th
5
Grade
Shenandoah Kolbe
Maxine Weiss
Ana Sanchez
Heather Tinker
Amy Horn
Dan Scurlock
frac·tion
ˈfrakSHən/
noun
noun: fraction; plural noun: fractions; noun: Fraction;
noun: the Fraction
1. a numerical quantity that is not a whole number (e.g., 1/2,
0.5).
Common
Denominator
Factor
Denominator
Unit
Fraction
Mixed
Number
Numerator
Equivalent
Fractions
Least Common
Denominator
Operation
Improper
Fraction
Area
Reciprocal
Importance of Math Vocabulary
 The language of mathematics uses three linguistic tools that are each a form of
text:
 words
 symbols
 diagrams
 ELA is needed in addition to symbols and diagrams.
 Language in mathematics is important because it is necessary for:
 communication
 mathematics reasoning
 Precision
 Words are not just for story problems; math uses words with specific
applications that have very different meanings in other settings (odd, even,
radical, obtuse, circle, rational).
•
Words, symbols, and diagrams must map onto each other.
www.doe.virginia.gov
Word Walls
Concept Mapping
Interactive Math Journals
ADDING AND SUBTRACTING
FRACTIONS - 5.NF.A.1
Add and subtract fractions with
unlike denominators (including mixed
numbers) by replacing given fractions
with equivalent fractions in such a way
as to produce an equivalent sum or
difference of fractions with like
denominators.
Misconceptions-5.NF.1 & 2
 Students often mix models when adding, subtracting,
or comparing fractions
 Students tend to want to add the denominators
ADDING AND SUBTRACTING
FRACTIONS - 5.NF.A.2
Solve word problems involving
addition and subtraction of fractions
referring to the same whole, including
cases of unlike denominators by using
visual fraction models or equations to
represent the problem.
Use benchmark fractions and number
sense of fractions to estimate mentally
and assess the reasonableness of
answers.
INTERPRETING FRACTIONS AS AN
IMPLIED DIVISION – 5.NF.3
Interpret a fraction as division of the
numerator by the denominator
(a/b = a ÷ b). Solve word problems
involving division of whole numbers
leading to answers in the form of
fractions or mixed numbers, e.g., by using
visual fraction models or equations to
represent the problem.
MULTIPLYING FRACTIONS 5.NF.4
Apply and extend previous understandings of
multiplication to multiply a fraction or whole
number by a fraction.
a. Interpret the product (a/b) × q as a parts of
a partition of q into b equal parts; equivalently
as the result of a sequence of operations
a × q ÷ b.
b. Find the area of a rectangle with fractional
side lengths by tiling it with unit squares of the
appropriate unit fraction side lengths, and show
that the area is the same as would be found by
multiplying the side lengths. Multiply fractional
side lengths to find areas of rectangles, and
represent fraction products as rectangular areas.
MULTIPLYING FRACTIONS 5.NF.5
Interpret multiplication as scaling (resizing), by:
a. Comparing the size of a product to the size of
one factor on the basis of the size of the other
factor, without performing the indicated
multiplication.
b. Explaining why multiplying a given number by a
fraction greater than 1 results in a product
greater than the given number (recognizing
multiplication by whole numbers greater than 1 as
a familiar case); explaining why multiplying a given
number by a fraction less than 1 results in a
product smaller than the given number; and
relating the principle of fraction equivalence a/b =
(n × a)/(n × b) to the effect of multiplying a/b by 1.
MULTIPLYING FRACTIONS 5.NF.6
Solve real world problems involving
multiplication of fractions and mixed
numbers, e.g., by using visual fraction
models or equations to represent the
problem.
DIVIDING WITH FRACTIONS 5.NF.7
Apply and extend previous understandings of
division to divide unit fractions by whole
numbers and whole numbers by unit fractions.
a. Interpret division of a unit fraction by a nonzero whole number and compute such
quotients.
b. Interpret division of a whole number by a unit
fraction, and compute such quotients.
c. Solve real world problems involving division of
unit fractions by non-zero whole numbers and
division of whole numbers by unit fractions,
e.g., by using visual fraction models and
equations to represent the problem.
Misconceptions-5.NF.3-7
 Students may believe that multiplication results in a
larger number and that division always results in a
smaller number
Larry has ½ of a fruit bar
and wants to give half of it
to his brother. How much of
the whole fruit bar will
Larry give to his brother?
This problem can be solved by thinking
of ½ of ½.
http://www.learner.org/courses/learningmath/number/session9/part_a/try.html
Ava has ½ of a pizza. She
eats 2/3 of the pizza she
has. How much of the whole
pizza did she eat?
To solve this problem, think of 2/3
times ½.
http://www.learner.org/courses/learningmath/number
/session9/part_a/try.html
One informal assessment on:
CCSS.Math.Content.5.NF.A.1 Add and subtract fractions with
unlike denominators (including mixed numbers) by
replacing given fractions with equivalent fractions in such a
way as to produce an equivalent sum or difference of
fractions with like denominators.
CCSS.Math.Content.5.MD.B.2 Make a line plot to display a
data set of measurements in fractions of a unit (1/2, 1/4, 1/8).
The outcome about five different levels on the learning
trajectory.
4,3,2,1 based on:
1. Understanding
the problem
2.Strategies
3. Accuracy
Self
Assessment
checklist
based on
Polya’s
problem
solving
method
1. The student was able to
partition the number line
into eighths, but do not
consider the range of the
data or plot the data.
2. The student added up all
the data, regardless of the
denominator.
3. The student attempted a
fraction bar strategy, but
failed to realize that the 2
15/52 would not match.
1. The student was able to
partition the number line and
included equivalent fractions,
but failed to plot the data.
2. The student may have the
misconception that ¼ is smaller
than 1/8.
3. The student was able to
compare the most frequent
term with mode.
4. The student was able to
combine fractions with like
denominators, but then added
different denominators across.
1. The student partition
the number line according
to the range of the data,
failed to attend to
precision
2. Evidence is clear that
the student was able to
convert all fractions to
eighths and was able to
recognize the improper
fractions and simplified
1. There is evidence of
partitioning of eighths with
equivalent fractions, and some
of the data is plotted correctly.
2. There may be vocabulary
issues with least and most
frequent
3. The student was able to add
unlike denominators
4. Evidence of algorithm
strategy with multiples and
concept of wholes
5. Teacher guided to review
final answer since there was
an improper fraction
1. The student was able to
create a line plot, with a
minor precision issue with
labeling
2. The student used mental
strategies to create whole
numbers
Fraction Checklist
Recognizing fractions using benchmarks
Compare Fractions using Benchmarks
Rename fractions to have common denominators
and be in simplest form
Estimate sums and differences of mixed numbers
using benchmarks
Order fractions
Use a number-line model to solve fractions
Use an area model to solve multiplication
problems
Add and subtract fractions with unlike
denominators
Display data on a line plot and identify the data
landmarks
Interpret data displayed in line plots with
fraction units
Assess
Progre
ss
Comments
Resources
 EngageNewYork.org
 O'Malley, . (n.d.). Authentic Assessment for English Language Learners. N.p.:
Addison-Wesley.
 Howard County (No URL, search)
 http://www.learner.org/courses/learningmath/number/session9/part_a/try.ht
ml