SCUSD Curriculum Map - Last Updated 3/22/2016
Curriculum
Map
DRAFT Last Updated August 1, 2014
Grade 7 Mathematics
Common Core
Mathematics
Grade 7
Sacramento City Unified School District
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SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics
Table of Contents
7th Grade Year-at-a-Glance .....................................................................................................................................................................................................................................................................................................3
Unit #1: Proportional Reasoning and Relationships ...............................................................................................................................................................................................................................................................4
Unit #2: Applying Proportional Reasoning to Problems with Percents ..................................................................................................................................................................................................................................8
Unit #3: Operations with Rational Numbers – Addition and Subtraction ........................................................................................................................................................................................................................... 11
Unit #4: Operations with Rational Numbers – Multiplication and Division ........................................................................................................................................................................................................................ 15
Unit #5: Equivalent Expressions ........................................................................................................................................................................................................................................................................................... 19
Unit #6: Problem Solving with Equations and Inequalities .................................................................................................................................................................................................................................................. 22
Unit #7: Data Analysis .......................................................................................................................................................................................................................................................................................................... 26
Unit #8: Probability .............................................................................................................................................................................................................................................................................................................. 30
Unit #9: 2-Dimensional and 3-Dimensional Geometric Figures........................................................................................................................................................................................................................................... 34
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SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics
7th Grade Year-at-a-Glance
District Benchmark 1
*Alignment TBD
Month
Unit
Content Standards
September
Unit #1
Proportional Reasoning and Relationships
7.RP.1
7.RP.2
7.G.1
October
Unit #2
Applying Proportional Reasoning to Problems with Percents
Unit #3
Operations with Rational Numbers –Addition and Subtraction
Unit #4
Operations with Rational Numbers –Multiplication and Division
Unit #5
Equivalent Expressions
Unit #6
Problem Solving with Equations and Inequalities
November
District Benchmark 2
*Alignment TBD
December
January
February
District Benchmark 3
*Alignment TBD
CAASPP
(Smarter Balanced Summative Test)
March
Unit #7
Data Analysis
April
Unit #8
Probability
May/June
Unit #9
2-Dimensional and 3-Dimensional Geometric Figures
7.RP.3
7.NS.1
7.NS.3
7.NS.2
7.NS.3
7.EE.1
7.EE.2
7.EE.3
7.EE.4
7.SP.1
7.SP.2
7.SP.3
7.SP.4
7.SP.5
7.SP.6
7.SP.7
7.SP.8
7.G.1
7.G.2
7.G.3
7.G.4
7.G.5
7.G.6
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SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics
Unit #1: Proportional Reasoning and Relationships
(Approx. # of Days ___)
Content Standards: 7.RP.1,2 and 7.G.1
In this unit, students will be able to use ratios and proportions appropriately
Common Core State Standards-Mathematics:
Ratios and Proportional Relationships
7.RP
Analyze proportional relationships and use them to solve real-world and mathematical problems.
1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour,
compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
2. Recognize and represent proportional relationships between quantities.
a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight
line through the origin.
b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost
and the number of items can be expressed as t = pn.
d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate
Geometry
7.G
Draw, construct, and describe geometrical figures and describe the relationships between them.
1. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
Standards for Mathematical Practice of Emphasis:
SMP.1 - Make Sense of Problems and Persevere in Solving Them
SMP.2 - Reason Abstractly and Quantitatively
SMP.4 - Model with Mathematics
ELD Standards to Support Unit:
Part I: Interacting in Meaningful Ways:
A. Collaborative:
2. Interacting with others in written English in various communicative forms
4. Adapting language choices to various contexts
B. Interpretive:
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SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics
5. Listening actively to spoken English in a range of social and academic contexts.
C. Productive:
11. Supporting own opinions and evaluating others’ opinions in speaking and writing.
Part II: Learning About How English Works
A. Expanding and Enriching Ideas
5. Modifying to add details.
B. Connecting and Condensing Ideas
6. Connecting Ideas
7. Condensing Ideas
SEL Competencies:
Self-awareness
Self-management
Social awareness
Relationship skills
Responsible decision making
Unit #1 Proportional Reasoning and Relationships
Essential Questions
Assessments for Learning
Assessments/Tasks aligned to
learning outcomes
Note: These Assessments are
suggested, not required.
Sequence of Learning Outcomes
7.RP.1, 7.RP.2, 7.G.1
Students will be able to….
Strategies for Teaching and Learning
Differentiation
e.g. EL, SpEd, GATE
Differentiation Support
for Unit:
Use of math journals for
differentiation and
formative assessment
(use link below)
https://www.teaching
channel.org/videos/m
ath-journals
Flexible grouping:
 Content
 Interest
 Project/product
Resources
CCSS to Support Unit:
CA Mathematics Framework Gr. 7
p. 6 – 14
Progressions for the Common Core – Ratios
and Proportional Relationships Gr. 6-7
North Carolina
7th Grade Math Unpacked Content: pgs. 69, 25-26
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SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics
Unit #1 Proportional Reasoning and Relationships
Essential Questions




Assessments for Learning
What is the role of
unit rate in solving
problems?
How do you know
which of the two
unit rates is
important for a
problem?
What makes a
relationship
proportional?
http://www.illustrativemathe
matics.org/illustrations/82
How do you know
which of the two
unit rates is
important for a
problem?
http://www.illustrativemathe
matics.org/illustrations/101
For Learning Outcomes 1-5:
http://www.engageny.org
(this link is to a module that
has a variety of tasks that
relate to the learning
outcomes)
Sequence of Learning Outcomes
7.RP.1, 7.RP.2, 7.G.1
1) Identify and utilize unit rates to
solve real-world problems with
proportional relationships
containing whole numbers,
fractions and decimals by using
visual representations.
(Framework p.12)
7.RP.1
1) Use their understanding of unit
rates and proportionality to create
equations, both in the form
a d
 and y = kx, to solve
b c
real-world problems. (Framework
p.12)
7.RP.2

What makes a
relationship
proportional?
http://www.illustrativemathe
matics.org/illustrations/107
2) Identify, utilize and write
equations with unit rates
developed from scale drawings to
solve problems and reproduce a
scale drawing at a different scale.
(Framework p.35, 36)
7.G.1
Strategies for Teaching and Learning
Differentiation
e.g. EL, SpEd, GATE
Teaching Ratios through Tape Diagrams
 Level
(Heterogeneous/
and Double Number Lines:
Homogeneous)
http://math.kennesaw.edu/~twatanab/
Tiered:
DeKalb%20Title%20I%20Summit%202
 Independent
012.pdf
Management Plan
(Must Do/May Do)
Video on Teaching Unit Rate with Tape
 Grouping
Diagrams:
o Content
https://learnzillion.com/lessons/841-cre
o Rigor w/in the
ate-unit-rate-using-tape-diagram
concept
o Project-based
learning
o Homework
o Grouping
o Formative
Assessment
Anchor Activities:
 Content-related
tasks for early
finishers
o Game
o Investigation
o Partner
Activity
Video on Scale Drawings:
o
Stations
http://www.virtualnerd.com/middle-ma
Depth
and
Complexity
th/ratios-proportions-percent/scale-dra
wings-models/scale-drawing-definition Prompts/Icons:
 Depth
o Language of
the Discipline
Resources
Big Ideas Math 7th grade TE:
Section 5.1:
p.152-163 – exploratory activities
p. 164 – definition
p. 167-169 – practice finding the unit rate
p. 171 – activity 3 – examples of when to
use the unit rate
http://www.virtualnerd.com/middle-math/
all/ (See Ratios, Proportions, and Percent)
Big Ideas Math 7th grade TE:
Section 5.3
p. 178 – 184
Section 5.6
p. 199 – Activity 2 & 3 – Real World
Examples of Direct Variation
p. 200 – Identifying Direct Variation
p. 201 – Real Life Application
Big Ideas Math 7th grade TE:
Section 7.5
p. 300 – Definition of Scale Models &
Drawings
p. 301 – Definition of Scale Factor/Unit
Rate
p. 303 – 304 – Examples of Scale Drawings
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SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics
Unit #1 Proportional Reasoning and Relationships
Essential Questions


