Palm Springs Unified School District
Math 5 Course Guide
Traditional and Modified Calendars
2013 - 2014
MATH 5
Table of Contents
Preface - Important Note to Teachers……………………………………………………...3
Using the Released Test Questions......................................................................................4
Purpose and Use of Pacing Guide…………………………………………………………5
National Educational Technology Standards Grades Pre-K - 12.........................................6
California Standards Test (CST) Blueprint………………………………………………..8
California Content Standards at a Glance………………………………………………...12
California Content Standards Unpacked…………………………………………………13
Instructional Segments…………………………………………………………….……..19
CST Blueprint Color-Coded by Instructional Segments………......................…….….....25
Trimester 1 Assessment at a Glance………………………….…………………………..28
Vocabulary by Instructional Segments……………….……………………………….….29
Vocabulary in Spanish by Instructional Segments…………………………………….…30
Pacing Guide………………………………………………………………………….….31
Please direct any questions or comments to:
Cinthia Ruiz
K-12 Math Specialist
cruiz@psusd.us
(760) 285-5528
Sandi Enochs
Coordinator, Assessment and Data Analysis
senochs@psusd.us
(760) 416-6066
2
IMPORTANT!
.
THIS PACING GUIDE IS INTENDED TO BE FLEXIBLE!!!!
Although a Pacing Guide has been created with a suggested order for teaching the textbook lessons,
site grade level teams may change the order of the lessons being taught WITHIN an Instructional
Segment. The only requirement is that all lessons within each Instructional Segment be completed
(and standards mastered) prior to that Instructional Segment’s Closing Date.
The Instructional Segment’s Closing Date is the absolute last date by which the Segment’s
Assessment must be administered and results entered into OARS. These are OARS deadline dates,
not just dates by which the exams must be administered to your students. Feel free to administer
the Assessment any time prior to this date.
Throughout this document, the standards that have been designated Key Standards by the California
Department of Education are highlighted in bold print and with an asterisk (*) following the standard
number. These represent the high impact standards and comprise a minimum of 70% of the
California Standards Test (CST).
This Course Guide highlights the Key Standards, unpacks the standards, and can be very helpful to
teachers in making instructional decisions about focus areas. All teachers need to keep track of
whatever is and is not working, for consideration during the next revision of this Course Guide. This
is critical, if we are to make useful changes in the future.
Please note: Benchmark Exam #2 has been replaced with a CST Mirror Test. During the time
between the administration of the CST Mirror Test and the administration of the actual CST teachers
will continue to teach new content while providing interventions as indicated by the results of the
CST Mirror Test. This Course Guide is NOT suggesting that all content be taught prior to the CST
Mirror Test administration date.
A Scope and Sequence of the National Educational Technology Standards, Grades Pre-K - 12, has
been added to all Course Guides. It clearly identifies the Technology Standards that should be
integrated into all subject areas at the appropriate grade levels.
The Textbook column of the Pacing Guide refers to our adopted textbook; enVision, by Pearson
Scott, Foresman. The two far right columns (Other Resources and # of Days) on the Pacing Guide
have been intentionally left blank. These columns are intended to be used by teachers when planning
individually or collaboratively.
A column, entitled RTQ’s, has been added to the Pacing Guide. It references the specific Released
Test Question(s) that align to the lesson being taught at that point in time. If you need a copy of the
Grade 5 Mathematics STAR Released Test Questions, you may download them from the CDE
website:
http://www.cde.ca.gov/ta/tg/sr/documents/cstrtqmath5.pdf
Please see the following page for some suggestions of how to use the RTQ’s.
3
Using the Released Test Questions throughout the School Year
It is highly recommended that you use the Released Test Questions as a wrap-up of instruction on a
particular standard. Close the lesson with “Now let’s see how the state might test this concept (or
standard)”. After the students have answered the question(s) and selected their responses, thoroughly
review the question and answer choices with them. Discover how many (and which) students
answered the question(s) correctly. Then have a frank and open discussion about the distracters and
why each student chose a particular distracter




Did they totally not understand the concept (standard)?
Did they not know a particular vocabulary word (academic or content-specific)?
Did they miss a step in the process of solving the problem?
Did they not finish solving the problem, because one of the distracters was the answer they
received when they were only part-way through solving the problem?
 Did they arrive at a perfectly good answer, but it was not the answer to the problem?
Try and discover all errors and misconceptions now, so that they can be corrected immediately and
not continue throughout the school year.
Please keep in mind that most standards encompass several (if not many) concepts, as evidenced by
the Unpacked Standards in your Course Guide. These Released Test Questions may only assess some
of these concepts. That does not mean that these are the only aspects of the standard that will be
tested on the CST. These are the questions that CDE chose to release at this point in time. This is not
necessarily an indication of which concepts to stress or an indication of which part of the standard
will be tested. You may need to generate or find additional questions to assess the other portions of
the standard.
These questions (and the students’ responses to the questions) should be a focus of your PLC
collaborative discussions. They will generate a wealth of information to be shared by the team. Here
are some facts quoted from Robert Marzano’s book Classroom Assessment and Grading that Work
(pp.5 – 6):
 When students receive feedback on a classroom assessment that simply tells them whether
their answers are correct or incorrect, learning is negatively influenced.
 When students are provided with the correct answer, learning is influenced in a positive
direction. This practice is associated with a gain of 8.5 percentile points in student
achievement.
 Providing students with explanations as to why their responses are correct or incorrect is
associated with a gain of 20 percentile points in student achievement.
 Asking students to continue responding to an assessment until they correctly answer the items
is associated with a gain of 20 percentile points.
 Displaying assessment results graphically can go a long way to helping students take control
of their own learning. However, this practice can also help teachers more accurately judge
students’ levels of understanding and skill. It is associated with a gain of 26 percentile points
in student achievement.
 Teachers within a school or a district should have rigorous and uniform ways of interpreting
the results of classroom assessments. If the interpretation of assessment results is done by a
set of rules, student achievement is enhanced by 32 percentile points.
4
Purpose and Use of this Pacing Guide
1. Emphasis for 2013-2014:
a. More emphasis is being placed on the Key Standards.
b. There are three common Instructional Segment Closing Dates.
c. Instructional Segment Assessment data will provide teachers with information to
improve and drive instruction through team and department collaboration.
d. Instructional Segment Assessment data may be used to provide information to assist
with grading, but should not be the only data used in determining grades.
2. Course Guide Format:
a. A scope and sequence of the National Educational Technology Standards has been
included to assist with the integration of the appropriate technology standards into 5th
grade math lessons.
b. The actual CST Blueprint from the California Department of Education has been
reproduced for this document. It lists all the fifth grade math standards and the number
of items per standard that are on the CST. It also identifies with an asterisk the Key
Standards (high impact standards) which comprise a minimum of 70% of the test.
c. Immediately following this official document is an “At a Glance” version of the
standards, which provides a one-page abbreviated summary of the standards.
d. The next section, CA Content Standards Unpacked, restates the standards, followed by
a listing of the individual skills and/or objectives encompassed by each standard. This
may be utilized as a checklist, to check off all components of each standard as they are
mastered. Teachers may even reproduce this section as a checklist for students to keep
in their notebook to keep track of their individual progress.
e. The Pacing Guide is separated into three Instructional Segments. An overview of the
three Instructional Segments is placed at the beginning of the next section. Each
Instructional Segment summary includes the Main Topics and Standards that must be
taught prior to the end of that Instructional Segment, with a space to record the sitespecific Essential Standards.
f. The next section contains a color-coded version of the CST Blueprint, aligning each
standard with the Instructional Segment where it is taught.
g. This is followed by a Benchmark Exam at a Glance page. This chart lists the CA
content standards tested on the first Instructional Segment Assessment, along with the
number of questions per standard on this assessment.
h. The CA content standards (with correlated textbook sections) to be mastered before
the end of each Instructional Segment are clearly shown on the Pacing Guide. This
pacing guide focuses on the textbook lessons needed to teach the fifth grade CA
content standards for mathematics and includes an alignment to the Released Test
Questions.
5
National Educational Technology Standards Grades Pre-K - 12
Scope and Sequence (H = Help / I = Introduce / D = Develop / IU = Independent Use)
Integration and Projects
PK K 1 2 3 4 5
Create developmentally appropriate multimedia
products with support from teachers or student
H
partners
Use technology resources for problem solving,
communication, & illustration of thoughts, ideas
H
& stories
Work responsibly, independently & as part of a
group in developing projects
Use teacher-created rubric for assessment of
project
Use technology for individual & collaborative
writing, communication & publishing activities to
create knowledge products for audiences inside &
outside the classroom.
