Following a shipwreck you have been
stranded on a deserted island. You were
able to bring one mathematical tool to
the island.
Think of the tool that you would
bring and why you selected that item.
Tool Time Link
 Fractions
and algebra are two topics in
school mathematics that are considered
critical to the curriculum and difficult to
learn (National Council of Teachers of
Mathematics, 1998, 2000).
 According
to a recent Math Panel report,
for instance, the ability to perform
fraction computations easily and quickly
is one of the most critical foundations for
algebra (U.S. Department of Education,
2008).
“For students in the upper elementary grades
and even middle school, fractions present a
considerable challenge. It is in the area of
fractions that students often give up trying to
understand and resort instead to rules. However,
if approached in a developmental manner,
students in the primary grades can be helped to
construct a firm foundation for fraction
concepts….”
K-3,
Lovin
~Teaching Student-Centered Mathematics
John A. Van de Walle, LouAnn H.
 Why
do you think that students have such
a difficult time understanding fractions?
 Take
5 minutes and discuss with your
partner.
 1/6
1/3

1
4/3

3/6 1/2

1/7
2/7

3/10 ½

½
4/6
Part/whole:
Ex: This class has 19 students. 18 are females. What
fraction of the class is female?
Quotient Implies “division”
Ex 1: Pizza for a group of friends: $12 ÷ 3 people
(or $ 12/3 each)
Ratio Conceptually different and doesn’t imply
dividing a whole into parts or division.
Ex.:Weekend days to school days is 2:5 or 2/5.
Weekend to whole week is 2:7 or 2/7.
3 different models
Region
Length
Set
 One
of the best ways to help a kid solve a
fraction problem is to draw a diagram. But,
one of the worst ways to confuse a student
is to draw the wrong model!
If this is 2/5, draw 1 whole.
Jake bought three kinds of pizza (one of each
kind) for a party. Each pizza was the same size.
People were not very hungry, and at the end of
the party there was 3/4 of each pizza left. How
much pizza was left in all?
 At your table solve the problem.
 Create an equation that represents the
situation.
 Use two different strategies to solve the
problem.
 Identify a Mathematical Practice that could
be used to solve the problem.
 At
your table decide which standard or
standards does this problem align.
 Identify the concepts and skills that align
to the standard(s).
 What prerequisite standard is necessary
for the students to be successful with this
concept?
 Where will the students go from here?
 What misconceptions might a student
have about this problem?
1.
2.
3.
4.
5.
6.
7.
8.
9.
In what MAFS grade level does the study of
fractions begin?
What is the name of the Domain in the grade level
where fractions begins?
Which grade level has the most fraction standards?
What grade level do they begin adding fractions?
What grade level do they begin comparing
fractions?
What grade level do students begin partitioning
fractions?
What grade level do students divide fractions?
In what standard do students recognize that equal
shares of an identical whole do not need to have the
same shape?
When do students begin using fractions on a
number line?
1. In what MAFS grade level does the study of
fractions begin?
Kindergarten, indirectly through Geometry
2. What is the name of the Domain in the grade
level where fractions begins?
Geometry Domain, Kindergarten
3. Which grade level has the most fraction
standards?
5th grade, 7 standards
4. What grade level do they begin adding
fractions?
4th grade
5. What grade level do they begin comparing
fractions?
3rd Grade
6. What grade level do students begin partitioning
fractions?
1st Grade
7. What grade level do students divide fractions?
5th Grade
8. In what standard do students recognize that
equal shares of an identical whole do not need to
have the same shape?
2nd Grade MAFS.2.g.1.3
9. When do students begin using fractions on a
number line?
3rd Grade
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