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

Lesson 2.11Add and Subtract Decimals

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can add and subtract decimals by lining up the place values and the decimal points.

Start hereWords for this lesson

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

WordWhat it meansExample
DecimalSpanish: Decimal A number with a dot, like 0.5, that shows a part less than one. 3.75 means 3 ones + 7 tenths + 5 hundredths — it is between 3 and 4
Place valueSpanish: Valor posicional What a digit is worth based on where it sits in a number. In 4.38: the 4 = 4 ones, the 3 = 3 tenths (0.3), the 8 = 8 hundredths (0.08)
TenthsSpanish: Décimas The first spot after the decimal point. It shows parts out of 10. 0.7 = 7/10 — like 7 slices of a pizza cut into 10 equal slices
HundredthsSpanish: Centésimas The second spot after the decimal point. It shows parts out of 100. 0.05 = 5/100 — like 5 pennies out of a dollar (100 pennies)
Annex zerosSpanish: Agregar ceros Adding zeros at the end of a decimal so numbers line up evenly. 15.7 becomes 15.70 so you can subtract 15.70 − 8.36 with aligned place values

How it worksWorked example

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

The tank has 128.75 liters. A shuttle adds 46.8 liters. I line up the decimal points and annex a zero: 46.80.

  1. I add: 128.75 + 46.80 = 175.55 liters.
  2. Now the thrusters use 19.35 liters, so I subtract: 175.55 − 19.35 = 156.20.
  3. The final fuel level is 156.20 liters. I check with estimation: about 130 + 47 − 19 = 158, which 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 add 12.45 and 7.8. First, how do we write 7.8 with two decimal places? (7.80.)

Answer:

Say it and write itSentence starters

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

  • When I add to , I move to the right on the number line and land on .

Word bank DecimalPlace valueTenthsHundredthsAnnex zerosdecimalplace valueline uptenthshundredthsrightleft

Watch outA common mistake

A common mistake in Add and Subtract Decimals is lining up the last digits (the right edges) of each number instead of lining up the decimal points — for example, adding 8.3 and 2.45 as if the 3 and the 5 belong in the same column. Before you add or subtract, add zeros so every number has the same number of decimal places (write 8.3 as 8.30), then check that the decimal points sit directly above one another.

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

Lesson 2.11Add and Subtract Decimals

Version ASupported practice

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

Learning target I can add and subtract decimals by lining up the place values and the decimal points.

Part 1Understand the ideamodels and meaning
  1. 1Mark and label each value on the number line.

    Show 6.5 − 2.8 and 3.25 + 1.5 on the number line

    012345678

    Hint Each label shows an operation — work out the value first, then find that exact spot between the whole numbers.

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

    What is 14.6 + 3.85?

    1. A17.45
    2. B18.35
    3. C18.45
    4. D18.55

    Hint Notice the mismatch: 14.6 has one decimal place but 3.85 has two. Lining up the POINTS is the whole trick here.

    Line up the place values
    1. 1Line upPoints under points.
    2. 2Fill gapsWrite in the zeros.
    3. 3OperateRight to left.
    4. 4Bring the point downStraight down.
  2. 3Circle the letter of the best answer. Show how you know.

    What is 9.05 + 4.7?

    1. A13.12
    2. B13.57
    3. C13.75
    4. D14.75

    Hint Watch the middle zero in 9.05 and the missing hundredths in 4.7 — align the decimal POINTS, never the last digits.

    Line up the place values
    1. 1Line upPoints under points.
    2. 2Fill gapsWrite in the zeros.
    3. 3OperateRight to left.
    4. 4Bring the point downStraight down.
Part 3Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    What is 20.3 − 7.48?

    1. A12.18
    2. B12.82
    3. C12.92
    4. D13.82

    Hint 20.3 stops at the tenths but 7.48 has hundredths — you can't subtract from an empty column until you annex a zero.