Determine when technology is useful & select the
appropriate tools & technology resources to
address a variety of tasks & problems
Use information literacy skills to research &
evaluate the accuracy, relevance, appropriateness,
comprehensiveness & bias of information sources
concerning real-world problems
Save, find & retrieve work in different formats via
email, network & online sources for project work
Develop & use student-created rubrics for
assessment
Take on specific role & manage different group
activities & rotation strategies as part of a project
Develop essential & subsidiary questions as part
of projects
Properly cite all information sources
Design, develop, publish & present real-world
products using technology resources that
demonstrate & communicate curriculum concepts
to audiences inside & outside the classroom
Select appropriate technology tools for research,
information analysis, problem-solving &
decision-making in content learning as part of
project-based learning
Compile projects in electronic portfolio
6
7
8
9 10 11 12
H I D D D IU IU IU IU IU IU IU IU
H I D D D D IU IU IU IU IU IU IU
H I D D D IU IU IU IU IU IU IU
H I D D D D IU IU IU IU IU IU
H H I D D D IU IU IU IU IU IU
H H H I D D D IU IU IU IU IU
H H H I
D D D IU IU IU IU
H H H I
D D D IU IU IU IU
H H H I
D D D IU IU IU IU
H H H
I
D D D IU IU IU
H H H
I
D D D IU IU IU
H H H
I
D D D IU IU IU
H H H
I
D D D D IU
H H H
I
D D D D IU
H H H
I
D D D D
6
National Educational Technology Standards Grades Pre-K - 12
Scope and Sequence ( H = Help / I = Introduce / D = Develop / IU = Independent Use)
Social & Ethical Use
Understand and follow rules & procedures for
technology use
Work cooperatively & collaboratively with
others when using technology in the classroom
Demonstrate positive social & ethical behaviors
when using technology
Practice responsible use of technology systems
& software
Discuss responsible use of technology &
information & describe consequences of
inappropriate use
Demonstrate knowledge of current changes in
information technologies & the effect those
changes have on the workplace & society
Exhibit legal & ethical behaviors when using
information & technology & discuss
consequences of misuse
Understand & follow proper use of copyrighted
material & use netiquette when using email
Cite resources properly
Identify capabilities & limitations of emerging
technology resources & assess the potential of
these systems & services to address personal,
lifelong learning, & workplace needs
Access & use primary & secondary sources of
information for an activity
Demonstrate & advocate for legal & ethical
behaviors among peers, family & community
regarding the use of technology & information
PK K 1 2 3 4
5
6
7
8
9 10 11 12
H
I D D D IU IU IU IU IU IU IU IU IU
H
I D D D IU IU IU IU IU IU IU IU IU
H H I D D D IU IU IU IU IU IU IU IU
H H I D D
D
IU IU IU IU IU IU IU
H H H I D
D
D IU IU IU IU IU IU
H H H I
D
D
D IU IU IU IU IU
H H H H
I
D
D D IU IU IU IU
H H H
H
I
D D D IU IU IU
H H H
H
I
D D D IU IU IU
H H
H
H
I
D D D IU IU
H
H
H
I
D D D IU IU
H
H
H
I
D D D IU
7
CALIFORNIA STANDARDS TEST
GRADE 5 MATHEMATICS
(Blueprint adopted by the State Board of Education 10/02)
CALIFORNIA CONTENT STANDARDS: GRADE 5
# of
Items
%
By the end of grade five, students increase their facility with the four basic
arithmetic operations applied to fractions, decimals, and positive and negative
numbers. They know and use common measuring units to determine length and
area and know and use formulas to determine the volume of simple geometric
figures. Students know the concept of angle measurement and use a protractor
and compass to solve problems. They use grids, tables, graphs, and charts to
record and analyze data.
Number Sense
Standard Set 1.0 Students compute with very large and very
small numbers, positive integers, decimals, and fractions
and understand the relationship between decimals,
fractions, and percents. They understand the relative
magnitudes of numbers:
1.1
Estimate, round, and manipulate very large (e.g., millions)
and very small (e.g., thousandths) numbers.
1.2* Interpret percents as a part of a hundred; find decimal and
percent equivalents for common fractions and explain why
they represent the same value; compute a given percent
of a whole number.
1.3
Understand and compute positive integer powers of
nonnegative integers; compute examples as repeated
multiplication.
1.4* Determine the prime factors of all numbers through 50
and write the numbers as the product of their prime
factors by using exponents to show multiples of a factor
(e.g., 24 = 2 × 2 × 2 × 3 = 23 × 3).
1.5* Identify and represent on a number line decimals,
fractions, mixed numbers, and positive and negative
integers.
Standard Set 2.0 Students perform calculations and solve
problems involving addition, subtraction, and simple
multiplication and division of fractions and decimals:
2.1* Add, subtract, multiply, and divide with decimals; add with
negative integers; subtract positive integers from negative
integers; and verify the reasonableness of the results.
2.2* Demonstrate proficiency with division, including division
with positive decimals and long division with multi-digit
divisors.
*
Key standards comprise a minimum of 70% of the test
** Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
*** Not assessable in a multiple-choice format
Embedded: Content of standard is embedded within items in other strands.
© California Department of Education
29
45%
1
5
1
3
2
7
3
8
CALIFORNIA STANDARDS TEST
GRADE 5 MATHEMATICS
(Blueprint adopted by the State Board of Education 10/02)
CALIFORNIA CONTENT STANDARDS: GRADE 5
2.3*
2.4
2.5
Solve simple problems, including ones arising in concrete
situations, involving the addition and subtraction of
fractions and mixed numbers (like and unlike
denominators of 20 or less), and express answers in the
simplest form.
Understand the concept of multiplication and division of
fractions.
Compute and perform simple multiplication and division of
fractions and apply these procedures to solving problems.
# of
Items
5
1
1
Algebra and Functions
Standard Set 1.0 Students use variables in simple
expressions, compute the value of the expression for
specific values of the variable, and plot and interpret the
results:
1.1
Use information taken from a graph or equation to answer
questions about a problem situation.
1.2* Use a letter to represent an unknown number; write and
evaluate simple algebraic expressions in one variable by
substitution.
1.3
Know and use the distributive property in equations and
expressions with variables.
1.4* Identify and graph ordered pairs in the four quadrants of
the coordinate plane.
1.5* Solve problems involving linear functions with integer
values; write the equation; and graph the resulting
ordered pairs of integers on a grid.
17
Measurement and Geometry
Standard Set 1.0 Students understand and compute the
volumes and areas of simple objects:
1.1* Derive and use the formula for the area of a triangle and of
a parallelogram by comparing it with the formula for the
area of a rectangle (i.e., two of the same triangles make a
parallelogram with twice the area; a parallelogram is
compared with a rectangle of the same area by cutting
and pasting a right triangle on the parallelogram).
1.2* Construct a cube and rectangular box from twodimensional patterns and use these patterns to compute
the surface area for these objects.
15
*
Key standards comprise a minimum of 70% of the test
** Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
*** Not assessable in a multiple-choice format
Embedded: Content of standard is embedded within items in other strands.
© California Department of Education
%
26%
1
6
1
4
5
23%
2 1/2**
1/2**
9
CALIFORNIA STANDARDS TEST
GRADE 5 MATHEMATICS
(Blueprint adopted by the State Board of Education 10/02)
CALIFORNIA CONTENT STANDARDS: GRADE 5
Understand the concept of volume and use the
appropriate units in common measuring systems (i.e.,
cubic centimeter[cm3], cubic meter[m3], cubic inch[in3],
cubic yard[yd3]) to compute the volume of rectangular
solids.
1.4 Differentiate between and use appropriate units of
measures for, two- and three- dimensional objects (i.e.,
find perimeter, area, volume).
Standard Set 2.0 Students identify, describe, and classify
the properties of, and the relationships between, plane and
solid geometric figures:
2.1* Measure, identify, and draw angles, perpendicular and
parallel lines, rectangles, and triangles by using
appropriate tools (e.g., straightedge, ruler, compass,
protractor, drawing software).
2.2* Know that the sum of the angles of any triangle is 180°
and the sum of the angles of any quadrilateral is 360° and
use this information to solve problems.
2.3
Visualize and draw two-dimensional views of threedimensional objects made from rectangular solids.
# of
Items
%
1.3*
Statistics, Data Analysis, and Probability
Standard Set 1.0 Students display, analyze, compare, and
interpret different data sets, including data sets of different
sizes:
1.1 Know the concepts of mean, median, and mode; compute
and compare simple examples to show that they may
differ.
1.2 Organize and display single-variable data in appropriate
graphs and representations (e.g., histogram, circle graphs)
and explain which types of graphs are appropriate for
various data sets.
1.3
Use fractions and percentages to compare data sets of
different sizes.
1.4* Identify ordered pairs of data from a graph and interpret
the meaning of the data in terms of the situation depicted
by the graph.
1.5* Know how to write ordered pairs correctly; for example,
(x, y).
*
Key standards comprise a minimum of 70% of the test
** Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
*** Not assessable in a multiple-choice format
Embedded: Content of standard is embedded within items in other strands.
© California Department of Education
3
1
3
4
1
4
6%
1/3**
1/3**
1/3**
2 1/2**
1/2**
10
CALIFORNIA STANDARDS TEST
GRADE 5 MATHEMATICS
(Blueprint adopted by the State Board of Education 10/02)
CALIFORNIA CONTENT STANDARDS: GRADE 5
Mathematical Reasoning
Standard Set 1.0 Students make decisions about how to
approach problems:
1.1
Analyze problems by identifying relationships,
distinguishing relevant from irrelevant information,
sequencing and prioritizing information, and observing
patterns.
1.2
Determine when and how to break a problem into simpler
parts.
Standard Set 2.0 Students use strategies, skills, and
concepts in finding solutions:
2.1
Use estimation to verify the reasonableness of calculated
results.
2.2 Apply strategies and results from simpler problems to
more complex problems.
2.3
Use a variety of methods, such as words, numbers,
symbols, charts, graphs, tables, diagrams, and models, to
explain mathematical reasoning.
2.4
Express the solution clearly and logically by using the
appropriate mathematical notation and terms and clear
language; support solutions with evidence in both verbal
and symbolic work.
2.5
Indicate the relative advantages of exact and approximate
solutions to problems and give answers to a specified
degree of accuracy.
2.6
Make precise calculations and check the validity of the
results from the context of the problem.
Standard Set 3.0 Students move beyond a particular
problem by generalizing to other situations:
3.1
Evaluate the reasonableness of the solution in the context
of the original situation.
3.2 Note the method of deriving the solution and demonstrate
a conceptual understanding of the derivation by solving
similar problems.