What makes a
relationship
proportional?
How is the
constant of
proportionality
represented in a
graph, table and
equation?
Assessments for Learning
http://www.illustrativemathe
matics.org/illustrations/1527
Sequence of Learning Outcomes
7.RP.1, 7.RP.2, 7.G.1
Strategies for Teaching and Learning
3) Use unit rate or constant of
Video on Understanding Unit Rates:
proportionality to determine if a
https://learnzillion.com/lessons/2410
relationship is proportional.
Students should explore a variety
of non-examples including: no
relationship, linear but not
proportional, inverse
relationships, non-similar figures.
(Framework p.8,9)
7.RP.2
http://map.mathshell.org/mat 4) Given a real-world example, work
erials/download.php?fileid=10
simultaneously with a graph, table
70
and equation. Determine if there
is a constant of proportionality in
each representation. If so, identify
the constant of proportionality in
each representation, giving careful
attention to the point (1, r) on a
graph.
7.G.1
Differentiation
e.g. EL, SpEd, GATE
o
o
Patterns
Unanswered
Questions
o Rules
o Trends
o Big Ideas
 Complexity
See Differentiation
Resources at:
http://scusd-math.wik
ispaces.com/home
Resources
Big Ideas Math 7th grade TE:
Section 5.2
p. T-164 – Example 2 Discusses a common
error. This can be used as an entry point
to discuss which unit rate is important for
the problem.
p. 170 & 171 – Determining Proportions
p. 172 – Comparing Ratios by simplifying to
simplest form
p. 173 – Example 3 Comparing Unit Rates to
Determine Proportionality
p. 176 – Graphing Proportions
Big Ideas Math 7th grade TE:
Section 5.6
p. 201 – Example 3
p. 203 & T-203 – Practice with proportions
using multiple representations
Proportional Reasoning Sample Lesson:
http://math.serpmedia.org/dragonfly/drag
onfly.pdf
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SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics
Unit #2: Applying Proportional Reasoning to Problems with Percents
(Approx. # of Days ___)
Content Standards: 7.RP.3
In this unit, students will be able to apply proportions.
Common Core State Standards-Mathematics:
Ratios and Proportional Relationships
7.RP
Analyze proportional relationships and use them to solve real-world and mathematical problems.
3. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent
error.
Standards for Mathematical Practice:
SMP.1 - Make Sense of Problems and Persevere in Solving Them
SMP.3 - Construct Viable Arguments and Critique the Reasoning of Others
SMP.4 - Model with Mathematics
SMP.5 - Use Appropriate Tools Strategically
ELD Standards to Support Unit:
SEL Competencies:
Self-awareness
Self-management
Social awareness
Relationship skills
Responsible decision making
Part I: Interacting in Meaningful Ways:
5) Collaborative:
3. Interacting with others in written English in various communicative forms
6. Adapting language choices to various contexts
6) Interpretive:
7. Listening actively to spoken English in a range of social and academic contexts.
7) Productive:
11. Supporting own opinions and evaluating others’ opinions in speaking and writing.
Part II: Learning About How English Works
C. Expanding and Enriching Ideas
5. Modifying to add details.
D. Connecting and Condensing Ideas
6. Connecting Ideas
7. Condensing Ideas
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SCUSD Curriculum Map - Last Updated 3/22/2016
Essential Questions
Assessments for Learning
Assessments/Tasks aligned to
learning outcomes:
Grade 7 Mathematics
Unit #2 Applying Proportional Reasoning to Problems with Percents
Sequence of Learning Outcomes Strategies for Teaching and Learning
Differentiation
7.RP.3
e.g. EL, SpEd, GATE
Students will be able to….
Note: These Assessments are
suggested, not required.



How can you
check for
reasonableness as
you solve a
problem and in
your answer?
How do you round
percentages
strategically to
estimate?
What are the
connections
between bar
modeling, double
number lines and
the algorithmic
procedure?
http://www.illustrativemathem 1) Estimate and calculate tips, simple
atics.org/illustrations/106
interest, tax, fees and mark ups
using bar modeling, double
http://map.mathshell.org/mate
number lines and algorithmic
rials/download.php?fileid=1042
procedures. (Framework p.14, 15)
7.RP.3
Videos (click on links below):
 Estimating Percents Using Bar
Modeling
 Finding Cost After Tax
 Percent Increase/Decrease
Differentiation Support
for Unit:
Use of math journals for
differentiation and
formative assessment
(use link below)
https://www.teachingc
hannel.org/videos/mat
h-journals
Flexible grouping:
 Content
 Interest
 Project/product
 Level
(Heterogeneous/
Homogeneous)
Tiered:
 Independent
Management Plan
(Must Do/May Do)
 Grouping
o Content
o Rigor w/in the
concept
o Project-based
learning
o Homework
o Grouping
o Formative
Assessment
Anchor Activities:
 Content-related
Resources
CCSS to Support Unit:
CA Mathematics Framework Gr. 7
p. 14 – 16
Progressions for the Common Core – Ratios
and Proportional Relationships Gr. 6-7
North Carolina
7th Grade Math Unpacked Content: p. 1013
7th Grade Common Core State Standards
Flip Book
Big Ideas Math TE
Building background knowledge: Lessons
6.1-6.4 (for changing % to decimals,
reinforce the concept of why we move
the decimal twice)
Lessons 6.4, 6.6 and 6.7
For tax: Need p. 250 problem #3 and p. 251
problems #24 & #25
For tip: See CA Framework p. 15
Relationships between decimals, fractions,
and percentages:
http://www.mathsisfun.com/decimal-fracti
on-percentage.html
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SCUSD Curriculum Map - Last Updated 3/22/2016



