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CCSD Math Department
7th Grade “roadmap”
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Apply and extend previous
understandings of operations with
fractions to + , – , × , ÷ rational numbers:

Apply and extend previous
understandings of addition and
subtraction to add and subtract rational
numbers – 7.NS.1

Represent addition and subtraction on a
horizontal or vertical number line
diagram – 7.NS.1

Describe situations in which opposite
quantities combine to make 0
– 7.NS.1a

Understand p + q as the number
located a distance |q| from p, in the
positive or negative direction
depending on whether q is positive or
negative – 7.NS.1b

Show that a number and its opposite
have a sum of 0 (are additive inverses)
– 7.NS.1b

Interpret sums of rational numbers by
describing real-world contexts
– 7.NS.1b

Understand subtraction of rational
numbers as adding the additive inverse;
p – q = p + (-q) – 7.NS.1c

Show that the distance between two
rational numbers on a number line is
the absolute value of their difference,
and apply this principle to real-world
contexts – 7.NS.1c

Apply properties of operations as
strategies to add and subtract rational
numbers – 7.NS.1d

Apply and extend previous
understandings of multiplication and
division and of fractions to multiply
and divide rational numbers – 7.NS.2
Use properties of operations to generate
equivalent expressions:

Apply properties of operations as
strategies to add, subtract, factor, and
expand linear expressions with rational
coefficients – 7.EE.1

Understand that rewriting an expression
in different forms in a problem context
can shed light on the problem and how
the quantities in it are related – 7.EE.2
Solve real-life and mathematical problems
involving angle measure, area:

Solve real-world and mathematical
problems involving area of 2D objects
composed of:
o triangles
o quadrilaterals
o polygons
– 7.G.6
Solve real-life and mathematical problems
involving area:

Know the formulas for the area and
circumference of a circle – 7.G.4

Use the formulas for circles to solve
problems
– 7.G.4

Give an informal derivation of the
relationship between the circumference
and area of a circle
– 7.G.4
Solve real-life and mathematical problems
involving angle measure,:

Use facts about:
o supplementary angles
o complementary angles
o vertical angles
o adjacent angles
in a multi-step problem
– 7.G.5

Write and solve simple equations for an
unknown angle in a figure – 7.G.5
Use random sampling to draw inferences about a
population:

Understand that statistics can be used to gain
information about a population by examining a
sample of the population – 7.SP.1

Generalizations about a population from a
sample are valid only if the sample is
representative of that population – 7.SP.1

Understand that random sampling tends to
produce representative samples and support valid
inferences – 7.SP.1

Use data from a random sample to draw
inferences about a population with an unknown
characteristic of interest – 7.SP.2

Generate multiple samples (or simulated
samples) of the same size to gauge the variation
in estimates or predictions – 7.SP.2
Draw informal comparative inferences about two
populations:

Informally assess the degree of visual overlap of
two numerical data distributions with similar
variabilities, measuring the difference between
the centers – 7.SP.3

Express the overlap as a multiple of a measure of
variability (mean absolute deviation) – 7.SP.3
Use measures of center (mean and/or median) and
measures of variability (interquartile range and/or
mean absolute deviation) for numerical data from
random samples to draw informal comparative
inferences about two populations – 7.SP.4
Quarter 1 (cont.)
Quarter 2 (cont.)
Quarter 3 (cont.)
Quarter 4 (cont.)
Solve real-life and mathematical problems
using numerical and algebraic expressions
and equations:

Solve multi-step real-life mathematical
problems posed with positive and
negative rational numbers in any form
using tools strategically:
o whole numbers
o fractions
o decimals
– 7.EE.3

Apply properties of operations to
calculate with numbers in any form
– 7.EE.3

Convert between forms as appropriate
– 7.EE.3

Assess the reasonableness of answers
using mental computation and
estimation strategies – 7.EE.3

Use variables to represent quantities in a
real-world or mathematical problem
– 7.EE.4

Construct simple equations and
inequalities to solve problems by
reasoning about the quantities
– 7.EE.4

Solve word problems leading to
equations of the form px + q = r and
p(x + q) = r, where p, q, and r are
specific rational numbers – 7.EE.4a

