Lesson 14 | Addition and Subtraction of Fractions/Decimals | 5th Grade Mathematics

Objective

Subtract decimals.

Common Core Standards

Core Standards

The core standards covered in this lesson

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.

Number and Operations in Base Ten

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

The foundational standards covered in this lesson

5.NBT.A.1

Number and Operations in Base Ten

5.NBT.A.1 — Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
5.NBT.A.4

Number and Operations in Base Ten

5.NBT.A.4 — Use place value understanding to round decimals to any place.
4.NF.C.5

Number and Operations—Fractions

4.NF.C.5 — Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

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

Tips for Teachers

Suggestions for teachers to help them teach this lesson

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

Tasks designed to teach criteria for success of the lesson, and guidance to help draw out student understanding

Problem 1

a. Solve.

3 eighths – 1 fourth = ___________
3 fifths – 1 half = ___________
3 tenths – 1 hundredth = ___________

b. What do you notice about Part (a) above? What do you wonder?

Guiding Questions

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Problem 2

a. Estimate the following differences.

0.8 – 0.2
0.94 – 0.6
2 – 0.34
73.73 – 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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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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Problem Set

Problem Set

Answer Keys

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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 Michael correct? What error did he make?
Look at #4. Was Peter correct? How can you prove him wrong without calculating the actual difference?
Look at #8. Who thinks they have the smallest difference? Did anyone get a smaller difference? What was your strategy?

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

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.

Extra Practice Problems

Extra Practice Problems

Answer Keys

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Word Problems and Fluency Activities

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Lesson 13

Lesson 15

Lesson Map

Topic A: Addition and Subtraction of Fractions

Recognize and generate equivalent fractions.

5.NF.A

Add fractions with like denominators.

5.NF.A

Subtract fractions with like denominators.

5.NF.A

Add fractions with unlike denominators whose sum is less than 1.

5.NF.A.1 5.NF.A.2

Subtract fractions from fractions less than 1 with unlike denominators.

5.NF.A.1 5.NF.A.2

Add fractions with unlike denominators whose sum is less than 2.

5.NF.A.1 5.NF.A.2

Subtract fractions from fractions less than 2 with unlike denominators.

5.NF.A.1 5.NF.A.2

Add fractions with unlike denominators whose sum is greater than 2.

5.NF.A.1 5.NF.A.2

Subtract fractions from fractions greater than 2 with unlike denominators.

5.NF.A.1 5.NF.A.2

Use benchmark fractions and number sense to estimate mentally and assess the reasonableness of answers.

5.NF.A.2

Add and subtract more than two fractions.

5.NF.A.1

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

5.NF.A.2

Topic B: Addition and Subtraction of Decimals

Add decimals.

5.NBT.B.7

Subtract decimals.

5.NBT.B.7

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

5.NBT.B.7

Addition and Subtraction of Fractions/Decimals

Objective

Common Core Standards

Core Standards

Number and Operations in Base Ten

Foundational Standards

Number and Operations in Base Ten

Number and Operations in Base Ten

Number and Operations—Fractions

Criteria for Success

Tips for Teachers

Anchor Tasks

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Discussion of Problem Set

Target Task

Student Response

Additional Practice

Extra Practice Problems

Word Problems and Fluency Activities

Lesson Map

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