Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.NOS.3

Lesson 2.12Multiply Decimals

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can multiply decimals and place the decimal point correctly in the product.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
ProductSpanish: Producto The answer when you multiply. 4 × 7 = 28, so the product is 28
Decimal pointSpanish: Punto decimal The dot that splits the whole number from the part after it. In 3.25, the decimal point separates 3 (ones) from 25 (tenths and hundredths)
EstimateSpanish: Estimar A close answer you get by rounding first. 3.7 × 4.2: round to 4 × 4 = 16, so the exact answer should be near 16
Place valueSpanish: Valor posicional What a digit is worth based on where it sits in a number. In 0.36: the 3 is in the tenths place (0.3) and the 6 is in the hundredths place (0.06)
Decimal placesSpanish: Cifras decimales How many digits come after the decimal point. 3.4 (1 place) × 2.6 (1 place) = 8.84 (2 places total)

How it worksWorked example

These numbers are not on your problems. The steps are. Follow them with your own numbers.

I want 4.5 × 12.60, the cost of 4.5 meters at $12.60 each.

  1. First I multiply without points, like whole numbers: 45 × 1260 = 56,700.
  2. Now I count decimal places: 4.5 has 1, and 12.60 has 2, so 1 + 2 = 3 decimal places.
  3. I put the point 3 places from the right in 56,700: that gives 56.700, or $56.70.
  4. I check with an estimate: 5 × $13 = $65, and $56.70 is close, so my answer is reasonable.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

Let's multiply 0.4 × 0.7. First multiply like whole numbers: what is 4 × 7? (28.)

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • I estimated x by rounding to x = , which told me the product is than 20.

Word bank ProductDecimal pointEstimatePlace valueDecimal placesestimaterounddecimal placesproductmultiplyreasonable

Watch outA common mistake

A common mistake in Multiply Decimals is counting decimal places from only one factor instead of adding the decimal places from BOTH factors. For example, in 0.4 × 0.06, a student multiplies 4 × 6 = 24, then places the decimal point using just one factor's place count (1 place), writing 0.24 instead of the correct answer: 0.4 has 1 decimal place and 0.06 has 2 decimal places, for a total of 3, so 24 becomes 0.024. Before you submit, count the decimal places in EACH factor separately and add them together — that total is how many decimal places belong in your final answer.

Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.NOS.3

Lesson 2.12Multiply Decimals

Version ASupported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can multiply decimals and place the decimal point correctly in the product.

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Multiply as whole numbers, then place the decimal point.

    ProblemWhole Number ProductTotal Decimal PlacesFinal Answer
    2.5 × 4
    1.2 × 0.3
    6.1 × 0.5

    Hint The columns show the whole strategy in order: whole-number product first, then count decimal places, then place the point.

    Show your work
Part 2Practice the skillshow every step
  1. 2Circle the letter of the best answer. Show how you know.

    What is 3.4 × 2.6?

    1. A0.884
    2. B8.48
    3. C8.84
    4. D88.4

    Hint Decimal multiplication is two jobs: multiply the digits, then place the point. Count the decimal places in BOTH factors first.

    Show each partial product, then add them
    1. 1SplitBreak one factor apart.
    2. 2MultiplyOne part at a time.
    3. 3AddAdd the parts.
  2. 3Circle the letter of the best answer. Show how you know.

    What is 0.7 × 1.5?

    1. A0.105
    2. B1.05
    3. C1.50
    4. D10.5

    Hint Both factors are close to 1, so expect an answer near 1 — a quick estimate protects you from decimal-point slips.

    Show each partial product, then add them
    1. 1SplitBreak one factor apart.
    2. 2MultiplyOne part at a time.
    3. 3AddAdd the parts.
  3. 4Circle the letter of the best answer. Show how you know.

    What is 5.3 × 4?

    1. A2.12
    2. B20.12
    3. C21.2
    4. D212

    Hint Only ONE factor has a decimal here: 5.3 has one place and 4 has none, so the product needs exactly one decimal place.

