MTSD
5.NF.4 Intervention Guide
Draft Dated 9.4.13.mh
Intervention Guide
5.NF.4
Apply and extend previous understandings of multiplication and division to multiply and divide
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. For example, use a visual fraction model to
show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) ×
(4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
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.
If students are struggling to understand skills and concepts related to 5.NF.4 they may need to back
up to the following:
3.MD.5
Recognize area as an
attribute of plane figures
and understand concepts
of area measurement.
a. A square with side
length 1 unit, called “a
unit square,” is said to
have “one square unit” of
area, and can be used to
measure area.
b. A plane figure which
can be covered without
gaps or overlaps by n unit
squares is said to have an
area of n square units.
Howard County 3.MD.5
Resources
https://grade3commonc
oremath.wikispaces.hcps
s.org/3.MD.5
https://grade3commonc
oremath.wikispaces.hcps
s.org/Assessing+3.MD.5
3.MD.7
Relate area to the operations of
multiplication and addition.
a.Find the area of a rectangle with wholenumber side lengths by tiling it, and show
that the area is the same as would be
found by multiplying the side lengths.
b. Multiply side lengths to find areas of
rectangles with whole- number side
lengths in the context of solving real world
and mathematical problems, and
represent whole-number products as
rectangular areas in mathematical
reasoning.
c. Use tiling to show in a concrete case
that the area of a rectangle with wholenumber side lengths a and b + c is the sum
of a × b and a × c. Use area models to
represent the distributive property in
mathematical reasoning.
Howard County 3.MD.7 Resources
https://grade3commoncoremath.wikispac
es.hcpss.org/3.MD.7
https://grade3commoncoremath.wikispac
es.hcpss.org/Assessing+3.MD.7
4.NF.4
Apply and extend previous
understandings of multiplication to
multiply a fraction by a whole
number.
A. Understand a fraction a/b as a
multiple of 1/b.For example, use a
visual fraction model to represent 5/4
as the product 5 × (1/4), recording the
conclusion by the equation 5/4 = 5 ×
(1/4).
B. Understand a multiple of a/b as a
multiple of 1/b, and use this
understanding to multiply a fraction
by a whole number. For example, use
a visual fraction model to express 3 ×
(2/5) as 6 × (1/5), recognizing this
product as 6/5. (In general, n × (a/b) =
(n × a)/b.)
Howard County 4.NF.4 Resources
https://grade4commoncoremath.wiki
spaces.hcpss.org/4.NF.4
https://grade4commoncoremath.wiki
spaces.hcpss.org/Assessing+4.NF.4
MTSD
5.NF.4 Intervention Guide
Draft Dated 9.4.13.mh
Resources to support intervention work around 5.NF.4
Resource #1
Conceptua Big Idea 8 – Multiplying With Fractions
 Paper/Pencil Tasks are posted on MTSD RtI Website
 You will need your teacher login
 A “class” will need to be created for you in Conceptua. Email first and last names and grades
of your students to Melissa.
https://www.conceptuamath.com/app/curriculum
Resource #2
Conceptua Tool Library – Multiplying Fractions -- Use this tool to help students build conceptual
understanding of what it means to multiply with fractions. Present contexts in the form of story
problems, assist students in paraphrasing the problems, then use models to clearly represent the
problems and the product. The tool easily represents the use of multiplication to find the product for
both “groups of” and “parts of” problems.
https://www.conceptuamath.com/app/tool/multiplying-fractions-tool
Resource #3
Area Word Problems – Solving multiplication of fraction story problems using the area model.
http://www.k-5mathteachingresources.com/support-files/area-word-problems-fractional-sidelengths-5nf4b.pdf
Resource #4
Mixed Number Multiplication Story Problems – some can be done as a group and some can be done
individually. Use the Conceptua Multiplying Fractions Tool (Resource #2) to model and solve these
problems.
http://www.k-5mathteachingresources.com/support-files/fraction-x-mixed-no.-word-problems5nf6.pdf
Resource #5
Mini-lesson - Modeling mixed number multiplication using Cuisenaire rods. See Melissa for Cuiseniare
rods.
http://www.k-5mathteachingresources.com/support-files/Mixed-Number-x-Fraction-Models.pdf
Resource #6
Fraction x fraction word problems. Students should solve using visual models and equations. Students
may do their work on white boards or use the Conceptua Multiplying Fraction Tool (Resource #2).
http://www.k-5mathteachingresources.com/support-files/fraction-x-fraction-word-problems.pdf
Resource #7
Mini-lesson -- Multiplying a fraction by a fraction using arrays
http://www.k-5mathteachingresources.com/support
files/multiplyingfractionsbydividingrectangles5.nf4a.pdf
MTSD
5.NF.4 Intervention Guide
Draft Dated 9.4.13.mh
Resource #8
Howard County Math Wiki Grade 5 Assessing 5.NF.4 There are 6 assessment tasks on this site that
can be downloaded. All can be used as instructional tasks. Students should solve using visual models
and equations. Students may do their work on white boards or use the Conceptua Multiplying
Fraction Tool (Resource #2).
https://grade5commoncoremath.wikispaces.hcpss.org/Assessing+5.NF.4