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

Lesson 2.122.12 Small Group · Group 2

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, explain why the method works, and use it on a problem I have not seen before.

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.

A bead is 0.08 inch wide. A smaller bead is 0.5 times as wide. How wide is the smaller bead? Find 0.5 × 0.08.

  1. Multiply like whole numbers: 5 × 8 = 40
  2. Add the decimal places in both factors: 1 + 2 = 3
  3. Write a zero in front to get 3 places: 40 → 0.040
  4. Drop the zero at the end: 0.040 = 0.04
  5. Check the size of the answer: 0.04 < 0.08
  6. The smaller bead is 0.04 inch wide.

Now you trySame steps, your turn

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

Multiply 0.4 × 0.7.

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 2.122.12 Small Group · Group 2

Group 2Challenge 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, explain why the method works, and use it on a problem I have not seen before.

Part 1Practice the skillshow every step
  1. 1Complete each step, then write the final answer.

    Find 0.08 × 0.6.

    Show your work
    Final answer:
  2. 2Complete each step, then write the final answer.

    Find 1.25 × 0.4.

    Show your work
    Final answer:
Part 2Apply itreal-world problems
  1. 3Complete each step, then write the final answer.
    00.0020.0040.0060.0080.010.0120.0140.0160.0180.020.02
    0.3 of 0.02 is a small part of 0.02.

    Multiply 0.3 × 0.02.

    1. 1Multiply like whole numbers. What is 3 × 2?
    2. 2How many decimal places are in both factors together?
    3. 36 has only 1 digit. Write zeros in front. What is the product?
    Final answer:
  2. 4Complete each step, then write the final answer.
    0.621.20.50.3
    Add the two parts to check the product.

    Multiply 2.5 × 0.6.

    1. 1Multiply 25 × 6. Then count the decimal places in both factors.
    2. 2Place the point in 150. What is the product?
    3. 3Why must you place the point before you drop the zero?
    Final answer:
  3. 5Complete each step, then write the final answer.
    Meters16.2Cost ($)3.45?× ?× ?

    Wire costs $3.45 per meter. The crew needs 6.2 meters. What is the total cost?

    Show your work
    Final answer:
  4. 6Complete each step, then write the final answer.

    Ana says 4.8 × 0.25 is 12. Use an estimate to decide if she is right. What is the correct product?

    Show your work
    Final answer:

Explain your thinkingIs the product of two decimals always less than both factors? Use 0.3 × 0.02 and 2.5 × 0.6 to explain.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

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