Download Grade 6 Elementary Complete B1-B3

Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
Number Sense
1.1a SAM06101 (BM1)
Compare and order
positive fractions,
decimals, and mixed
numbers; solve problems
involving fractions, ratios,
proportions, and
percentages: Compare
and order whole
numbers, fractions and
decimals. (1.1)
Ca. Standards
1.1 Compare and order
positive and negative
fractions, decimals, and
mixed numbers and place
them on a number line.
Compare and order
positive and negative
fractions, decimals, and
mixed numbers; solve
problems involving
fractions, ratios,
proportions, and
percentages: Compare
and order positive and
negative fractions,
decimals, and mixed
numbers and place them
on a number line (1.1)
Compare and order
positive and negative
Mastering Skills &
Concepts: Course
IV
Module: Fractions
Unit: Proper and
Improper Fractions
Session 1: Proper
Fractions
Session 2: Improper
Fractions
Session 3: Equivalent
Fractions
Session 4: Ordering
and Rounding
Fractions
Module: Fractions
Unit: Essentials of
Fractions
Session 1:
Recognizing a
Fraction
Session 2: Exploring
Proper and Improper
Fractions
Session 3: Working
with Mixed Numbers
Module: Decimals
Unit: Introduction
Session 1: Tenths,
Hundredths, and
Thousandths
Session 2: Ordering
and Rounding
1.1b SAM06101 (BM3)
1.2 SAM06102 (BM2)
Mastering Skills &
Concepts: Course III
The Graphing Tool
1.2 Interpret and use ratios
in different contexts (e.g.,
batting averages, miles per
hour) to show the relative
Module: Decimals
Unit: Introduction
Session 3: Ratios,
Decimals, and
1
Mastering Skills &
Concepts: Course V
Module: Fractions
Unit: Equivalent
Fractions
Session 1: Identifying
the Factors of a
Number
Session 2:
Expressing Fractions
in Lowest Terms
Session 3: Writing
and Comparing
Equivalent Fractions
Module: Decimals
Unit: Essentials of
Decimals
Session 1:
Investigating Decimal
Place Values
Session 2: Rounding
Decimals
Session 3: Exploring
Repeating and
Terminating Decimals
The Graphing Tool
Module: Percents
Unit: Finding
Percents of
Quantities
Module: Ratio and
Proportion
Unit: Ratio
Session 1: Defining
Mastering Algebra I:
Course 1
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
fractions, decimals, and
mixed numbers; solve
problems involving
fractions, ratios,
proportions, and
percentages: Use
appropriate notations
with positive fractions,
decimals and mixed
numbers to show relative
sizes of two quantities
(1.2)
Ca. Standards
sizes of two quantities,
using appropriate notations
(a/b, a to b, a:b).
Mastering Skills &
Concepts: Course III
Percents
Mastering Skills &
Concepts: Course
IV
Session 3:
Expressing Ratios as
Percents
Mastering Skills &
Concepts: Course V
Ratio
Session 2:
Expressing Ratios as
Equivalent Fractions
and Decimals
Session 3: Forming
Ratios Between
Unlike Quantities
1.2 SAM06102 (BM3)
Compare and order
positive and negative
fractions, decimals, and
mixed numbers; solve
problems involving
fractions, ratios,
proportions, and
percentages: Interpret
and use ratios in different
contexts (e.g., batting
averages, miles per hour)
to show the relative sizes
of two quantities, using
appropriate notations (e.
g., a/b, a to b, a:b). (1.2)
1.3 SAM06103 (BM2)
Compare and order
positive and negative
fractions, decimals, and
mixed numbers; solve
problems involving
fractions, ratios,
proportions, and
percentages: Use
proportions to solve
problems with positive
fractions, decimals and
mixed numbers by cross
Module: Ratio and
Proportion
Unit: Proportion
Session 1: Defining a
Proportion
Session 2: Solving for
a Variable in a
Proportion
Session 3: Applying
the Means/Extremes
Property
1.3 Use proportions to
solve problems (e.g.,
determine the value of
N if 4/7 = N/21, find the
length of a side of a
polygon similar to a
known polygon). Use
cross-multiplication as
a method for solving
such problems,
understanding it as the
multiplication of both
sides of an equation by
Module: Ratio and
Proportion
2
Mastering Algebra I:
Course 1
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
multiplication (1.3)
Ca. Standards
Mastering Skills &
Concepts: Course III
Mastering Skills &
Concepts: Course
IV
a multiplicative inverse.
Unit: Similar
Polygons
Session 1: Defining
Similarity
Session 2: Identifying
Equivalent Ratios
Session 3: Setting Up
and Solving
Proportions in Similar
Polygons
1.3 SAM06103 (BM3)
Compare and order
positive and negative
fractions, decimals, and
mixed numbers; solve
problems involving
fractions, ratios,
proportions, and
percentages: Use
proportions to solve
problems (e.g., determine
the value of n if 4/7 = n/21;
find the length of a side of
a polygon similar to a
known polygon); use
cross-multiplication as a
method for solving such
problems, understanding
it as the multiplication of
both sides of an equation
by a multiplicative inverse
(1.3)
1.4a SAM06104 (BM3)
Compare and order
positive and negative
fractions, decimals, and
mixed numbers; solve
problems involving
fractions, ratios,
proportions, and
percentages: Calculate
given percentages of
quantities and solve
problems involving
discounts at sales,
interest earned, and tips
(1.4) .
