Scope and Sequence
Grade 5 Second Edition Library
The Accelerated Math™ Second Edition scope and sequence is based on extensive mathematics and
standards research and consultation from mathematics educators, mathematicians, and university
researchers. You're sure to find objectives that reinforce the skills you are teaching, regardless of
what instructional materials you use. Accelerated Math makes it easy to select and organize objectives
to suit your textbook and your own teaching approach. This Accelerated Math library provides the
following scope and sequence of objectives:
•
Topic 1 - Number Sense and
Operations
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Determine if a number to 50 is prime or
composite
Determine a complete list of whole number
factor pairs for a number to 50
Determine all the factors of a whole number
to 50
Determine the prime factorization of a
number to 50
Determine the common factors for two
whole numbers to 50
Determine the greatest common factor of
two whole numbers to 50
Determine the multiple(s) of a number
Determine common multiples for two whole
numbers
Determine the least common multiple of
two whole numbers
Apply divisibility rules for 2, 5, or 10
Multiply a 3- or 4-digit whole number by a
3-digit whole number
WP: Multiply a 3- or 4-digit whole number
by a 3-digit whole number
Divide a multi-digit whole number by
multiples of 100 or 1,000
Divide a multi-digit whole number by a 1digit number, with no remainder and at
least one zero in the quotient
Divide a multi-digit whole number by a 1digit number, with a remainder and at least
one zero in the quotient
Divide a multi-digit whole number by a 1digit number and express the quotient as a
mixed number
Divide a multi-digit whole number by a 1digit number and express the quotient as a
decimal
Divide a multi-digit whole number by a 2digit whole number, with no remainder and
no zeros in the quotient
Divide a multi-digit whole number by a 2digit whole number, with a remainder and
no zeros in the quotient
Page 1 of 5
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
v. 2.0 03/06/2009
Divide a multi-digit whole number by a 2digit whole number, with no remainder and
