5th GradeShenandoah Kolbe

Maxine WeissAna Sanchez

Heather TinkerAmy Horn

Dan Scurlock

Vocabularyfrac·tionˈfrakSHən/nounnoun: fraction; plural noun: fractions; noun: Fraction; noun: the Fraction1. a numerical quantity that is not a whole number (e.g., 1/2, 0.5).

CommonDenominato

r

Factor Denominator

UnitFraction

Mixed Number

Numerator Equivalent Fractions

Least Common

Denominator

Operation ImproperFraction

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 withunlike denominators (including mixed numbers) by replacing given fractions

with equivalent fractions in such a way

as to produce an equivalent sum ordifference of fractions with likedenominators. 

Misconceptions-5.NF.1 & 2Students often mix models when adding,

subtracting, or comparing fractionsStudents tend to want to add the

denominators

ADDING AND SUBTRACTING FRACTIONS - 5.NF.A.2

Solve word problems involvingaddition and subtraction of fractionsreferring to the same whole, includingcases of unlike denominators by using visual fraction models or equations torepresent the problem. Use benchmark fractions and numbersense of fractions to estimate mentallyand assess the reasonableness of answers. 

INTERPRETING FRACTIONS AS AN IMPLIED DIVISION – 5.NF.3

Interpret a fraction as division of thenumerator by the denominator(a/b = a ÷ b). Solve word problemsinvolving division of whole numbers leading to answers in the form offractions or mixed numbers, e.g., by

usingvisual fraction models or equations torepresent the problem. 

MULTIPLYING FRACTIONS 5.NF.4Apply and extend previous understandings ofmultiplication to multiply a fraction or wholenumber 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.5Interpret 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 involvingmultiplication of fractions and mixednumbers, e.g., by using visual fraction

models or equations to represent theproblem.

DIVIDING WITH FRACTIONS 5.NF.7Apply and extend previous understandings

ofdivision to divide unit fractions by wholenumbers and whole numbers by unit

fractions.a. Interpret division of a unit fraction by a

non- zero 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.3-7Students 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

Assessing Fraction KnowledgeOne 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 Assessmentchecklistbased 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 Assess

Progress

Comments

Compare Fractions using BenchmarksRename fractions to have common denominators and be in simplest formEstimate sums and differences of mixed numbers using benchmarksOrder fractionsUse a number-line model to solve fractionsUse an area model to solve multiplication problemsAdd and subtract fractions with unlike denominatorsDisplay data on a line plot and identify the data landmarksInterpret data displayed in line plots with fraction units

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/par

t_a/try.html