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					                             Mathematics Alignment Lesson
                              Grade 5 Quarter 3 Day 97

       Common Core State Standard(s)                                   Alignment Lesson
   5.NF.1 Add and subtract fractions with unlike       Adding and Subtracting Mixed Numbers with Models
   denominators (including mixed numbers) by
   replacing given fractions with equivalent        1. Today’s lesson builds on activities from Days 94 and 95
   fractions in such a way as to produce an            by incorporating mixed numbers into the models.
   equivalent sum or difference of fractions with
   like denominators.
                                                       Reference those activities in the beginning of the lesson
   For example, 2/3 + 5/4 = 8/12 +15/12 =              to remind students of their work with pattern blocks and
   23/12. (In general, a/b + c/d = (ad + bc)/bd.)      grid or area models to represent the addition and
                                                       subtraction of fractions. Students may need particular
    Standards for Mathematical Practice                support understanding what the grid or area models will
   Standard 2 - Reason abstractly and                  look like when they are drawing models involving mixed
                quantitatively.                        numbers.
   Standard 4 - Model with mathematics.
   Standard 7 - Look for and make use of            2. Display Transparency/Blackline Master, “Adding and
                structure.                             Subtracting Mixed Numbers,” and have students work
   Standard 8 - Look for and express regularity        with a partner to solve the first problem. Once pairs have
                in repeated reasoning.                 solved the problem, engage students in Math Talk using
                                                       the following questions:
               Materials Needed:                            Which pattern blocks did you use to model the
                                                               first mixed number?
      Blackline Masters, “Adding and
           Subtracting Mixed Numbers with
                                                            Which pattern blocks did you use to model the
              Models,” “Adding and                             second mixed number?
                 Subtracting Mixed Numbers                  How did you find the sum using the pattern
                    with Models Journal                        blocks?
                       Prompt”
      Transparency/Blackline Master,               3. Follow the same instructions and use similar questioning
           “Adding and Subtracting Mixed               to have students work through problems 2, 3, and 4 on
              Numbers”                                 Transparency/Blackline Master, “Adding and
      Pattern Blocks (hexagons, trapezoids            Subtracting Mixed Numbers.”
       (red & brown), rhombi, triangles (green
       & purple))                                   4. Use the remaining time for students to practice and
                                                       discuss using Blackline Master “Adding and Subtracting
                    Assessment                         Mixed Numbers with Models.”
   Informal:
    Independent student work                       5. Students should complete Blackline Master, “Adding and
    Student discussion during Math Talk               Subtracting Mixed Numbers with Models Journal
                                                       Prompt,” for homework.
                    Homework
   Blackline Master- “Adding and Subtracting
     Mixed Numbers with Models Journal
         Prompt”



                    Vocabulary                          Source: Teacher Created
                  None Referenced

Wake County Public School System, 2012
                  Transparency/Blackline Master   Grade 5   Day 97   Standard 5.NF.1

                                                                Name: ________________________
                                                                 Date: ________________________

                 Adding and Subtracting Mixed Numbers
                           1     2
    1. Find the value of 1 6 + 1 3 using pattern blocks.




                           1      1
    2. Find the value of 3 12 – 1 2 using pattern blocks.




                           1     3
    3. Find the value of 2 3 + 1 5 using a grid or area model.




                           3     5
    4. Find the value of 4 4 – 1 6 using a grid or area model.




Wake County Public School System, 2012
                  Transparency/Blackline Master   Grade 5   Day 97   Standard 5.NF.1




Wake County Public School System, 2012
                                Answer Key                  Grade 5   Day 97   Standard 5.NF.1


                 Adding and Subtracting Mixed Numbers
                              Answer Key
                                1             2
    1. Find the value of 1 6 + 1 3 using pattern blocks.

        Use one hexagon and one green triangle to model the first mixed number. Use one hexagon
        and two rhombi to model the second mixed number. To find the sum, trade the two rhombi for
        four green triangles and combine everything to make two hexagons and five green triangles.

