Addition and Subtraction of Fractions/Decimals

Lesson 13

Math

Unit 4

5th Grade

Lesson 13 of 15

Objective


Add decimals.

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 add quantities, they must have the same unit (which in the case of decimals, are their place values). 
  2. Add 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). 
  3. Estimate sums of decimals. 
  4. Understand that the commutative and associative properties still hold with decimal addition (MP.7). 
  5. Solve one-step word problems involving the addition 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.

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Anchor Tasks


Problem 1

a.   Solve. 

  1. 3 eighths + 1 fourth = ___________
  2. 3 fifths + 1 half = ___________
  3. 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 sums. 

  1. 0.3 + 0.5 
  2. 0.64 + 0.7
  3. 0.2 + 15
  4. 4.99 + 56.123 + 123.01 + 3.7

b.   Solve for the actual sums 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 addends on the left-hand side of each equation below. Place a decimal point in each addend to make the equation true. 

a.   3419 + 267 = 60.89

b.   5 + 361 + 47 + 20 = 10.36

Guiding Questions

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Problem Set


Answer Keys

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Discussion of Problem Set

  • Look at #2d. If someone got 64 as an answer, how would you explain to them that their answer is unreasonable? 
  • Look at #3. Is Jeremy’s answer reasonable? How do you know? What mistake did he make? 
  • Look at #4. Did anyone solve without actually adding any values together? How were you able to do that? 
  • Look at #5. When I added, I got 16.00, but I don’t see that as an option. What mistake did I make? 
  • Look at #7. Why does this strategy work? When might it be helpful to use?
  • Look at #8. Who thinks they have the smallest sum? Did anyone get a smaller sum? What was your strategy?

Target Task


Solve.

a.   4.7 + 3.60 = __________

b.   43.56 + 7.85 = __________

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

Answer Keys

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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.

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Lesson 12

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Lesson 14

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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