Fractions, Decimals and Percents Mini-course

1
Fractions, Decimals and Percents Mini-course

• Session Two

2
Objectives

• To promote conversation and success with
  mathematical endeavors.
• To use color tiles as a manipulative for
  illustrating fraction concepts.
• To explore the fraction concepts of equivalence,
  simplest form, and common denominators.
• To introduce NCTMs Problem Solving Standard.

3

• Fractions Decimals - Percents
• Any new ideas to share go ahead and post
• Keep watching and listening for uses in your
  everyday world!

• Tangram Follow-up
• Share at tables
• Volunteers to share with large group.

4
Using objects pictures to represent fractions

• If you were going to explain the fraction ½ to a
  child, how might you do it?
• What objects or pictures might you use?
• What words would you use in your explanation?

5
Colored Tiles Activity

• Make a collection of the following tiles
• 1 Red
• 1 Blue
• 6 Green
• 4 Yellow

Compare the number of RED tiles to the total
number. What fraction do the RED represent?
BLUE?
GREEN?
YELLOW?
6
What is a Fraction?

•  

7
Names for GREEN tiles

• Based on this picture, what fraction name would
  you assign to Green?

G
G
G
G
G
G
R
Y
Y
Y
Y
B
8
Names for GREEN tiles

• Do you see another fraction name for Green?

G
G
G
G
G
G
Y
Y
Y
Y
B
R
9
Names for GREEN tiles

• And yet another name for Green?

G
G
G
G
G
G
Y
Y
B
R
Y
Y
10
Equivalent Fractions

•  

Lets do same for Yellow at your tables.
11
New Set of Tiles

• Make a collection of the following tiles
• 4 Red
• 5 Blue
• 3 Green
• 8 Yellow

Find new fractional names for each color.
RED?
BLUE?
GREEN?
YELLOW?
12
Simplest form

• Why is it that some fractions (like 3/20 in the
  previous example) have no equivalent names that
  can be demonstrated in this tile collection?

• When a color has several equivalent names (like
  red in the previous example), which fraction do
  you think is the easiest to work with or might be
  considered the simplest name?

13
Equivalent Fraction Activity

• Suppose you were told that a collection of tiles
  has
• 1/2 Red
• 1/5 Blue
• 3/10 Yellow

• How many tiles should we use?
• Is there another collection that would also work?
• How can you prove that another collection also
  works?

14
Equivalent Fraction Activity

• Suppose you were told that a collection of tiles
  has
• 1/2 Red
• 1/5 Blue
• 3/10 Yellow

• Answer
• 5 Red, 2 Blue, 3 Yellow
• What equivalent fractions did you discover?

15
Color Tile Collections (worksheet received
tonight)

• Work in small groups to solve problems.
• Write equivalent fraction names for each color
  using the total number of tiles as the
  denominator.
• OK if you dont finish all go a pace for good
  discovery! Can finish at home.
• Will be looking for volunteers to share solutions
  and explain thinking.

16
Color Tile Mysteries (worksheet received tonight)

• Work in small groups to solve problems.
• OK if you dont finish all go a pace for good
  discovery! Can finish at home.
• Will be looking for volunteers to share solutions
  and explain thinking.

17
NCTM Problem Solving Standard

• Build new mathematical knowledge through problem
  solving.
• Apply and adapt a variety of appropriate
  strategies to solve problems.

18
Reflection Closing

• Think about the problem solving standard.
• How do the activities of this session and the
  previous class promote this standard?
• How have the color tiles helped your
  understanding of fractions?
• Bringing Mathematics Home 2 Complete the three
  problems on Fraction Problems I, using color
  tiles or other objects and share your solutions
  in session three.