3.3
Develop generalizations of the results obtained and apply
them in other circumstances.
GRADE 5 TOTAL
*
Key standards comprise a minimum of 70% of the test
** Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
*** Not assessable in a multiple-choice format
Embedded: Content of standard is embedded within items in other strands.
© California Department of Education
# of
Items
%
Embedded
Embedded
Embedded
Embedded
Embedded
Embedded
Embedded
Embedded
Embedded
Embedded
Embedded
Embedded
65
100%
11
# CST
Items
65
STD
29
45%
1
NS1.1
5
NS1.2*
1
NS1.3
3
NS1.4*
2
NS1.5*
7
NS2.1*
3
NS2.2*
5
NS2.3*
1
NS2.4
1
NS2.5
17
26%
1
AF1.1
6
AF1.2*
1
AF1.3
4
AF1.4*
5
AF1.5*
15
23%
2 1/2 MG1.1*
1/2 MG1.2*
3
MG1.3*
1
MG1.4
3
MG2.1*
4
MG2.2*
1
MG2.3
4
6%
1/3
SP1.1
1/3
SP1.2
1/3
SP1.3
2 1/2 SP1.4*
1/2
SP1.5*
Embedded
MR1.1
MR1.2
MR2.1
MR2.2
MR2.3
MR2.4
MR2.5
MR2.6
MR3.1
MR3.2
MR3.3
*
**
Math 5 Standards at a Glance
Standard
NUMBER SENSE
Estimate and Round Very Large and Very Small Numbers
Percents
Exponents
Prime Factorization of Numbers through 50
Number Line
Operations with Decimals, Positive and Negative Integers
Division, including Decimals and Long Division
Solve Problems: Addition and Subtraction of Fractions and Mixed Numbers
Understand Multiplication and Division of Fractions
Multiply and Divide Fractions
ALGEBRA and FUNCTIONS
Interpret Graphs and Equations
Write and Evaluate Simple Algebraic Expressions
Distributive Property
Identify and Graph Ordered Pairs
Solve and Graph Simple Linear Equations
MEASUREMENT and GEOMETRY
Area of Triangle and Parallelogram
Surface Area of Cube and Rectangular Box
Volume of Rectangular Solids
Appropriate Units of Measures for Two- and Three-Dimensional Objects
Measure, Identify and Draw Geometric Figures
Sum of the Angles of a Triangle and Quadrilateral
Draw Two-Dimensional Views of Three-Dimensional Rectangular Solids
STATISTICS, DATA ANALYSIS, AND PROBABILITY
Mean, median and mode
Histograms and Circle Graphs
Compare Data Sets using Fractions and Percentages
Interpret Data from a Graph
Write Ordered Pairs
MATHEMATICAL REASONING
Analyze Problems
Break a Problem into Simpler Parts
Estimation to Verify Reasonableness
Use Simpler Problems to Solve Complex Problems
Variety of Methods to Explain Mathematical Reasoning
Appropriate Mathematical Notation and Terms
Advantages of Exact and Approximate Solutions
Precise Calculations and Check Validity of Results
Reasonableness of Solution
Methods of Deriving a Solution to Solve Similar Problems
Generalize Results and Apply to Other Circumstances
Key standards comprise a minimum of 70% of the test
Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
12
STD
# CST
Items
Math 5 CA Content Standards Unpacked
STANDARD
45%
NS1.1
65
29
NUMBER SENSE
Estimate, round, and manipulate very large (e.g., millions) and very small (e.g.,
thousandths) numbers.
1
Estimate very large numbers
Estimate very small numbers
Round very large numbers
Round very small numbers
Manipulate very large numbers
Manipulate very small numbers
Interpret percents as a part of a hundred; find decimal and percent equivalents for
NS1.2* common fractions and explain why they represent the same value; compute a given
percent of a whole number.
5
Interpret percents as a part of a hundred
Find decimal equivalents for common fractions
Find percent equivalents for common fractions
Explain why decimal and percent equivalents represent the same value as fraction
Compute a given percent of a whole number
NS1.3
Understand and compute positive integer powers of nonnegative integers; compute
examples as repeated multiplication.
1
Understand positive integer powers of nonnegative integers
Compute positive integer powers of nonnegative integers
Compute positive integer powers of nonnegative integers as repeated multiplication
Determine the prime factors of all numbers through 50 and write the numbers as
NS1.4* the product of their prime factors by using exponents to show multiples of a factor
(e.g., 24 = 2 × 2 × 2 × 3 = 23 × 3).
3
Determine the prime factors of all numbers through 50
Write the numbers through 50 as the product of their prime factors using exponents
NS1.5*
Identify and represent on a number line decimals, fractions, mixed numbers, and
positive and negative integers.
2
Identify decimals on a number line
Identify fractions on a number line
Identify mixed numbers on a number line
Identify positive integers on a number line
Identify negative integers on a number line
Represent decimals on a number line
Represent fractions on a number line
Represent mixed numbers on a number line
Represent positive integers on a number line
Represent negative integers on a number line
Add, subtract, multiply, and divide with decimals; add with negative integers;
NS2.1* subtract positive integers from negative integers; and verify the reasonableness of
the results.
*
**
Key standards comprise a minimum of 70% of the test
Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
7
13
STD
# CST
Items
Math 5 CA Content Standards Unpacked
Add decimals and verify reasonableness of results
Subtract decimals and verify reasonableness of results
Multiply decimals and verify reasonableness of results
Divide decimals and verify reasonableness of results
Add with negative integers and verify reasonableness of results
Subtract positive integers from negative integers and verify reasonableness of results
NS2.2*
Demonstrate proficiency with division, including division with positive decimals and
long division with multi-digit divisors.
3
Demonstrate proficiency with division
Demonstrate proficiency with division using positive decimals
Demonstrate proficiency with long division using multi-digit divisors
Solve simple problems, including ones arising in concrete situations, involving the
NS2.3* addition and subtraction of fractions and mixed numbers (like and unlike
denominators of 20 or less), and express answers in the simplest form.
5
Solve word problems involving addition of fractions with like denominators and simplify
Solve word problems involving addition of fractions with unlike denominators of 20 or less and simplify
Solve word problems involving subtraction of fractions with like denominators and simplify
Solve word problems involving subtraction of fractions with unlike denominators of 20 or less and simplify
Solve word problems involving addition of mixed numbers with like denominators and simplify
Solve word problems involving addition of mixed numbers with unlike denominators of 20 or less and
simplify
Solve word problems involving subtraction of mixed numbers with like denominators and simplify
Solve word problems involving subtraction of mixed numbers with unlike denominators of 20 or less and
simplify
NS2.4
1
Understand the concept of multiplication and division of fractions.
Understand the concept of multiplication of fractions
Understand the concept of division of fractions
NS2.5
Compute and perform simple multiplication and division of fractions and apply
these procedures to solving problems.
1
Compute and perform simple multiplication of fractions
Compute and perform simple division of fractions
Solve word problems involving simple multiplication of fractions
Solve word problems involving simple division of fractions
26%
AF1.1
ALGEBRA and FUNCTIONS
Use information taken from a graph or equation to answer questions about a
problem situation.
17
1
Use information taken from a graph to answer questions about a problem situation
Use information taken from an equation to answer questions about a problem situation
AF1.2*
*
**
Use a letter to represent an unknown number; write and evaluate simple algebraic
expressions in one variable by substitution.
Use a letter to represent an unknown number
Write simple algebraic expressions in one variable
Evaluate simple algebraic expressions in one variable by substitution
Key standards comprise a minimum of 70% of the test
Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
6
14
STD
Math 5 CA Content Standards Unpacked
# CST
Items
AF1.3
Know and use the distributive property in equations and expressions with variables.
1
Know the distributive property
Use the distributive property in equations and expressions with variables
AF1.4*
Identify and graph ordered pairs in the four quadrants of the coordinate plane.
4
Identify ordered pairs in the four quadrants of the coordinate plane
Graph ordered pairs in the four quadrants of the coordinate plane
AF1.5*
Solve problems involving linear functions with integer values; write the equation;
and graph the resulting ordered pairs of integers on a grid.
5
Solve problems involving linear functions with integer values
Write the equation for problems involving linear functions
Graph ordered pairs of linear functions on the coordinate plane
23%
MEASUREMENT and GEOMETRY
Derive and use the formula for the area of a triangle and of a parallelogram by
comparing it with the formula for the area of a rectangle (i.e., two of the same
MG1.1* triangles make a parallelogram with twice the area; a parallelogram is compared
with a rectangle of the same area by cutting and pasting a right triangle on the
parallelogram).
15
2 1/2
Derive the formula for the area of a triangle by comparing it with the formula for the area of a rectangle
Derive the formula for the area of a parallelogram by comparing it with the formula for the area of a
rectangle
Use the formula for the area of a triangle
Use the formula for the area of a parallelogram
MG1.2*
Construct a cube and rectangular box from two-dimensional patterns and use these
patterns to compute the surface area for these objects.
1/2
Construct a cube from two-dimensional patterns
Compute the surface area of a cube using the two-dimensional patterns
Construct a rectangular box from two-dimensional patterns
Compute the surface area of a rectangular box using the two-dimensional patterns
Understand the concept of volume and use the appropriate units in common
MG1.3* measuring systems (i.e., cubic centimeter[cm3], cubic meter[m3], cubic inch[in3],
cubic yard[yd3]) to compute the volume of rectangular solids.
3
Understand the concept of volume
Use appropriate units in common measuring systems to compute the volume of rectangular solids
MG1.4
Differentiate between and use appropriate units of measures for, two- and threedimensional objects (i.e., find perimeter, area, volume).
