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Actions with Fractions

- Drew Polly
- UNC-Charlotte

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?

Cookie Jar ProblemAdapted from Deborah Ball

- Approaches/Strategies?

Cookie Jar ProblemAdapted from Deborah Ball

- Mathematics Content?

Cookie Jar ProblemAdapted from Deborah Ball

- Adapting the Task for Differentiation?

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!!

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?

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?

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

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

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?

Adding Marbles

- Approaches?
- How could we modify this task?

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?

Spinner Probabilities

- Modifications?

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?

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.

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?

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.

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.

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?

Area (Region) Models

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.

Area (Region) Models

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.

Area (Region) Models

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?

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

4

25

9

1

Contact Information

- Drew Polly
- abpolly_at_uncc.edu
- http//education.uncc.edu/abpolly/