Mastering Skills &
Concepts: Course V
Module: Percents
Unit: Essentials of
Percents Session:
Investigating the
Meaning of Percent
Session: Expressing
Percents as Proper
Fractions
Session: Expressing
Percents greater than
100% as Improper
Fractions
1.4 Calculate given
percentages of quantities
and solve problems
involving discounts at sales,
interest earned, and tips.
Module: Percents
Unit: Finding
Percents of
Quantities
3
Mastering Algebra I:
Course 1
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
2.1a SAM06105 (BM2)
Calculate and solve
problems involving
addition, subtraction,
multiplication, and
division: Solve problems
involving addition,
subtraction,
multiplication, and
division of positive
fractions and explain why
a particular operation was
used for a given situation
(2.1)
Ca. Standards
2.1 Solve problems
involving addition,
subtraction, multiplication,
and division of positive
fractions and explain why a
particular operation was
used for a given situation.
Mastering Skills &
Concepts: Course III
Module: Fractions
Unit: Addition and
Subtraction
Session 1: Sums
Involving Like
Denominators
Session 2:
Differences Involving
Like Denominators
Session 3: Working
with Unlike
Denominators
Module: Fractions
Unit: Multiplication
and Division
Session 1: Finding
Products
Session 2: Quotients
and Remainders
4
Mastering Skills &
Concepts: Course
IV
Session: Finding
Percents of a Whole
Session: Expressing
Ratios as Percents
Session: Calculating
the Whole from a Part
and a Percent
Module: Percents
Unit: Increasing and
Decreasing Percents
Session 1:
Calculating Percent
Increases
Session 2:
Calculating Percent
Decreases
Session 3:
Calculating Simple
Interest
Module: Fractions
Unit: Multiplying
Fractions
Session 1: Finding
Products of Fractions,
Whole Numbers, and
Mixed Numbers
Session 2: Using the
GCF in Finding
Products
Session 3:
Representing
Multiplication
Module: Fractions
Unit: Dividing
Fractions
Session 1: Estimating
Quotients of
Fractions
Session 2: Using
Multiplicative
Inverses
Session 3: Solving
Mastering Skills &
Concepts: Course V
Mastering Algebra I:
Course 1
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
Ca. Standards
Mastering Skills &
Concepts: Course III
Mastering Skills &
Concepts: Course
IV
Missing Value
Problems when
Dividing Fractions
Module: Fractions
Unit: Adding
Fractions
Session 1: Adding
with Like
Denominators
Session 2: Adding
with Unlike
Denominators
Session 3: Solving
Missing Value
Problems when
Adding Fractions
2.2 SAM06106 (BM2)
Calculate and solve
problems involving
addition, subtraction,
multiplication, and
division: Explain the
meaning of multiplication
and division of positive
fractions and perform the
calculations (e.g.,
5/8÷15/16 = 5/8 x 16/15 =
2/3). (2.2)
2.2 Explain the meaning of
multiplication and division of
positive fractions and
perform the calculations
(e.g., 5/8  15/16 = 5/8 X
16/15 = 2/3).
Module: Fractions
Unit: Multiplication
and Division
Session 1: Finding
Products
Session 2: Quotients
and Remainders
5
Module: Fractions
Unit: Subtracting
Fractions
Session 1:
Subtracting with Like
Denominators
Session 2:
Subtracting with
Unlike Denominators
Session 3: Solving
Missing Value
Problems when
Subtracting Fractions
Module: Fractions
Unit: Multiplying
Fractions
Session 1: Finding
Products of Fractions,
Whole Numbers, and
Mixed Numbers
Session 2: Using the
GCF in Finding
Products
Session 3:
Representing
Multiplication
Mastering Skills &
Concepts: Course V
Mastering Algebra I:
Course 1
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
2.3a SAM06107 (BM2)
Calculate and solve
problems involving
addition, subtraction,
multiplication, and
division: Solve addition,
subtraction,
multiplication, and
division problems,
including those arising in
concrete situations, that
use positive and negative
integers and
combinations of these
operations (2.3)
Ca. Standards
2.3 Solve addition,
subtraction, multiplication,
and division problems,
including those arising in
concrete situations, that use
positive and negative
integers and combinations
of these operations.
