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.

Why This Matters The space station's main fuel tank reads 128.75 liters. A resupply shuttle delivers 46.8 liters of fuel, but the thrusters used 19.35 liters during docking. What is the fuel level after both events?

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 out!A 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

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

Lesson 2.11Add and Subtract Decimals

Level 0Most support · every hint printed

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.

Why This Matters The space station's main fuel tank reads 128.75 liters. A resupply shuttle delivers 46.8 liters of fuel, but the thrusters used 19.35 liters during docking. What is the fuel level after both events?

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.
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

    00.81.62.43.244.85.66.47.28
    Steps to try
    1. Each label shows an operation — work out the value first, then find that exact spot between the whole numbers.
    2. For 6.5 − 2.8: take away 2 first to reach 4.5, then remove the extra 0.8. For 3.25 + 1.5: add 1 first, then 0.5 more.
    3. Start with 6.5 − 2 = 4.5, then count back 8 tenths from 4.5 — notice you cross below 4. Place that mark, then build the sum the same way.
    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
    Steps to try
    1. Notice the mismatch: 14.6 has one decimal place but 3.85 has two. Lining up the POINTS is the whole trick here.
    2. Write 14.6 as 14.60 so both numbers show hundredths, stack the decimal points, and add column by column from the right.
    3. Set up 14.60 + 3.85 with the points stacked. Add the hundredths (0 + 5) first, then the tenths (6 + 8) — that column carries.
    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
    Steps to try
    1. Watch the middle zero in 9.05 and the missing hundredths in 4.7 — align the decimal POINTS, never the last digits.
    2. Write 4.7 as 4.70, stack the two numbers with the points lined up, then add each column starting from the right.
    3. Stack 9.05 over 4.70. Add hundredths (5 + 0), then tenths (0 + 7), then the ones — watch that last sum spill into a tens place.
    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
    Steps to try
    1. 20.3 stops at the tenths but 7.48 has hundredths — you can't subtract from an empty column until you annex a zero.
    2. Rewrite the problem as 20.30 − 7.48, stack the decimal points, and subtract right to left, borrowing when the top digit is smaller.
    3. Start at the hundredths: 0 − 8 doesn't work, so borrow from the tenths to make it 10 − 8. Keep borrowing leftward as needed.
    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.

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 ___.

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