1
Differentiate between appropriate units of measures for two- and three- dimensional objects
Use appropriate units of measures for two- and three- dimensional objects
Find perimeter
Find area
Find volume
*
**
Key standards comprise a minimum of 70% of the test
Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
15
STD
# CST
Items
Math 5 CA Content Standards Unpacked
Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and
MG2.1* triangles by using appropriate tools (e.g., straightedge, ruler, compass, protractor,
drawing software).
3
Identify angles
Identify perpendicular lines
Identify parallel lines
Identify rectangles
Identify triangles
Measure angles using appropriate tools
Measure rectangles using appropriate tools
Measure triangles using appropriate tools
Draw angles using appropriate tools
Draw perpendicular lines using appropriate tools
Draw parallel lines using appropriate tools
Draw rectangles using appropriate tools
Draw triangles using appropriate tools
MG2.2*
Know that the sum of the angles of any triangle is 180° and the sum of the angles of
any quadrilateral is 360° and use this information to solve problems.
4
Know that the sum of the angles of any triangle is 180°
Know that the sum of the angles of any quadrilateral is 360°
Solve problems using the sum of the angles of a triangle
Solve problems using the sum of the angles of a quadrilateral
MG2.3
Visualize and draw two-dimensional views of three-dimensional objects made from
rectangular solids.
1
Visualize two-dimensional views of three-dimensional objects made from rectangular solids
Draw two-dimensional views of three-dimensional objects made from rectangular solids
6%
SP1.1
STATISTICS, DATA ANALYSIS, AND PROBABILITY
Know the concepts of mean, median, and mode; compute and compare simple
examples to show that they may differ.
4
1/3
Know the concept of mean
Compute mean
Know the concept of median
Compute median
Know the concept of mode
Compute mode
Compare simple examples to show that mean, median and mode may differ
SP1.2
*
**
Organize and display single-variable data in appropriate graphs and representations
(e.g., histogram, circle graphs) and explain which types of graphs are appropriate for
various data sets.
Organize single-variable data in appropriate graphs and representations (e.g., histogram, circle graphs)
Display single-variable data in appropriate graphs and representations (e.g., histogram, circle graphs)
Explain which types of graphs are appropriate for various data sets
Key standards comprise a minimum of 70% of the test
Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
16
1/3
STD
SP1.3
# CST
Items
Math 5 CA Content Standards Unpacked
1/3
Use fractions and percentages to compare data sets of different sizes.
Use fractions to compare data sets of different sizes
Use percentages to compare data sets of different sizes
SP1.4*
Identify ordered pairs of data from a graph and interpret the meaning of the data in
terms of the situation depicted by the graph.
2 1/2
Identify ordered pairs of data from a graph
Interpret the meaning of the data in terms of the situation depicted by a graph
SP1.5*
Know how to write ordered pairs correctly; for example, (x, y).
1/2
Write ordered pairs correctly; for example (x, y)
MR1.1
MATHEMATICAL REASONING
Analyze problems by identifying relationships, distinguishing relevant from
irrelevant information, sequencing and prioritizing information, and observing
patterns.
Embed
Analyze problems by identifying relationships
Analyze problems by distinguishing relevant from irrelevant information
Analyze problems by sequencing and prioritizing information
Analyze problems by observing patterns
MR1.2
Determine when and how to break a problem into simpler parts.
Determine when to break a problem into simpler parts
Determine how to break a problem into simpler parts
MR2.1
Use estimation to verify the reasonableness of calculated results.
Use estimation to verify the reasonableness of calculated results
MR2.2
Apply strategies and results from simpler problems to more complex problems.
Apply strategies from simpler problems to more complex problems
Apply results from simpler problems to more complex problems
MR2.3
Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables,
diagrams,
Use words to explain mathematical reasoning
Use numbers to explain mathematical reasoning
Use symbols to explain mathematical reasoning
Use charts to explain mathematical reasoning
Use graphs to explain mathematical reasoning
Use tables to explain mathematical reasoning
Use diagrams to explain mathematical reasoning
Use models to explain mathematical reasoning
MR2.4
Express the solution clearly and logically by using the appropriate mathematical
notation and terms and clear language; support solutions with evidence in both
verbal and symbolic work.
Express solutions clearly and logically by using the appropriate mathematical notation and terms
Express solutions clearly and logically by using clear language
Support solutions with evidence in verbal work
*
**
Key standards comprise a minimum of 70% of the test
Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
17
STD
# CST
Items
Math 5 CA Content Standards Unpacked
Support solutions with evidence in symbolic work
MR2.5
Indicate the relative advantages of exact and approximate solutions to problems and
give answers to a specified degree of accuracy.
Indicate the relative advantages of exact and approximate solutions to problems
Give answers to a specified degree of accuracy
MR2.6
Make precise calculations and check the validity of the results from the context of
the problem.
Make precise calculations
Check the validity of results from the context of the problem
MR3.1
Evaluate the reasonableness of the solution in the context of the original situation.
Evaluate the reasonableness of the solution in the context of the original situation
MR3.2
Note the method of deriving the solution and demonstrate a conceptual
understanding of the derivation by solving similar problems.
Note the method of deriving the solution
Demonstrate a conceptual understanding of the derivation of a solution by solving similar problems
MR3.3
Develop generalizations of the results obtained and apply them in other
circumstances.
Develop generalizations of the results obtained
Apply generalizations of the results in other circumstances
*
**
Key standards comprise a minimum of 70% of the test
Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
18
INSRTUCTIONAL SEGMENT 1 – Math 5
Benchmark Exam #1 Closing Dates
Traditional: November 22, 2013
Modified: November 1, 2013
Main Topics
 Numeration (Topic 1)
 Addition and Subtraction Number Sense (Topic 2)
 Multiplication (Topics 3, 6)
 Division (Topics 4, 7)
Standards
Topic 1 Numeration
 NS 1.1 Estimate, round, and manipulate very large (e.g., millions) and very small (e.g., thousandths)
numbers.
Topic 2 Addition and Subtraction Number Sense
 NS 1.1 Estimate, round, and manipulate very large (e.g., millions) and very small (e.g., thousandths)
numbers.
 NS 2.1* Add, subtract, multiply, and divide with decimals; add with negative integers; subtract
positive integers from negative integers; and verify the reasonableness of the results.
Topic 3 Multiplication of Whole Numbers
 NS 1.1 Estimate, round, and manipulate very large (e.g., millions) and very small (e.g., thousandths)
numbers.
 NS 1.3 Understand and compute positive integer powers of nonnegative integers; compute examples as
repeated multiplication.
Topic 6 Multiplying Decimals
 NS 2.1* Add, subtract, multiply, and divide with decimals; add with negative integers; subtract
positive integers from negative integers; and verify the reasonableness of the results.
Topic 4 Division of Whole Numbers
 NS 1.1 Estimate, round, and manipulate very large (e.g., millions) and very small (e.g., thousandths)
numbers.
 NS 2.2* Demonstrate proficiency with division, including division with positive decimals and long
division with multi-digit divisors.
*
**
Key standards comprise a minimum of 70% of the test
Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
19
Topic 7 Dividing Decimals
 NS 1.1 Estimate, round, and manipulate very large (e.g., millions) and very small (e.g., thousandths)
numbers.
 NS 2.1* Add, subtract, multiply, and divide with decimals; add with negative integers; subtract
positive integers from negative integers; and verify the reasonableness of the results.
 NS 2.2* Demonstrate proficiency with division, including division with positive decimals and long
division with multi-digit divisors.
Essential Standards
*
**
Key standards comprise a minimum of 70% of the test
Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
20
INSTRUCTIONAL SEGMENT 2 – Math 5
CST Mirror Test Closing Dates
Traditional: March 7, 2014
Modified: February 28, 2014
Please Note: This entire Instructional Segment should be completed before
the administration of the CST Mirror Test. Topics 8 and 14 from the next
Instructional Segment should be completed before the administration of the
actual CST.
Main Topics
 Factors and Multiples (Topic 9)
 Fractions, Mixed Numbers, and Decimals (Topic 10)
 Adding and Subtracting Fractions and Mixed Numbers (Topic 11)
 Percents (Topic 17)
 Integers (Topic 15)
 Variables and Expressions (Topic 5)
 Equations (Topic 16)
 Equations and Graphs (Topic 18)
 Graphs and Data (Topic 19)
Standards
Topic 9 Factors and Multiples
 NS 1.4* Determine the prime factors of all numbers through 50 and write the numbers as the
product of their prime factors by using exponents to show multiples of a factor (e.g., 24 =
2 × 2 × 2 × 3 = 23 × 3).
Topic 10 Fractions, Mixed Numbers, and Decimals
 NS 1.5* Identify and represent on a number line decimals, fractions, mixed numbers, and positive
and negative integers.
Topic 11 Adding and Subtracting Fractions and Mixed Numbers
 NS 2.3* Solve simple problems, including ones arising in concrete situations, involving the
addition and subtraction of fractions and mixed numbers (like and unlike denominators
of 20 or less), and express answers in the simplest form.
Topic 17 Percents
 NS 1.2* Interpret percents as a part of a hundred; find decimal and percent equivalents for
common fractions and explain why they represent the same value; compute a given
percent of a whole number.
Topic 15 Integers
 NS 1.5* Identify and represent on a number line decimals, fractions, mixed numbers, and positive
and negative integers.
 NS 2.1* Add, subtract, multiply, and divide with decimals; add with negative integers; subtract
positive integers from negative integers; and verify the reasonableness of the results.
*
**
Key standards comprise a minimum of 70% of the test
Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
21
 AF 1.2* Use a letter to represent an unknown number; write and evaluate simple algebraic
expressions in one variable by substitution.