                            1         2             5
                        1   6   + 1   3       = 2   6



                                 1         1
    2. Find the value of 3      12   –    12      using pattern blocks.

        Use three hexagons and one purple right triangle to model the first mixed number. To find the
        difference, you need to take away one hexagon and the equivalent of one red trapezoid. One of the
        three hexagons must first be traded for two red trapezoids. Once the trade has been made, you
        have two hexagons, two red trapezoids, and one purple right triangle. To model taking away 1½,
        take away one hexagon and one red trapezoid. You are left with one hexagon, one red trapezoid,
        and one purple right triangle. In order to state the answer as one mixed number, you need to have
        a common shape for the fractional part (or a common denominator). To do this, trade the red
        trapezoid for six purple right triangles. The resulting difference is one hexagon and seven purple
        right triangles.

                            1             1             7
                        3 12 – 1 2 = 1 12


                                1             3                           using a grid or area model.
    3. Find the value of 2 3 + 1 5




        Each addend is represented with a different color. The grid shows that 1/3 = 5/15 and
        3/5 = 9/15. Because the resulting fraction is less than 1, the fractional part of both addends can
        be represented on one grid.

                            1         3             14
                        2   3   + 1   5       =   3 15




Wake County Public School System, 2012
                              Answer Key         Grade 5    Day 97       Standard 5.NF.1



                 Adding and Subtracting Mixed Numbers
                          Answer Key (page 2)
                              3        5
    4. Find the value of 4    4   –   16   using a grid or area model.




        The grid model shows 1 and 5/6 subtracted from 4 and 3/4, leaving 2 + 1/6 + 3/4, which can be
        changed to 2 + 2/12 + 9/12 = 2 11/12.

                          3           5     11
                        4 4 – 1 6 = 2 12




Wake County Public School System, 2012
                         Blackline Master   Grade 5   Day 97   Standard 5.NF.1

                                                                 Name: ________________________
                                                                  Date: ________________________

     Adding and Subtracting Mixed Numbers with Models
Complete each of the following problems using pattern blocks or an area (grid) model. If you use
pattern blocks, you must draw a picture of the pattern blocks to show your work. Show your
drawings for each problem on a separate sheet of paper.


         7      1
    1. 2 12 + 1 2 = __________




         2     1
    2. 2 3 – 1 6 = __________




         1     5
    3. 3 4 + 1 6 = __________




         1     5
    4. 3 2 – 1 6 = __________




         5      3
    5. 4 12 – 2 4 = __________



Wake County Public School System, 2012
                         Blackline Master   Grade 5   Day 97   Standard 5.NF.1




Wake County Public School System, 2012
                                     Answer Key   Grade 5   Day 97   Standard 5.NF.1


     Adding and Subtracting Mixed Numbers with Models
                        Answer Key
    Student grid or area representations may all look slightly different. Circulate and view student work
    to determine if their models depict a correct representation of the problem.

            7         1          1
    1. 2   12   + 1   2   = 4   12

    Pattern Blocks: Use two hexagons and seven purple right triangles to model the first mixed number.
    Use one hexagon and one red trapezoid to model the second mixed number. To find the sum, trade
    the red trapezoid for six purple right triangles and combine everything to make three hexagons and
    thirteen purple right triangles. Trade twelve purple right triangles for one hexagon to make four
    hexagons and one purple right triangle.


           2      1         1
    2. 2 3 – 1 6 = 1 2

    Pattern Blocks: Use two hexagons and two rhombi to model the first mixed number. To find the
    difference, you need to take away one hexagon and the equivalent of one green triangle. To do this,
    you must first trade the two rhombi for four green triangles. Then, take away one hexagon and one
    green triangle. The resulting difference is one hexagon and three green triangles, which is equivalent
    to one hexagon and one red trapezoid.


