Curriculum  /  Math  /  5th Grade  /  Unit 4: Addition and Subtraction of Fractions/Decimals  /  Lesson 16

Addition and Subtraction of Fractions/Decimals

Lesson 16

Math

Unit 4

5th Grade

Lesson 16 of 17

Objective

Subtract decimals where the total is greater than 2.

Common Core Standards

Core Standards

  • 5.NBT.B.7 — Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Foundational Standards

  • 5.NBT.A.1
  • 5.NBT.A.4
  • 4.NF.C.5

Criteria for Success

  1. Understand that in order to subtract quantities, they must have the same unit (which in the case of decimals, are their place values).
  2. Subtract like units with decimals using the standard algorithm, aligning places correctly (which results in the decimal points being aligned) (MP.5, MP.6).
  3. Estimate differences of decimals.
  4. Use the relationship between addition and subtraction to check the solution to a decimal subtraction problem (MP.7).
  5. Solve one-step word problems involving the subtraction of two decimals (MP.4).

Tips for Teachers

  • Instead of using language like “aligning the decimal points” when discussing how to set up these computations vertically, instead use language like “aligning like units” or “aligning places” (i.e., ones with ones, tenths with tenths, etc.). Aligning like units results in decimal points being aligned, of course, but it’s because of the need to add and subtract like units that this happens, not the other way around.
  • When subtraction requires decomposition, doing all necessary decomposition before subtracting will help to avoid errors. Take 4.25 – 2.78, for example. “The total 4.25 does not have enough tenths or hundredths to subtract the 7 tenths or 8 hundredths in 2.78. Therefore 1 one is decomposed to make 10 tenths and 1 tenths is decomposed to make 10 hundredths. These decompositions can be done and written in either order; starting from the left is shown because many students prefer to operate in that order. In the middle step, 1 one has been decomposed (making 3 ones, 11 tenths, 15 hundredths) so that the 2 ones 7 tenths and 8 hundredths in 2.78 can be subtracted. These subtractions of like units can also be done in any order. When students alternate decomposing and subtracting like units, they may forget to decompose entirely or in a given column after they have just subtracted (e.g., after subtracting 8 hundredths from 15 hundredths to get 7 hundredths, they move left to the tenths column and see a 1 on the top and a 7 on the bottom and write 6 because they are in subtraction mode, having just subtracted the hundredths)” (NBT Progression, p. 10, modified to make it a decimal computation as original was with whole numbers). Thus, decomposing first both allows students to decompose in any order as well as avoid common errors. This process would look like this:

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Anchor Tasks

25-30 minutes

Problem 1

a.   Find the value of 2.8 – 1.53.

b.   Joanie used the standard algorithm to subtract decimals. This is Joanie’s work. Describe what Joanie did in each step.

Step 1:

Step 2:

Step 3:

Guiding Questions

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Student Response

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References

Open Up Resources Grade 5 Unit 5 Lesson 15 — Activity 2

Grade 5 unit 5 Lesson 15 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed June 17, 2024, 11:18 a.m..

Modified by Fishtank Learning, Inc.

Problem 2

a.   Estimate the following differences.

  1. 9.58 – 4.72
  2. 17.64 – 2.8
  3. 95 – 7.68
  4. 73.03 – 41.123

b.   Solve for the actual differences in Part (a) above. Are your answers reasonable? Why or why not?

Guiding Questions

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Student Response

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Problem 3

The decimal points have been erased from the minuend and subtrahend on the left-hand side of each equation below. Place a decimal point in each value on the left-hand side to make the equation true. 

a.   1272 – 59 = 6.82

b.   21 – 63 = 1.47

Guiding Questions

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Student Response

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Problem Set

15-20 minutes

Discussion of Problem Set

  • Look at #2d. I wasn’t able to subtract since 10 has no tenths or hundredths. Do you agree or disagree?
  • Look at #3. Was Peter correct? How can you prove him wrong without calculating the actual difference?
  • Who did you agree with in #6b? What mistake did Elena make?
  • Look at #7. Who thinks they have the smallest difference? Did anyone get a smaller difference? What was your strategy?

Target Task

5-10 minutes

Solve.

a.   54.37 − 16.5 = __________

b.   8 − 0.26 = __________

Student Response

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Additional Practice

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Next

Solve two- and multi-step word problems involving addition and subtraction of decimals.

Lesson 17
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Addition and Subtraction of Fractions

Topic B: Addition and Subtraction of Decimals

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