Topic 5 Variables and Expressions
 AF 1.1 Use information taken from a graph or equation to answer questions about a problem situation.
 AF 1.2* Use a letter to represent an unknown number; write and evaluate simple algebraic
expressions in one variable by substitution.
 AF 1.3 Know and use the distributive property in equations and expressions with variables.
Topic 16 Solving and Writing Equations
 AF 1.2* Use a letter to represent an unknown number; write and evaluate simple algebraic
expressions in one variable by substitution.
 AF 1.5* Solve problems involving linear functions with integer values; write the equation; and
graph the resulting ordered pairs of integers on a grid.
Topic 18 Equations and Graphs
 AF1.4* Identify and graph ordered pairs in the four quadrants of the coordinate plane.
 AF 1.5* Solve problems involving linear functions with integer values; write the equation; and
graph the resulting ordered pairs of integers on a grid.
 SDP1.4* Identify ordered pairs of data from a graph and interpret the meaning of the data in
terms of the situation depicted by the graph.
 SDP1.5* Know how to write ordered pairs correctly; for example, (x, y).
Topic 19 Graphs and Data
 AF 1.1 Use information taken from a graph or equation to answer questions about a problem situation.
 SDP1.1 Know the concepts of mean, median, and mode; compute and compare simple examples to
show that they may differ.
 SDP1.2 Organize and display single-variable data in appropriate graphs and representations (e.g.,
histogram, circle graphs) and explain which types of graphs are appropriate for various data
sets.
 SDP1.3 Use fractions and percentages to compare data sets of different sizes.
 SDP1.4* Identify ordered pairs of data from a graph and interpret the meaning of the data in
terms of the situation depicted by the graph.
Essential Standards
*
**
Key standards comprise a minimum of 70% of the test
Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
22
INSTRUCTIONAL SEGMENT 3 - Math 5
Site-Based End of Year Assessments Closing Dates
Traditional: June 13, 2014
Modified: June 26, 2014
PLEASE COMPLETE TOPICS 8 AND 14 BEFORE THE
ADMINISTRATION OF THE CST.
Main Topics
 Shapes (Topic 8)
 Solids (Topic 14)
 CST Review and Administration
 Construction (Topic 20)
 Multiplying and Dividing Fractions and Mixed Numbers (Topic 12)
 Length, Perimeter and Area (Topic 13)
Standards
Topic 8 Shapes
 MG2.1* Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and
triangles by using appropriate tools (e.g., straightedge, ruler, compass, protractor,
drawing software).
 MG2.2* Know that the sum of the angles of any triangle is 180° and the sum of the angles of any
quadrilateral is 360° and use this information to solve problems.
Topic 14 Solids
 MG1.2* Construct a cube and rectangular box from two-dimensional patterns and use these
patterns to compute the surface area for these objects.
 MG1.3* Understand the concept of volume and use the appropriate units in common measuring
systems (i.e., cubic centimeter[cm3], cubic meter[m3], cubic inch[in3], cubic yard[yd3]) to
compute the volume of rectangular solids.
 MG 2.3 Visualize and draw two-dimensional views of three-dimensional objects made from rectangular
solids.
Topic 20 Constructions
 MG2.1* Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and
triangles by using appropriate tools (e.g., straightedge, ruler, compass, protractor,
drawing software).
Topic 12 Multiplying and Dividing Fractions and Mixed Numbers
 NS 2.4 Understand the concept of multiplication and division of
fractions.
 NS 2.5 Compute and perform simple multiplication and division of fractions and apply these
procedures to solving problems.
*
**
Key standards comprise a minimum of 70% of the test
Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
23
Topic 13 Length, Perimeter and Area
 MG1.1* Derive and use the formula for the area of a triangle and of a parallelogram by comparing
it with the formula for the area of a rectangle (i.e., two of the same triangles make a
parallelogram with twice the area; a parallelogram is compared with a rectangle of the
same area by cutting and pasting a right triangle on the parallelogram).
 MG 1.4 Differentiate between and use appropriate units of measures for, two- and three- dimensional
objects (i.e., find perimeter, area, volume).
Essential Standards
*
**
Key standards comprise a minimum of 70% of the test
Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
24
CALIFORNIA STANDARDS TEST - GRADE 5 MATHEMATICS
INSTRUCTIONAL SEGMENT 1
INSTRUCTIONAL SEGMENT 2
INSTRUCTIONAL SEGMENT 3
CALIFORNIA CONTENT STANDARDS: GRADE 5
# of
Items
%
By the end of grade five, students increase their facility with the four basic
arithmetic operations applied to fractions, decimals, and positive and negative
numbers. They know and use common measuring units to determine length and
area and know and use formulas to determine the volume of simple geometric
figures. Students know the concept of angle measurement and use a protractor
and compass to solve problems. They use grids, tables, graphs, and charts to
record and analyze data.
Number Sense
Standard Set 1.0 Students compute with very large and very
small numbers, positive integers, decimals, and fractions
and understand the relationship between decimals,
fractions, and percents. They understand the relative
magnitudes of numbers:
1.1
Estimate, round, and manipulate very large (e.g., millions)
and very small (e.g., thousandths) numbers.
1.2* Interpret percents as a part of a hundred; find decimal and
percent equivalents for common fractions and explain why
they represent the same value; compute a given percent
of a whole number.
1.3
Understand and compute positive integer powers of
nonnegative integers; compute examples as repeated
multiplication.
1.4* Determine the prime factors of all numbers through 50
and write the numbers as the product of their prime
factors by using exponents to show multiples of a factor
(e.g., 24 = 2 × 2 × 2 × 3 = 23 × 3).
1.5* Identify and represent on a number line decimals,
fractions, mixed numbers, and positive and negative
integers.
Standard Set 2.0 Students perform calculations and solve
problems involving addition, subtraction, and simple
multiplication and division of fractions and decimals:
2.1* Add, subtract, multiply, and divide with decimals; add with
negative integers; subtract positive integers from negative
integers; and verify the reasonableness of the results.
2.1* Add, subtract, multiply, and divide with decimals; add with
negative integers; subtract positive integers from negative
integers; and verify the reasonableness of the results.
2.2* Demonstrate proficiency with division, including division
with positive decimals and long division with multi-digit
divisors.
*
Key standards comprise a minimum of 70% of the test
** Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
*** Not assessable in a multiple-choice format
© California Department of Education
29
45%
1
5
1
3
2
7
7
3
25
CALIFORNIA STANDARDS TEST - GRADE 5 MATHEMATICS
INSTRUCTIONAL SEGMENT 1
INSTRUCTIONAL SEGMENT 2
INSTRUCTIONAL SEGMENT 3
CALIFORNIA CONTENT STANDARDS: GRADE 5
2.3*
2.4
2.5
Solve simple problems, including ones arising in concrete
situations, involving the addition and subtraction of
fractions and mixed numbers (like and unlike
denominators of 20 or less), and express answers in the
simplest form.
Understand the concept of multiplication and division of
fractions.
Compute and perform simple multiplication and division of
fractions and apply these procedures to solving problems.
# of
Items
5
1
1
Algebra and Functions
Standard Set 1.0 Students use variables in simple
expressions, compute the value of the expression for
specific values of the variable, and plot and interpret the
results:
1.1
Use information taken from a graph or equation to answer
questions about a problem situation.
1.2* Use a letter to represent an unknown number; write and
evaluate simple algebraic expressions in one variable by
substitution.
1.3
Know and use the distributive property in equations and
expressions with variables.
1.4* Identify and graph ordered pairs in the four quadrants of
the coordinate plane.
1.5* Solve problems involving linear functions with integer
values; write the equation; and graph the resulting
ordered pairs of integers on a grid.
17
Measurement and Geometry
Standard Set 1.0 Students understand and compute the
volumes and areas of simple objects:
1.1* Derive and use the formula for the area of a triangle and of
a parallelogram by comparing it with the formula for the
area of a rectangle (i.e., two of the same triangles make a
parallelogram with twice the area; a parallelogram is
compared with a rectangle of the same area by cutting
and pasting a right triangle on the parallelogram).
1.2* Construct a cube and rectangular box from twodimensional patterns and use these patterns to compute
the surface area for these objects.
15
*
Key standards comprise a minimum of 70% of the test
** Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
*** Not assessable in a multiple-choice format
© California Department of Education
%
26%
1
6
1
4
5
23%
2 1/2**
1/2**
26
CALIFORNIA STANDARDS TEST - GRADE 5 MATHEMATICS
INSTRUCTIONAL SEGMENT 1
INSTRUCTIONAL SEGMENT 2
INSTRUCTIONAL SEGMENT 3
CALIFORNIA CONTENT STANDARDS: GRADE 5
Understand the concept of volume and use the
appropriate units in common measuring systems (i.e.,
cubic centimeter[cm3], cubic meter[m3], cubic inch[in3],
cubic yard[yd3]) to compute the volume of rectangular
solids.
1.4 Differentiate between and use appropriate units of
measures for, two- and three- dimensional objects (i.e.,
find perimeter, area, volume).
Standard Set 2.0 Students identify, describe, and classify
the properties of, and the relationships between, plane and
solid geometric figures:
2.1* Measure, identify, and draw angles, perpendicular and
parallel lines, rectangles, and triangles by using
appropriate tools (e.g., straightedge, ruler, compass,
protractor, drawing software).
2.2* Know that the sum of the angles of any triangle is 180°
and the sum of the angles of any quadrilateral is 360° and
use this information to solve problems.
2.3
Visualize and draw two-dimensional views of threedimensional objects made from rectangular solids.
# of
Items
%
1.3*
Statistics, Data Analysis, and Probability
Standard Set 1.0 Students display, analyze, compare, and
interpret different data sets, including data sets of different
sizes:
1.1 Know the concepts of mean, median, and mode; compute
and compare simple examples to show that they may
differ.