When bar
modeling, how do
you decide how to
“chunk” the
percents in the
model? (Ex: How
is 15%
represented? Is it
10% + 5% or 10%
+ 1% +1% +1%
+1% +1% or….)
http://www.illustrativemathem 2) Estimate and calculate discounts, Videos (click on links below):
atics.org/illustrations/105
markdowns and sales using bar
 Estimate Percent Using Bar
modeling, double number lines
Modeling
http://map.mathshell.org/mate
and algorithmic procedures.
 Tax, Tips, and Discounts
rials/download.php?fileid=1524
7.RP.3
Which quantity
http://map.mathshell.org/mate 3) Estimate and calculate percent
represents the
rials/download.php?fileid=79
change including identifying the
whole (or 100%)?
4
original value and comparing the
How can you check
difference in two values to the
for reasonableness
starting price. (Framework p.15,
as you solve a
16)
problem and in your
7.RP.3
answer?
Grade 7 Mathematics
tasks for early
finishers
o Game
o Investigation
o Partner Activity
o Stations
Depth and Complexity
Prompts/Icons:
 Depth
o Language of
the Discipline
o Patterns
o Unanswered
Questions
o Rules
o Trends
o Big Ideas
 Complexity
See Differentiation
Resources at:
http://scusd-math.wiki
spaces.com/home
Big Ideas Math 7th grade TE:
Lessons 6.4 and 6.6
Big Ideas Math 7th grade TE:
Lessons 6.5
Refer to 6.1 for Fraction, decimal, percent
conversions
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SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics
Unit #3: Operations with Rational Numbers – Addition and Subtraction
(Approx. # of Days ____)
Content Standards: 7.NS.1, 3
In his unit, students will be able to add & subtract integers
Common Core State Standards-Mathematics:
The Number System
7.NS
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.
b. 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. Show that a number and its opposite have a
sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.
c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of
their difference, and apply this principle in real-world contexts.
d. Apply properties of operations as strategies to add and subtract rational numbers.
3. Solve real-world and mathematical problems involving the four operations with rational numbers.
Standards for Mathematical Practice:
SMP.1 - Make Sense of Problems and Persevere in Solving Them
SMP.2 - Reason Abstractly and Quantitatively
SMP.3 - Construct Viable Arguments and Critique the Reasoning of Others
SMP.4 - Model with Mathematics
SMP.5 - Use Appropriate Tools Strategically
SMP.6 - Attend to Precision
SMP.7 - Look For and Make Use of Structure
SMP.8 - Look For and Express Regularity in Repeated Reasoning
ELD Standards to Support Unit:
Part I: Interacting in Meaningful Ways:
8) Collaborative:
4. Interacting with others in written English in various communicative forms
8. Adapting language choices to various contexts
9) Interpretive:
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SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics
9. Listening actively to spoken English in a range of social and academic contexts.
10) Productive:
11. Supporting own opinions and evaluating others’ opinions in speaking and writing.
Part II: Learning About How English Works
E. Expanding and Enriching Ideas
5. Modifying to add details.
F. Connecting and Condensing Ideas
6. Connecting Ideas
7. Condensing Ideas
Essential Questions
Assessments for Learning
SEL Competencies:
Self-awareness
Self-management
Social awareness
Relationship skills
Responsible decision making
Unit #3 Operations with Rational Numbers – Addition and Subtraction
Sequence of Learning Outcomes
Strategies for Teaching and Learning
Differentiation
7.NS.1, 7.NS.3
e.g. EL, SpEd, GATE
Assessments/Tasks aligned to Students will be able to…
learning outcomes:
Note: These Assessments are
suggested, not required.


What is a zero
pair?
How can you use
http://map.mathshell.org/ma 1) Understand and develop fluency
terials/lessons.php?taskid=45
adding rational numbers (integers,
3#task453
fractions and decimals) by creating
Strategies for adding and subtracting
positive and negative numbers (click on
links):
Differentiation Support
for Unit:
Use of math journals for
differentiation and
formative assessment
(use link below)
https://www.teachingc
hannel.org/videos/mat
h-journals
Flexible grouping:
 Content
 Interest
 Project/product
 Level
(Heterogeneous/
Homogeneous)
Tiered:
 Independent
Management Plan
Resources
CCSS Support for Unit:
CA Mathematics Framework Gr. 7
p. 18 – 28
http://www.cde.ca.gov/ci/ma/cf/docume
nts/aug2013gradeseven.pdf
Progressions for the Common Core – The
Number System gr. 6-8
North Carolina
7th Grade Math Unpacked Content: p. 14
–17
7th Grade Common Core State Standards
Flip Book
Big Ideas Math 7th grade TE:
Lesson 1.2
p. 8 and 9
12
SCUSD Curriculum Map - Last Updated 3/22/2016
Essential Questions






zero pairs to solve
problems?
How do you know
which number to
decompose when
creating zero
pairs?
How do zero pairs
and number lines
compare and
contrast?
What is the most
efficient method
to use for any
given problem?
Assessments for Learning
http://www.illustrativemathe
matics.org/illustrations/46
http://www.illustrativemathe
matics.org/illustrations/998
http://www.illustrativemathe
matics.org/illustrations/317
Grade 7 Mathematics
Unit #3 Operations with Rational Numbers – Addition and Subtraction
Sequence of Learning Outcomes
Strategies for Teaching and Learning
Differentiation
7.NS.1, 7.NS.3
e.g. EL, SpEd, GATE
zero pairs using counting chips, the
number line, decomposition and
mental math. Apply understanding
to solve real-world problems.
(Framework p.20-21)
7.NS.1, 7.NS.3






Counting Chips
T-Charts
Decomposition
Number Line
Reading the problem aloud
Making connections to real-world
problems (i.e. problems involving
money, debt, etc.)
Stay away from rote memorization
techniques or mnemonic devices (e.g.,
“keep-change-change”, etc.)
2) Understand and develop fluency
Strategies for adding and subtracting
How can you
subtracting
rational
numbers
positive and negative numbers:
subtract
(integers, fractions and decimals) by
something that
 Counting Chips
creating zero pairs using counting
isn’t there? (Ex: -3
 “Taking Away”
chips and the number line, with an
– 2, how can you
emphasis on “taking away” and by
subtract 2
seeing subtraction as the inverse of
positives from 3
addition (c – b = a means a + b = c).
negatives?)
Apply understanding to solve
How do you know
real-world problems. (Framework
how many zero
p.22, 23)
pairs to add to a
7.NS.1, 7.NS.3
problem in order
to subtract (take
away)?
Why is subtracting http://www.illustrativemathe 3) Compare and contrast work with
matics.org/illustrations/310
addition and subtraction of rational
a negative
(Must Do/May Do)
Grouping
o Content
o Rigor w/in the
concept
o Project-based
learning
o Homework
o Grouping
o Formative
Assessment
Anchor Activities:
 Content-related
tasks for early
finishers
o Game
o Investigation
o Partner Activity
o Stations
Depth and Complexity
Prompts/Icons:
 Depth
o Language of
the Discipline
o Patterns
o Unanswered
Questions
o Rules
o Trends
o Big Ideas
 Complexity
See Differentiation
Resources
(focuses only on integers)

The remainder of this lesson is more
applicable to learning outcome 4
Lesson 2.2
p. 50
(includes all rational numbers) Students
have experience with adding and
subtracting all positive rational numbers
in earlier grades so these two lessons can
be taught simultaneously.
Big Ideas Math 7th grade TE:
Lesson 1.3
p.14 only
This lesson focuses primarily on learning
outcome 3 and does not sufficiently
meet the expectations of this outcome
Big Ideas Math 7th grade TE:
Lesson 1.3
13
SCUSD Curriculum Map - Last Updated 3/22/2016
Essential Questions
equivalent to
adding a positive?

