Common Core Mathematics 6
Year at Glance
WHAT STUDENTS LEARN IN Mathematics 6
Mathematics Gr. 6 CA Framework
Overview
In grade six, instructional time should focus on four critical areas: (1) connecting ratio, rate, and percentage to whole number
multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of
fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing,
interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking (CCSSO 2010, Grade 6
Introduction).
Students also work toward fluency with multi-digit division and multi-digit decimal operations. A critical area of instruction in grade
six is to connect ratio, rate, and percentage to whole number multiplication and division and use concepts of ratio and rate to solve
problems. Students’ prior understanding of and skill with multiplication, division, and fractions contribute to their study of ratios,
proportional relationships, unit rates, and percent in grade six. In grade seven these concepts will extend to include scale
drawings, slope, and real-world percent problems. In grade six students complete their understanding of division of fractions and
extend the notion of number to the system of rational numbers, which includes negative numbers. Students also work toward
fluency with multi-digit division and multi-digit decimal operations. A critical area of instruction at grade six is writing, interpreting
and using expressions and equations. In previous grades students wrote numerical equations and simple equations involving one
operation with a variable. In grade six students start the systematic study of equations and inequalities and methods to solve them.
Students understand that mathematical expressions express calculations with numbers.
Some numbers might be given explicitly, like 2 or .75. Other numbers are represented by letters, such as x, y, P or n. The
calculation an expression represents might use a single
operation, as in 4 + 3 or 3x, or a series of nested or parallel operations, as in 3(a + 9) −9/b . An expression can consist of a single
number, even 0.
Students understand an equation is a statement that two expressions are equal. It is an important aspect of equations that the two
expressions on either side of the equal sign might not actually always be equal; that is, the equation might be a true statement for
some values of the variable(s) and a false statement for others (Adapted from Progressions 6-8 EE 2011.) In grade six students
extend their understanding of length, area, and volume as they solve problems by applying formulas for the area of triangles and
parallelograms and volume of rectangular prisms. A critical area of instruction in grade six is developing understanding of
statistical thinking. Students build on their knowledge and experiences in data analysis as they work with statistical variability and
represent and analyze data distributions. They continue to think statistically, viewing statistical reasoning as a four-step
investigative process.
IMP CC Mathematics Gr. 6 Course Outline 2014-15 FUESD Sixth Grade Math Instructional Timeline
1
Mathematics 6
Year at Glance
Unit
Length
Unit Name & Sub-topics
Standards
Addressed
Prior Knowledge
Assessment
Guideline
M = Major Cluster
A/S = Additional
or Supporting
Cluster
1 Week
Aug. 11th
3 Weeks
Aug. 18 to
Sept. 5
6 Weeks
Sept. 8th to
Oct. 17th
0: Introductory Week
 Setting the tone
 Establishing Routines
1: Rational Numbers (Negative Numbers)
 Concept of a negative number
 Seeing a number and its opposite as
equal distances from 0 on a number line.
 Zero pairs
 Plotting rational numbers on a number line
 Plotting coordinates in all four quadrants
as an extension of the horizontal number
line.
 Absolute Value with the number line
 Seeing the symbol for “negative” as
“opposite”
 Comparing Rational Numbers
2: Operations: Whole Numbers, Fractions
and Decimals
 Demonstrate fluency in division of whole
numbers.
 Word problems involving all 4 operations
NS 5, 6a, 6b, 6c,
7a, 7b, 7c, 7d, 8
(part)
All Major Clusters
 Plotting positive,
rational numbers on
the number line
 Graphing
coordinates in
quadrant 1
Unit 1
NS 1, 2, 3, 4
NS 1- Major
NS 2-4, A/S
 Operations with
Whole Numbers
 Operations with
Decimals (excluding
decimal divisors)
Unit 2
IMP CC Mathematics Gr. 6 Course Outline 2014-15 FUESD Sixth Grade Math Instructional Timeline
Unit 3
Maybe given separately or
together at the end of unit.
2

4 Weeks
Oct. 20th to
Nov. 14th
Nov. 17 – 21
4 Weeks
Dec. 1 to
Jan. 9th
Distributive Property of multiplication over
addition
 Greatest Common Factor, Lowest
Common Multiple
 See fraction operations as similar to whole
number operations.
 Division of fractions
 See decimal operations as similar to
whole number operations.
 Add, subtract, multiply and divide with
decimals.
 Connect multiplication and division of
decimals in terms of moving decimal point
to those operations with fractions.
3: Expressions, Exponents & Properties
EE 1, 2a, 2b, 2c,
with Variables
3, 4, 6,
All Major Clusters
 Read, write and evaluate expressions
containing variables
 Vocabulary- terms, sum, product, factor,
coefficient, variable, quotient, difference,
constant, equation, expression, inequality.