1.2 Organize and display single-variable data in appropriate
graphs and representations (e.g., histogram, circle graphs)
and explain which types of graphs are appropriate for
various data sets.
1.3
Use fractions and percentages to compare data sets of
different sizes.
1.4* Identify ordered pairs of data from a graph and interpret
the meaning of the data in terms of the situation depicted
by the graph.
1.5* Know how to write ordered pairs correctly; for example,
(x, y).
GRADE 5 TOTAL
*
Key standards comprise a minimum of 70% of the test
** Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
*** Not assessable in a multiple-choice format
© California Department of Education
3
1
3
4
1
4
6%
1/3**
1/3**
1/3**
2 1/2**
1/2**
65
100%
27
MATH 5 BENCHMARK EXAM #1 AT A GLANCE
Benchmark Exam #1 Closing Dates:
Traditional: November 22, 2013
Modified: November 1, 2013
#
Items
STD
4
NS1.1
4
NS1.3
6
NS2.1*
7+
NS2.2*
+One
STANDARD
Estimate, round, and manipulate very large (e.g., millions) and very small (e.g.,
thousandths) numbers.
Understand and compute positive integer powers of nonnegative integers; compute
examples as repeated multiplication.
Add, subtract, multiply, and divide with decimals; and verify the
reasonableness of the results.
Demonstrate proficiency with division, including division with positive
decimals and long division with multi-digit divisors.
of the questions for this standard is an open-ended, constructed response question.
*
Key standards comprise a minimum of 70% of the test
** Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years)
*** Not assessable in a multiple-choice format
© California Department of Education
28
MATH 5 VOCABULARY
Instructional Segment 1
Instructional Segment 2
Instructional Segment 3
Topic 1: digits, value, standard
form, expanded form, word
form, equivalent decimals
Topic 9: factor pair, divisible,
prime number, composite
number, prime factorization,
common factor, greatest
common factor
Topic 10: Common Factor,
Greatest Common Factor
(GCF),
Fraction, mixed number,
simplest form, improper
fraction, benchmark fraction
Topic 11: common
denominator, denominator,
numerator, common multiple,
least common multiple, least
common denominator
Topic 8: algebraic expression,
line, ray, parallel lines,
intersecting lines, point, line
segment, plane , angle, acute
angle, right angle, obtuse angle,
straight angle, vertex,
protractor, degrees, polygon,
regular polygon, triangle,
quadrilateral, pentagon,
hexagon, octagon, equilateral
triangle, isosceles triangle,
scalene triangle, right triangle,
acute triangle, obtuse triangle,
parallelogram, trapezoid,
rectangle, square,
generalization
Topic 2: Commutative
Property,
Associative Property,
compensation, compatible
numbers, rounding
Topic 3: equation, factors,
product, Commutative Property
of Multiplication, Associative
Property of Multiplication,
Identity Property of
Multiplication, Zero Property of
Topic 17: ratio, equal ratios,
Multiplication, overestimate,
percent
underestimate, power, base,
Topic 15: inverse, integers
exponent, exponential notation,
standard form, expanded form
Topic 5: compatible numbers,
algebraic expression, variable,
Distributive Property, order of
operations
Topic 6: equivalent fractions,
Topic 16: equality, inverse
factors, mixed numbers
operations, equation, Addition
Property of Equality,
Subtraction Property of
Equality, Multiplication
Property of Equality, Division
Property of Equality
Topic 4: Dividend, divisor,
Topic 18: coordinate grid,
quotient, remainder
ordered pair, coordinate plane,
x-axis, y-axis, origin, xcoordinate, y-coordinate, trend,
data, line graph, table of values,
linear equations
Topic 7: tenths, thousandths
Topic 19: bar graph, picture
graph, scale, interval,
histogram, circle graph, mean,
median, mode, range, tree
diagram, sample space,
probability, equally likely
Topic 14: solid figure, face,
edge, vertex, cube, prism,
cylinder, cone, pyramid, net,
surface area, volume, cubic unit
Topic 20: mean, median, mode,
construction
Topic 12: improper fraction,
reciprocal, multiplicative
inverse
Topic 13: perimeter, formula,
area, base, height
29
MATH 5 VOCABULRY IN SPANISH
Instructional Segment 1
Instructional Segment 2
Instructional Segment 3
Topic 1: dígitos, valor, forma
estándar, forma ampliada, forma
escrita, decimales equivalentes
Topic 9: par de factores,
divisible, número primo, número
compuesto, factorización prima,
factor común, el más grande
factor común
Topic 2: Propiedad Comutativa,
Propiedad Associativa,
compensación, números
compatibles, redondear
Topic 10: factor común, el más
grande factor común, fracción,
número mixto, forma simple,
fracción impropia, fracción de
Topic 8: expreción algebráica,
linea, rayo, lineas paralelas, lineas
intersectantes, punto, segmento
linear, plano, ángulo, ángulo
agudo, ángulo recto, ángulo
obtuso, ángulo llano, vértice,
transportador, grados, polígono,
polígono regular, triángulo,
cuadrilátero, pentágono,
hexágono, octágono, triángulo
equilátero, triángulo isósceles,
triángulo escaleno, triángulo recto,
triángulo agudo, triángulo obtuso,
paralelogramo, trapezoide,
rectángulo, cuadrado,
referencia
Topic 3: ecuación, factores,
producto, Propiedad Comutativa
de la Multiplicación, Propiedad
Associativa de la Multiplicación,
Propiedad de Identidad de la
Multiplicación, Propiedad de Cero
de la Multiplicación, sobreestimar,
subestimar, potencia, base,
exponente, notación exponencial,
forma estándar, forma ampliada
Topic 6: fracciones equivalentes,
factores, números mixtos
Topic 4: dividendo, divisor,
cociente, resto
Topic 7: décimos, milésimos
Topic 11: denominador común,
denominador, numerador, común
múltiplo, mínimo común múltiplo,
mínimo común denominador
Topic 17: razón, razones
equivalentes, porciento
Topic 15: inverso, numeros
enteros
Topic 5: números compatibles,
expreción algebráica, variable,
propiedad distributiva, orden de
operación
Topic 16: igualdad, operaciones
inversas, ecuación, Propiedad
Aditiva de Igualdad, Propiedad de
Resta de Igualdad, Propiedad
Multiplicativa de Igualdad,
Propiedad de División de
Igualdad
Topic 18: rejilla coordenada, par
ordenado, plano coordenado, eje de
la x, eje de la y, origen, coordenada
de la x, coordenada de la y,
tendencia, datos, diagrama de
linea, cuadro de los valores,
ecuaciones lineales
Topic 19: gráfica de barra,
pictografia, escala, intervalo,
histogramo, gráfica circular,
promedio, media, moda, gama,
diagrama de árbol, muestra,
probabilidad, probabilidad
generalización
Topic 14: figura sólida, cara,
borde, vértice, cubo, prisma,
cilíndro, cono, pirámide, red, área
superficial, volumen, unidad cúbica
Topic 20: promedio, media,
moda, construcción
Topic 12: fracción impropia,
recíproco, inverso multiplicativo
Topic 13: perímetro, fórmula,
área, base, altura
equivalente
30
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INSTRUCTIONAL SEGMENT 1
RTQ’s
Other
Resources
# of
Days
VOCABULARY LIST 1
Grade level teams may determine order of topics taught WITHIN each Instructional Segment.
Focus on word problems and problem solving strategies throughout this Instructional Segment
TOPIC 1
NUMERATION
Estimate, round, and manipulate very large (e.g., millions) and very small
(e.g., thousandths) numbers.
Place value
1.1
Comparing and ordering whole numbers
1.2
Decimal place value
1.3
Comparing and ordering decimals
Analyze problems by identifying relationships, distinguishing relevant
Embed MR 1.1 from irrelevant information, sequencing and prioritizing information, and
observing patterns.
Problem Solving: Look for a pattern
1.4
1
NS 1.1
Review/reteach/enrich/assess
1.5
pp. 18-20
TOPIC 2
ADDITION AND SUBTRACTION NUMBER SENSE
Review
1
NS 1.1
Review
Mental math (optional)
Estimate, round, and manipulate very large (e.g., millions) and very small
(e.g., thousandths) numbers.
Rounding whole numbers and decimals
2.1
Estimating sums and differences
2.3
Adding and subtracting
2.4
2.2
Grade 4 Standard
1, 2
Grade 4 Standard
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Add, subtract, multiply, and divide with decimals; add with negative
NS 2.1* integers; subtract positive integers from negative integers; and verify
the reasonableness of the results.
Embed MR 2.1 Use estimation to verify the reasonableness of calculated results.
7
Adding decimals
2.5
Subtracting decimals
Use a variety of methods, such as words, numbers, symbols, charts,
Embed MR 2.3
graphs, tables, diagrams and models, to explain mathematical reasoning.
Problem Solving: Draw a picture and write an equation
2.6
Review/reteach/enrich/assess
23, 26
2.7
pp. 46-48
TOPIC 3
REVIEWING MULTIPLICATION OF WHOLE NUMBERS
6th Grade
1
Embed
1
Multiplication properties (optional)
Estimate, round, and manipulate very large (e.g., millions) and very small
(e.g., thousandths) numbers
Estimating products
3.1
Review
Multiplying by 1-digit numbers (optional)
3.3
Grade 4 Standard
Review
Multiplying by 2-digit numbers (optional)
3.4
Grade 4 Standard
NS 1.1
Grade 6 Standard
3.2
MR 2.1 Use estimation to verify the reasonableness of calculated results.