Mastering Skills &
Concepts: Course III
Module: Operations
with Numbers
Unit: The Integers
Session 1: Integer
Sums
Session 2:
Differences Between
Integers
Mastering Skills &
Concepts: Course
IV
Module: Fractions
Unit: Dividing
Fractions
Session 1: Estimating
Quotients of
Fractions
Session 2: Using
Multiplicative
Inverses
Session 3: Solving
Missing Value
Problems when
Dividing Fractions
Module: Integers &
Order of Operations
Unit: Adding and
Subtracting Signed
Numbers
Session 1: Exploring
the Number Line and
Absolute Value
Session 2: Adding
with Absolute Value
Session 3:
Subtracting with
Absolute Value
Module: Integers &
Order of Operations
Unit: Multiplying and
Dividing Signed
Numbers
Session 1: Finding
Products of Signed
Numbers
Session 2:
Representing the
Multiplication of
Signed Numbers
Session 3: Finding
Quotients Using
Reciprocals
6
Mastering Skills &
Concepts: Course V
Mastering Algebra I:
Course 1
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
2.4 SAM06108 (BM2)
Calculate and solve
problems involving
addition, subtraction,
multiplication, and
division: Determine the
least common multiple
and greatest common
divisor of whole numbers;
use them to solve
problems with fractions
(e.g., to find a common
denominator to add two
fractions or to find the
reduced form for a
fraction. (2.4, 2.3)
Ca. Standards
2.4 Determine the least
common multiple and the
greatest common divisor of
whole numbers; use them
to solve problems with
fractions (e.g., to find a
common denominator to
add two fractions or to find
the reduced form for a
fraction).
Mastering Skills &
Concepts: Course III
Module: Numbers
and Number Sense
Unit: Numbers as
Factors
Session 3: Identifying
Common Factors
Module: Fractions
Unit: Proper and
Improper Fractions
Session 3: Equivalent
Fractions
Session: Ordering
and Rounding
Fractions
Module: Fractions
Unit: Addition and
Subtraction
Session 3: Working
with Unlike
Denominators
Module: Fractions
Unit: Multiplication
and Division
Session: Finding
Products
Session: Quotients
and Remainders
Mastering Skills &
Concepts: Course
IV
Module: Fractions
Unit: Essentials of
Fractions
Session: Working
with Mixed Numbers
Module: Fractions
Unit: Multiplying
Fractions
Session: Finding
Products of Fractions,
Whole Numbers, and
Mixed Numbers
Session: Using the
GCF in Finding
Products
Session:
Representing
Multiplication
Module: Fractions
Unit: Equivalent
Fractions
Session 1: Identifying
the Factors of a
Number
Session 2:
Expressing Fractions
in Lowest Terms
Session 3: Writing
and Comparing
Equivalent Fractions
Module: Fractions
Unit: Adding
Fractions
Session 2: Adding
with Unlike
Denominators
Session 3: Solving
Missing Value
Problems when
Adding Fractions
ALGEBRA AND FUNCTIONS
7
Mastering Skills &
Concepts: Course V
Mastering Algebra I:
Course 1
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
1.1 SAM06201a (BM1)
Write verbal expressions
and sentences as
algebraic expressions
and equations; evaluate
algebraic expressions,
solve simple linear
equations, and graph and
interpret results: Evaluate
simple linear equations in
problem solving
situations with one
variable (1.1)
Ca. Standards
Mastering Skills &
Concepts: Course III
1.1 Write and solve onestep linear equations in one
variable.
Mastering Skills &
Concepts: Course V
Mastering Algebra I:
Course 1
Module: Essentials
of Algebra
Unit: Algebra
Fundamentals
Session 1:
Introducing Variables
Module: The
Language of
Algebra
Unit: Variables,
Expressions, and
Equations
Session 1:
Translating Words
into Expressions
Module: Essentials
of Algebra
Unit: Simple
Equations
Session 1: Using
Variables to Express
Relationships
Session 3: Solving
Simple Equations
1.1 SAM06201 (BM3)
Write verbal expressions
and sentences as
algebraic expressions
and equations; evaluate
algebraic expressions,
solve simple linear
equations, and graph and
interpret results: Write
and solve one-step linear
equations in one variable
(1.1)
1.2 SAM06202a (BM2)
Write verbal expressions
and sentences as
algebraic expressions
and equations; evaluate
algebraic expressions,
solve simple linear
equations, and graph and
interpret results: Write
and evaluate an algebraic
expression for a given
situation, using one
variable (1.2)
Mastering Skills &
Concepts: Course
IV
Module: Essentials
of Algebra
Unit: Algebra
Fundamentals
Session 2: Identifying
Components of
Algebraic
Expressions
Session 3: Replacing
Variables in a
Formula
1.2 Write and evaluate an
algebraic expression for a
given situation, using up to
three variables.
