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Actions with Fractions

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Then Tommy comes and eats half of the remaining cookies. ... Activity 1: If you removed half of the eggs, draw what the egg carton would look ... – PowerPoint PPT presentation

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Title: Actions with Fractions


1
Actions with Fractions
  • Drew Polly
  • UNC-Charlotte

2
Cookie Jar ProblemAdapted from Deborah Ball
  • There are some cookies in the jar. Susan eats
    3/12 of them. Then Tommy comes and eats half of
    the remaining cookies. Monique then eats 4/6 of
    the remaining cookies. Lastly, Fethi eats one
    cookie. If there were three cookies left how many
    were there at the beginning?

3
Cookie Jar ProblemAdapted from Deborah Ball
  • Approaches/Strategies?

4
Cookie Jar ProblemAdapted from Deborah Ball
  • Mathematics Content?

5
Cookie Jar ProblemAdapted from Deborah Ball
  • Adapting the Task for Differentiation?

6
Fractions of a Set
  • Candy sort
  • Take a bag of candy (Jolly Ranchers, MMs) and
    have students calculate fractions based on the
    colors of the candy pieces.
  • MM Graphing Activity
  • Sort by color
  • Bar graph, pie graph
  • Integrate fractions!!

7
Fractions of a Set- Egg CartonsAdapted from NCTM
Illuminations
  • Activity 1 If you removed half of the eggs, draw
    what the egg carton would look like.
  • What does it look like to have half of the eggs
    missing?
  • How many are left?
  • What if we only removed one-third of the eggs.
    Draw what that would look like.
  • How many are left?

8
Fractions of a Set- Egg CartonsAdapted from NCTM
Illuminations
  • Activity 2 Give students 5 pieces of card stock
    that are the size of the egg carton.
  • Students will cut the pieces into
  • 1/12, 1/6, 1/4, 1/3, 1/2
  • Cover half of the carton with 1/3 pieces and half
    with 1/6 pieces. What do you notice about the
    number of pieces needed?
  • Can you think of another?

9
Fractions of a Set
  • Attribute Pieces
  • Given a set of attribute pieces, students
    determine fractions for various categories (e.g.,
    color, size, shape)
  • Making your own Attribute Pieces
  • Squares, Circles, Triangles
  • Modify by color
  • Modify by size- large and small.
  • 3 shapes, 2 colors, 2 sizes 12 different pieces

10
Fractions of a Set
  • Given a set of attribute pieces, students
    determine fractions for various categories
  • 12 pieces

What can we write fractions for?
Large red square Large red circle Large red
triangle Small red square Small red circle Small
red triangle
Large blue square Large blue circle Large blue
triangle Small blue square Small blue
circle Small blue triangle
11
Adding Marbles
  • A bag contains five red marbles, three green
    marbles, and four blue marbles. How many green
    marbles must be added so that the probability of
    drawing a green marble is 3/4?

12
Adding Marbles
  • Approaches?
  • How could we modify this task?

13
Spinner Probabilities
  • You have a spinner with five unequal areas. The
    area of Region A is 1/4. The area of Region B is
    1/6. The area of Region C is 1/12. The areas of
    Region D and Region E are unknown.
  • What do we know about the total area of both
    regions?
  • What are some possible answers of Region D and
    Region E?

14
Spinner Probabilities
  • Modifications?

15
Spinner Probabilities
  • Simplified version
  • You have a spinner with three unequal areas. The
    area of Region A is 1/2 of the total area. The
    areas of Region B and C is unknown.
  • What do we know about the total area of both
    regions?
  • What are some possible answers of Region D and
    Region E?

16
Area (Region) Models
  • Pattern blocks- Introduction
  • What relationships do you notice among shapes?
  • Pattern blocks- Cover the hexagon
  • Cover the hexagon. Write a number sentence to
    represent the values of the pieces that cover the
    hexagon, which equals one.

17
Area (Region) Models
  • Pattern blocks- Changing the whole
  • If the triangle is the whole (unit), what is the
    value of the different shapes?
  • If the parallelogram is the whole (unit), what is
    the value of the different shapes?

18
Area (Region) Models
  • Composing and decomposing shapes
  • The triangle below represents 1/4 the area of a
    shape. Draw what the entire shape might look like.

19
Area (Region) Models
  • Composing and decomposing shapes
  • The triangle below represents 1/4 the area of a
    shape. Draw what the entire shape might look like.

20
Area (Region) Models
  • Geoboard (4x4 that has 5 pegs across)
  • Divide your entire geoboard into 4 regions of
    equal area that do not overlap?
  • Can you use only triangles?

21
Area (Region) Models
22
Area (Region) Models
  • Geoboard (4x4 that has 5 pegs across)
  • Divide your geoboard into various regions only
    using two different sizes of areas- small and
    large. The small shapes must be half the area of
    the large shapes.

23
Area (Region) Models
24
Area (Region) Models
  • Geoboard (4x4 that has 5 pegs across)
  • Divide your geoboard into various regions only
    using three different sizes of areas- small,
    medium, and large. The small shapes must be half
    the area of the medium shapes, and the medium
    shapes have to be half the area of the large
    shapes.

25
Area (Region) Models
26
Area (Region) Models
If the smallest square is 1 unit by 1 unit, what
fraction represents the area of smallest square
compared to the area of the largest square? What
fraction represents the area of the smallest
square compared to the entire figure?
27
Area (Region) Models
If the smallest square is 1 unit by 1 unit, what
fraction represents the area of smallest square
compared to the area of the largest square? What
fraction represents the area of the smallest
square compared to the entire figure?
64
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Contact Information
  • Drew Polly
  • abpolly_at_uncc.edu
  • http//education.uncc.edu/abpolly/
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