How can you
transition from
using a particular
method to solve a
problem to just
knowing the
answer?
Assessments for Learning
Grade 7 Mathematics
Unit #3 Operations with Rational Numbers – Addition and Subtraction
Sequence of Learning Outcomes
Strategies for Teaching and Learning
Differentiation
7.NS.1, 7.NS.3
e.g. EL, SpEd, GATE
numbers to build the understanding
that p – q = p + (-q) for the purpose
of thinking of any subtraction
problem as an addition problem
with a negative quantity. Apply
understanding to solve real-world
problems.
7.NS.1, 7.NS.3
4) Synthesize the work they have done
with addition and adding the
opposite to create an algorithm
around comparing quantities of
rational numbers and either adding
or subtracting. (Framework p.21)
7.NS.1
Resources
Resources at:
p.14 (integers only)
http://scusd-math.wiki
spaces.com/home
lesson 2.3
p. 58 (all rational numbers)
*see note in outcome 1 about teaching
the lessons simultaneously.
Big Ideas 7th grade TE:
Lesson 1.2
Starting on p. 10
14
SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics
Unit #4: Operations with Rational Numbers – Multiplication and Division
(Approx. # of days ____)
Content Standards: 7.NS.2, 3
In this unit, students will be able to multiply and divide integers
Common Core State Standards-Mathematics:
The Number System
7.NS
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property,
leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–
p)/q = p/(–q). Interpret quotients of rational numbers by describing real world contexts.
c. Apply properties of operations as strategies to multiply and divide rational numbers.
d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.
3. Solve real-world and mathematical problems involving the four operations with rational numbers.
Standards for Mathematical Practice:
SMP.1 - Make Sense of Problems and Persevere in Solving Them
SMP.2 - Reason Abstractly and Quantitatively
SMP.3 - Construct Viable Arguments and Critique the Reasoning of Others
SMP.4 - Model with Mathematics
SMP.5 - Use Appropriate Tools Strategically
SMP.6 - Attend to Precision
SMP.7 - Look For and Make Use of Structure
SMP.8 - Look For and Express Regularity in Repeated Reasoning
ELD Standards to Support Unit:
Part I: Interacting in Meaningful Ways:
11) Collaborative:
5. Interacting with others in written English in various communicative forms
15
SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics
10. Adapting language choices to various contexts
12) Interpretive:
11. Listening actively to spoken English in a range of social and academic contexts.
13) Productive:
11. Supporting own opinions and evaluating others’ opinions in speaking and writing.
Part II: Learning About How English Works
G. Expanding and Enriching Ideas
5. Modifying to add details.
H. Connecting and Condensing Ideas
6. Connecting Ideas
7. Condensing Ideas
Essential Questions Assessments for Learning
Assessments/Tasks aligned
to learning outcomes:
SEL Competencies:
Self-awareness
Self-management
Social awareness
Relationship skills
Responsible decision making
Unit #4 Operations with Rational Numbers – Multiplication and Division
Sequence of Learning Outcomes
Strategies for Teaching and Learning
Differentiation
7.NS.2, 7.NS.3
e.g. EL, SpEd, GATE
Students will be able to…
Note: These Assessments are
suggested, not required.

Where do the
rules of signed
numbers come
from?
1) Understand and develop fluency
Definition of multiplication for integers,
of multiplication of integers
for example:
through definition of integers and 3(-4) is three groups of negative four or
multiplication as repeated
-4 + -4 + -4 = -12 and -3(-4) is the
addition. Additional methods that
opposite of three groups of negative
Differentiation Support
for Unit:
Use of math journals for
differentiation and
formative assessment
(use link below)
https://www.teachingc
hannel.org/videos/mat
h-journals
Flexible grouping:
 Content
 Interest
 Project/product
 Level
(Heterogeneous/
Homogeneous)
Tiered:
Resources
CCSS Support for Unit:
CA Mathematics Framework Gr. 7
p. 18 – 28
http://www.cde.ca.gov/ci/ma/cf/documents/a
ug2013gradeseven.pdf
Progressions for the Common Core – The
Number System gr. 6-8
North Carolina
7th Grade Math Unpacked Content: p. 14 – 1 7
Big Ideas Math 7th grade TE:
Lesson 1.4
p. 22
It is essential here that the conceptual
16
SCUSD Curriculum Map - Last Updated 3/22/2016
Essential Questions Assessments for Learning

Why is the
product of two
negative
numbers a
positive number?
Grade 7 Mathematics
Unit #4 Operations with Rational Numbers – Multiplication and Division
Sequence of Learning Outcomes
Strategies for Teaching and Learning
Differentiation
7.NS.2, 7.NS.3
e.g. EL, SpEd, GATE
should be explored include using
four or –(-4 + -4 + -4) = -(-12) = 12.
patterns in products of integers
and the proof of why (-1)(-1) = 1. Videos:
(CA Framework p. 25, 26)
Understanding multiplication using
7.NS.2 number lines:
http://www.youtube.com/watch?v=K_J
qdw3NpEw
Multiplication using decomposition:
http://www.youtube.com/watch?v=Q_V1
brQtxT0
Proof of (-1)(-1) = 1
https://www.khanacademy.org/math/arit
hmetic/absolute-value/mult_div_negati
ves/v/why-a-negative-times-a-negative-i
s-a-positive



What are
examples of
multiplying and
dividing signed
rational numbers
in real life?
How can you
extend the rules
for integers to all
rational
numbers?
How do the rules
for multiplying
signed numbers
2) Develop the rules for multiplying
integers and extend that
understanding to all rational
numbers for the purpose of
fluency. Apply rules of signed
numbers to real-world contexts.
7.NS.2
3) Extend the rules of multiplication
to division of integers using the
inverse relationship between
Students look for patterns of products in
integers.

Independent
Management Plan
(Must Do/May Do)
 Grouping
o Content
o Rigor w/in the
concept
o Project-based
learning
o Homework
o Grouping
o Formative
Assessment
Anchor Activities:
 Content-related
tasks for early
finishers
o Game
o Investigation
o Partner Activity
o Stations
Depth and Complexity
Prompts/Icons:
 Depth
o Language of
the Discipline
o Patterns
o Unanswered
Questions
o Rules
o Trends
o Big Ideas
Resources
understanding is built and this leads to the
discovery of the rules mentioned in outcome
2.
Proof for (-1)(-1) = 1
p.64
Big Ideas Math 7th grade TE:
Lesson 1.5
p. 28
17
SCUSD Curriculum Map - Last Updated 3/22/2016
Essential Questions Assessments for Learning
help you know
the rules for
dividing signed
numbers?