Module: Essentials
of Algebra
Unit: Evaluating an
Algebraic Expression
Session 1:
1.2 SAM06202 (BM3)
Write verbal expressions
8
Module: The
Language of
Algebra
Unit: Linear
Equations in One
Variable
Session 1: Applying
Inverse Operations
Module: The
Language of
Algebra
Unit: Variables,
Expressions, and
Equations
Session 1:
Translating Words
into Expressions
Session 3: Evaluating
and Simplifying
Expressions
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
Ca. Standards
Mastering Skills &
Concepts: Course III
and sentences as
algebraic expressions
and equations; evaluate
algebraic expressions,
solve simple linear
equations, and graph and
interpret results: Write
and evaluate an algebraic
expression using up to
Mastering Skills &
Concepts: Course
IV
Mastering Skills &
Concepts: Course V
Representing the
Dimensions and Area
of a Rectangle
Session 2: Combining
Like Terms
Session 3: Evaluating
Expressions Using
Substitution
Module: Essentials
of Algebra
Unit: Simple
Equations
Session: Using
Variables to Express
Relationships
Session: Simplifying
Algebraic
Expressions
Session: Solving
Simple Equations
three variables (1.2)
Module: Essentials
of Algebra
Unit: Variables on
Both Sides of the
Equation
Session 1: Writing
Equations
Session: Simplifying
Both Sides of an
Equation
Session: Checking
the Solution to an
Equation
Module: Essentials
of Algebra
Unit: Solving Literal
Equations
Session 1: Identifying
the Variables in a
Given Formula
Session 2: Rewriting
9
Mastering Algebra I:
Course 1
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
Ca. Standards
Mastering Skills &
Concepts: Course III
Mastering Skills &
Concepts: Course
IV
1.3 SAM06203 (BM1)
Write verbal expressions
and sentences as
algebraic expressions
and equations; evaluate
algebraic expressions,
solve simple linear
equations, and graph and
interpret results: Apply
algebraic order of
operations and the
commutative, associative,
and distributive
properties to evaluate
expressions; justify each
step in the process. (1.3)
1.3 Apply algebraic order
of operations and the
commutative, associate,
and distributive properties
to evaluate expressions;
and justify each step in the
process.
Module: Integers &
Order of Operations
Unit: Order of
Operations
Session 1:
Simplifying
Expressions
Session 2:
Introducing the
Distributive Property
Session 3: Using
Grouping Symbols
(not associative
property)
1.4 SAM06204 (BM1)
Write verbal expressions
and sentences as
algebraic expressions
and equations; evaluate
algebraic expressions,
solve simple linear
equations, and graph and
interpret results: Solve
problems manually by
using the correct order of
operations or by using a
scientific calculator. (1.4)
1.4 Solve problems
manually by using the
correct order of operations
or by using a scientific
calculator.
Module: Integers
and Order of
Operations
Unit: Order of
Operations Session:
Simplifying
Expressions
Session: Introducing
the Distributive
Property
Session: Using
Grouping Symbols
Mastering Skills &
Concepts: Course V
a Formula in Terms
of a Different Variable
Session 3:
Substituting Values
and Solving an
Equation
Module: Essentials
of Algebra
Unit: Simple
Equations
Session 2:
Simplifying Algebraic
Expressions
(not associative
property)
Session: Solving
Simple Equations
Module: Essentials
of Algebra
Unit: Evaluating an
Algebraic Expression
Session: Combining
Like Terms
Module: Essentials
of Algebra
Unit: Simple
Equations
Session: Simplifying
Algebraic
Expressions
Session 3: Solving
Simple Equations
Module: Essentials
of Algebra
Unit: Variables on
Both Sides of the
Equation
10
Mastering Algebra I:
Course 1
Module: The
Language of
Algebra
Unit: Variables,
Expressions, and
Equations
Session 2: Applying
Properties of Real
Numbers
Session: Evaluating
and Simplifying
Expressions
Module: The
Language of
Algebra
Unit: Variables,
Expressions, and
Equations
Session: Applying
Properties of Real
Numbers
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
Ca. Standards
Mastering Skills &
Concepts: Course III
Mastering Skills &
Concepts: Course
IV
Mastering Skills &
Concepts: Course V
Mastering Algebra I:
Course 1
Session 2:
Simplifying Both
Sides of an Equation
Session 3: Checking
the Solution to an
Equation
The Calculator Tool
2.1 SAM06205 (BM2)
Analyze and use tables,
graphs, and rules to solve
problems involving rates
and proportions: Convert
one unit of measurement
to another (e.g., from feet
to miles, from centimeters
to inches). (2.1)
2.1 Convert one unit of
measurement to another
(e.g., from feet to miles,
from centimeters to inches).
2.2 SAM06206 (BM2)
Analyze and use tables,
graphs, and rules to solve
problems involving rates
and proportions:
Demonstrate an
understanding that rate is
a measure of one quantity
per unit value of another
quantity. (2.2)
2.2 Demonstrate an
understanding that rate is a
measure of one quantity per
unit value of another
quantity.
2.3 SAM06207 (BM3)
Analyze and use tables,
graphs, and rules to solve
problems involving rates
and proportions: Solve
problems involving rates,
average speed, distance,
and time. (2.3)
2.3 Solve problems involving
rates, average speed,
distance, and time.
