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

Lesson 2.112.11 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can add and subtract decimals by lining up the place values and the decimal points — one step at a time, with support.

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 fuel tank has 128.75 liters. A shuttle adds 46.8 liters. How many liters are in the tank now?

  1. Line up the decimal points: 128.75 + 46.8
  2. Write a zero so both numbers have hundredths: 46.8 = 46.80
  3. Add each column from right to left: 128.75 + 46.80 = 175.55
  4. Check with an estimate: 130 + 47 = 177
  5. The tank has 175.55 liters.
  6. The tank now has 175.55 liters. The thrusters use 19.35 liters. How many liters are left?
  7. Line up the decimal points: 175.55 − 19.35
  8. Subtract each column from right to left: 175.55 − 19.35 = 156.20
  9. Check with an estimate: 176 − 19 = 157
  10. 156.20 liters are left. That is the same as 156.2 liters.

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 1

Group 1Supported practice

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

Learning target With my small group, I can add and subtract decimals by lining up the place values and the decimal points — one step at a time, with support.

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

    Find 4.3 + 2.5.

    Show your work

    Hint Line up the decimal points. Add the tenths, then the ones.

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

    Find 52.8 + 17.45.

    Show your work

    Hint Write 52.8 as 52.80 so both numbers have hundredths.

    Final answer:
Part 2Apply itreal-world problems
  1. 3Complete each step, then write the final answer.
    TensOnes.TenthsHundredths
    23.60
    +5.47
    =??.??
    23.6 is written as 23.60 so the places match.

    Add 23.6 and 5.47.

    1. 1How do we write 23.6 with two decimal places?
    2. 2Line up the points. Add the hundredths, then the tenths. What do you regroup?
    3. 3Add the ones and the tens. What is the sum?
    Final answer:
  2. 4Complete each step, then write the final answer.
    Ones.TenthsHundredths
    9.50
    −3.26
    =?.??
    This time we subtract. 9.5 is written as 9.50.

    Find 9.5 − 3.26.

    1. 1Write 9.5 with two decimal places.
    2. 2Subtract the hundredths. 0 is less than 6. What do you do?
    3. 3Finish subtracting. What is the difference?
    Final answer:
  3. 5Complete each step, then write the final answer.

    A water bottle holds 1.5 liters. Ty drinks 0.65 liter. How much water is left?

    Show your work

    Hint Subtract. Write 1.5 as 1.50 and line up the decimal points.

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

    Eva adds 3.4 + 1.25. She lines up the last digits and gets 1.59. What is the correct sum?

    Show your work

    Hint Line up the decimal points, not the last digits. Write 3.4 as 3.40.

    Final answer:

Explain your thinkingWhy do we line up the decimal points and not the last digits? Use Eva's mistake to explain.

Sentence starter I line up the decimal points so that ___. · Eva got 1.59, but the sum is ___ because ___.

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