Introduction
Multiplying by Multiples of 10 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 multiplying by multiples of 10.
What Is Multiplying by Multiples of 10?
Multiplying by Multiples of 10 means understanding equal groups, arrays, and repeated addition as multiplication.
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 Multiplying by Multiples of 10
Before solving, students should slow down and decide what each number, shape, unit, or label represents.
- Name the equal groups before choosing an operation.
- Use arrays, repeated addition, or related facts to explain the work.
- Connect multiplication and division as inverse operations.
- Check that the answer fits the story problem.
Visual Models
Visual Model 1
Question: How many stars are there? Skip count by \(10\)s to find the total.
- A. \(13\)
- B. \(103\)
- C. \(31\)
- D. \(30\)
Why it works: Skip count by \(10\)s: \(10, 20, 30\). There are \(3\) groups of \(10\) stars, so \(3\times10=30\) stars total.
Answer: \(30\)
Visual Model 2
Question: This array has \(2\) rows. Each row has \(50\) squares. How many squares in total?
- A. \(52\)
- B. \(25\)
- C. \(100\)
- D. \(1000\)
Why it works: \(2\) rows of \(50\) squares \(= 2\times50=100\) squares. Multiply \(2\times5=10\), then multiply by \(10\) to get \(100\).
Answer: \(100\)
Worked Examples
Example 1
Question: Sam has \(8\) groups of \(10\) stickers. How many stickers does Sam have in total?
| Tens | Ones |
|---|---|
| 08 | 00 |
- A. \(18\)
- B. \(108\)
- C. \(810\)
- D. \(80\)
- \(8\) groups of \(10 = 8 \times 10 = 80\) stickers.
- The place-value chart shows 8 tens and 0 ones, which equals 80.
Answer: \(80\)
Example 2
Question: Look at this number bond. What value should replace the question mark?
- A. \(6\); divide by \(10\)
- B. \(600\); multiply by \(10\)
- C. \(60\); add
- D. \(10\); multiply
- \(60 = 6 \times 10\).
- The number bond shows that \(60\) can be decomposed into \(6\) and another factor; that factor is \(10\).
- You multiply \(6\times10\) to get \(60\).
Answer: \(10\); multiply
Example 3
Question: There are \(4\) rows of apples. Each row has \(10\) apples. How many apples are there?
- A. \(14\)
- B. \(401\)
- C. \(410\)
- D. \(40\)
- The array shows 4 rows with 10 apples each: \(4\times10=40\) apples.
Answer: \(40\)
Real-World Word Problems
Problem 1
Question: Noah buys \(7\) packs of pencils. Each pack has \(10\) pencils. How many pencils does Noah buy?
- A. \(17\)
- B. \(701\)
- C. \(710\)
- D. \(70\)
Why it works: \(7\) packs of \(10\) pencils \(= 7 \times 10 = 70\) pencils.
Answer: \(70\)
Problem 2
Question: Lily buys \(3\) packages of toy cars. Each package has \(40\) toy cars. How many toy cars does Lily buy?
- A. \(34\)
- B. \(43\)
- C. \(120\)
- D. \(1200\)
Why it works: \(3\) packages of \(40\) cars \(= 3 \times 40 = 120\) cars. Multiply \(3\times4=12\), then add one zero.
Answer: \(120\)
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 is \(6\times40\)? Show your thinking: \(6\times40 = 6\times(4\times10) = (6\times4)\times10\).
- A. \(46\)
- B. \(64\)
- C. \(240\)
- D. \(2400\)
Question 2
Which repeated addition matches \(5\times10\)?
- A. \(5+5+5\)
- B. \(10+5\)
- C. \(10+10+10+10+10\)
- D. \(5+10\)
Question 3
Quinn calculated \(7\times30\) and got \(710\). What error did Quinn make?
- A. Quinn forgot to multiply at all.
- B. Quinn wrote the zero in the wrong place.
- C. Quinn multiplied correctly but added an extra zero.
- D. Quinn wrote down the digits \(7\) and \(30\) instead of multiplying them.
Question 4
Which shows why \(4\times20\) equals \(80\)?
- A. \((4+2) \times 10 = 60\)
- B. \(4 + 2 + 10 = 16\)
- C. \(4 \times (2+10) = 48\)
- D. \((4\times2) \times 10 = 8 \times 10 = 80\)
Question 5
What is \(9\times30\)?
- A. \(27\) (forgot to add zero)
- B. \(2700\) (added two zeros)
- C. \(270\)
- D. \(39\) (added instead of multiplying)
Question 6
Ava makes \(5\) sets of picture cards. Each set has \(20\) cards. How many cards does Ava make?
- A. \(25\)
- B. \(52\)
- C. \(100\)
- D. \(1000\)
Full Answer Explanations Click to show all answers and explanations
Question 1
Answer: \(240\)
Multiply \(6\times4=24\), then multiply by \(10\) to get \(240\): \(6\times40 = 24\times10 = 240\). You decompose \(40\) as \(4\times10\), then use the associative property.
Question 2
Answer: \(10+10+10+10+10=50\)
\(5\times10\) means \(5\) groups of \(10\), which is the same as adding \(10\) five times: \(10+10+10+10+10=50\). This shows that multiplication is repeated addition.
Question 3
Answer: Digit concatenation error
\(7\times30=210\) (multiply \(7\times3=21\), then multiply by \(10\)). Quinn wrote \(7\) and \(30\) together as \(730\) instead. The correct answer is \(210\).
Question 4
Answer: \((4\times2) \times 10 = 80\)
\(4\times20 = 4\times(2\times10) = (4\times2)\times10 = 8\times10 = 80\). This uses associative property: you break \(20\) into \(2\times10\), multiply the single digits first, then multiply by \(10\).
Question 5
Answer: \(270\)
Multiply \(9\times3=27\), then multiply by \(10\): \(9\times30=270\). Add exactly one zero—not zero zeros, and not two zeros.
Question 6
Answer: \(100\)
\(5\) sets of \(20\) cards \(= 5 \times 20 = 100\) cards. Multiply \(5\times2=10\), then add one zero.
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
Multiplying by Multiples of 10 becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
GOLDEN RULE
Equal groups make multiplication make sense.
