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

Lesson 2.112.11 Small Group · Group 2

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, 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
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.

A water tank holds 30 liters. The crew uses 12.46 liters. How many liters are left?

  1. Write 30 with a decimal point and two zeros: 30 = 30.00
  2. Line up the decimal points: 30.00 − 12.46
  3. Regroup across the zeros: 30.00 → 2 tens, 9 ones, 9 tenths, 10 hundredths
  4. Subtract each column from right to left: 30.00 − 12.46 = 17.54
  5. Check by adding: 17.54 + 12.46 = 30.00
  6. 17.54 liters are left.

Now you trySame steps, your turn

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

Add 12.45 and 7.8.

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 2.112.11 Small Group · Group 2

Group 2Challenge 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, 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.
    TensOnes.TenthsHundredths
    7.50
    +12.38
    +0.90
    =??.??
    Three numbers, one column for each place.

    Find 7.5 + 12.38 + 0.9.

    1. 1Write each number with two decimal places.
    2. 2Line up the points and add. What is the sum?
    3. 3Why is 0.9 not the same as 0.09?
    Final answer:
  2. 2Complete each step, then write the final answer.

    Find 0.6 + 0.47.

    Show your work
    Final answer:
Part 2Apply itreal-world problems
  1. 3Complete each step, then write the final answer.
    TensOnes.TenthsHundredths
    10.00
    −6.85
    =?.??
    10 is written as 10.00 so every place has a digit.

    A runner's goal is 10 kilometers. She has run 6.85 kilometers. How far does she still need to run?

    1. 1Write 10 with a decimal point and two zeros.
    2. 2There are no hundredths to take from. How do you regroup 10.00?
    3. 3Subtract each column. How far is left?
    Final answer:
  2. 4Complete each step, then write the final answer.

    Find 45 − 18.72.

    Show your work
    Final answer:
  3. 5Complete each step, then write the final answer.

    Mia spent $4.75 on lunch. She has $8.60 left. How much money did she have before lunch?

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

    Raj says 6 − 2.35 is 4.35. He subtracted the ones and copied the .35. What is the correct difference?

    Show your work
    Final answer:

Explain your thinkingWhen you subtract a decimal from a whole number, why do you write zeros after the decimal point? Use Raj's mistake.

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