How do you
know if a number
is rational?
Grade 7 Mathematics
Unit #4 Operations with Rational Numbers – Multiplication and Division
Sequence of Learning Outcomes
Strategies for Teaching and Learning
Differentiation
7.NS.2, 7.NS.3
e.g. EL, SpEd, GATE
 Complexity
See Differentiation
Resources at:
http://scusd-math.wikisp
aces.com/home
multiplication and division. Apply
division of integers to real-world
contexts.
7.NS.2
4) Apply rules of multiplication and
division to all rational numbers.
Solve real-world problems
involving both operations.
7.NS.2
Resources
Multiplying fractions:
3 5
 1  5 
  3  
4 7
 4  7 
Big Ideas Math 7th grade TE:
Lesson 2.4
p. 66
http://www.illustrativemath 5) Convert rational numbers to
ematics.org/illustrations/60
decimals using long division; know
4
that the decimal form of a rational
number terminates in 0’s or
http://www.illustrativemath
repeats.
ematics.org/illustrations/5
7.NS.2
93
Big Ideas Math 7th grade TE:
Lesson 2.1
p.46
http://www.illustrativemath 6) Solve real-world and
ematics.org/illustrations/29
mathematical problems involving
8
the four operations with rational
numbers. (Framework p.28)
7.NS.2
Embedded into the practice of each of the
above mentioned lessons.
18
SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics
Unit #5: Equivalent Expressions
(Approx. # of Days ____)
Content Standards: 7.EE.1,2
In this unit, students will be able to identify and generate equivalent expressions.
Common Core State Standards-Mathematics:
Expressions and Equations
7.EE
Use properties of operations to generate equivalent expressions.
1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
2. 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. For example, a + 0.05a = 1.05a means that “increase
by 5%” is the same as “multiply by 1.05.”
Standards for Mathematical Practice:
SMP.3 - Construct Viable Arguments and Critique the Reasoning of Others
SMP.7 - Look For and Make Use of Structure
SMP.8 - Look For and Express Regularity in Repeated Reasoning
ELD Standards to Support Unit:
SEL Competencies:
Self-awareness
Self-management
Social awareness
Relationship skills
Responsible decision making
Part I: Interacting in Meaningful Ways:
14) Collaborative:
6. Interacting with others in written English in various communicative forms
12. Adapting language choices to various contexts
15) Interpretive:
13. Listening actively to spoken English in a range of social and academic contexts.
16) Productive:
11. Supporting own opinions and evaluating others’ opinions in speaking and writing.
Part II: Learning About How English Works
I. Expanding and Enriching Ideas
5. Modifying to add details.
J. Connecting and Condensing Ideas
6. Connecting Ideas
7. Condensing Ideas
19
SCUSD Curriculum Map - Last Updated 3/22/2016
Essential Questions
Assessments for Learning
Grade 7 Mathematics
Unit #5 Equivalent Expressions
Sequence of Learning Outcomes
Strategies for Teaching and Learning
7.EE.1, 7.EE.2
Assessments/Tasks aligned to Students will be able to…
learning outcomes:


Differentiation
e.g. EL, SpEd, GATE
Differentiation
Support for Unit:
Use of math journals
Note: These Assessments are
for differentiation
suggested, not required.
and formative
assessment (use link
below)
https://www.teachin
gchannel.org/videos/
math-journals
Flexible grouping:
 Content
 Interest
http://www.illustrativemathe 1) Generate equivalent expressions
Use pattern problems like the “Pool
Of the many
 Project/product
containing rational numbers by
Border Problem” (Framework p. 31).
possible equivalent matics.org/illustrations/541
 Level
combining like terms in
expressions, how
(Heterogeneous/
mathematical and real-world
Possible use of manipulatives: Integer
does each
Homogeneous)
problems. Compare the meaning of
tiles
represent the
Tiered:
each equivalent expression in the
meaning of a given
 Independent
context of real-world problems.
Other real-world problems could include:
situation?
Management
(Framework p.29)
 Perimeter/Area Problems
Plan (Must
7.EE.2
 Cell Phone Plans
Do/May Do)
 Grouping
o Content
o Rigor w/in
http://www.illustrativemathe 2) Generate equivalent expressions
Of the many
the concept
containing rational numbers using
possible equivalent matics.org/illustrations/543
o Project-base
the distributive property, both
expressions, which http://www.illustrativemathe
d learning
matics.org/illustrations/1450
expanding and factoring, in
of them best
o Homework
mathematical and real-world
represents the
o Grouping
problems. Compare the meaning of
meaning of the
o Formative
each equivalent expression in the
situation?
Resources
CCSS Support for Unit:
CA Mathematics Framework Gr. 7
p. 28 – 31
Progressions for the Common Core –
Expressions and Equations Gr. 6 – 8
North Carolina
7th Grade Math Unpacked Content: p. 18 – 2 0
7th Grade Common Core State Standards Flip
Book
20
SCUSD Curriculum Map - Last Updated 3/22/2016
Essential Questions

Assessments for Learning
Grade 7 Mathematics
Unit #5 Equivalent Expressions
Sequence of Learning Outcomes
Strategies for Teaching and Learning
7.EE.1, 7.EE.2
context of real-world problems.
(CA Framework p.29)
7.EE.2
How does changing http://www.illustrativemathe 3) Generate equivalent expressions
matics.org/illustrations/433
containing rational numbers using
one term of an
the distributive property, addition
expression change
and subtraction, i.e. 8 – 2(0.5x + 1)
the meaning of the
in mathematical and real-world
context?
problems. Compare the meaning of
each equivalent expression in the
context of real-world problems.
7.EE.1
Differentiation
e.g. EL, SpEd, GATE
Resources
Assessment
Anchor Activities:
 Content-related
tasks for early
finishers
o Game
o Investigation
o Partner
Activity
o Stations
Depth and Complexity
Prompts/Icons:
 Depth
o Language of
the Discipline
o Patterns
o Unanswered
Questions
o Rules
o Trends
o Big Ideas
 Complexity
See Differentiation
Resources at:
http://scusd-math.wi
kispaces.com/home
21
SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics
Unit #6: Problem Solving with Equations and Inequalities
(Approx. # of Days ____)
Content Standards: 7.EE.3,4
In this unit, students will be able to identify, create, and solve equations and inequalities.
Common Core State Standards-Mathematics:
Expressions and Equations
7.EE
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of
operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a
woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a
door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
a. 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. Solve equations of these forms fluently. Compare an algebraic
solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
Standards for Mathematical Practice:
SMP-1. Make Sense of Problems and Persevere in Solving Them
SMP-2. Reason Abstractly and Quantitatively
SMP-4. Model with Mathematics
SMP-5. Use Appropriate Tools Strategically
SMP-7. Look For and Make Use of Structure
ELD Standards to Support Unit:
SEL Competencies:
Part I: Interacting in Meaningful Ways:
17) Collaborative:
7. Interacting with others in written English in various communicative forms
14. Adapting language choices to various contexts
18) Interpretive:
15. Listening actively to spoken English in a range of social and academic contexts.
19) Productive:
11. Supporting own opinions and evaluating others’ opinions in speaking and writing.
Part II: Learning About How English Works
Self-awareness
Self-management
Social awareness
Relationship skills
Responsible decision making
22
SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics
K. Expanding and Enriching Ideas
5. Modifying to add details.
L. Connecting and Condensing Ideas
6. Connecting Ideas
7. Condensing Ideas
Essential Questions
Assessments for
Learning
Assessments/Tasks
aligned to learning
outcomes:
Unit #6 Problem Solving with Equations and Inequalities
Sequence of Learning Outcomes
Strategies for Teaching and Learning
7.EE.3, 7.EE.4
Students will be able to…
Note: These
Assessments are
suggested, not
required.