 Whole number exponents (any base)write and evaluate
 Properties (distributive, associative,
commutative) with variables
 Order of Operations (but not PEMDAS
short-cut)
 Equivalent Expressions with variables
Review, catch up, move forward
 Operations with
Fractions (excluding
dividing fractions by
fractions)
 Properties with
numeric expressions
 Manipulating
numeric expressions
 Basic order of
operations (multiply
and divide before add
and subtract)
Unit 4
4: Equations and Inequalities
 Concept of Solving a linear equation
 Solving one-step linear equations
 Writing and graphing inequalities based
 Graphing data from
a table onto a
coordinate plane.
Unit 5
EE 5, 6, 7, 8, 9
All Major Clusters
IMP CC Mathematics Gr. 6 Course Outline 2014-15 FUESD Sixth Grade Math Instructional Timeline
May consider a
performance task or OARs
assessment to examine
performance on EE6
3
6 Weeks
Jan. 12th to
Feb. 20th
2 Weeks
Feb. 23rd to
Mar. 6th
upon real world constraints
 Graphing data from two linear equations.
 Dependent vs. independent variables.
 Discrete vs. continuous data
 Data in tables, graphs and equations (real
world situations)
5: Ratios and Their Applications
 Concept of a Ratio- multiplicative/relative
thinking vs. additive or absolute thinking.
 Ratios as part to whole vs. part to part
 Unit rate
 Rate (always with units)
 Equivalent Ratios
 Tables to study and problem solve with
equivalent ratios
 Tape diagrams to study and solve
problems with equivalent ratios.
 Use unit rate to solve proportions and to
show two ratios are equivalent.
 Conversions within and between
measurement systems.
 Double number lines to solve proportions
with different units.
 Equations to represent and solve
problems with equivalent ratios.
6: Percent
 Concept of percent as “per 100”
 Using benchmark percents to solve
problems
 Finding the whole, percent or part
 Using double sided number lines to solve
percent problems.
Unit 6
RP 1, 2, 3a, 3b,
3d
All Major Clusters
RP 3c
Major Cluster
 Multiplicative
comparisons (how
many times larger is
__ than __)
 Units of measure
 Equivalent
Fractions
 Graphing on
coordinate plane (gr.
6)
 Solving basic
equations (gr. 6)
 Ratios and
proportions (gr. 6)
IMP CC Mathematics Gr. 6 Course Outline 2014-15 FUESD Sixth Grade Math Instructional Timeline
Performance task
or OARs
assessment
Team created or found in
Synced
Unit 7
4

Mar. 9 - 13
3 Weeks
Mar. 16 to
Apr. 10th
3 Weeks
Apr. 13th to
May 1st
2 Weeks
May 4th to
May 15th
component
Real world contexts with percent
problems (single-step only)
Review, catch up or move forward
7: Statistics
 What is a good statistical question?
 Distribution of data (center, spread,
overall shape)
 Measures of center (mean and median)
 Measures of variability (MAD and IQR)
 Displaying data- histograms, box plots,
dot plots
 Summarize results of data collection and
display
8: Area and Perimeter (including on
coordinate plane)
 Derive formula for area of right triangles
and other triangles.
 Use triangles and rectangles to derive
area of trapezoids and parallelograms.
 Solve real world problems involving area
of triangles and quadrilaterals.
 Graph polygons on the coordinate plane
and find distances (horizontal or vertical)
between points.
 Absolute Value and distance on
coordinate plane
 Find the area and perimeter of polygons
graphed on the coordinate plane.
9: Volume and Surface Area
 Use nets to build prisms.
 Use nets to find surface area of solids
with rectangle and triangle faces
 Derive formula for volume of
SP 1, 2, 3,
SP 4, 5a, 5b, 5c,
5d
All A/S Cluster
 Representing data
with a graph
G 1, 3, NS 8
(distance)
All A/S Cluster
 Area of rectangles
 Perimeter of
polygons
 Graphing on
coordinate plane and
finding distance (gr. 6)
Performance task
or OARs
assessment
 Volume of
rectangular prisms
Unit 10
G 2, 4
All A/S Cluster
Unit 8
Unit 9
May give separately or
together at the end of the
unit
IMP CC Mathematics Gr. 6 Course Outline 2014-15 FUESD Sixth Grade Math Instructional Timeline
Team created or found in
Synced
5
3&4
May 18-28
rectangular prism
 Problem solve with volume of
rectangular prisms with fractional edge
lengths.
 Modeling with volume and surface
area
Review, catch up
 Indicates pre-units to be taught to address standards that were taught in prior grades, but have moved grade levels and for
which students need a first-teaching, or in which students need review. Pre-units may be phased out over time.
IMP CC Mathematics Gr. 6 Course Outline 2014-15 FUESD Sixth Grade Math Instructional Timeline
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