Solve equations of the two forms
specified above fluently
– 7.EE.4a
7th Grade
May 5, 2017
Continued - Apply and extend previous
understandings of operations with
fractions to + , – , × , ÷ rational numbers:

Understand that multiplication is
extended from fractions to rational
numbers by requiring that operations
continue to satisfy the properties of
operations (in particular-the
distributive property) leading to the
rules for multiplying signed numbers
– 7.NS.2a

Interpret products of rational numbers
by describing real-world contexts
– 7.NS.2a

Understand that integers can be
divided, provided that the divisor is not
zero – 7.NS.2b

Understand that every quotient of
integers (with a non-zero divisor) is a
rational number – 7.NS.2b

If p and q are integers, then –(p\q) = (p)\q = p\(-q) – 7.NS.2b

Interpret quotients of rational numbers
by describing real-world contexts
– 7.NS.2b

Apply properties of operations as
strategies to multiply and divide
rational numbers – 7.NS.2c

Convert a rational number to a decimal
using long division – 7.NS.2d

Know that the decimal form of a
rational number terminates in 0’s or
eventually repeats – 7.NS.2d

Solve real-world and mathematical
problems involving the four operations
with rational numbers – 7.NS.3
NOTE: computations with
rational numbers extend the rules
for manipulating fractions to
complex fractions
Continued - Solve real-life and
mathematical problems using numerical
and algebraic expressions and equations:

Compare an algebraic solution to an
arithmetic solution, identifying the
sequence of the operations used in each
approach – 7.EE.4a

Solve word problems leading to
inequalities of the form px + q > r or
px + q < r, where p, q, and r are specific
rational numbers – 7.EE.4b

Graph a solution set of the inequality
– 7.EE.4b

Interpret the solution of an inequality in
the context of the problem – 7.EE.4b
Analyze proportional relationships and
use them to solve real-world and
mathematical problems:

Compute unit rates associated with
ratios of fractions, including ratios of
lengths, areas, and other quantities
measured in like or different units
– 7.RP.1

Recognize and represent proportional
relationships between quantities
– 7.RP.2

Decide whether two quantities are in a
proportional relationship by:
o testing for equivalent ratios in a
table
o graphing on a coordinate plane
o observing whether the graph is a
straight line through the origin
– 7.RP.2a

Identify the constant of proportionality
(unit rate) of proportional relationships
in:
o tables
○ equations
o graphs
○ diagrams
o verbal descriptions
– 7.RP.2b

Represent proportional relationships by
equations – 7.RP.2c

Explain what a point (x, y) on the graph
of a proportional relationship means in
terms of the situation – 7.RP.2d

Give special attention to the points (0,0)
and (1,r) where r is the unit rate on a
graph – 7.RP.2d

Use proportional relationships to solve
multi-step ratio and percent problems
7th Grade
Draw, construct, and describe geometrical
figures and describe the relationships
between them:

Solve problems involving scale
drawings of geometric figures – 7.G.1

Compute actual lengths and areas from
a scale drawing – 7.G.1

Reproduce a scale drawing at a different
scale – 7.G.1
Draw, construct, and describe geometrical
figures and describe the relationships
between them:

Describe the 2D figures that result from
slicing 3D figures:
o in plane sections of right
rectangular prisms
o in plane sections of right
rectangular pyramids
– 7.G.3
Solve real-life and mathematical problems
involving surface area, and volume:

Solve real-world and mathematical
problems involving volume, and surface
area of 3D objects composed of:
o cubes
o right prisms
– 7.G.6
Draw, construct, and describe geometrical
figures and describe the relationships
between them:

Draw geometric shapes with given
conditions using:
o freehand
o ruler and protractor
o technology
– 7.G.2

Focus on constructing triangles form
three measures of angles or sides,
noticing when the conditions determine:
o a unique triangle
o more than one triangle
o no triangle
– 7.G.2
May 5, 2017
Investigate chance processes and develop, use, and
evaluate probability models:

Understand that the probability of a chance event
is a number between 0 and 1 that expresses the
likelihood of the event occurring, specifically:
o larger numbers indicate a greater likelihood
o a probability near 0 indicates an unlikely
event
o a probability around ½ indicates an event
that is neither unlikely or likely
o a probability near 1 indicates a likely event
– 7.SP.5

Approximate the probability of a chance event
by:
o collecting data on the chance process that
produces it
o observing its long-run relative frequency
o predict the approximate relative frequency
given the probability
– 7.SP.6

Develop a probability model and use it to find
probabilities of events – 7.SP.7

Compare probabilities from a model to observed
frequencies; if the agreement is not good, explain
possible sources of the discrepancy – 7.SP.7

Develop a uniform probability model by
assigning equal probability to all outcomes, and
use the model to determine probabilities of
events – 7.SP.7a

Develop a probability model (which may not be
uniform) by observing frequencies in data
generated from a chance process – 7.SP.7b
Continued: Investigate chance processes and
develop, use, and evaluate probability models:

Find probabilities of compound events using
organized lists, tables, tree diagrams, and
simulations – 7.SP.8

Understand that, just as with simple events, the
probability of a compound event is the fraction of
outcomes in the sample space for which the
compound event occurs – 7.SP.8a

Represent sample spaces for compound events
using methods such as:
o organized lists
o tables
o tree diagrams
– 7.SP.8b

For an event described in everyday language,
identify the outcomes in the sample space which
compose the event – 7.SP.8b

Design and use a simulation to generate
frequencies for compound events – 7.SP.8c
that include:
o simple interest ○ tax
o gratuities
○ commissions
o fees
○ percent error
o markups and markdowns
o percent increase or decrease
–
7.RP.3
Quarter 1 Quarter 2 Quarter 3
(cont.)
(cont.)
(cont.)
Quarter 4 (cont.)

Embedded Throughout: Mathematical Practices

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


Practice 1:
Practice 2:
Practice 3:
Practice 4:
Practice 5:
Practice 6:
Practice 7:
Practice 8:
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Plan with these in mind (as they pertain to you):
Literacy Emphasis:
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
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





Balance informational and literary text; increase reading of informational text
Build strong content knowledge in all disciplines
Respond to the varying demands of audience, task, purpose, and discipline
Use resources that have high text complexity (grade appropriate)
Increase writing from sources
•
•
•
•
Engage in high level, text-based discussions
Argument through text-based evidence/answers
Use technology and digital media strategically and capably
Use academic vocabulary to build understanding of complex texts
Literacy Standards Embedded Throughout
RST.7.2 Determine the central ideas or conclusion of a text; provide an accurate summary of the text distinct from prior knowledge or opinions
RST.7.3 Follow precisely a multistep procedure when performing technical tasks
RST.7.4 Determine meaning of symbols, key terms, and other domain-specific words and phrases
RST.7.7 Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (graphs, tables, diagrams, models,
flow charts, etc.)
WHST.7.2 Write informative/explanatory texts including the narration of technical processes with emphasis on:
o a. Introduce a topic clearly while organizing ideas and concepts
o d. Use precise language and domain-specific vocabulary to inform about or explain the topic
o e. Establish and maintain a formal style and objective tone
o f. Provide a concluding statement or section that follows from and supports the information or explanation presented
7th Grade
May 5, 2017


WHST.7.4 Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience
WHST.7.9 Draw evidence from informational texts to support analysis reflection and research
Embedded Throughout: Mathematical Practices
Plan with these in mind:




Practice
Practice
Practice
Practice
Quarter
1:
2:
3:
4:
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Unit
Benchmark(s)
Subunit/
Topic



Decimal &
fraction
operations
(≈ 4 weeks)
7.NS.1d
7.NS.2d
7.NS.3



Q1

Integers
(≈ 3 weeks)
7.NS.1
7.NS.2
7.NS.3
•
•
•
•



5:
6:
7:
8:
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Models/ Strategies
Know key terms for operations
Add, subtract, multiply, and divide fractions
and decimals
Convert between fractions, decimals, and
percents when applying the properties of
operations
Order a list of values (mixed with fractions,
decimals, and percents) from least to
greatest and vice versa
Order of operations
Include real-life multi-step
situations/everyday life situations (where
students have to choose what operation(s)
to do to answer the question)
Be familiar with the categories of rational
numbers (natural, whole, integer, and
rational)
All four operations using integers
Extend using operations to rational
numbers (positive and negative fractions &
decimal values)
Solve real-world problems involving the
four operations with rational numbers
7th Grade
Practice
Practice
Practice
Practice
Resources
Assessment




