Download 5.NF.B.5a

Mathematics Curriculum Supplement
Grade 5 (5.NF.B.5ab)
Grade: 5
Highly-Leveraged Standard1
Mathematics
5.NF.B.5. Interpret multiplication as scaling (resizing), by:
5.NF.B.5a 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.
5.NF.B.5b 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b) to the effect of
multiplying a/b by 1.
Student Learning Targets:
5.NF.B.5a Interpret multiplication as scaling (resizing), by 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.
 understand and identify the parts of a multiplication problem. (e.g., factor and product)
 recall the strategy of working with rectangular areas with fractions.
 determine how a given number would be scaled, or resized, in a situation (e.g., 2/3 x 3 means 2/3 will
triple its size and 2/3 will then increase; however, 2/3 x 1/3 means 2/3 will be a third of its size and the
size of 2/3 will then decrease).
5.NF.B.5b Interpret multiplication as scaling (resizing), by 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b) to the effect of multiplying a/b by 1.
 understand that multiplying whole numbers and fractions result in products that depend on the size of
the factors.
 draw a conclusion that multiplying a fraction greater than one will result in a product greater than the
given number.
 draw a conclusion that when you multiply a fraction by any version of one, the resulting fraction is
equivalent.
 draw a conclusion that when you multiply a fraction less than one by a fraction less than one, the
product will be smaller than either fraction.
Performance Level Descriptor
Standard
Minimally Proficient
The Minimally
Proficient student
DOMAIN
5.NF.B [4
to 5]
shows the product of a
fraction by a whole
number by repeated
addition, using visual
fraction models.
Interprets
multiplication scaling
by comparing the size
of a product to the size
of one factor on the
basis of the size of the
second factor, without
Partially Proficient
The Partially Proficient
student
Proficient
The Proficient student
Highly Proficient
The Highly Proficient
student
shows the product of
two fractions by using
an area model.
Interprets
multiplication scaling
by comparing the size
of a product to the size
of one factor on the
basis of the size of the
second factor, without
performing the
indicated
shows the product of
two fractions using an
area model and creates
a story context for the
product. Finds the area
of a rectangle with
fractional side lengths
by tiling it with
squares with unit
fraction side lengths,
and shows that the
area is the same as
creates a real-world
context and models
representing
multiplication of
fractions.
Demonstrates
reasoning about
fractions in both an
additive and
multiplicative sense
with different wholes,
and displays the
TUSD Department of Curriculum and Instruction Curriculum 3.0
Revised 5/15/2017 2:41 PM
Page 1
Mathematics Curriculum Supplement
Grade 5 (5.NF.B.5ab)
performing the
indicated
multiplication (where
both factors are whole
numbers).
multiplication (where
one factor is a fraction
less than one).
would be found by
multiplying the side
lengths. Multiplies
fractional side lengths
to find areas of
rectangles, and
represents fraction
products as
rectangular areas.
Interprets
multiplication scaling
by comparing the size
of a product to the size
of one factor on the
basis of the size of the
second factor, without
performing the
indicated
multiplication.
quantities with visual
models. Interprets
multiplication scaling
by comparing the size
of a product to the size
of one factor on the
basis of the size of the
second factor by
performing the
indicated
multiplication with 2
fractions.
1
Highly-Leveraged Standards are the most essential for students to learn because they have endurance, leverage and essentiality.
This definition for highly-leveraged standards was adapted from the website of Millis Public Schools, K-12, in Massachusetts, USA.
http://www.millis.k12.ma.us/services/curriculum_assessment/brochures
Specifically for mathematics, the Highly-Leveraged Standards are the Major Content/Clusters as defined by the AZCCRS Grade
Level Focus documents. They should encompass a range of at least 65%-75% for Major Content/Clusters and a range of 25%-35%
for Supporting Cluster Instruction. See the Grade Level Focus documents at: http://www.azed.gov/azccrs/files/2015/01/k-8-majorand-supporting-content-emphasis.pdf
2
Supporting Standards are related standards that support the highly leverage standards in and across grade levels.
TUSD Department of Curriculum and Instruction Curriculum 3.0
Revised 5/15/2017 2:41 PM
Page 2