Worked Example 7
Problem: Create a simple Grade 4 example about Using inverse operations using the numbers 9 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 Using inverse operations.
Worked Example 8
Problem: Create a simple Grade 4 example about Using inverse operations 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 Using inverse operations.
Worked Example 9
Problem: Create a simple Grade 4 example about Using inverse operations using the numbers 19 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 inverse operations.
Worked Example 10
Problem: Create a simple Grade 4 example about Using inverse operations using the numbers 16 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 inverse operations.
Practice Exercise
Create and solve one new example of Using inverse operations. 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.
35.8 Using models to solve equations
Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal. 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: Solve n + 5 = 12.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 7
Worked Example 2
Problem: Solve n + 1 = 3.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 2
Worked Example 3
Problem: Solve n + 6 = 13.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 7
Worked Example 4
Problem: Solve n + 3 = 15.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 12
Worked Example 5
Problem: Solve n + 1 = 14.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 13
Worked Example 6
Problem: Solve n + 10 = 20.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 10
Worked Example 7
Problem: Solve n + 6 = 13.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 7
Worked Example 8
Problem: Solve n + 1 = 16.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 15
Worked Example 9
Problem: Solve n + 2 = 8.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 6
Worked Example 10
Problem: Solve n + 1 = 13.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 12
Practice Exercise
Create and solve one new example of Using models to solve equations. 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.
35.9 Guess check and improve
Guess check and improve is an important Grade 4 mathematics idea in Solving Equations with Whole Numbers to 50. 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 Guess check and improve using the numbers 18 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 Guess check and improve.
Worked Example 2
Problem: Create a simple Grade 4 example about Guess check and improve using the numbers 3 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 Guess check and improve.
Worked Example 3
Problem: Create a simple Grade 4 example about Guess check and improve 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 Guess check and improve.
Worked Example 4
Problem: Create a simple Grade 4 example about Guess check and improve 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 Guess check and improve.
Worked Example 5
Problem: Create a simple Grade 4 example about Guess check and improve using the numbers 15 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 Guess check and improve.
Worked Example 6
Problem: Create a simple Grade 4 example about Guess check and improve using the numbers 7 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 Guess check and improve.
Worked Example 7
Problem: Create a simple Grade 4 example about Guess check and improve 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 Guess check and improve.
Worked Example 8
Problem: Create a simple Grade 4 example about Guess check and improve 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 Guess check and improve.
Worked Example 9
Problem: Create a simple Grade 4 example about Guess check and improve using the numbers 9 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 Guess check and improve.
Worked Example 10
Problem: Create a simple Grade 4 example about Guess check and improve using the numbers 17 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 Guess check and improve.
Practice Exercise
Create and solve one new example of Guess check and improve. 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.
35.10 Verifying by substitution
Verifying by substitution is an important Grade 4 mathematics idea in Solving Equations with Whole Numbers to 50. 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 Verifying by substitution using the numbers 18 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 Verifying by substitution.
Worked Example 2
Problem: Create a simple Grade 4 example about Verifying by substitution using the numbers 12 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 Verifying by substitution.
Worked Example 3
Problem: Create a simple Grade 4 example about Verifying by substitution using the numbers 13 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 Verifying by substitution.
Worked Example 4
Problem: Create a simple Grade 4 example about Verifying by substitution 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 Verifying by substitution.
Worked Example 5
Problem: Create a simple Grade 4 example about Verifying by substitution using the numbers 3 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 Verifying by substitution.
Worked Example 6
Problem: Create a simple Grade 4 example about Verifying by substitution using the numbers 18 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 Verifying by substitution.
Worked Example 7
Problem: Create a simple Grade 4 example about Verifying by substitution using the numbers 20 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 Verifying by substitution.
Worked Example 8
Problem: Create a simple Grade 4 example about Verifying by substitution using the numbers 2 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 Verifying by substitution.
Worked Example 9
Problem: Create a simple Grade 4 example about Verifying by substitution 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 Verifying by substitution.
Worked Example 10
Problem: Create a simple Grade 4 example about Verifying by substitution using the numbers 12 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 Verifying by substitution.
Practice Exercise
Create and solve one new example of Verifying by substitution. 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.
35.11 Equation word problems
Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal. 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: Solve n + 3 = 8.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 5
Worked Example 2
Problem: Solve n + 5 = 15.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 10
Worked Example 3
Problem: Solve n + 9 = 19.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 10
Worked Example 4
Problem: Solve n + 7 = 11.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 4
Worked Example 5
Problem: Solve n + 9 = 12.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 3
Worked Example 6
Problem: Solve n + 9 = 21.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 12
Worked Example 7
Problem: Solve n + 9 = 14.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 5
Worked Example 8
Problem: Solve n + 1 = 14.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 13
Worked Example 9
Problem: Solve n + 9 = 13.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 4
Worked Example 10
Problem: Solve n + 2 = 15.
- Use the inverse operation.
- Subtract the same number from both sides.
Very beginner explanation: The solution makes both sides of the equation equal.
Answer: n = 13
Practice Exercise
Create and solve one new example of Equation 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.
35.12 Explaining why a solution is true
Explaining why a solution is true is an important Grade 4 mathematics idea in Solving Equations with Whole Numbers to 50. 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 Explaining why a solution is true 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 Explaining why a solution is true.