Be open to using and understanding
multiple strategies
Charts (organization)
100-grids


Number line
Integer tiles



May 5, 2017
Embedded Throughout: Mathematical Practices
Plan with these in mind:




Practice
Practice
Practice
Practice
Quarter
1:
2:
3:
4:
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Unit
Benchmark(s)
(≈2 weeks)
7.G.2
7.G.6






Q2

Solving
Equations
(≈2-3 weeks)
7.EE.1
7.EE.2
7.EE.3
7.EE.4
Practice
Practice
Practice
Practice
5:
6:
7:
8:
Subunit/
Topic


2D Geometry:
•
•
•
•



Models/
Strategies
Draw geometric shapes with given conditions
Construct various types of triangles (with and without the
protractor) when given:

three angle measures

three side length measures

a combination of three measurements
Distinguish how many different triangles are possible with
the given conditions
Include descriptive vocabulary when describing triangles:

equilateral, isosceles, scalene

equiangular, acute, right, obtuse
Use specific math notation and vocabulary to name (lines,
segments, edges, vertices, parallel, perpendicular, etc…)
Introduce angle relationships
Understand that rewriting expressions can provide different
perspectives in order to help solve problems (some forms
may be more useful than others)
Write expressions using whole numbers, fractions, and
decimals
Write equivalent expressions using:

addition/subtraction

factoring

distributive property

combine like terms

use rational coefficients
Solve multi-step linear equations (one variable) that include:

Positive and negative rational numbers (whole
numbers, fractions, and decimals)

2-step equations fluently

Using distributive property fluently

Using combining like terms

Variables on both sides
Compare solving situations algebraically (using an equation)
and arithmetically (table, diagram, ect…)
Use word problems to construct simple equations to solve
problems (focus on formats of 2-step and using distributive
7th Grade
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
May 5, 2017




Spaghetti (to investigate
possible triangle side
lengths)
Geoboard
Geometer’s Sketchpad
Resources
Assessment




property)
Quarter 2 Continued:
Unit
Benchmark(s)
Subunit/
Topic
Models/
Strategies

Area
(≈3 weeks)

Understand formula and calculate area of:

triangles

quadrilaterals (squares, rectangles, parallelograms, and
trapezoids) – emphasize parallelograms and
trapezoids

polygons (pentagons, hexagons, and octagons; regular
and/or irregular)

Understand that rewriting expressions and inequalities can
provide different perspectives in order to help solve
problems (some forms may be more useful than others)
Write inequalities using whole numbers, fractions, and
decimals
Write equivalent expressions and inequalities using:

addition/subtraction

factoring

distributive property

combine like terms

use rational coefficients
Solve multi-step linear inequalities (one variable) that
include:

Positive and negative rational numbers (whole
numbers, fractions, and decimals)

2-step equations fluently

Using distributive property fluently

Using combining like terms

Variables on both sides
Compare solving situations algebraically (using an equation)
and arithmetically (table, diagram, ect…)
Use word problems to construct simple inequalities to solve
problems (focus on formats of 2-step and using distributive
property)
Graph inequality solutions on a number line and interpret
7.G.2
7.G.6
Q2


Solving
Inequalities
(≈2 weeks)
7.EE.1
7.EE.2
7.EE.3
7.EE.4




7th Grade
May 5, 2017


Use different models to
understand area of
trapezoid
1. split a trapezoid
into two triangles
(drawing the
diagonal)
2. joining two
congruent
trapezoids together
to form a rectangle
Resources
Assessment




solutions in the context of the problem
Embedded Throughout: Mathematical Practices
Plan with these in mind:




Practice
Practice
Practice
Practice
Quarter
1:
2:
3:
4:
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Unit
Benchmark(s)


