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					                           Mathematics Alignment Lesson
                            Grade 5 Quarter 1 Day 33

       Common Core State Standard(s)                                  Alignment Lesson
   5.NBT.7 Add, subtract, multiply, and divide      Adding & Subtracting Decimals in a Real-World Context
   decimals to hundredths, using concrete
   models or drawings and strategies based on      1. Discuss Journal Prompt question from yesterday’s homework.
   place value, properties of operations, and/or          Why is it important to write numbers with the same place
   the relationship between addition and                  value beneath each other when you are subtracting
   subtraction; relate the strategy to a written          decimals using a vertical format? Use appropriate math
   method and explain the reasoning used.                 vocabulary in your explanation.
                                                   2. Display Transparency/Blackline Master, “Distance Covered”
    Standards for Mathematical Practice               and explain the task to students being careful not to make
   1. Make sense of problems and persevere in         sense of the problem for them.
      solving them.                                3. Give students ample time to solve the problem using the three
   2. Reason abstractly and quantitatively.           different representations specified.
   3. Construct viable arguments and critique
                                                   4. Strategically divide students into groups of 2 or 3 and instruct
      the reasoning of others.
                                                      them to each share their different representations of the
                                                      problem. Do not spend more than 2-3 minutes on this step.
              Materials Needed:                    5. Explain that each group will create a “final copy” on chart
                                                      paper of one of their strategies to share with the class. Each
      Blackline Masters, “Real-World                 group will need to determine which strategy they want to
          Decimal Addition and Subtraction            share. Their final copy can be a combined representation of
            Problems”, “ Adding and                   that strategy from all members of their group, or they can
              Subtracting Decimals in a Real-         choose to use one person’s representation that they think
                  World Context Journal               accurately reflects strong thinking and good problem solving.
                     Prompt”                       6. As students are working, circulate and choose 3 groups who
      Transparency/Blackline Master,                 will verbally share their final copies with the class later in the
           “Distance Covered”                         lesson. Try to choose one from each of the three different
      Chart paper and markers                        representations if possible.
      Base Ten Blocks available for each
                                                   7. Post final copies around the room and invite students to take a
       student as needed (flats, rods, units)
                                                      quick gallery walk.
                                                   8. Invite each of the three groups of students you strategically
                                                      selected to share their final copies. As students share, engage
                  Assessment                          the class in Math Talk, incorporating some of the following
   Informal:                                          questions as appropriate:
    Written student solutions from the                    What connections do you notice between the three
       Distance Covered problem                                different representations?
    Journal Prompt explanation                            Which representation appeals to you most? Why?
                                                           How do the different representations help you make
                                                               sense of the problem?
                   Homework
                                                   9. Use the remaining time for students to practice and discuss
      Finish “Real-World Decimal Addition
                                                      using Blackline Master “Real-World Decimal Addition and
       and Subtraction Problems”
                                                      Subtraction Problems.” Students should finish any remaining
      “Adding and Subtracting Decimals in a
                                                      problems and the journal prompt for homework.
       Real-World Context Journal Prompt”


                  Vocabulary                         Source: Teacher Created – Draft and Final Copy activity
                None Referenced                      adapted with permission from NCSU Project AIM


Wake County Public School System, 2012
                 Transparency/Blackline Master   Grade 5   Day 33   Standard 5.NBT.7

                                                                Name: ________________________
                                                                 Date: ________________________


                                         Distance Covered
William walked 1.25 miles to work, 0.9 miles to the store, and
0.47 miles home. Rebecca ran 2.75 miles for exercise at the
school track. Who covered more distance? How much more
distance did that person cover?




Individually, solve the problem using the following steps:

    1. Reread the problem and determine what the problem is
       asking you to find.

    2. Predict/Estimate the solution.

    3. Solve the problem using the 3 different representations of
       pictures, words, and numbers.

    4. Review your solution and determine if it is reasonable.




Wake County Public School System, 2012
                            Answer Key Grade 5   Day 33   Standard 5.NBT.7

                                      Distance Covered
                                     Answer Key (page 1)
Pictures:




First, shade 1.25 + 0.9 +                                      0.47 by breaking the numbers
into wholes, tenths, and                                       hundredths.




Then, subtract 2.75 – 2.62 by shading the larger number and crossing out the smaller
number on the base ten grids.




