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.

Why This Matters The station needs 4.5 meters of heat shielding that costs $12.60 per meter. Commander Diaz needs to calculate the total cost before submitting the supply order. What is the total cost of the shielding?

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 out!A 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

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

Lesson 2.12Multiply Decimals

Level 0Most support · every hint printed

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.

Why This Matters The station needs 4.5 meters of heat shielding that costs $12.60 per meter. Commander Diaz needs to calculate the total cost before submitting the supply order. What is the total cost of the shielding?

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.
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
    Steps to try
    1. The columns show the whole strategy in order: whole-number product first, then count decimal places, then place the point.
    2. Count decimal places across BOTH factors: 1.2 × 0.3 has 1 + 1 = 2 places, so its product needs two decimal digits.
    3. Row 1: multiply 25 × 4 ignoring the point, then count the decimal places in 2.5 × 4 (just one) and shift the point once.
    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
    Steps to try
    1. Decimal multiplication is two jobs: multiply the digits, then place the point. Count the decimal places in BOTH factors first.
    2. Multiply 34 × 26 as whole numbers, then give the product one decimal place for each factor — two places in total.
    3. Compute 34 × 26 by splitting it: 34 × 20 plus 34 × 6. Then move the decimal point two places left in that product.
    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
    Steps to try
    1. Both factors are close to 1, so expect an answer near 1 — a quick estimate protects you from decimal-point slips.
    2. Multiply 7 × 15 first, ignoring the points, then count the decimal places in 0.7 and 1.5 to place the point.
    3. Compute 7 × 15. Then count one decimal place from each factor — two total — and shift the point that many spots left.
    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
    Steps to try
    1. Only ONE factor has a decimal here: 5.3 has one place and 4 has none, so the product needs exactly one decimal place.
    2. Multiply 53 × 4 as whole numbers, then place the decimal so the answer shows one decimal place.
    3. Estimate to check yourself: 5.3 is close to 5, and 5 × 4 = 20 — so your final answer should land near 20.
    Show each partial product, then add them
    1. 1SplitBreak one factor apart.
    2. 2MultiplyOne part at a time.
    3. 3AddAdd the parts.

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.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help