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SAUSD Curriculum Map 2015-2016: Math 7
Math 7
These curriculum maps are designed to address CCSS Mathematics and Literacy outcomes. The
overarching focus for all curriculum maps is building student’s content knowledge and literacy skills as
they develop knowledge about the world. Each unit provides several weeks of instruction. Each unit also
includes various assessments. Taken as a whole, this curriculum map is designed to give teachers
recommendations and some concrete strategies to address the shifts required by CCSS.
Instructional Shifts in Mathematics
Focus:
Focus strongly
where the
Standards focus
Coherence:
Think across
grades, and link
to major topics
within grades
Rigor:
In major topics,
pursue
conceptual
understanding,
procedural skills
and fluency, and
application
Focus requires that we significantly narrow and deepen the scope of content in
each grade so that students experience concepts at a deeper level.
 Instruction engages students through cross-curricular concepts and application. Each

unit focuses on implementation of the Math Practices in conjunction with math content.
Effective instruction is framed by performance tasks that engage students and promote
inquiry. The tasks are sequenced around a topic leading to the big idea and essential
questions in order to provide a clear and explicit purpose for instruction.
Coherence in our instruction supports students to make connections within and
across grade levels.



Problems and activities connect clusters and domains through the art of questioning.
A purposeful sequence of lessons build meaning by moving from concrete to abstract,
with new learning built upon prior knowledge and connections made to previous
learning.
Coherence promotes mathematical sense making. It is critical to think across grades
and examine the progressions in the standards to ensure the development of major
topics over time. The emphasis on problem solving, reasoning and proof,
communication, representation, and connections require students to build
comprehension of mathematical concepts, procedural fluency, and productive
disposition.
Rigor helps students to read various depths of knowledge by balancing
conceptual understanding, procedural skills and fluency, and real-world
applications with equal intensity.



