# q3-5.nf.1-day97

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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?
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
   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
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: ________________________

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

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

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

Adding and Subtracting Mixed Numbers with Models
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
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
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

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.

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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