    Show each partial product, then add them
    1. 1SplitBreak one factor apart.
    2. 2MultiplyOne part at a time.
    3. 3AddAdd the parts.
Part 3Apply itreal-world problems
  1. 5Circle the letter of the best answer. Show how you know.

    Which estimate is closest to 4.8 × 3.2?

    1. A4 × 3 = 12
    2. B5 × 3 = 15
    3. C5 × 4 = 20
    4. D48 × 32 = 1,536

    Hint 'Estimate' means round each factor to its nearest whole number BEFORE multiplying — no exact work needed.

    Show your work
Part 4Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake — Counting Decimal Places

    1. 1Problem0.3 × 0.6
    2. 2Multiply as whole numbers3 × 6 = 18
    3. 3Count decimal places0.3 has 1 decimal place and 0.6 has 1 decimal place → 1 total
    4. 4Place the decimal pointMove the point 1 place in 18 to get 1.8

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Hint Add the decimal places in BOTH factors: how many does 0.3 have, and how many does 0.6 have?

    Correct work
    Correct answer:

Explain your thinkingHow did estimating by rounding help you sort the products? How do you decide where to place the decimal in the exact product?

Sentence starter I estimated ___ x ___ by rounding to ___ x ___ = ___, which told me the product is ___ than 20.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.NOS.3

Lesson 2.12Multiply Decimals

Version BCore practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can multiply decimals and place the decimal point correctly in the product.

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each expression to its product.

    1. 2.5 × 4
    2. 1.2 × 0.3
    3. 3.6 × 0.5
    4. 4.8 × 2.5
    5. 0.6 × 0.8
    6. 7.5 × 1.2
    • A10
    • B0.36
    • C1.8
    • D12
    • E0.48
    • F9
  2. 2Complete the table. Show how you found each value.

    Complete each decimal multiplication.

    ProblemProduct
    6.4 × 3.5
    0.25 × 0.4
    8.3 × 2.1
    12.5 × 0.8
    Show your work
  3. 3Write the name of the correct group on each line.

    Sort: when you multiply two decimals, is the product GREATER than both factors, or LESS than at least one factor?

    Groups: Product Greater Than Both Factors Product Less Than at Least One Factor
    • 3.5 × 4
    • 6 × 2.5
    • 10 × 1.5
    • 0.5 × 8
    • 0.3 × 0.4
    • 0.7 × 6
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    A car travels 55.5 miles per hour for 2.4 hours. How far does it go?

    1. A13.32 miles
    2. B57.9 miles
    3. C133.2 miles
    4. D1,332 miles
    per 1
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake — Placing the Decimal Point

    1. 1Problem1.5 × 2.4
    2. 2Multiply as whole numbers15 × 24 = 360
    3. 3Count decimal places1.5 has 1 decimal place and 2.4 has 1 decimal place → 2 total
    4. 4Place the decimal pointMove the point 2 places in 360 to get 0.36

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingHow did estimating by rounding help you sort the products? How do you decide where to place the decimal in the exact product?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help
Grade 6 Mathematics · Unit 2: Understanding the World Around Us Through StatisticsStandard 6.NOS.3

Lesson 2.12Multiply Decimals

ChallengeExtension

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can multiply decimals and place the decimal point correctly in the product.

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Find the missing factor.

    EquationMissing Factor
    ___ × 0.5 = 3.5
    2.4 × ___ = 7.2
    ___ × 1.5 = 4.5
    Show your work
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find Kai's Mistake

    1. 1Problem2.4 × 3.15
    2. 2Multiply as whole numbers24 × 315 = 7,560
    3. 3Count decimal places2.4 has 1 decimal place, 3.15 has 2 decimal places → 2 total
    4. 4Place decimal75.60

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    A driver buys 9.5 gallons of gas at $3.40 per gallon. Show how to find the total cost. Use estimation to check if your answer is reasonable.

    Write your answer

Explain your thinkingHow did estimating by rounding help you sort the products? How do you decide where to place the decimal in the exact product?

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help