MTSD
5.NF.1 & 5.NF.2 Intervention Guide
Draft Dated 9.9.13.mh
Intervention Guide
5.NF.1 & 5.NF.2
Use equivalent fractions as a strategy to add and subtract fractions.
5.NF.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. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b +
c/d = (ad + bc)/bd.)
5.NF.2. Solve word problems involving addition and subtraction of fractions referring to the same
whole, including cases of unlike denominators, e.g., 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. For example, recognize an incorrect result 2/5 + 1/2 = 3/7,
by observing that 3/7 < 1/2.
As you prepare to intervene around Grade 5 standards that target addition and subtraction of
fractions, keep in mind the following:
 In order to add and subtract two fractions with unlike denominators, students must understand
how to find equivalent fractions. They need to know that the same fraction can be named in many
different ways.*
 As you intervene around these standards attend to the fact that students need a visual
representation of the fractions. Make a fraction kit by folding fraction strips out of equal-sized
paper strips. Create a strip to represent the whole. Fold other strips to represent halves, fourths,
eighths, thirds and sixths. Line the sentence strips up so students can see the relationship between
equivalent fractions. Have them use the strips as they add and subtract unlike fractions.*
 When first introducing adding and subtracting with unlike denominators, present students with
problem such as 3/8 + 1/4. Let them use models to find the solution. Ask questions such as, How
can we change this problem to look like fractions that have the same denominator? Using models,
let the students discover that 3/8 + 1/4 is the exact same problem as 3/8 + 2/8 which equals 5/8.
Then students need to work with problems where both denominators need to be changed.
Problems such as 3/4 + 1/3. Focus attention on finding a problem that is exactly the same problem
as 3/4 + 1/3 but in a different representation. Students should use their understanding of
equivalent fractions and find out that 3/4 + 1/3 is the same problem as 9/12 + 4/12 which is equal
to 13/12 or 1 1/12.*
 Benchmark fractions help students know the value of fractions. Students need to know where
fractions fall on a number line using benchmark fractions. Benchmark fractions are 1/4., 1/2, and
3/4 and 1. Students need to know that one whole is represented by fractions like 3/3, 4/4, etc.
When comparing fractions, students need to say the fraction is close to zero, one-half, or one
whole. Understanding this also helps when estimating sums and differences. Students should be
able to explain that 3/4 + 2/3 is more than one whole because both fractions are more than onehalf.*
*Information adapted from Howard County 5.NF.1 and 5.NF.2 Math Wikis
https://grade5commoncoremath.wikispaces.hcpss.org/5.NF.1
https://grade5commoncoremath.wikispaces.hcpss.org/5.NF.2
MTSD
5.NF.1 & 5.NF.2 Intervention Guide
Draft Dated 9.9.13.mh
If students are struggling to understand skills and concepts related to 5.NF.1 and 5.NF.2 they may
need to back up to the following:
3.NF.2
Understand a fraction as a
number on the number line;
represent fractions on a
number line diagram.
Note:
* This helps represent and
make sense of adding and
subtracting fractions.
* Adding and subtracting
fractions on a number line
connects with previous
grade level representations
of adding and subtracting
whole numbers.
3.NF.3
4.NF.3
Explain equivalence of fractions in special
cases, and compare fractions by
reasoning about their size.
a. Understand two fractions as
equivalent (equal) if they are the same
size, or the same point on a number
line.
b. Recognize and generate simple
equivalent fractions, e.g., 1/2 = 2/4,
4/6 = 2/3). Explain why the fractions
are equivalent, e.g., by using a visual
fraction model.
c. Express whole numbers as fractions,
and recognize fractions that are
equivalent to whole numbers.
Examples: Express 3 in the form 3 =
3/1; recognize that 6/1 = 6; locate 4/4
and 1 at the same point of a number
line diagram.
d. Compare two fractions with the same
numerator or the same denominator
by reasoning about their size.
Recognize that comparisons are valid
only when the two fractions refer to
the same whole. Record the results of
comparisons with the symbols >, =, or
<, and justify the conclusions, e.g., by
using a visual fraction model.
Understand a fraction a/b with a >
1 as a sum of fractions 1/b.
A. Understand addition and
subtraction of fractions as joining
and
separating parts referring to the
same whole.
B. Decompose a fraction into a sum
of fractions with the same
denominator in more than one
way, recording each decomposition
by an equation. Justify
decompositions, e.g., by using a
visual fraction model. Examples:
3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 +
2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8
+ 1/8.
Resources to support intervention work around 5.NF.1 and 5.NF.2
Prior to working with students you may wish to review these online resources as you may find them
helpful to your planning:
(1) Teaching Channel video that shows a Grade 4 teacher working on subtracting fractions from
whole number and from mixed numbers. This video offers a primer on using a context, visual models
and equations to help students understand this difficult topic.
https://www.teachingchannel.org/videos/fractions-with-borrowing?fd=1
(2) The YouTube video shows how to use Thinking Blocks website to model addition of fractions with
unlike denominators.
http://www.youtube.com/watch?v=eQa2S92ftNo&feature=related
MTSD
5.NF.1 & 5.NF.2 Intervention Guide
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(3) Learn Zillion
A good website to support using visual models to add and subtract fractions:
http://learnzillion.com/lessons/1051-use-a-model-to-solve-word-problems-involving-addition-offractions-with-unlike-denominators
Lessons 3 through 8 offer 3-4 minute “mini-lessons” showing how to solve addition and subtraction of
fraction story problems using different models including number lines and tape diagrams. The links
are found on the left side of the screen.
(4) Thinking Blocks – will give you story problems and modeling tools
Accessing Thinking Blocks:
Step #1: http://www.mathplayground.com/NewThinkingBlocks/thinking_blocks_fractions.html
Step #2:
Click on either
“Adding Fractions
with Like
Denominators” or
“Adding Fractions
with Unlike
Denominators.” .”