Module: Data
Analysis and
Probability
Unit: Modeling and
Displaying Events
Session: Displaying
and Analyzing Data
Module: Fractions
Unit: Multiplying
Fractions
Session: Using the
GCF in Finding
Products
Module: Decimals
Unit: Dividing
Decimals
Session: Estimating
and Finding
Quotients
Session: Dividing by
Powers of 10
Module: The
Language of
Algebra
Unit: Linear
Equations in One
Variable
Session:
Transforming
Equations using
Multiple Operations
Module: The
Language of
Algebra
Unit: Linear
Equations in One
Variable
Session:
Transforming
Equations using
Multiple Operations
11
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
3.1 SAM06208 (BM3)
Investigate geometric
patterns and describe
them algebraically: Use
variables in expressions
describing geometric
quantities (e.g., P = 2W +
2L, A = 1/2 BH, C = π D –
the formulas for the
perimeter of a rectangle,
the area of a triangle, and
the circumference of a
circle, respectively) (3.1)
Ca. Standards
3.1 Use variables in
expressions describing
geometric quantities (e.g.,
P  2w  2l ,
A  1 / 2bh, C  d -
the formulas for the
perimeter of a rectangle,
the area of a triangle, and
the circumference of a
circle, respectively.
Mastering Skills &
Concepts: Course III
3.2 Express in symbolic
form simple relationships
arising from geometry.
Mastering Skills &
Concepts: Course V
Module: Numbers
and Number Sense
Unit: Numbers as
Factors
Session: Finding
Factors
Module: Essentials
of Algebra
Unit: Algebra
Fundamentals
Session 1:
Introducing Variables
Module: Operations
with Numbers
Unit: Multiplication
and Division of Whole
Numbers
Session: Two-Digit
Multipliers
Session: Introduction
to Long Division
Module: Essentials
of Algebra
Unit: Evaluating an
Algebraic Expression
Session 1:
Representing the
Dimensions and Area
of a Rectangle
Session: Combining
Like Terms
Session: Evaluating
Expressions Using
Substitution
Module: Fractions
Unit: Multiplication
and Division
Session: Finding
Products
3.2 SAM06209 (BM3)
Investigate geometric
patterns and describe
them algebraically:
Express in symbolic form
simple relationships
arising from geometry.
(3.2)
Mastering Skills &
Concepts: Course
IV
Module: Geometry
Unit: Measurement
Session 1: Lines,
Angles, and Circles
Session 2:
Rectangles and
Squares
Session: Triangles
12
Module: Essentials
of Algebra
Unit: Solving Literal
Equations
Session: Identifying
the Variables in a
Given Formula
Session: Rewriting a
Formula in Terms of
a Different Variable
Module:
Fundamentals of
Geometry
Unit: Geometry
Fundamentals
Session 2: Defining
Complementary and
Supplementary
Angles
Session 3:
Recognizing
Congruent Angles
Mastering Algebra I:
Course 1
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
Ca. Standards
Mastering Skills &
Concepts: Course III
Mastering Skills &
Concepts: Course
IV
Mastering Skills &
Concepts: Course V
Module:
Fundamentals of
Geometry
Unit: Triangles
Session 1:
Classifying Triangles
by Sides
Session 2: Exploring
the Area of a Triangle
Session 3:
Classifying Triangles
by Angles
Module:
Fundamentals of
Geometry
Unit: Volume and
Surface Area
Session 1:
Calculating the
Volume of a Right
Triangular Prism
Session 2:
Calculating the
Surface Area of a
Right Triangular
Prism
Session 3:
Calculating the
Volume and Surface
Area of a Right
Cylinder
MEASUREMENT AND GEOMETRY
1.1 SAM06301 (BM3)
1.1 Understand the concept
Deepen the
of a constant such as  ,
understanding of the
know the formulas for the
measurement of plane
circumference and area of a
and solid shapes and use
circle.
this understanding to
solve problems:
Understand the concept
of a constant such as
(PIE), know the formulas
for the circumference and
Module: Decimals
Unit: Essentials of
Decimals
Session 2: Rounding
Decimals
13
Module:
Fundamentals of
Geometry
Unit: Volume and
Surface Area
Session 3:
Calculating the
Volume and Surface
Area of a Right
Cylinder
(advanced level)
Mastering Algebra I:
Course 1
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
Ca. Standards
Mastering Skills &
Concepts: Course III
Mastering Skills &
Concepts: Course
IV
Mastering Skills &
Concepts: Course V
area of a circle. (1.1)
1.2 SAM06302 (BM3)
Deepen the
understanding of the
measurement of plane
and solid shapes and use
this understanding to
solve problems: Know
common estimates of ?