Problem solving strategies for real-world
What are some arithmetic http://www.illustrativ 1) Solve multi-step, real-life and
mathematical problems by using
context problems (click on links, where
tools you can use to solve emathematics.org/illu
strations/997
arithmetic methods such as bar
available):
real-life problems?
modeling,
Guess
and
Check,
 Bar Modeling (video)
When is it appropriate to
drawing a picture or other tools  Drawing a picture
use arithmetic tools and
instead of creating an equation.  Make a table
when is it appropriate to
Use estimation to assess the
solve equations
 Guess and Check
reasonableness of answers.
algebraically?
 Estimation (3/7 of $105 is about ½ of
7.EE.3
For equations such as
$100)
5x  10  25 and
 Integer Tiles
 Side-by-side instruction
 Multiple Representations
Differentiation
e.g. EL, SpEd, GATE
Differentiation
Support for Unit:
Use of math journals
for differentiation
and formative
assessment (use
link below)
https://www.teachi
ngchannel.org/vide
os/math-journals
Flexible grouping:
 Content
 Interest
 Project/produc
t
 Level
(Heterogeneou
s/
Homogeneous)
Tiered:
 Independent
Management
Plan (Must
Do/May Do)
Resources
CCSS Support for Unit:
CA Mathematics Framework Gr. 7
p. 31 – 33
Progressions for the Common Core – Expressions
and Equations Gr. 6 – 8
North Carolina
7th Grade Math Unpacked Content: p. 21 – 24
7th Grade Common Core State Standards Flip
Book
Using multiple representations to solve problems:
http://www.acoe.org/acoe/files/EdServices/Math
/OneStepEquationsMultipleApproachesV3.pdf
23
SCUSD Curriculum Map - Last Updated 3/22/2016
Essential Questions
Assessments for
Learning
Grade 7 Mathematics
Unit #6 Problem Solving with Equations and Inequalities
Sequence of Learning Outcomes
Strategies for Teaching and Learning
7.EE.3, 7.EE.4





Resources

2
9 x  6  10 , what are
3
different methods for
solving algebraically?
When solving a problem
using both methods
(arithmetic tools and
algebraically), where do
you see relationships in
your work?
How do you interpret the
graph of an inequality in
terms of the context of
the problem?
What is the purpose of
using inverse operations?
Differentiation
e.g. EL, SpEd, GATE
http://www.illustrativ 2) Generate equations equivalent to
emathematics.org/illu
px + q = r with rational
strations/108
coefficients and solve
mathematical and real-life
situations using inverse
operations.
7.EE.4
What does your solution http://www.illustrativ 3) Generate equations equivalent to
p(x + q) = r with rational
mean in the context of the emathematics.org/illu
strations/478
coefficients and solve
problem?
mathematical and real-life
situations using inverse
operations.
7.EE.4
http://www.illustrativ 4) Compare and contrast the use of
emathematics.org/illu
arithmetic (see 1) versus
strations/712
algebraic methods (see 2 and 3)
Grouping
o Content
o Rigor w/in
the
concept
o Project-bas
ed learning
o Homework
o Grouping
o Formative
Assessmen
t
Anchor Activities:
 Content-relate
d
tasks for early
finishers
o Game
o Investigatio
n
o Partner
Activity
o Stations
Use inverse operations to solve algebraic
Depth and
equations (i.e. creating zeroes and ones).
Complexity
Warn against the language of “cancel out.”
Prompts/Icons:
 Depth
o Language
of the
Discipline
Learning Experience 4 can be embedded in
o Patterns
Experiences 2 and 3
o Unanswere
24
SCUSD Curriculum Map - Last Updated 3/22/2016
Essential Questions
Assessments for
Learning
Grade 7 Mathematics
Unit #6 Problem Solving with Equations and Inequalities
Sequence of Learning Outcomes
Strategies for Teaching and Learning
7.EE.3, 7.EE.4
of solving equations equivalent to
px + q = r and p(x + q) = r in
mathematical and real-life
situations. *
7.EE.4


Use investigation to help students
Why and when would you http://www.illustrativ 5) Generate and solve inequalities
emathematics.org/illu
with
rational
numbers,
in
the
understand the reason for reversing
reverse an inequality
strations/643
form of px + q < r and px + q > r
inequality symbols when multiplying or
symbol?
(including < and >) that arise from dividing by negative numbers.
When solving equations
real world problems. Graph the
https://www.youtube.com
and inequalities, using
solution region and interpret the
inverse operations, how
meaning of solutions in the
do you know whether to
context of the problem.
create a zero or a one?
7.EE.4
Differentiation
e.g. EL, SpEd, GATE
Resources
d
Questions
o Rules
o Trends
o Big Ideas
 Complexity
See Differentiation
Why the inequality sign changes when
Resources at:
multiplying or dividing by a negative number:
http://scusd-math. http://www.algebra.com/algebra/homework/Ine
wikispaces.com/ho
qualities/Inequalities.faq.question.203735.html
me
25
SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics
Unit #7: Data Analysis
(Approx. # of Days ____)
Content Standards: 7.SP.1,2,3,4
In this unit, students will be able to gather, sort, and appropriately interpret data
Common Core State Standards-Mathematics:
Statistics and Probability
7.SP
Use random sampling to draw inferences about a population.
1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is
representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the
variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled
survey data. Gauge how far off the estimate or prediction might be.
Draw informal comparative inferences about two populations.
3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of
variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on
either team; on a dot plot, the separation between the two distributions of heights is noticeable.
4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a
chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.
Standards for Mathematical Practice:
SMP.1 - Make Sense of Problems and Persevere in Solving Them
SMP.2 - Reason Abstractly and Quantitatively
SMP.3 - Construct Viable Arguments and Critique the Reasoning of Others
SMP.4 - Model with Mathematics
SMP.5 - Use Appropriate Tools Strategically
SMP.6 - Attend to Precision
SMP.7 - Look For and Make Use of Structure
SEL Competencies:
Self-awareness
Self-management
Social awareness
Relationship skills
Responsible decision making
ELD Standards to Support Unit:
Part I: Interacting in Meaningful Ways:
20) Collaborative:
26
SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics
8. Interacting with others in written English in various communicative forms
16. Adapting language choices to various contexts
21) Interpretive:
17. Listening actively to spoken English in a range of social and academic contexts.
22) Productive:
11. Supporting own opinions and evaluating others’ opinions in speaking and writing.
Part II: Learning About How English Works
M. Expanding and Enriching Ideas
5. Modifying to add details.
N. Connecting and Condensing Ideas
6. Connecting Ideas
7. Condensing Ideas
Essential Questions
Assessments for Learning
Unit #7 Data Analysis
Sequence of Learning Outcomes
Strategies for Teaching and Learning
7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4
Assessments/Tasks aligned to Students will be able to
learning outcomes:
Note: These Assessments are
suggested, not required.

How do you
conduct a random
sample to most
For Learning Outcomes 1 – 4:
Random Sampling of a Population:
http://www.engageny.org
1) Determine if a given random sample http://www.glencoe.com (from Glencoe
(pg: 82 – 157)
is representative of a population,
textbook
Differentiation
e.g. EL, SpEd, GATE
Differentiation
Support for Unit:
Use of math journals
for differentiation
and formative
assessment (use link
below)
https://www.teachi
ngchannel.org/video
s/math-journals
Flexible grouping:
 Content
 Interest
 Project/product
 Level
(Heterogeneous
Resources
CCSS Support for Unit:
CA Mathematics Framework Gr. 7
p. 38 – 42
Progressions for the Common Core –
Statistics and Probability Gr. 6-8
North Carolina
7th Grade Math Unpacked Content: p. 34 –
38
7th Grade Common Core State Standards
Flip Book
27
SCUSD Curriculum Map - Last Updated 3/22/2016
Essential Questions