at least one zero in the quotient
Divide a multi-digit whole number by a 2digit whole number, with a remainder and
at least one zero in the quotient
Divide a multi-digit whole number by a 2digit whole number and express the
quotient as a mixed number
WP: Divide a whole number, with no
remainder
WP: Divide a whole number and interpret
the remainder
WP: Solve a 2-step problem involving whole
numbers
Know the effects of rounding
Estimate a quotient using compatible
numbers
Estimate a quotient using any method
WP: Estimate a quotient using any method
Relate a sharing situation to a fraction
Determine equivalent fractions not in
simplest form
Determine the simplest form of a fraction
Compare fractions with unlike denominators
Order fractions with unlike denominators in
ascending or descending order
Add fractions with like denominators
greater than 10 and simplify the sum
Add fractions with unlike denominators
using a model and do not simplify the sum
Add fractions with unlike denominators and
do not simplify the sum
Add fractions with unlike denominators that
have factors in common and simplify the
sum
Add fractions with unlike denominators that
have no factors in common
Subtract fractions with like denominators
greater than 10 and simplify the difference
Subtract fractions with unlike denominators
using a model and do not simplify the
difference
Subtract fractions with unlike denominators
and do not simplify the difference
 2009 Renaissance Learning, Inc.
Scope and Sequence
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Subtract fractions with unlike denominators
that have factors in common and simplify
the difference
Subtract fractions with unlike denominators
that have no factors in common
WP: Add or subtract fractions with like
denominators and simplify the sum or
difference
WP: Add or subtract fractions with unlike
denominators that have no factors in
common
Convert a mixed number to an improper
fraction
Convert an improper fraction to a mixed
number
Add mixed numbers with like denominators
and simplify the sum
Add mixed numbers with unlike
denominators and simplify the sum
Subtract mixed numbers with like
denominators and simplify the difference
Subtract mixed numbers with unlike
denominators and simplify the difference
WP: Add or subtract mixed numbers with
like denominators and simplify the sum or
difference
WP: Add or subtract mixed numbers with
unlike denominators that have no factors in
common
Round a fraction to a benchmark number of
0, 1/2, or 1
Estimate a fraction sum using benchmark
numbers 0, 1/2, and 1
Estimate a fraction difference using
benchmark numbers 0, 1/2, and 1
WP: Estimate a fraction sum or difference
using benchmark numbers 0, 1/2, and 1
Multiply a whole number by a unit fraction
using a model
Multiply a whole number by a unit fraction
Multiply a proper fraction by a whole
number using a model
Multiply a proper fraction by a whole
number
Divide a whole number by a unit fraction
using a model
Divide a whole number by a unit fraction
Divide a unit fraction by a whole number
Divide a whole number by a fraction, with a
whole number quotient using a model
Divide a whole number by a fraction, with a
whole number quotient
WP: Multiply or divide a whole number by a
unit fraction
Page 2 of 5
Grade 5 Second Edition Library
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
v. 2.0 03/06/2009
Determine the value of a digit in a decimal
number to thousandths
Determine a decimal number represented in
expanded form
Represent a decimal number in expanded
form
Compare decimal numbers to thousandths
represented in expanded form
Compare decimal numbers of differing
places to thousandths
Order decimal numbers of differing places
to thousandths in ascending or descending
order
Add two decimal numbers of differing
places to thousandths
Add three or more decimal numbers
Add decimal numbers and whole numbers
Subtract two decimal numbers of differing
places to thousandths
Subtract a decimal number from a whole
number or a whole number from a decimal
number
WP: Add or subtract decimal numbers
through thousandths
WP: Add or subtract a decimal number
through thousandths and a whole number
Round a decimal number to a specified
decimal place to thousandths
Estimate the sum of two decimal numbers
through thousandths and less than 1 by
rounding to a specified place
Estimate the difference of two decimal
numbers through thousandths and less
than 1 by rounding to a specified place
WP: Estimate the sum or difference of two
decimal numbers through thousandths
using any method
Multiply a decimal number through
thousandths by 10, 100, or 1,000
WP: Multiply a decimal through thousandths
by 10, 100, or 1,000
Multiply a money amount by a 2- or 3-digit
whole number
WP: Multiply a money amount by a 2-digit
whole number
Convert a decimal number through
thousandths to a simplified fraction
Convert a fraction with a denominator that
is a factor of 10, 100, or 1,000 to decimal
notation
Determine a model of a percent on a 100
grid
Determine the percent represented by a
model on a 100 grid
 2009 Renaissance Learning, Inc.
Scope and Sequence
•
•
•
•
Relate an equivalent fraction and percent
given a grid
Relate an equivalent decimal and percent
given a grid
Evaluate a numerical expression involving
three operations, with no parentheses,
using order of operations
Evaluate a numerical expression involving
three operations, with parentheses, using
order of operations
Topic 2 - Algebra
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Use a variable expression with one
operation to represent a verbal expression
Use a verbal expression to represent a
variable expression with one operation
WP: Use a variable expression with one
operation to represent a situation
Evaluate a 1-variable expression, involving
one operation, using whole number
substitution
Evaluate a 2-variable expression, involving
one operation, using whole number
substitution
WP: Evaluate a 1-variable expression with
one operation using a whole number value
WP: Evaluate a 2-variable expression with
one operation using whole number values
WP: Extend a pattern to solve a problem
Generate a table of paired numbers based
on a variable expression with one operation
Generate a table of paired numbers based
on a variable expression with two
operations
Determine the variable expression with one
operation for a table of paired numbers
WP: Generate a table of paired numbers
based on a variable expression with one
operation
WP: Determine the variable expression with
one operation for a table of paired numbers
Use a first quadrant graph to represent the
values from a table generated in context
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Determine an appropriate unit of measure
Convert between customary units of length
using fractional amounts
Convert between customary units of
capacity using fractional amounts
Convert between customary units of weight
using fractional amounts
Page 3 of 5
•
•
Topic 3 - Geometry and
Measurement
•
•
Grade 5 Second Edition Library
•
•
•
•
v. 2.0 03/06/2009
Convert between metric units of capacity
using decimal amounts
Convert between metric units of mass using
decimal amounts
Convert between millimeters or centimeters
and meters, or meters and kilometers using
decimal amounts
WP: Compare customary units of length,
weight, or capacity using fractional
amounts
WP: Compare metric units of length, mass,
or capacity using decimal amounts
Calculate elapsed time using a.m. and p.m.