(3.14; 22/7) and use these
values to estimate and
calculate the
circumference and the
area of circles; compare
with actual
measurements. (1.2)
1.3 SAM06303 (BM3)
Deepen the understanding
of the measurement of
plane and solid shapes and
use this understanding to
solve problems: Know and
use the formulas for the
volume of triangular prisms
and cylinders (area of base
x height); compare these
formulas and explain the
similarity between them
and the formula for the
volume of a rectangular
solid. (1.3)
2.1 SAM06304 (BM3)
Identify and describe the
properties of twodimensional figures:
Identify angles as vertical,
adjacent, complementary,
or supplementary and
provide descriptions of
these terms. (2.1)
Module: Decimals
Unit: Essentials of
Decimals
Session 2: Rounding
Decimals
1.2 Know common
estimates of  , (3.14,
22/7) and use these values
to estimate and calculate
the circumference and the
area of circles; compare
with actual measurements.
Module:
Fundamentals of
Geometry
Unit: Volume and
Surface Area
Session 3:
Calculating the
Volume and Surface
Area of a Right
Cylinder
1.3 Know and use the
formulas for the volume of
triangular prisms and
cylinders (area of base X
height); compare these
formulas and explain the
similarity between them and
the formula for the volume of
a rectangular solid.
Module:
Fundamentals of
Geometry
Unit: Volume and
Surface Area
Session 1:
Calculating the
Volume of a Right
Triangular Prism
Session 3:
Calculating the
Volume and Surface
Area of a Right
Cylinder
2.1 Identify angles as
vertical, adjacent,
complementary, or
supplementary and provide
descriptions of these terms.
Module:
Fundamentals of
Geometry
Unit: Geometry
Fundamentals
Session 2: Defining
Complementary and
Supplementary
Angles
Session 3:
Recognizing
Congruent Angles
14
Mastering Algebra I:
Course 1
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
Ca. Standards
2.2 SAM06305 (BM3)
2.2 Use the properties of
Identify and describe the
complementary and
properties of twosupplementary angles and
dimensional figures: Use
the sum of the angles of a
the properties of
triangle to solve problems
complementary and
involving an unknown
supplementary angles
angle.
and the sum of the angles
of a triangle to solve
problems involving an
unknown angle. (2.2)
2.3 SAM06306 (BM2)
2.3 Draw quadrilaterals and
Identify and describe the
triangles from given
properties of twoinformation about them (e.g.,
dimensional figures: Draw
a quadrilateral having equal
quadrilaterals and triangles
sides but no right angles, a
from given information
right isosceles triangle).
about them (e.g., a
quadrilateral having equal
sides but no right angles, a
right isosceles triangle).
(2.3)
STATISTICS, DATA ANALYSIS, AND PROBABILITY
1.1 SAM06401 (BM1)
1.1 Compute the range,
Compute and analyze
mean, median, and mode of
statistical measurement
data sets.
for data sets: Compute
the range, mean, median,
and mode of data sets.
(1.1)
Mastering Skills &
Concepts: Course III
Mastering Skills &
Concepts: Course
IV
Mastering Skills &
Concepts: Course V
Module:
Fundamentals of
Geometry
Unit: Triangles
Session 3:
Classifying Triangles
by Angles
Module: Geometry
Unit: Measurement
Session 2:
Rectangles and
Squares
Session 3:
Triangles
Session 4:
Parallelograms and
Trapezoids
Module:
Fundamentals of
Geometry
Unit: Triangles
Session 1:
Classifying Triangles
by Sides
Session 3:
Classifying Triangles
by Angles
Module: Data
Analysis and
Probability
Unit: Modeling and
Displaying Events
Session 1: Displaying
and Analyzing Data
Module:
Fundamentals of
Statistics
Unit: The Mean,
Median, and Mode
Session 1: Defining
the Mean and Median
Session 2: Defining
the Mode
Session 3:
Calculating the Mean,
Median, and Mode
Module:
Fundamentals of
Statistics
Unit: Frequency
Distribution and
Histograms
Session: Creating &
Interpreting a
15
Mastering Algebra I:
Course 1
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
Ca. Standards
1.2 SAM06402 (BM2)
Compute and analyze
statistical measurement
for data sets: Understand
how additional data
added to data sets may
affect these computations
of measures of central
tendency. (1.2)
1.2 Understand how
additional data added to
data sets may affect these
computations of measures
of central tendency.
1.3 SAM06403 (BM3)
Compute and analyze
statistical measurement
for data sets: Understand
how the inclusion or
exclusion of outliers
affects measures of
central tendency. (1.3)
1.3 Understand how the
inclusion or exclusion of
outliers affects measures of
central tendency.
2.1 SAM06405 (BM3) Use
data samples of a
population and describe
the characteristics and
limitations of the
samples: Compare
different samples of a
population with the data
from the entire population
and identify a situation in
which it makes sense to
use a sample. (2.1)
2.1 Compare different
samples of a population
with the data from the entire
population and identify a
situation in which it makes
sense to use a sample.