The program will
provide a story
problem and
modeling tools.
Resource #1
Conceptua Fractions
Adding and Subtracting Fractions
This sequence of lesson begins with a very brief review of adding and subtracting related fractions
and creating equivalent fractions. Students eventually complete Big Idea 7: Adding and Subtacting
Improper Fractions/Mixed Numbers with Uncommon Denominators.
***Pacing Guide is found on MTSD Math RtI Resources under Grade 5 Number and Operations
Fractions. It is labeled “5.NF.1 and 5.NF.2 Pacing Guide.”
https://www.conceptuamath.com/app/curriculum
MTSD
5.NF.1 & 5.NF.2 Intervention Guide
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Resource #2
Conceptua Fractions Tool Library
(1) Adding Fractions with Uncommon Denominators
Use this tool to help students build conceptual understanding of adding fractions with uncommon
denominators by linking visual models to procedures. Students make use of fractions with a “one”
fraction.
https://www.conceptuamath.com/app/tool/adding-fractions-with-uncommon-denominators
(2) Subtracting Fractions with Uncommon Denominators
Use this tool to help students build conceptual understanding of subtracting fractions with
uncommon denominators by linking visual models to procedures. Students make use of a “one”
fraction.
https://www.conceptuamath.com/app/tool/subtracting-fractions-with-uncommon-denominators
Resource #3
The Rational Number Project
Lesson #5 Addition with Fractions Using Fraction Circles **Use fractions strips instead of circles
Students transition from using fraction circles and symbols to adding fractions using only symbols.
Connections between concrete model and symbols are emphasized.
http://www.cehd.umn.edu/ci/rationalnumberproject/RNP2/Lesson05.pdf
Resource #4
The Rational Number Project
Lesson #6 Subtraction Fractions
Students build on their understanding of adding fractions with symbols to subtract fractions.
Connections between concrete model and symbols are included. Lesson includes 3 story problems. A
very nice lesson.
http://www.cehd.umn.edu/ci/rationalnumberproject/RNP2/Lesson06.pdf
Resource #5
The Rational Number Project
Lesson #7 Students solve story problems involving addition and subtraction. The subtraction stories
go beyond the take away model used in lesson 6.
http://www.cehd.umn.edu/ci/rationalnumberproject/RNP2/Lesson07.pdf
Resource #6
The Rational Number Project
Lesson #8 Addition and Subtraction of Fraction Story Problems - Students have developed a strategy
for adding and subtracting fractions using their equivalence ideas in previous lessons. This lesson
extends their work to special cases: fractions> 1; sums > 1; differences with fractions > 1; sums of
more than two fractions.
http://www.cehd.umn.edu/ci/rationalnumberproject/RNP2/Lesson08.pdf
MTSD
5.NF.1 & 5.NF.2 Intervention Guide
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Resource #7
Utah Education Network – Assessment Tasks are very nice. They are found at the end of the pdf. This
guide also has links to 2 Illuminations Tasks and 2 links to the National Library of Virtual
Manipulatives found under Instructional Strategies Used.
http://www.uen.org/core/math/downloads/5NF1.pdf
Resource #8
Teaching Student-Centered Mathematics Grades 3-5 Vol II (Van de Walle, et al., 2014)
Activity 13.3 The Gold Prize – p. 238
You will need pattern blocks to play this game and a number cube that has 1/6, 1/3, ½, 2/6, 2/3,
and 5/6 on its sides. This game reinforces the finding of common denominators if students make
equivalent fractions before subtracting a piece.
Activity 13.4 Jumps on the Ruler – p. 239
Activity 13.5 Common Multiple Cards p. 241
Resource #6
Illustrative Mathematics – Finding Common Denominators to Add
A teaching task that engages students in adding fractions by discussing the need for common
denominators. Visual models support the work.
http://www.illustrativemathematics.org/illustrations/848
Resource #7
Illustrative Mathematics – Finding Common Denominators to Subtract
A teaching task that engages students in subtracting fractions by discussing the need for common
denominators. Visual models support the work.
http://www.illustrativemathematics.org/illustrations/859
Resource #8
Illustrative Mathematics
A teaching task that uses the context of a camping trip and making s’mores to engage students in
adding and subtracting fractions.
http://www.illustrativemathematics.org/illustrations/861
Resource #9
1
3
Asks students to add 1 3 + 2 5 in 2 different ways; The visual models (horizontal bar models AKA tape
diagrams) are make the mathematics very clear. Could be used whole group if needed or for small
group differentiation
http://www.illustrativemathematics.org/illustrations/847
MTSD
5.NF.1 & 5.NF.2 Intervention Guide
Draft Dated 9.9.13.mh
Resource #10
K-5 Math Teaching Resources
Adding and Subtraction of Fractions Story Problems with Unlike Denominators These problems could
be solved using Thinking Blocks website or Conceptua Tools for Adding and Subtracting Fractions with
Uncommon Denominators. (See Resource #2 for Conceptua links.)
http://www.k-5mathteachingresources.com/support-files/fraction-word-problems-unlikedenominator.pdf
Resource #11
K-5 Math Teaching Resources
Magic Squares with Fractions
http://www.k-5mathteachingresources.com/support-files/magicsquaresadditionfractions.pdf
Resource #12
Howard County “Assessing 5.NF.1” and “Assessing 5.NF.2” provides assessment tasks that can easily
be used as teaching tasks.
https://grade5commoncoremath.wikispaces.hcpss.org/Assessing+5.NF.1
https://grade5commoncoremath.wikispaces.hcpss.org/Assessing+5.NF.2