Wake County Public School System, 2012
                            Answer Key Grade 5   Day 33   Standard 5.NBT.7

                                      Distance Covered
                                     Answer Key (page 2)
Words:
William walked 1.25 miles to work and then 0.9 miles to the store. At that point, he had
walked 2.15 miles. I added to find this out. Then, he walked 0.47 miles home. When I add
0.47 to 2.15, I know his total walking distance was 2.62 miles. 2.62 miles is less than
Rebecca’s 2.75 miles. To find out how much farther Rebecca went I subtracted 2.62 from
2.75. She covered 0.13 more miles than William did.

Note: Students may also choose to explain a base ten grids or a base ten models
representation for their words. The above explanation provides just one example of many
ways of thinking.




Numbers:

        William walked:                          Rebecca ran: 2.75 miles

             1.25                                Difference: 2.75
             0.9                                           – 2.62
           + 0.47                                            0.13 miles
             2.62 miles

        Rebecca covered 0.13 miles more than William.




Wake County Public School System, 2012
                         Blackline Master   Grade 5   Day 33   Standard 5.NBT.7

                                                                  Name: ________________________
                                                                   Date: ________________________

  Real-World Decimal Addition and Subtraction Problems
Directions: Solve the following problems. Use estimation to determine if your answers
            make sense.

    1. At the grocery store, Jerome bought 1.4 pounds of potatoes, 0.9 pounds of tomatoes,
       and 1.3 pounds of bananas. How many pounds of produce did Jerome purchase?




    2. Clarissa improved her time running a mile in gym class from 6.3 minutes to 5.78
       minutes. By how much time did she improve?




    3. At the bookstore, Paul bought 2 books for $8.95 and a magazine for $3.99. How
       much money did he spend at the bookstore?




    4. Andy plans to buy a new road bike and has found two different bikes he likes. Bike
       A weighs 22.7 pounds and Bike B weighs 21.85 pounds. Which bike is lighter?
       How much lighter is it?




    5. At the beginning of the month, Kendra’s credit card balance was $125.43. She sent
       a check to the credit card company to pay off $75 of her debt. Then, she used her
       credit card to purchase shoes for $31.55 and a sweater for $23.98. What is Kendra’s
       new credit card balance?




Wake County Public School System, 2012
                            Answer Key Grade 5   Day 33   Standard 5.NBT.7

  Real-World Decimal Addition and Subtraction Problems
                      Answer Key

    1. At the grocery store, Jerome bought 1.4 pounds of potatoes, 0.9 pounds of tomatoes,
       and 1.3 pounds of bananas. How many pounds of produce did Jerome purchase?

                1.4 + 0.9 + 1.3 = 3.6 pounds


    2. Clarissa improved her time running a mile in gym class from 6.3 minutes to 5.78
       minutes. By how much time did she improve?

                6.3 – 5.78 = 0.52 minutes


    3. At the bookstore, Paul bought 2 books for $8.95 and a magazine for $3.99. How
       much money did he spend at the bookstore?

                $8.95 + $8.95 + $3.99 = $21.89


    4. Andy plans to buy a new road bike and has found two different bikes he likes. Bike
       A weighs 22.7 pounds and Bike B weighs 21.85 pounds. Which bike is lighter?
       How much lighter is it?

                22.7 – 21.85 = 0.85 pounds       Bike B is lighter by 0.85 pounds.


    5. At the beginning of the month, Kendra’s credit card balance was $125.43. She sent
       a check to the credit card company to pay off $75 of her debt. Then, she used her
       credit card to purchase shoes for $31.55 and a sweater for $23.98. What is Kendra’s
       new credit card balance?

                $125.43 – $75 = $50.43

                $50.43 + $31.55 + $23.98 = $105.96




Wake County Public School System, 2012
                         Blackline Master   Grade 5   Day 33   Standard 5.NBT.7

                                                                  Name: ________________________
                                                                   Date: ________________________

Adding and Subtracting Decimals in a Real-World Context
                    Journal Prompt


        Choose one of the problems from the Real-World Decimal Addition and
        Subtraction Problems activity. Explain how you solved the problem and
        how estimation helped you determine if your answer made sense. Use
        appropriate math vocabulary in your explanation.




Wake County Public School System, 2012

				
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