2.2 SAM06406 (BM3) Use
2.2 Identify different ways
Mastering Skills &
Concepts: Course III
Mastering Skills &
Concepts: Course
IV
Mastering Skills &
Concepts: Course V
Frequency Table
Session: Defining a
Histogram
Module:
Fundamentals of
Statistics
Unit: The Mean,
Median, and Mode
Session 1: Defining
the Mean and Median
Session 2: Defining
the Mode
Session 3:
Calculating the Mean,
Median, and Mode
Module:
Fundamentals of
Statistics
Unit: The Mean,
Median, and Mode
Session 1: Defining
the Mean and Median
Session 2: Defining
the Mode
Session 3:
Calculating the Mean,
Median, and Mode
(These sessions do
not mention outliers
by name.)
16
Mastering Algebra I:
Course 1
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
data samples of a
population and describe
the characteristics and
limitations of the
samples: Identify different
ways of selecting a
sample (e.g., convenience
sampling, responses to a
survey, random sampling)
and which method makes
a sample more
representative for a
population. (2.2)
2.3 SAM06407 (BM2) Use
data samples of a
population and describe the
characteristics and
limitations of the samples:
Analyze data displays, and
explain why the way in
which the question was
asked might have
influenced the results
obtained and why the way
in which the results were
displayed might have
influenced the conclusions
reached. (2.3)
Ca. Standards
Mastering Skills &
Concepts: Course III
Mastering Skills &
Concepts: Course
IV
Mastering Skills &
Concepts: Course V
of selecting a sample (e.g.,
convenience sampling,
responses to a survey,
random sampling) and
which method makes a
sample more representative
for a population.
2.3 Analyze data displays
and explain why the way in
which the question was asked
might have influenced the
results obtained and why the
way in which the results were
displayed might have
influenced the conclusions
reached.
Module: Data
Analysis and
Probability
Unit: Modeling and
Displaying Events
Session: Displaying
and Analyzing Data
Module:
Fundamentals of
Statistics
Unit: Interpreting and
Constructing Graphs
Session 1: Exploring
Line Graphs
Session 2: Exploring
Bar Graphs
Session 3:
Interpreting Pie
Charts
Module:
Fundamentals of
Statistics
Unit: The Mean,
Median, & Mode
Session 2: Defining
the Mode
Module:
Fundamentals of
Statistics
Unit: Frequency
Distribution and
Histograms
Session: Creating &
Interpreting a
Frequency Table
Session: Defining a
17
Mastering Algebra I:
Course 1
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
Ca. Standards
Mastering Skills &
Concepts: Course III
Mastering Skills &
Concepts: Course
IV
Mastering Skills &
Concepts: Course V
Histogram
2.4 SAM06408 (BM3) Use
data samples of a
population and describe
the characteristics and
limitations of the
samples: Identify data
that represent sampling
errors and explain why
the sample (and the
display) might be biased.
(2.4)
2.4 Identify data that
represent sampling errors
and explain why the sample
(and the display) might be
biased.
2.5 SAM06409 (BM3) Use
data samples of a
population and describe
the characteristics and
limitations of the
samples: Identify claims
based on statistical data
and, in simple cases,
evaluate the validity of
the claims. (2.5)
2.5 Identify claims based
on statistical data and, in
simple cases, evaluate the
validity of the claims.
3.1 SAM06410 (BM2)
Determine theoretical and
experimental probabilities
and use these to make
predictions about events:
Represent all possible
outcomes for compound
events in an organized
way (e.g., tables, grids,
tree diagrams) and
express the theoretical
probability of each
outcome. (3.1)
3.1 Represent all possible
outcomes for compound
events in an organized way
(e.g., tables, grids, tree
diagrams) and express the
theoretical probability of
each outcome.
Module: Data
Analysis and
Probability
Unit: Modeling and
Displaying Events
Session 2: Looking at
Chance
Module:
Fundamentals of
Probability
Unit: Simple
Probability
Session 1: Defining
and Expressing
Probability
Session 2:
Calculating
Probabilities on a
Color Wheel
Session 3:
Determining
Probability of
Complementary
Events
Module:
Fundamentals of
Probability
18
Mastering Algebra I:
Course 1
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
3.2 SAM06411 (BM3)
Determine theoretical and
experimental probabilities
and use these to make
predictions about events:
Use data to estimate the
probability of future
events (e.g., batting
averages or number of
accidents per mile
driven). (3.2)
Ca. Standards
Mastering Skills &
Concepts: Course III
Mastering Skills &
Concepts: Course
IV
Mastering Skills &
Concepts: Course V
Unit: Probability of
Combined Events
Session 1:
Calculating the
Probability of
Independent Events
Session 2:
Determining the
Sample Space of an
Experiment
Session 3:
Calculating the
Probability of
Mutually Exclusive
Events
Module:
Fundamentals of
Probability
Unit: Simple
Probability Session:
Defining &
Expressing
Probability
Session: Calculating
Probabilities on a
Color Wheel
Session: Determining
Probabilities of
Complementary
Events
3.2 Use data to estimate
the probability of future
events (e.g., batting
averages or number of
accidents per mile driven).
