Fractions, Decimals and
Percents Mini-course
Session Two
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 NCTM`s Problem Solving
Standard.
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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.
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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?
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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?
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What is a Fraction?
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Names for GREEN tiles:
• Based on this picture, what fraction name
would you assign to Green?
GGGGGG
Y Y Y Y B R
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Names for GREEN tiles:
• Do you see another fraction name for
Green?
GGG
GGG
Y Y Y
Y B R
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Names for GREEN tiles:
• And yet another name for Green?
GG GG GG
Y Y Y Y B R
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Equivalent Fractions
Let’s do same for
Yellow at your tables.
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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?
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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?
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Equivalent Fraction Activity
• Suppose you were told that a collection of
tiles has
– 1/2 Red
• How many tiles should we
– 1/5 Blue
use?
– 3/10 Yellow • Is there another collection
that would also work?
• How can you prove that
another collection also
works?
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Equivalent Fraction Activity
• Suppose you were told that a collection of
tiles has
– 1/2 Red
• Answer:
– 1/5 Blue
5 Red, 2 Blue, 3 Yellow
– 3/10 Yellow
What equivalent fractions
did you discover?
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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 don’t finish all – go a pace for
good discovery! Can finish at home.
• Will be looking for volunteers to share
solutions and explain thinking.
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Color Tile Mysteries
(worksheet received tonight)
• Work in small groups to solve
problems.
• OK if you don’t finish all – go a pace
for good discovery! Can finish at
home.
• Will be looking for volunteers to share
solutions and explain thinking.
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NCTM Problem Solving Standard
• Build new mathematical knowledge
through problem solving.
• Apply and adapt a variety of
appropriate strategies to solve
problems.
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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.
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