Assessments for Learning
Grade 7 Mathematics
Unit #7 Data Analysis
Sequence of Learning Outcomes
Strategies for Teaching and Learning
7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4
Differentiation
e.g. EL, SpEd, GATE
Resources
accurately reflect a (This module contains a
and make generalizations about the Videos (Random Sampling):
/
population?
variety of tasks that relate
population based on characteristics http://learnzillion.com/lessons/2716-take-a
Homogeneous)
to multiple learning
of the sample.
-simple-random-sample
Tiered:
How do you know
outcomes.)
7.SP.2
 Independent
if a random sample
http://learnzillion.com/lessons/3206-gener
Management
is representative of
Possible Unit Project:
ate-survey-data-through-simulations
Plan (Must
a population?
http://www.ciese.org/curricu
Do/May Do)
lum/tempproj/
 Grouping
o Content
2) Make predictions about a
How do you know
o Rigor w/in
population given data from a
if your inferences
the concept
random sample, and then generate
and predictions
o Project-base
and analyze data from additional
about a population
d learning
random samples representing the
are valid?
o
Homework
same population to determine the
Why might you
o Grouping
validity of the predictions.
conduct more than
o Formative
(Framework,
p.
39,
40)
one random
Assessment
7.SP.1
sample of the same
Anchor Activities:
population?
 Content-related
tasks for early
3) Make inferences, predictions, and
Videos (click on links below):
What kinds of
finishers
comparisons from visual
Dot Plots
inferences or
o Game
representations (for example, dot
Box Plots
predictions can you
o Investigatio
plots and box plots) of given data
Interquartile Range
make from looking
n
sets.
at visual
o
Partner
7.SP.3
representations of
Activity
given data sets (for
o
Stations
example, dot
Depth and Complexity
plots)?
Prompts/Icons:
4) Determine if the averages (mean or Video (click on link below):
How can you use
 Depth
median) of two or more given data Mean Absolute Deviation
the mean absolute
o Language of
sets serve as a valuable reference
deviation (MAD) of
the
for comparison based on the
a given data set?
28
SCUSD Curriculum Map - Last Updated 3/22/2016
Essential Questions

When is it
appropriate to use
the different
measures of center
(mean and median)
and when is it
appropriate to use
the different
measures of
variability (MAD
and inter-quartile
range)?
Assessments for Learning
Grade 7 Mathematics
Unit #7 Data Analysis
Sequence of Learning Outcomes
Strategies for Teaching and Learning
7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4
variance (mean absolute deviation
or inter-quartile range) of the data
set. (Framework, p. 41, 42).
7.SP.4
Differentiation
e.g. EL, SpEd, GATE
Resources
Discipline
Patterns
Unanswered
Questions
o Rules
o Trends
o Big Ideas
 Complexity
See Differentiation
Resources at:
http://scusd-math.w
ikispaces.com/home
o
o
29
SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics
Unit #8: Probability
(Approx. # of Days ____)
Content Standards: 7.SP.5,6,7,8
In this unit, students will be able to identify, develop, and use probability to measure outcomes.
Common Core State Standards- Mathematics:
Statistics and Probability
7.SP
Investigate chance processes and develop, use, and evaluate probability models.
5. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0
indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given
the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.
7. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the
discrepancy.
a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from
a class, find the probability that Jane will be selected and the probability that a girl will be selected.
b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny
will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?
8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
a. 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.
b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify
the outcomes in the sample space which compose the event.
c. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have
type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?
Standards for Mathematical Practice:
SMP-1. Make Sense of Problems and Persevere in Solving Them
SMP-2. Reason Abstractly and Quantitatively
SMP-3. Construct Viable Arguments and Critique the Reasoning of Others
SMP-4. Model with Mathematics
SMP-5. Use Appropriate Tools Strategically
SMP-6. Attend to Precision
SMP-7. Look For and Make Use of Structure
30
SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics
ELD Standards to Support Unit:
Part I: Interacting in Meaningful Ways:
23) Collaborative:
9. Interacting with others in written English in various communicative forms
18. Adapting language choices to various contexts
24) Interpretive:
19. Listening actively to spoken English in a range of social and academic contexts.
25) Productive:
11. Supporting own opinions and evaluating others’ opinions in speaking and writing.
Part II: Learning About How English Works
O. Expanding and Enriching Ideas
5. Modifying to add details.
P. Connecting and Condensing Ideas
6. Connecting Ideas
7. Condensing Ideas
Essential Questions Assessments for Learning
Assessments/Tasks aligned
to learning outcomes:
Note: These Assessments are
suggested, not required.
Sequence of Learning Outcomes
7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8
Students will be able to…
SEL Competencies:
Self-awareness
Self-management
Social awareness
Relationship skills
Responsible decision making
Unit #8 Probability
Strategies for Teaching and Learning
Differentiation
e.g. EL, SpEd, GATE
Differentiation
Support for Unit:
Use of math journals
for differentiation
and formative
assessment (use link
below)
https://www.teachin
gchannel.org/videos/
math-journals
Flexible grouping:
 Content
Resources
CCSS Support for Unit:
Technology for random sampling:
http://www.randomizer.org/
http://stattrek.com/statistics/random-number-ge
nerator.aspx
CA Mathematics Framework Gr. 7
p. 42 – 45
Progressions for the Common Core – Statistics
and Probability Gr. 6-8
31
SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics






1) Determine the probability of a
Why does it make http://www.engageny.org
(pp. 1 - 82)
chance event and represent it as a
sense that the
(This module contains a
number between 0 and 1 (for
probability of a
variety of tasks that relate
example, the probability of flipping
chance event is
to multiple learning
heads on a quarter is ½), and
represented as a
experiences.)
understand that a probability near
number between
zero is an unlikely event, while a
0 and 1?
probability near 1 is a likely event.
How do you know http://www.illustrativemath
ematics.org/illustrations/1
7.SP.5
if your predictions
581
based on
observed
frequencies are
valid?
What is a
reasonable
number of data
points to collect in
order to make a
prediction about
the probability of
a chance event?
http://www.illustrativemath 2) Collect data from a chance event
ematics.org/illustrations/1
(for example, rolling a die),
216
calculate the probability based on
the observed frequencies, and use
proportional reasoning to make
predictions.
7.SP.6
Conduct class discussions about
observed data (e.g. flipping a coin),
paying attention to similarities and
differences between students’
observations, and focusing on any
predictions that can be made.
Possible chance events:
 Rolling dice
 Flipping coins
 Choosing cards from a deck
 Choosing colored objects
 Spinner (video)
Interest
Project/product
Level
(Heterogeneous/
Homogeneous)
Tiered:
 Independent
Management
Plan (Must
Do/May Do)
 Grouping
o Content
o Rigor w/in
the concept
o Project-base
d learning
o Homework
o Grouping
o Formative
Assessment
Anchor Activities:
 Content-related
tasks for early
finishers
o Game
o Investigation
o Partner
Activity
o Stations
Depth and Complexity
Prompts/Icons:
 Depth
o Language of
the Discipline
o Patterns
North Carolina
7th Grade Math Unpacked Content: p. 39 – 43
Videos (click on links below)
Using organized lists
Using tables
Using tree diagrams
32
SCUSD Curriculum Map - Last Updated 3/22/2016

Grade 7 Mathematics
http://map.mathshell.org/m 3) Compare the theoretical probability
aterials/tasks.php?taskid=
of a chance event to the probability
367#task367
based on observed frequencies,
http://map.mathshell.org/m
and explain any possible sources of
aterials/lessons.php?taski
discrepancies.
d=225&subpage=concept
7.SP.7
http://www.illustrativemath 4) Find probabilities of compound
What are some
ematics.org/illustrations/8
events using organized lists, tables,
similarities and
85
and tree diagrams.
differences when
7.SP.8
using an organized
list, a table, and a
tree diagram to
find probabilities
of compound
events?