           1      5             1
    3. 3 4 + 1 6 = 5 12

    Pattern Blocks: Use three hexagons and one brown right trapezoid to model the first mixed number.
    Use one hexagon and five green triangles to model the second mixed number. To find the sum, trade
    the brown right trapezoid for three purple right triangles and trade the five green triangles for ten
    purple right triangles. Combine everything to make four hexagons and thirteen purple right triangles.
    Trade twelve purple right triangles for one hexagon to make five hexagons and one purple right
    triangle.


           1      5         2
    4. 3 2 – 1 6 = 1 3

    Pattern Blocks: Use three hexagons and one red trapezoid to model the first mixed number. To find
    the difference, you need to take away one hexagon and five green triangles. One of the three
    hexagons must first be traded for six green triangles. Once the trade has been made, you have two
    hexagons, six green triangles, and one red trapezoid. To model taking away 1 and 5/6, take away one
    hexagon and five green triangles. You are left with one hexagon, one green triangle, and one red
    trapezoid. In order to state the answer as one mixed number, you need to have a common shape for
    the fractional part (or a common denominator). To do this, trade the red trapezoid for three green


Wake County Public School System, 2012
                           Answer Key Grade 5 Day 97 Standard 5.NF.1
    triangles. The resulting difference is one hexagon and four green triangles, which is equivalent to one
    hexagon and two blue rhombi.



     Adding and Subtracting Mixed Numbers with Models
                   Answer Key (page 2)
            5         3         2
    5. 4   12   – 2   4   = 1   3

    Pattern Blocks: Use four hexagons and five purple right triangles to model the first mixed number.
    To find the difference, you need to take away two hexagons and three brown right trapezoids. One of
    the four hexagons must first be traded for four brown right trapezoids. Once the trade has been
    made, you have three hexagons, four brown right trapezoids, and five purple right triangles. To
    model taking away 2¾, take away two hexagons and three brown right trapezoids. You are left with
    one hexagon, one brown right trapezoid, and five purple right triangles. In order to state the answer
    as one mixed number, you need to have a common shape for the fractional part (or a common
    denominator). To do this, trade the brown right trapezoid for three purple right triangles. The
    resulting difference is one hexagon and eight purple right triangles, which is equivalent to one
    hexagon and two blue rhombi.




Wake County Public School System, 2012
                         Blackline Master   Grade 5   Day 97   Standard 5.NF.1

                                                                 Name: ________________________
                                                                  Date: ________________________

     Adding and Subtracting Mixed Numbers with Models
                      Journal Prompt


        Today you used pattern blocks to model addition problems with mixed
        numbers. Explain how your modeled representation of the problem helps
        you find the common denominators you need to solve the problem. Use
        appropriate math vocabulary in your explanation.




Wake County Public School System, 2012
                            Answer Key   Grade 5   Day 97   Standard 5.NF.1

     Adding and Subtracting Mixed Numbers with Models
                      Journal Prompt
                        Answer Key


        Today you used pattern blocks to model addition problems with mixed
        numbers. Explain how your modeled representation of the problem helps
        you find the common denominators you need to solve the problem. Use
        appropriate math vocabulary in your explanation.

       When modeling an addition problem with pattern blocks, you have to create a model

       of each of the addends and then combine them to find the total sum. When the

       denominators are not the same in each of the addends, the model contains two

       different shapes for the fractional parts. In order to find the answer as a whole

       number and a fraction, you have to trade the pattern blocks for other pattern blocks

       that represent the same thing. This is the same as finding common denominators

       in a fraction addition problem. For example, if I am adding 2/3 and 1/6, the 2/3 is

       represented by 2 rhombi and the 1/6 is represented by 1 green triangle. In order to

       combine them, I have to trade the 2 rhombi for 4 green triangles so that I have all

       green triangles. This is the same as making 2/3 into 4/6. They are equivalent

       fractions and then I have the common denominator of 6 in both of my addends.




Wake County Public School System, 2012

				
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