Q3
(≈ 5-6 weeks)
7.RP.1
7.RP.2
7.RP.3
7.G.1
Practice
Practice
Practice
Practice
5:
6:
7:
8:
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Subunit/
Topic





Proportions
•
•
•
•




Models/
Strategies
Review rates, ratios, and unit rates
Review converting fractions/decimals/percents
Calculate unit rates with rational numbers
Definition of a proportional relationship
Decide whether two quantities have a proportional relationship
(using tables and graphs)
Identify the constant unit rate of a proportional relationship
when given various formats:

tables

diagrams

graphs

verbal descriptions

equations
Represent proportional relationships by writing equations when
given:

diagrams

tables

verbal descriptions

graphs
Explain the relationship between the origin, the unit rate,r, (1,r),
and any point (x,y) on a graph in terms of the situation
Use proportional relationships to solve multi-step problems
involving:

Simple interest

Tax

Markups and markdowns

Gratuities and commissions

Fees

Percent increase or decrease

Percent error

Scale factors (maps, blueprints, perimeter, area)

Similar figures (missing dimensions)
Reproduce a scale drawing at a different scale
Incorporate measurement conversions
7th Grade
May 5, 2017



Coordinate plane
Tables
Resources

Assessment



3D Geometry
(≈3 weeks)
7.G.3
7.G.6


Practice
Practice
Practice
Practice
Quarter
1:
2:
3:
4:
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Unit
Benchmark(s)
(≈2 weeks)
7.G.4





Q4
Angle
Relationships
(≈2 weeks)
7.G.5

Stats
(≈ 4 weeks)
7.SP.1
7.SP.2
7.SP.3
7.SP.4
•
•
•
•
Practice
Practice
Practice
Practice
5:
6:
7:
8:
Geoblocks
Dot paper
Grid paper
3D Shape Bait


Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Subunit/
Topic

Circles




Embedded Throughout: Mathematical Practices
Plan with these in mind:




3D vocabulary (face, vertex, edge, net, etc…)
Volume and Surface Area

cubes

right prisms (triangular, rectangular, trapezoidal, hexagonal,
ect…)
Solve real-world problems involving 2D and 3D figures
Slice 3D figures and describe resulting 2D faces (right
rectangular prisms and right rectangular pyramids)


Models/
Strategies
Know circle vocabulary:

area

radius

pi

diameter

circumference
Understand the value of pi (ratio of circumference to diameter)
Understand the formulas for circumference and area of circles
Use formulas to calculate circumference and area in
mathematical problems and real-world problems
Analyze (informally) the relationship between circumference and
area
Know vocabulary:

vertical angles

supplementary angles

adjacent angles

complementary angles

parallel lines

congruent

transversal

intersecting lines

alternate interior

corresponding angles (ntk)
angles (ntk)

alternate exterior angles (ntk)
Find unknown angles using simple equations:

use geometric figures with unknown angle measure(s)

use unknown angle measure as a variable (i.e. “x”)

use unknown angle measure as an expression
(i.e. “3x + 2”)
Examine a sample of a population
Terms to know:

purpose of statistics

sample

population

random sample

representative population

valid inferences
7th Grade
May 5, 2017
Resources
Assessment









Use string to
measure diameter
and circumference
activity



Analyze data from random samples to make inferences
Take multiple samples of the same size from the same
population to analyze variation
Compare and draw informal inferences about two populations
using:

center (summarizes the data with one value; mean or
median)

spread/variation (how data’s values vary with a single
number; range, quartiles, or mean absolute deviation)

dot plots, histograms, and/or box and whisker plots
IF THERE IS ADDITIONAL TIME:
Unit
Q4
Probability
(≈4 weeks)
Benchmark(s)
7.SP.5
7.SP.6
7.SP.7
7.SP.8
Subunit/
Topic




Models/
Strategies
Definition/difference between probability and likelihood
Theoretical and experimental probability
Develop probability models and use a model(s) to find
probabilities of simple events
Find probabilities of compound events using:

organized lists

tables

tree diagrams

simulations
7th Grade
May 5, 2017

Resources

Assessment
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