    Line up the place values
    1. 1Line upPoints under points.
    2. 2Fill gapsWrite in the zeros.
    3. 3OperateRight to left.
    4. 4Bring the point downStraight down.
  2. 5Circle the letter of the best answer. Show how you know.

    What is 50 − 23.47?

    1. A26.53
    2. B26.63
    3. C27.47
    4. D27.53

    Hint 50 is a whole number but 23.47 has hundredths — you'll need to give 50 decimal places before you can subtract.

    Line up the place values
    1. 1Line upPoints under points.
    2. 2Fill gapsWrite in the zeros.
    3. 3OperateRight to left.
    4. 4Bring the point downStraight down.
Part 4Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Mistake — Missing Annex Zero

    1. 1ProblemAdd 8.3 + 2.45
    2. 2Set upLined up the right edges so the 3 sits under the 5
    3. 3Add8.3 + 2.45 = 8.75
    4. 4Final answer8.75

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

    Hint Check the Set up step. Are the decimal points lined up, or just the last digits on the right?

    Correct work
    Correct answer:

Explain your thinkingHow does a number line help you see what happens when you add or subtract decimals?

Sentence starter When I add ___ to ___, I move ___ to the right on the number line and land on ___.

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 2.11Add and Subtract Decimals

Version BCore practice

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

Learning target I can add and subtract decimals by lining up the place values and the decimal points.

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

    Compute each decimal sum or difference.

    ProblemAnswer
    5.63 + 2.7
    12.4 − 8.56
    9.08 + 4.925
    25.1 − 13.47
    7.006 + 3.94
    Show your work
  2. 2Write the name of the correct group on each line.

    Round each number to the nearest whole number to estimate the sum or difference. If the estimate equals 10, calculate the exact result before sorting. Sort by whether the actual result is greater than or less than 10.

    Groups: Result Greater Than 10 Result Less Than 10
    • 7.8 + 3.45
    • 6.25 + 5.9
    • 15.3 − 4.7
    • 8.4 − 2.15
    • 5.6 + 3.82
    • 12.1 − 4.95
  3. 3Write the letter of the matching item on each line.

    Match each expression to its answer.

    1. 8.5 + 3.75
    2. 15.2 − 6.8
    3. 4.06 + 7.94
    4. 20 − 13.45
    5. 9.99 + 0.01
    6. 11.3 − 4.8
    • A12.25
    • B8.4
    • C12
    • D6.55
    • E10
    • F6.5
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    A student buys items costing $4.59, $12.75, and $3.80. What is the total cost?

    1. A$20.14
    2. B$21.04
    3. C$21.14
    4. D$21.24
    Show your work
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Mistake — Subtracting Without a Placeholder

    1. 1ProblemSubtract 12.5 − 3.45
    2. 2Set upLeft 12.5 as one decimal place instead of annexing a zero
    3. 3Subtract12.5 − 3.45 = 9.5
    4. 4Final answer9.5

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

    Correct work
    Correct answer:

Explain your thinkingHow does a number line help you see what happens when you add or subtract decimals?

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 2.11Add and Subtract Decimals

ChallengeExtension

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

Learning target I can add and subtract decimals by lining up the place values and the decimal points.

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

    Find the missing number in each equation.

    EquationMissing Number
    4.7 + ___ = 10
    ___ − 3.85 = 6.15
    8.06 + ___ = 15
    Show your work
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find Tasha's Mistake

    1. 1Problem15.7 − 8.36
    2. 2Set up15.7 − 8.36
    3. 3Subtract15.7 − 8.36 = 7.41
    4. 4Final answer7.41

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

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

    A runner's lap times are 2.45 minutes, 2.6 minutes, and 2.38 minutes. Her personal record is 7.5 minutes total. Did she beat her record? Show all your work with decimal alignment and explain.

    Write your answer

Explain your thinkingHow does a number line help you see what happens when you add or subtract decimals?

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