Introduction
Unknown Number in Equations is an important Grade 3 math skill because students are moving from simple answers toward explaining how the math works.
In this lesson, students use models, real questions, worked examples, practice problems, and two online quizzes to build confidence with unknown number in equations.
What Is Unknown Number in Equations?
Unknown Number in Equations means using place value, operations, and equations to reason accurately with numbers.
The goal is not only to get the answer. Students should be able to show the idea, explain the strategy, and check whether the answer makes sense.
Understanding Unknown Number in Equations
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Read the question carefully and identify what is being asked.
- Choose a model, equation, table, or diagram that matches the situation.
- Solve one step at a time and keep units or labels attached.
- Use the answer explanation to check that the result makes sense.
Visual Models
Visual Model 1
Question: Look at the fact family: Which equation is part of this fact family?
| \(3\times8=24\) | \(8\times3=24\) |
|---|---|
| \(24\div3=8\) | \(24\div8=3\) |
- A. \(24\div 8 = 4\)
- B. \(24\div 4 = 8\)
- C. \(20\div 3 = 8\)
- D. \(24\div 3 = 8\)
Why it works: In this fact family, \(24\div3=8\). This is the division equation that matches the multiplication \(3\times8=24\).
Answer: \(24\div 3 = 8\)
Visual Model 2
Question: A bar shows 4 equal groups. Each group has 7 stickers. How many stickers are there in total?
- A. \(28\)
- B. \(25\)
- C. \(24\)
- D. \(30\)
Why it works: Multiply: \(4\times7=28\) stickers. The unknown is \(28\).
Answer: \(28\)
Worked Examples
Example 1
Question: A balance scale shows 3 equal weights on one side and 15 on the other. Each weight is the same. What is the unknown weight? \(\)\square\times3=15\(\)
- A. \(7\)
- B. \(6\)
- C. \(4\)
- D. \(5\)
- Divide: \(15\div3=5\).
- Each unknown weight is \(5\).
- Check: \(5\times3=15\).
Answer: \(5\)
Example 2
Question: Look at this array. It has 3 rows and \(\square\) columns. There are 21 dots in total. \(\)3\times\square=21\(\)
- A. \(9\)
- B. \(8\)
- C. \(6\)
- D. \(7\)
- Divide: \(21\div3=7\) columns.
- Check: \(3\times7=21\).
Answer: \(7\)
Example 3
Question: Look at the fact family table: If one factor is \(7\) and the product is \(42\), what is the other factor? \(\)7\times\square=42\(\)
| \(7\times6=42\) | \(6\times7=42\) |
|---|---|
| \(42\div7=6\) | \(42\div6=7\) |
- A. \(8\)
- B. \(7\)
- C. \(5\)
- D. \(6\)
- From the fact family, \(7\times6=42\).
Answer: \(6\)
Real-World Word Problems
Problem 1
Question: Ava has 6 bags of marbles. Each bag has the same number of marbles. She has 42 marbles in all. How many marbles are in each bag? \(\)6\times\square=42\(\)
- A. \(9\)
- B. \(6\)
- C. \(8\)
- D. \(7\)
Why it works: Divide: \(42\div6=7\) marbles per bag. Check: \(6\times7=42\).
Answer: \(7\)
Problem 2
Question: Ben saves $7 each week. After a certain number of weeks, he has saved $63. How many weeks did he save? \(\)\square\times 7=63\(\)
- A. \(10\)
- B. \(8\)
- C. \(7\)
- D. \(9\)
Why it works: Divide: \(63\div7=9\) weeks. Check: \(9\times 7=63\).
Answer: \(9\)
Common Mistakes
- Rushing before identifying what the numbers represent.
- Choosing an operation that does not match the situation.
- Dropping labels, units, or context from the answer.
- Skipping the estimate or reasonableness check.
Strategy Tips
- Underline the question being asked.
- Use a model before jumping to computation.
- Write an equation that matches the story or picture.
- Explain the final answer in a sentence.
Practice Questions
Question 1
What number makes the equation true? \(\)\square\times7=42\(\)
- A. \(8\)
- B. \(7\)
- C. \(5\)
- D. \(6\)
Question 2
What number makes the equation true? \(\)\square\times5=35\(\)
- A. \(9\)
- B. \(8\)
- C. \(6\)
- D. \(7\)
Question 3
What number makes the equation true? \(\)9\times\square=54\(\)
- A. \(8\)
- B. \(5\)
- C. \(7\)
- D. \(6\)
Question 4
What number makes the equation true? \(\)8\times\square=32\(\)
- A. \(4\)
- B. \(5\)
- C. \(6\)
- D. \(3\)
Question 5
What number makes the equation true? \(\)\square\times6=48\(\)
- A. \(10\)
- B. \(9\)
- C. \(7\)
- D. \(8\)
Question 6
What number makes the equation true? \(\)20\div4=\square\(\)
- A. \(4\)
- B. \(7\)
- C. \(6\)
- D. \(5\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(6\)
Think: \(42\div7=6\), so the unknown is \(6\). Check: \(6\times7=42\).
Question 2
Answer: \(7\)
Use the inverse: \(35\div5=7\). Check: \(7\times5=35\).
Question 3
Answer: \(6\)
Divide: \(54\div9=6\). Check: \(9\times6=54\).
Question 4
Answer: \(4\)
Think: \(32\div8=4\). Check: \(8\times4=32\).
Question 5
Answer: \(8\)
Divide: \(48\div6=8\). Check: \(8\times6=48\).
Question 6
Answer: \(5\)
Think: \(5\times4=20\), so \(20\div4=5\).
Connection to Standards
This lesson supports Grade 3 math expectations for reasoning, modeling, problem solving, and explaining answers clearly. It connects classroom skills to the kind of questions students see on state math assessments.
Summary
Unknown Number in Equations becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Understand the model before choosing the operation.
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