Module:
Fundamentals of
Probability
Unit: Probability of
Combined Events
Session 1:
Calculating the
Probability of
Independent Events
Session 2:
Determining the
Sample Space of an
Experiment
19
Mastering Algebra I:
Course 1
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
Ca. Standards
3.3 SAM06412 (BM2)
Determine theoretical and
experimental probabilities
and use these to make
predictions about events:
Represent probabilities
as ratios, proportions,
decimals between 0 and
1, and percentages
between 0 and 100 and
verify that the
probabilities computed
are reasonable; know that
if p is the probability of an
event, 1 p is the
probability of an event
not occurring (3.3)
3.3 Represent probabilities
as ratios, proportions,
decimals between 0 and 1,
and percentages between 0
and 100 and verify that the
probabilities computed are
reasonable; know that if P
is the probability of an
event, 1-P is the probability
of an event not occurring.
3.4 SAM06413 (BM2)
Determine theoretical and
experimental probabilities
and use these to make
predictions about events:
Understand that the
probability of either of
two disjoint events
occurring is the sum of
the two individual
probabilities and that the
probability of one event
following another, in
independent trials, is the
product of the two
probabilities. (3.4)
3.4 Understand that the
probability of either of two
disjoint events occurring is
the sum of the two
individual probabilities and
that the probability of one
event following another, in
independent trials, is the
product of the two
probabilities.
SAM06414 (BM2)
3.5 Determine theoretical
and experimental
probabilities and use
Determine theoretical and
experimental probabilities
Mastering Skills &
Concepts: Course III
Module: Data
Analysis and
Probability
Unit: Modeling and
Displaying Events
Session 2: Looking at
Chance
Module: Data
Analysis and
Probability
20
Mastering Skills &
Concepts: Course
IV
Mastering Skills &
Concepts: Course V
Session 3:
Calculating the
Probability of
Mutually Exclusive
Events
Module:
Fundamentals of
Probability
Unit: Simple
Probability
Session 1: Defining
and Expressing
Probability
(Workout Questions 3
and 5 only, using
SHOW ME feature)
Module:
Fundamentals of
Probability
Unit: Probability of
Combined Events
Session 1:
Calculating the
Probability of
Independent Events
Session 2:
Determining the
Sample Space of an
Experiment
Session 3:
Calculating the
Probability of
Mutually Exclusive
Events
Module:
Fundamentals of
Probability
Mastering Algebra I:
Course 1
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
and use these to make
predictions about events:
Understand the difference
between independent and
dependent events. (3.5)
Ca. Standards
these to make predictions
about events: Understand
the difference between
independent and
dependent events.
MATHEMATICAL REASONING
SAM6501 (BM2) Use
2.1 Use estimation to verify
strategies, skills and
the reasonableness of
concepts in finding
calculated results.
solutions: Use estimation
to verify reasonableness
of calculated results. (2.1)
Mastering Skills &
Concepts: Course III
Mastering Skills &
Concepts: Course
IV
Unit: Modeling and
Displaying Events
Session 2: Looking at
Chance
Module: Operations
with Numbers
Unit: Addition and
Subtraction of Whole
Numbers
Session: Whole
Number Sums
Session: Differences
Between Large
Numbers
Module: Operations
with Numbers Unit:
Multiplication and
Division of Whole
Numbers
Session: Introduction
to Long Division
Session: Two-Digit
Divisors
Module: Fractions
Unit: Addition and
Subtraction
Session: Sums
involving Like
Denominators
Session: Differences
involving Like
Denominators
Session: Working
with Unlike
21
Mastering Skills &
Concepts: Course V
Unit: Probability of
Combined Events
Session 1:
Calculating the
Probability of
Independent Events
Session 3:
Calculating the
Probability of
Mutually Exclusive
Events
Module: Fractions
Unit: Dividing
Fractions
Session: Estimating
Quotients of
Fractions
Module: Fractions
Unit: Adding
Fractions
Session: Adding with
like Denominators
Module: Decimals
Unit: Adding and
Subtracting Decimals
Session: Using Place
Value Grids
Module: Decimals
Unit: Dividing
Decimals
Session: Estimating
and Finding
Quotients
Module: Percents
Unit: Increasing and
Decreasing Percents
Session: Calculating
Percent Decreases
Mastering Algebra I:
Course 1
Alignment of Destination Math Courseware
with
GRADE 6 (Elementary) Benchmarks
Pomona Benchmarks
Ca. Standards
Mastering Skills &
Concepts: Course III
Denominators
Module: Fractions
Unit: Multiplication
and Division
Session: Finding
Products
Session: Quotients
and Remainders
Module: Decimals
Unit: Addition and
Subtraction
Session: Adding
Decimals
Session: Subtracting
Decimals
Module: Decimals
Unit: Multiplication
and Division
Session: Multiplying
Decimals
Session: Dividing
Decimals by Whole
Numbers
22
Mastering Skills &
Concepts: Course
IV
Mastering Skills &
Concepts: Course V
Mastering Algebra I:
Course 1