WP: Calculate elapsed time using a.m. and
p.m.
WP: Use a calendar to solve a problem
Measure an angle to the nearest 5 degrees
Determine the perimeter of a polygon
Use a formula to determine the area of a
triangle
Determine the area of a complex figure
divided into basic shapes
Use a formula to determine the area of a
parallelogram
WP: Determine the area of a triangle
WP: Determine the area of a square or
rectangle
WP: Determine a missing dimension given
the area and another dimension
Determine the volume of a rectangular
prism given a diagram
WP: Determine the volume of a rectangular
prism given a diagram
Determine the volume of a rectangular
prism
WP: Determine the volume of a rectangular
prism
Determine the volume of an object
composed of rectangular prisms by
counting units
Answer a question by analyzing a shape
made of cubes
Determine the surface area of a cube or a
rectangular prism given a net
Determine the surface area of a rectangular
prism
WP: Find the surface area of a rectangular
prism
Classify a triangle by its sides and angles
Determine the 3-dimensional shape that
can be formed from a net
Determine a net of a 3-dimensional shape
Determine the number of faces, edges, and
vertices in a 3-dimensional shape
 2009 Renaissance Learning, Inc.
Scope and Sequence
•
•
•
•
•
•
•
Identify a figure that has reflectional or
rotational symmetry
Determine the result of a reflection, a
rotation, or a translation on a grid
Determine the transformation that
generates the image of a figure on a grid
Locate a point by following compass
directions on a grid
Use compass directions to describe a path
to a point on a grid
Determine the location of an ordered pair in
the first quadrant
Determine the ordered pair of a point in the
first quadrant
Grade 5 Second Edition Library
•
•
•
•
•
•
•
•
•
Topic 4 - Data Analysis, Statistics,
and Probability
•
•
•
•
•
•
Answer a question using information from a
line graph that does not start at zero or has
a broken vertical scale
WP: Extend a line graph to solve a problem
Read a double- or stacked-bar graph
Use a double- or stacked-bar graph to
represent data
Page 4 of 5
•
v. 2.0 03/06/2009
Answer a question using information from a
double- or stacked-bar graph
Use information from a table or a chart to
solve a problem
Answer a question using information from a
Venn diagram
Determine the mode from a graph
Determine the range from a graph
Determine the mean of a set of whole
number data, whole number results
Determine the median of an odd number of
data values
Determine the mode of a set of whole
number data
Determine the range of a set of whole
number data
Determine all possible outcomes of a
compound event using a list
Determine all possible outcomes of a
compound event using a tree diagram
Determine the probability of a single event
given the total number of possible
outcomes
 2009 Renaissance Learning, Inc.
Scope and Sequence
Accelerated Math Libraries include an
almost unlimited supply of dynamic algorithmgenerated problems for both assisted-response
(multiple-choice) and free-response
assignments. Fifteen libraries are available:
Grade
Grade
Grade
Grade
Grade
Grade
Grade
Grade
1
2
3
4
5
6
7
8
Algebra
Algebra 2
Geometry
Probability & Statistics
Pre-Calculus
Calculus
Basic Math
Grade 5 Second Edition Library
Please call us toll-free at 1-800-338-4204
to order this Accelerated Math library or to
request the Scope and Sequence for other
libraries.
Accelerated Math Library
Accelerated Math Second Edition Grade 5
P.O. Box 8036
Wisconsin Rapids, WI 54495-8036
(800) 338-4204
www.renlearn.com
Page 5 of 5
v. 2.0 03/06/2009
 2009 Renaissance Learning, Inc.