Visual Model 1
Question: A number line shows where a product lands. What point represents \(0.5 \times 8\)?
- A. \(2\)
- B. \(3\)
- C. \(4\)
- D. \(5\)
How the model helps: \(0.5 \times 8 = 4\), so the point belongs exactly at \(4\) on the number line.
CH03-02 lesson
Multiplying Decimals Learning Activity
A focused Grade 5 learning session for Multiplying Decimals using visual models, worked examples, strategy guidance, and a short mastery check.
- 18
- minutes
- 6
- lesson parts
- 11
- practice items
Students will multiply decimals using powers of ten, models, and whole-number reasoning.
Student goal: I can multiply decimals and explain where the decimal point belongs.
Helpful first:
Patterns with Powers of Ten
Multiplying Multi-Digit Whole Numbers
Learn the Idea
Multiplying Decimals is the Grade 5 skill of students multiply decimals to hundredths using strategies based on place value and properties of operations. They use area models and place value patterns to understand why the product has the total number of decimal places from both factors.
Which place values matter most, and how does the decimal point guide the work?
Strong understanding comes from naming what the numbers, shapes, units, or data values represent, then showing the idea with a model or clear steps before solving.
The key to this topic is understanding the structure behind the work, not just following a rule. Students should be able to talk through what is happening, point to a model, and explain why the answer makes sense.
- Name the place of each important digit before comparing or computing.
- Use place value patterns to explain what happens when values shift.
- Estimate first so the final answer can be checked for reasonableness.
- Use the topic language from class discussions: Students multiply decimals to hundredths using strategies based on place value and properties of operations. They use area models and place value patterns to understand why the product has the total number of decimal places from both factors.
See the Math
Follow a Worked Example
Example 1
Question: A number line shows division. If you divide 4.5 by 5, where does the quotient fall?
- A. Between 0 and 1
- B. Between 1 and 2
- C. Between 2 and 3
- D. Between 4 and 5
- \(4.5 \div 5 = 0.9\), which is between 0 and 1.
Answer: Between 0 and 1
Example 2
Question: Which model correctly shows \(0.6 \times 4\)?
- A. Option A
- B. Option B
- C. Neither model
- D. Both models
- \(0.6 \times 4\) means four groups of \(0.6\).
- Option A shows \(0.6\) four times, which is \(2.4\) in all.
Answer: Option A
Connect It to a Real Situation
Problem 1
Question: Maria buys 5 erasers at $0.75 each. How much does she spend?
- $3.25
- $3.50
- $3.75
- $4.00
Answer: $3.75
Why it works: Multiply \(5 \times 0.75 = 3.75\). Since \(0.75\) has 2 decimal places and 5 has 0, the product has 2 decimal places: $3.75.
Avoid Mistakes and Choose a Strategy
- Starting the computation before identifying what the numbers, units, or parts represent.
- Ignoring place value by lining up digits incorrectly instead of aligning decimal points or decimal places.
- Forgetting to estimate, which makes it easier to miss an unreasonable answer.
- Stopping at a number without explaining what the answer means in context.
- Read the situation slowly and name what each number or label represents.
- Use place value charts or aligned digits to keep the decimal meaning clear.
- Estimate first so you already know the answer's approximate size.
- Check the answer with an inverse operation, another representation, or a sentence explanation.
- Say the math idea out loud in simple words before writing the final answer.
Remember the Key Idea
Multiplying Decimals gets easier when students read the model, track what each number means, and explain why the answer fits the situation.
GOLDEN RULE
Name the place value first, then compute or compare with aligned digits.
Solve before opening the answer
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
warmup
2 questionsWhat is \(4.7 \times 10\)?
- A 0.47
- B 4.7
- C 47
- D 470
Check answer and explanation
Answer C: 47
Multiplying by 10 moves the decimal point 1 place to the right: \(4.7 \times 10 = 47\).
What is \(0.45 \times 10\)?
- A 0.045
- B 45
- C 4.5
- D 450
Check answer and explanation
Answer C: 4.5
Multiplying by 10 moves the decimal point 1 place to the right: \(0.45 \times 10 = 4.5\).
guided
1 questionWhat is \(0.45 \times 100\)?
- A 4.5
- B 450
- C 4500
- D 45
Check answer and explanation
Answer D: 45
Multiplying by 100 moves the decimal point 2 places to the right: \(0.45 \times 100 = 45\).
practice
5 questionsWhat is \(0.45 \times 1000\)?
- A 45
- B 450
- C 4500
- D 45000
Check answer and explanation
Answer B: 450
Multiplying by 1000 moves the decimal point 3 places to the right: \(0.45 \times 1000 = 450\).
The place-value chart shows a number. When multiplied by 10, the digit 3 moves from the tenths place to which place?
- A Thousandths
- B Tenths
- C Hundredths
- D Ones
Check answer and explanation
Answer D: Ones
Multiplying by 10 moves each digit one place to the left, so 3 moves from tenths to ones place.
What is \(2.13 \times 10\)?
- A 2.13
- B 213
- C 21.3
- D 2130
Check answer and explanation
Answer C: 21.3
Move the decimal point 1 place right: \(2.13 \times 10 = 21.3\).
Which expression equals 5.6?
- A \(0.56 \times 10\)
- B \(0.56 \times 100\)
- C \(56 \times 10\)
- D \(560 \times 10\)
Check answer and explanation
Answer A: \(0.56 \times 10\)
\(0.56 \times 10 = 5.6\) (decimal moves 1 place right).
Use the arrow diagram. How many places does the decimal point move when multiplying by \(10^2\)?
- A 1 place
- B 2 places
- C 3 places
- D 10 places
Check answer and explanation
Answer B: 2 places
\(10^2 = 100\); multiplying by 100 moves the decimal 2 places to the right.
exit
3 questionsWhat is \(0.08 \times 10\)?
- A 0.8
- B 0.008
- C 8
- D 80
Check answer and explanation
Answer A: 0.8
Move the decimal 1 place right: \(0.08 \times 10 = 0.8\).
A metric conversion: 1.5 meters \(=\) \_\_\_ centimeters. (There are 100 cm in 1 m, so multiply by 100.) Which is correct?
- A \(1.5 \times 10 = 15\) cm
- B \(1.5 \div 100 = 0.015\) cm
- C \(1.5 \times 1000 = 1500\) cm
- D \(1.5 \times 100 = 150\) cm
Check answer and explanation
Answer D: \(1.5 \times 100 = 150\) cm
To convert meters to centimeters, multiply by 100: \(1.5 \times 100 = 150\) cm.
What is \(3.6 \times 100\)?
- A 36
- B 3600
- C 360
- D 36000
Check answer and explanation
Answer C: 360
Multiply by 100: move decimal 2 places right: \(3.6 \times 100 = 360\).