What are some
similarities and
differences
between simple
events and
compound
events?
5) Make connections between finding
the probability of a simple event
and finding the probability of a
compound event.
7.SP.8

How do you
design a
simulation that
represents a
compound event?
6) Design and use a simulation from a
compound event (for example,
rolling two dice) to generate
frequencies.
o
Unanswered
Questions
o Rules
o Trends
o Big Ideas
 Complexity
See Differentiation
Resources at:
http://scusd-math.wi
kispaces.com/home
7.SP.8
33
SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics
Unit #9: 2-Dimensional and 3-Dimensional Geometric Figures
(Approx. # of Days ____)
Content Standards: 7.G.1,2,3,4,5,6
In this unit, students will be able to identify, draw, classify, and understand common geometric figures.
Common Core State Standards- Mathematics:
Geometry
7.G
Draw, construct, and describe geometrical figures and describe the relationships between them.
1. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
2. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the
conditions determine a unique triangle, more than one triangle, or no triangle.
3. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
4. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
6. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Standards for Mathematical Practice:
SMP-3. Construct Viable Arguments and Critique the Reasoning of Others
SMP-5. Use Appropriate Tools Strategically
SMP-6. Attend to Precision
SMP-7. Look For and Make Use of Structure
SMP-8. Look For and Express Regularity in Repeated Reasoning
ELD Standards to Support Unit:
Part I: Interacting in Meaningful Ways:
26) Collaborative:
10. Interacting with others in written English in various communicative forms
20. Adapting language choices to various contexts
27) Interpretive:
21. Listening actively to spoken English in a range of social and academic contexts.
SEL Competencies:
Self-awareness
Self-management
Social awareness
Relationship skills
Responsible decision making
34
SCUSD Curriculum Map - Last Updated 3/22/2016
Grade 7 Mathematics
28) Productive:
11. Supporting own opinions and evaluating others’ opinions in speaking and writing.
Part II: Learning About How English Works
Q. Expanding and Enriching Ideas
5. Modifying to add details.
R. Connecting and Condensing Ideas
6. Connecting Ideas
7. Condensing Ideas
Essential Questions Assessments for Learning
Assessments/Tasks aligned
to learning outcomes:


Unit #9 2-Dimensional and 3-Dimensional Geometric Figures
Sequence of Learning Outcomes
Strategies for Teaching and Learning
7.G.1, 7.G.2, 7.G.3, 7.G.4, 7.G.5, 7.G.6
Students will be able to…
Differentiation
e.g. EL, SpEd, GATE
Differentiation
Support for Unit:
Use of math journals
Note: These Assessments are
for differentiation
suggested, not required.
and formative
assessment (use link
below)
https://www.teachin
gchannel.org/videos/
math-journals
Flexible grouping:
 Content
 Interest
http://map.mathshell.org/m 1) Draw triangles (freehand, with ruler and Informal introduction to triangle inequality  Project/product
What are the
 Level
aterials/lessons.php?taski
protractor and with technology) given
theorem.
criteria for 3 side
(Heterogeneous/
d=581&subpage=concept
three
out
of
six
possible
criteria,
for
http://www.mathopenref.com/triangleine
lengths to form a
Homogeneous)
example two side lengths and an angle. quality.html
triangle?
Tiered:
Determine if the triangle exists, is
What is an
 Independent
unique, or determines more than one
Informal introduction to triangle
example of a
Management
triangle.
congruence theorems: SSS, SSA, AAS, SAS,
situation where
Resources
CCSS Support for Unit:
GeoGebra
CA Mathematics Framework Gr. 7
p. 33 – 38
North Carolina
7th Grade Math Unpacked Content: p. 25 –
33
7th Grade Common Core State Standards
Flip Book
35
SCUSD Curriculum Map - Last Updated 3/22/2016
Essential Questions Assessments for Learning
you could be
given three
pieces of
information
about a triangle
and have more
than one possible
drawing that fit
the given
criteria?
Grade 7 Mathematics
Unit #9 2-Dimensional and 3-Dimensional Geometric Figures
Sequence of Learning Outcomes
Strategies for Teaching and Learning
7.G.1, 7.G.2, 7.G.3, 7.G.4, 7.G.5, 7.G.6
7.G.2 AAA.
http://www.regentsprep.org/Regents/mat
h/geometry/GP4/BegTriPrf.htm
2) Write and solve equations for unknown
angles in figures involving
supplementary, complementary, vertical
and adjacent angles.*
7.G.2, 7.G.5

What is  (pi)?
Why is it an
important
number and how
is it used?
3) Explore the relationship between the
circumference and diameter of circles to
discover .
7.G.4
http://www.illustrativemath 4) Build on understanding of
ematics.org/illustrations/15
circumference, diameter and  to
53
generate formulas for circumference
and area of circles and use them to solve
http://www.illustrativemath
mathematical and real-world problems.
ematics.org/illustrations/34
7.G.4
Videos (click on links below)
Explore and generate formulas for
circumference and area of a circle.
Finding Circumference
Finding the Area of a Circle
Differentiation
e.g. EL, SpEd, GATE
Plan (Must
Do/May Do)
 Grouping
o Content
o Rigor w/in
the concept
o Project-base
d learning
o Homework
o Grouping
o Formative
Assessment
Anchor Activities:
 Content-related
tasks for early
finishers
o Game
o Investigation
o Partner
Activity
o Stations
Depth and Complexity
Prompts/Icons:
 Depth
o Language of
the Discipline
o Patterns
o Unanswered
Questions
o Rules
o Trends
Resources
Use circles to explore supplementary,
complementary, vertical and adjacent
angles.
http://www.mathsisfun.com/geometry/circ
le-theorems.html
Exploration of Pi (lesson):
https://www.teachervision.com/math/less
on-plan/3430.html
36
SCUSD Curriculum Map - Last Updated 3/22/2016
Essential Questions Assessments for Learning


Grade 7 Mathematics
Unit #9 2-Dimensional and 3-Dimensional Geometric Figures
Sequence of Learning Outcomes
Strategies for Teaching and Learning
7.G.1, 7.G.2, 7.G.3, 7.G.4, 7.G.5, 7.G.6
5) Find the area of triangles, quadrilaterals, Compare the use of addition and
and other polygons, including composite subtraction when finding the area of
figures composed of triangles,
composite figures, for example:
quadrilaterals, and polygons, in the
context of real-world and mathematical
problems.
7.G.6
http://www.illustrativemath 6) Investigate relationships between side
What is the
ematics.org/illustrations/10
lengths and areas in scale drawings of
relationship
7
geometric figures, and reproduce a scale
between the
drawing at a diffe6ent scale.
ratios of side
7.G.1
lengths and areas http://map.mathshell.org/m
aterials/lessons.php?taskid=
of geometric
494&subpage=problem
figures in scale
drawings?
How do you
subdivide a
composite figure
to find its area?
Differentiation
e.g. EL, SpEd, GATE
Resources
o Big Ideas
 Complexity
See Differentiation
Sample Lesson:
Resources at:
http://cc.betterlesson.com/lesson/441863/
http://scusd-math.wiki
area-of-composite-shapes-using-a-grid
spaces.com/home
7) Identify the two-dimensional figure that
results from slicing a plane section of a
three-dimensional figure.
7.G.3

http://www.illustrativemath 8) Solve real-world and mathematical
What is the
ematics.org/illustrations/26
problems involving the surface area and
relationship
6
volume of cubes and right prisms, and
between area,
explore the relationship between
surface area, and
surface area and volume.
volume?
7.G.6
37