Estimating and multiplying with greater numbers
Understand and compute positive integer powers of nonnegative integers;
NS 1.3
compute examples as repeated multiplication.
Exponents
Analyze problems by identifying relationships, distinguishing relevant
MR 1.1 from irrelevant information, sequencing and prioritizing information, and
observing patterns.
MR 1.2 Determine when and how to break a problem into simpler parts.
3.5
Problem Solving: Multiple step problems
3.7
3.6
10
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pp. 72-74
TOPIC 6
MULTIPLYING DECIMALS
Add, subtract, multiply, and divide with decimals; add with negative
NS 2.1* integers; subtract positive integers from negative integers; and verify
the reasonableness of the results.
Multiplying decimals by 10, 100, 1000
6.1
Multiplying a whole number and a decimal
6.2
Estimating the product of a whole number and a decimal
6.3
Multiplying two decimals
6.4
MR 2.1 Use estimation to verify the reasonableness of calculated results.
Indicate the relative advantages of exact and approximate solutions to
Embed MR 2.5
problems and give answers to a specified degree of accuracy.
Make precise calculations and check the validity of the results from the
Embed MR2.6
context of the problem.
Problem Solving: Reasonableness
6.6
7
22, 25
20, 24, 27
Embed
Review/reteach/enrich/assess pp. 148-150
TOPIC 4
DIVISION OF WHOLE NUMBERS
3
1
3
Demonstrate proficiency with division, including division with positive
decimals and long division with multi-digit divisors.
Using patterns to divide
Estimate, round, and manipulate very large (e.g., millions) and very small
NS 1.1
(e.g., thousandths) numbers
Estimating quotients
Demonstrate proficiency with division, including division with positive
NS 2.2*
decimals and long division with multi-digit divisors.
Connecting models and symbols
NS 2.2*
4.1
4.2
4.3
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Dividing by one digit divisors
4.4
Zeros in the quotients
4.5
Dividing by two digit divisors
4.6
30, 31
More dividing by two digit advisors
Estimate, round, and manipulate very large (e.g., millions) and very small
1
NS 1.1
(e.g., thousandths) numbers
Estimating and dividing with greater numbers
Use a variety of methods, such as words, numbers, symbols, charts,
Embed MR 2.3
graphs, tables, diagrams and models, to explain mathematical reasoning.
Problem Solving: Draw a picture and write an equation
4.7
29
Other
Resources
# of
Days
4.8
4.9
Review/reteach/enrich/assess pp. 106-108
TOPIC 7
DIVIDING DECIMALS
Estimate, round, and manipulate very large (e.g., millions) and very small
(e.g., thousandths) numbers.
Add, subtract, multiply, and divide with decimals; add with negative
NS 2.1* integers; subtract positive integers from negative integers; and verify
the reasonableness of the results.
Demonstrate proficiency with division, including division with positive
NS 2.2*
decimals and long division with multi-digit divisors.
Dividing decimals by 10, 100, 1000
7.1
Dividing a decimal by a whole number
7.2
Estimation: Decimals divided by whole numbers
7.3
Dividing a decimal by a decimal
7.4
MR 1.2 Determine when and how to break a problem into simpler parts.
Use a variety of methods, such as words, numbers, symbols, charts,
Embed MR 2.3
graphs, tables, diagrams and models, to explain mathematical reasoning.
Problem Solving: Multi-step problems
7.5
1
7
3
NS 1.1
21
28
Embed
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Review/reteach/enrich/assess pp. 168-170
BENCHMARK EXAM #1 CLOSING DATES
Traditional: November 22, 2013
Modified: November 1, 2013
VOCABULARY LIST 1
BENCHAMRK EXAM #1 DATA ANALYSIS AND INTERVENTIONS
INSTRUCTIONAL SEGMENT 2
VOCABULARY LIST 2
Please Note: This entire Instructional Segment should be completed before the administration of the
CST Mirror Test. Topics 8 and 14 from the next Instructional Segment should be completed before the
administration of the actual CST.
TOPIC 9
FACTORS AND MULTIPLES
Review
Understanding factors (optional)
9.1
Grade 4 Standard
Prime and composite numbers (optional)
Determine the prime factors of all numbers through 50 and write the
NS 1.4* numbers as the product of their prime factors by using exponents to
show multiples of a factor (e.g., 24 = 2 × 2 × 2 × 3 = 23 × 3).
Finding prime factors
9.2
Grade 4 Standard
Review
3
th
6 Grade
Common factors and greatest common factor (optional)
Analyze problems by identifying relationships, distinguishing relevant
Embed MR 1.1 from irrelevant information, sequencing and prioritizing information, and
observing patterns.
Problem Solving: Try/check/revise
9.3
9.4
11 - 16
Grade 6 Standard
9.5
Review/reteach/enrich/assess pp. 208-210
35
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TOPIC 10
FRACTIONS, MIXED NUMBERS, AND DECIMALS
Review
Meanings of fractions
Identify and represent on a number line decimals, fractions, mixed
NS 1.5*
numbers, and positive and negative integers.
Fractions and division
10.1
Mixed numbers and improper fractions
10.3
Equivalent fractions (optional)
10.4
Grade 4 Standard
6 Grade
Comparing and ordering fractions and mixed numbers (optional)
10.5
Grade 6 Standard
6th Grade
Fractions in simplest form (optional)
Students compute with very large and very small numbers, positive
integers, decimals, and fractions and understand the relationship
between decimals, fractions, and percents. They understand the
relative magnitudes of numbers.
Tenths and hundredths
10.6
Grade 6 Standard
Thousandths
Identify and represent on a number line decimals, fractions, mixed
2 NS 1.5*
numbers, and positive and negative integers.
Fractions and decimals on the number line
Use a variety of methods, such as words, numbers, symbols, charts,
Embed MR 2.3
graphs, tables, diagrams and models, to explain mathematical reasoning.
Problem Solving: Writing to explain
10.8
2
Review
th
NS 1.0
Grade 4 Standard
10.2
10.7
10.9
18, 19
10.10
Review/reteach/enrich/assess pp. 240-242
36
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TOPIC 11
ADDING & SUBTRACTING FRACTIONS & MIXED NUMBERS
5
Solve simple problems, including ones arising in concrete situations,
involving the addition and subtraction of fractions and mixed
NS 2.3*
numbers (like and unlike denominators of 20 or less), and express
answers in the simplest form.
Adding and subtracting fractions with like denominators
th
6 Grade
11.1
Common multiples and LCM (optional)
Solve simple problems, including ones arising in concrete situations,
involving the addition and subtraction of fractions and mixed
NS 2.3*
numbers (like and unlike denominators of 20 or less), and express
answers in the simplest form.
Adding fractions with unlike denominators
11.2
Subtracting fractions with unlike denominators
11.4
Adding mixed numbers
11.5
33, 37
Subtracting mixed numbers
Analyze problems by identifying relationships, distinguishing relevant
Embed MR 1.1 from irrelevant information, sequencing and prioritizing information, and
observing patterns.
Problem Solving: Look for a pattern
11.6
35, 36
5
11.3
Grade 6 Standard
32, 34
11.7
Review/reteach/enrich/assess pp. 264-266
Note: You may want to briefly teach 12.1 through 12.4 here (multiply and divide fractions).
TOPIC 17
PERCENT
6th Grade
5
Understanding ratios (optional)
Interpret percents as a part of a hundred; find decimal and percent
NS 1.2* equivalents for common fractions and explain why they represent the
same value; compute a given percent of a whole number.
17.1
Grade 6 Standard
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Understanding percent
17.2
Percents, fractions, and decimals
17.3
4-8
Finding percents of a whole number
Analyze problems by identifying relationships, distinguishing relevant
Embed MR 1.1 from irrelevant information, sequencing and prioritizing information, and
observing patterns.
Use a variety of methods, such as words, numbers, symbols, charts,
Embed MR 2.3
graphs, tables, diagrams and models, to explain mathematical reasoning.
Problem Solving: Make a table and look for a pattern
17.4
3, 9
Other
Resources
# of
Days
17.5
Review/reteach/enrich/assess pp. 396-398
TOPIC 15
INTEGERS
Identify and represent on a number line decimals, fractions, mixed
numbers, and positive and negative integers.
Understanding integers
15.1
Comparing and ordering integers
15.2
Integers and the number line
Add, subtract, multiply, and divide with decimals; add with negative
NS 2.1* integers; subtract positive integers from negative integers; and verify
the reasonableness of the results.
Adding integers
15.3
Subtracting integers
Use a letter to represent an unknown number; write and evaluate
6 AF 1.2*
simple algebraic expressions in one variable by substitution
Simplifying expressions
Use a variety of methods, such as words, numbers, symbols, charts,
Embed MR 2.3
graphs, tables, diagrams and models, to explain mathematical reasoning.
Problem Solving: Work backward
15.5
2
7
NS 1.5*
17
15.4
15.6
15.7
38
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Review/reteach/enrich/assess pp. 358-360
TOPIC 5
VARIABLES AND EXPRESSIONS
1
6
Use information taken from a graph or equation to answer questions about
a problem situation.
Use a letter to represent an unknown number; write and evaluate
AF 1.2*
simple algebraic expressions in one variable by substitution
AF 1.1
43, 45, 47,
48, 50, 53
Variables and expressions
5.1
Patterns and expressions
5.2
More patterns and expressions
Know and use the distributive property in equations and expressions with
variables.
Distributive property
5.3
46, 49, 52
5.4
54 - 56
Order of operations (optional)
Use a variety of methods, such as words, numbers, symbols, charts,
Embed MR 2.3
graphs, tables, diagrams and models, to explain mathematical reasoning.