Worked Example 2
Problem: Create a simple Grade 4 example about Explaining why a solution is true using the numbers 11 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 Explaining why a solution is true.
Worked Example 3
Problem: Create a simple Grade 4 example about Explaining why a solution is true using the numbers 16 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 Explaining why a solution is true.
Worked Example 4
Problem: Create a simple Grade 4 example about Explaining why a solution is true 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 Explaining why a solution is true.
Worked Example 5
Problem: Create a simple Grade 4 example about Explaining why a solution is true using the numbers 20 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 Explaining why a solution is true.
Worked Example 6
Problem: Create a simple Grade 4 example about Explaining why a solution is true using the numbers 12 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 Explaining why a solution is true.
Worked Example 7
Problem: Create a simple Grade 4 example about Explaining why a solution is true using the numbers 16 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 Explaining why a solution is true.
Worked Example 8
Problem: Create a simple Grade 4 example about Explaining why a solution is true using the numbers 12 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 Explaining why a solution is true.
Worked Example 9
Problem: Create a simple Grade 4 example about Explaining why a solution is true using the numbers 16 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 Explaining why a solution is true.
Worked Example 10
Problem: Create a simple Grade 4 example about Explaining why a solution is true using the numbers 3 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 Explaining why a solution is true.
Practice Exercise
Create and solve one new example of Explaining why a solution is true. 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 Addition equations?
Answer: Addition combines quantities. Align place values, regroup when needed, and estimate first to predict a reasonable answer.
Q2. What is important to understand about Subtraction equations?
Answer: Subtraction finds what remains or the difference between quantities. Addition is a useful way to check.
Q3. What is important to understand about Multiplication equations?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q4. What is important to understand about Division equations?
Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.
Q5. What is important to understand about Unknown on the left side?
Answer: Unknown on the left side is an important Grade 4 mathematics idea in Solving Equations with Whole Numbers to 50. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q6. What is important to understand about Unknown on the right side?
Answer: Unknown on the right side is an important Grade 4 mathematics idea in Solving Equations with Whole Numbers to 50. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q7. What is important to understand about Using inverse operations?
Answer: Using inverse operations is an important Grade 4 mathematics idea in Solving Equations with Whole Numbers to 50. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q8. What is important to understand about Using models to solve equations?
Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.
Q9. What is important to understand about Guess check and improve?
Answer: Guess check and improve is an important Grade 4 mathematics idea in Solving Equations with Whole Numbers to 50. 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 Verifying by substitution?
Answer: Verifying by substitution is an important Grade 4 mathematics idea in Solving Equations with Whole Numbers to 50. 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 Equation word problems?
Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.
Q12. What is important to understand about Explaining why a solution is true?
Answer: Explaining why a solution is true is an important Grade 4 mathematics idea in Solving Equations with Whole Numbers to 50. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q13. How would you explain Addition equations?
Answer: Addition combines quantities. Align place values, regroup when needed, and estimate first to predict a reasonable answer.
Q14. How would you explain Subtraction equations?
Answer: Subtraction finds what remains or the difference between quantities. Addition is a useful way to check.
Q15. How would you explain Multiplication equations?
Answer: Multiplication combines equal groups. Arrays, place value, known facts, and breaking apart numbers can all help.
Q16. How would you explain Division equations?
Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.
Q17. How would you explain Unknown on the left side?
Answer: Unknown on the left side is an important Grade 4 mathematics idea in Solving Equations with Whole Numbers to 50. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q18. How would you explain Unknown on the right side?
Answer: Unknown on the right side is an important Grade 4 mathematics idea in Solving Equations with Whole Numbers to 50. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q19. How would you explain Using inverse operations?
Answer: Using inverse operations is an important Grade 4 mathematics idea in Solving Equations with Whole Numbers to 50. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q20. How would you explain Using models to solve equations?
Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.
Q21. How would you explain Guess check and improve?
Answer: Guess check and improve is an important Grade 4 mathematics idea in Solving Equations with Whole Numbers to 50. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q22. How would you explain Verifying by substitution?
Answer: Verifying by substitution is an important Grade 4 mathematics idea in Solving Equations with Whole Numbers to 50. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q23. How would you explain Equation word problems?
Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.
Q24. How would you explain Explaining why a solution is true?
Answer: Explaining why a solution is true is an important Grade 4 mathematics idea in Solving Equations with Whole Numbers to 50. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q25. What should a beginner check when working with Addition equations?
Answer: Addition combines quantities. Align place values, regroup when needed, and estimate first to predict a reasonable answer.
Q26. What should a beginner check when working with Subtraction equations?
Answer: Subtraction finds what remains or the difference between quantities. Addition is a useful way to check.
Q27. What should a beginner check when working with Multiplication equations?
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 Division equations?
Answer: Division means sharing equally or finding equal groups. Multiplication can be used to check the result.
Q29. What should a beginner check when working with Unknown on the left side?
Answer: Unknown on the left side is an important Grade 4 mathematics idea in Solving Equations with Whole Numbers to 50. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.
Q30. What should a beginner check when working with Unknown on the right side?
Answer: Unknown on the right side is an important Grade 4 mathematics idea in Solving Equations with Whole Numbers to 50. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.