Problem Solving: Act it out and use reasoning
5.5
1
AF 1.3
th
6 Grade
Grade 6 Standard
5.6
Review/reteach/enrich/assess pp. 130-132
TOPIC 16
SOLVING AND WRITING EQUATIONS
6th Grade
th
6 Grade
Solving addition and subtraction equations (optional)
Solving multiplication and division equations (optional)
Analyze problems by identifying relationships, distinguishing relevant
Embed MR 1.1 from irrelevant information, sequencing and prioritizing information, and
observing patterns.
Evaluate the reasonableness of the solution in the context of the
Embed MR 3.1
original situation.
16.1
Grade 6 Standard
16.2
Grade 6 Standard
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Problem Solving: Use reasoning
Use a letter to represent an unknown number; write and evaluate
AF 1.2*
simple algebraic expressions in one variable by substitution.
Solve problems involving linear functions with integer values; write
AF 1.5* the equation; and graph the resulting ordered pairs of integers on a
grid.
Patterns and equations
16.3
16.4
63, 65
More patterns and equations
Use a variety of methods, such as words, numbers, symbols, charts,
Embed MR 2.3
graphs, tables, diagrams and models, to explain mathematical reasoning.
Problem Solving: Draw a picture and write an equation
16.5
66
16.6
51, 67
6
5
Other
Resources
# of
Days
Review/reteach/enrich/assess pp. 380-382
TOPIC 18
EQUATIONS AND GRAPHS
Identify and graph ordered pairs in the four quadrants of the
coordinate plane.
1/2 SDP 1.5* Know how to write ordered pairs correctly; for example, (x, y).
4
AF 1.4*
2 1/2 SDP 1.4*
4
AF 1.4*
5
AF 1.5*
Embed
MR 1.1
Ordered pairs
Identify ordered pairs of data from a graph and interpret the meaning
of the data in terms of the situation depicted by the graph.
Line graphs
Identify and graph ordered pairs in the four quadrants of the
coordinate plane.
Solve problems involving linear functions with integer values; write
the equation; and graph the resulting ordered pairs of integers on a
grid.
Graphing equations
Analyze problems by identifying relationships, distinguishing relevant
from irrelevant information, sequencing and prioritizing information, and
18.1
57 – 62, 96
18.2
94
18.3
64
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observing patterns.
Problem Solving: Work backwards
18.4
Review/reteach/enrich/assess pp. 414-416
TOPIC 19
GRAPHS AND DATA
Use information taken from a graph or equation to answer questions about
a problem situation.
Organize and display single-variable data in appropriate graphs and
1/3 SDP 1.2 representations (e.g., histogram, circle graphs) and explain which types of
graphs are appropriate for various data sets.
Identify ordered pairs of data from a graph and interpret the meaning
2 1/2 SDP 1.4*
of the data in terms of the situation depicted by the graph.
Bar graphs and picture graphs
19.1
Histograms
19.2
1
AF 1.1
Circle graphs
Use a variety of methods, such as words, numbers, symbols, charts,
Embed MR 2.3
graphs, tables, diagrams and models, to explain mathematical reasoning.
Problem Solving: Make a graph
Know the concepts of mean, median, and mode; compute and compare
1/3 SDP 1.1
simple examples to show that they may differ
Mean
6th Grade
19.3
44, 95
92
19.4
19.5
Median, mode and range
19.6
Outcomes (optional)
19.7
91
Grade 6 Standard
1/3 SDP 1.3 Use fractions and percentages to compare data sets of different sizes.
Writing probability as a fraction
19.8
93
MR 1.2 Determine when and how to break a problem into simpler parts.
Apply strategies and results from simpler problems to more complex
Embed MR 2.2
problems.
Embed
41
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Problem Solving: Solve a simpler problem
Textbook
Lessons
RTQ’s
Other
Resources
# of
Days
19.9
Review/reteach/enrich/assess pp. 444-446
CST MIRROR TEST CLOSING DATES
Traditional: March 7, 2014
Modified: February 28, 2014
CST MIRROR TEST DATA ANALYSIS AND INTERVENTIONS
CST RELEASED TEST QUESTIONS and any or all of the following:
65
ALL
Multiple-choice test to assess students' understanding of the concepts and
skills taught in each Topic
65
ALL
Additional assessment options in Form A and B format for each Topic
65
ALL
Item Analysis for Diagnosis and Intervention chart for each Topic
Student text –
end of each
Topic
Teacher
Resource
Masters
Teacher
Edition - end
of each Topic
PLEASE COMPLETE TOPICS 8 AND 14 BEFORE THE ADMINISTRATION OF THE CST.
INSTRUCTIONAL SEGMENT 3
Vocabulary List 3
TOPIC 8
SHAPES
3
Measure, identify, and draw angles, perpendicular and parallel lines,
MG 2.1* rectangles, and triangles by using appropriate tools (e.g., straightedge,
ruler, compass, protractor, drawing software
Basic geometric ideas
8.1
83
Measuring and classifying angles
8.2
80 – 82
42
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4
Embed
Textbook
Lessons
RTQ’s
Know that the sum of the angles of any triangle is 180° and the sum of
MG 2.2* the angles of any quadrilateral is 360° and use this information to solve
problems.
Polygons
8.3
84
Triangles
8.4
85 – 88
Quadrilaterals
8.5
89
STD
MR 3.3
MATH 5 PACING GUIDE 2013 - 2014
Other
Resources
# of
Days
Develop generalizations of the results obtained and apply them in other
circumstances.
Problem Solving: Make and test generalizations
8.6
Review/reteach/enrich/assess pp. 188-190
TOPIC 14
SOLIDS
Review
Solids (optional)
14.1
Grade 4 Standard
Review
Relating shapes and solids (optional)
14.2
Grade 4 Standard
Construct a cube and rectangular box from two-dimensional patterns
and use these patterns to compute the surface area for these objects.
Surface area
14.3
73
Views of solids
14.4
90
Understand the concept of volume and use the appropriate units in
common measuring systems (i.e., cubic centimeter [cm3], cubic meter
MG 1.3*
[m3], cubic inch [in3], cubic yard [yd3]) to compute the volume of
rectangular solids.
Models and Volume
14.5
Volume
14.6
1/2 MG 1.2*
1
3
MG 2.3
Visualize and draw two-dimensional views of three-dimensional objects
made from rectangular solids.
74 - 77
43
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MR 1.2 Determine when and how to break a problem into simpler parts.
Problem Solving: Use objects and solve a simpler problem
14.7
Review/reteach/enrich/assess pp. 336-338
CST ADMINISTRATION
TOPIC 20
CONSTRUCTIONS
3
Embed
Measure, identify, and draw angles, perpendicular and parallel lines,
MG 2.1* rectangles, and triangles by using appropriate tools (e.g., straightedge,
ruler, compass, protractor, drawing software
Constructing angles
20.1
Constructing lines
20.2
Constructing shapes
20.3
MR 2.3
Use a variety of methods, such as words, numbers, symbols, charts,
graphs, tables, diagrams and models, to explain mathematical reasoning.
Problem Solving: Use objects
20.4
Review/reteach/enrich/assess pp. 464-466
TOPIC 12
MULTIPLYING & DIVIDING FRACTIONS & MIXED NUMBERS
1
NS 2.4 Understand the concept of multiplication and division of fractions.
1
NS 2.5
Compute and perform simple multiplication and division of fractions and
apply these procedures to solving problems
Multiplying fractions and whole numbers
12.1
42
Multiplying two fractions
12.2
40, 41
Dividing a whole number by a fraction
12.3
39
44
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12.4
38
Dividing two fractions
Other
Resources
# of
Days
Analyze problems by identifying relationships, distinguishing relevant
Embed MR 1.1 from irrelevant information, sequencing and prioritizing information, and
observing patterns.
Problem Solving: Missing or extra information
1
NS 2.4 Understand the concept of multiplication and division of fractions.
1
NS 2.5
Embed
MR 2.3
12.5
Compute and perform simple multiplication and division of fractions and
apply these procedures to solving problems
Multiplying mixed numbers
12.6
Dividing mixed numbers
12.7
Use a variety of methods, such as words, numbers, symbols, charts,
graphs, tables, diagrams and models, to explain mathematical reasoning.
Problem Solving: Draw a picture and write an equation
12.8
Review/reteach/enrich/assess pp. 290-292
TOPIC 13
LENGTH, PERIMETER AND AREA
1
MG 1.4
Differentiate between and use appropriate units of measures for, two- and
three- dimensional objects (i.e., find perimeter, area, volume).
Using customary units of length
13.1
Using metric units of length
13.2
Perimeter
13.3
79
78
Derive and use the formula for the area of a triangle and of a
parallelogram by comparing it with the formula for the area of a
2 1/2 MG 1.1* rectangle (i.e., two of the same triangles make a parallelogram with
twice the area; a parallelogram is compared with a rectangle of the
same area by cutting and pasting a right triangle on the parallelogram.
45
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STD
MR 2.3
MATH 5 PACING GUIDE 2013 - 2014
Textbook
Lessons
RTQ’s
Area of squares and rectangles
13.4
Area of parallelograms
13.5
68, 69, 72
Area of triangles
13.6
70, 71
Other
Resources
# of
Days
Use a variety of methods, such as words, numbers, symbols, charts,
graphs, tables, diagrams and models, to explain mathematical reasoning.
Problem Solving: Draw a picture and make an organized list
13.7
Review/reteach/enrich/assess pp. 312-314
SITE-BASED END OF YEAR ASSESSMENT CLOSING DATES
Traditional: June 13, 2014
Modified: June 26, 2014
END OF YEAR ASSESSMENT DATA ANALYSIS
46