Conceptual understanding underpins fluency; fluency is practiced in contextual
applications; and applications build conceptual understanding.
These elements may be explicitly addressed separately or at other times combined.
Students demonstrate deep conceptual understanding of core math concepts by
applying them in new situations, as well as writing and speaking about their
understanding. Students will make meaning of content outside of math by applying
math concepts to real-world situations.
Each unit contains a balance of challenging, multiple-step problems to teach new
mathematics, and exercises to practice mathematical skills
(Last updated May 18, 2015)
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SAUSD Curriculum Map 2015-2016: Math 7
8 Standards for Mathematical Practice
The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all
levels should seek to develop in their students. These practices rest on important “processes and
proficiencies” with longstanding importance in mathematics education. They describe how students should
learn the content standards, helping them to build agency in math and become college and career ready. The
Standards for Mathematical Practice are interwoven into every unit. Individual lessons may focus on
one or more of the Math Practices, but every unit must include all eight:
1. Make sense
of problems
and persevere
in solving
them
2. Reason
Abstractly and
quantitatively
3. Construct
viable
arguments
and critique
the reasoning
of others
Mathematically proficient students start by explaining to themselves the meaning of a problem and
looking for entry points to its solution. They analyze givens, constraints, relationships, and goals.
They make conjectures about the form and meaning of the solution and plan a solution pathway
rather than simply jumping into a solution attempt. They consider analogous problems, and try
special cases and simpler forms of the original problem in order to gain insight into its solution.
They monitor and evaluate their progress and change course if necessary. Older students might,
depending on the context of the problem, transform algebraic expressions or change the viewing
window on their graphing calculator to get the information they need. Mathematically proficient
students can explain correspondences between equations, verbal descriptions, tables, and graphs
or draw diagrams of important features and relationships, graph data, and search for regularity or
trends. Younger students might rely on using concrete objects or pictures to help conceptualize
and solve a problem. Mathematically proficient students check their answers to problems using a
different method, and they continually ask themselves, "Does this make sense?" They can
understand the approaches of others to solving complex problems and identify correspondences
between different approaches.
Mathematically proficient students make sense of quantities and their relationships in problem
situations. They bring two complementary abilities to bear on problems involving quantitative
relationships: the ability to decontextualize—to abstract a given situation and represent it
symbolically and manipulate the representing symbols as if they have a life of their own, without
necessarily attending to their referents—and the ability to contextualize, to pause as needed during
the manipulation process in order to probe into the referents for the symbols involved. Quantitative
reasoning entails habits of creating a coherent representation of the problem at hand; considering
the units involved; attending to the meaning of quantities, not just how to compute them; and
knowing and flexibly using different properties of operations and objects.
Mathematically proficient students understand and use stated assumptions, definitions, and
previously established results in constructing arguments. They make conjectures and build a logical
progression of statements to explore the truth of their conjectures. They are able to analyze
situations by breaking them into cases, and can recognize and use counterexamples. They justify
their conclusions, communicate them to others, and respond to the arguments of others. They
reason inductively about data, making plausible arguments that take into account the context from
which the data arose. Mathematically proficient students are also able to compare the effectiveness
of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—
if there is a flaw in an argument—explain what it is. Elementary students can construct arguments
using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can
make sense and be correct, even though they are not generalized or made formal until later grades.
Later, students learn to determine domains to which an argument applies. Students at all grades
can listen or read the arguments of others, decide whether they make sense, and ask useful
questions to clarify or improve the arguments.
(Last updated May 18, 2015)
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SAUSD Curriculum Map 2015-2016: Math 7
4. Model with
mathematics
5. Use
appropriate
tools
strategically
6. Attend to
precision
7. Look for
and make use
of structure
8. Look for
and express
regularity in
repeated
reasoning
Mathematically proficient students can apply the mathematics they know to solve problems arising
in everyday life, society, and the workplace. In early grades, this might be as simple as writing an
addition equation to describe a situation. In middle grades, a student might apply proportional
reasoning to plan a school event or analyze a problem in the community. By high school, a student
might use geometry to solve a design problem or use a function to describe how one quantity of
interest depends on another. Mathematically proficient students who can apply what they know are
comfortable making assumptions and approximations to simplify a complicated situation, realizing
that these may need revision later. They are able to identify important quantities in a practical
situation and map their relationships using such tools as diagrams, two-way tables, graphs,
flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions.
They routinely interpret their mathematical results in the context of the situation and reflect on
whether the results make sense, possibly improving the model if it has not served its purpose.
Mathematically proficient students consider the available tools when solving a mathematical
problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a
calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry
software. Proficient students are sufficiently familiar with tools appropriate for their grade or
course to make sound decisions about when each of these tools might be helpful, recognizing both
the insight to be gained and their limitations. For example, mathematically proficient high school
students analyze graphs of functions and solutions generated using a graphing calculator. They
detect possible errors by strategically using estimation and other mathematical knowledge. When
making mathematical models, they know that technology can enable them to visualize the results of
varying assumptions, explore consequences, and compare predictions with data. Mathematically
proficient students at various grade levels are able to identify relevant external mathematical
resources, such as digital content located on a website, and use them to pose or solve problems.
They are able to use technological tools to explore and deepen their understanding of concepts.
Mathematically proficient students try to communicate precisely to others. They try to use clear
definitions in discussion with others and in their own reasoning. They state the meaning of the
symbols they choose, including using the equal sign consistently and appropriately. They are
careful about specifying units of measure, and labeling axes to clarify the correspondence with
quantities in a problem. They calculate accurately and efficiently, express numerical answers with a
degree of precision appropriate for the problem context. In the elementary grades, students give
carefully formulated explanations to each other. By the time they reach high school they have
learned to examine claims and make explicit use of definitions.
Mathematically proficient students look closely to discern a pattern or structure. Young students,
for example, might notice that three and seven more is the same amount as seven and three more,
or they may sort a collection of shapes according to how many sides the shapes have. Later,
students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about
the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and
the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use
the strategy of drawing an auxiliary line for solving problems. They also can step back for an
overview and shift perspective. They can see complicated things, such as some algebraic
expressions, as single objects or as being composed of several objects. For example, they can see 5 3(x - y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be
more than 5 for any real numbers x and y.
Mathematically proficient students notice if calculations are repeated, and look both for general
methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that
they are repeating the same calculations over and over again, and conclude they have a repeating
decimal. By paying attention to the calculation of slope as they repeatedly check whether points are
on the line through (1, 2) with slope 3, middle school students might abstract the equation (y - 2)/(x
- 1) = 3. Noticing the regularity in the way terms cancel when expanding (x - 1)(x + 1), (x - 1)(x2 + x
+ 1), and (x - 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric
series. As they work to solve a problem, mathematically proficient students maintain oversight of
the process, while attending to the details. They continually evaluate the reasonableness of their
intermediate results.
(Last updated May 18, 2015)
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SAUSD Curriculum Map 2015-2016: Math 7
English Language Development Standards
The California English Language Development Standards (CA ELD Standards) describe the key
knowledge, skills, and abilities in core areas of English language development that students learning
English as a new language need in order to access, engage with, and achieve in grade‐level academic
content, with particular alignment to the key knowledge, skills, and abilities for achieving college‐ and
career‐readiness. ELs must have full access to high quality English language arts, mathematics, science,
and social studies content, as well as other subjects, at the same time as they are progressing through the
ELD level continuum. The CA ELD Standards are intended to support this dual endeavor by providing
fewer, clearer, and higher standards. The ELD Standards are interwoven into every unit.
Interacting in Meaningful Ways
A. Collaborative (engagement in dialogue with others)
1. Exchanging information/ideas via oral communication and conversations
B. Interpretive (comprehension and analysis of written and spoken texts)
5. Listening actively and asking/answering questions about what was heard
8. Analyzing how writers use vocabulary and other language resources
C. Productive (creation of oral presentations and written texts)
9. Expressing information and ideas in oral presentations
11. Supporting opinions or justifying arguments and evaluating others’ opinions or
arguments
(Last updated May 18, 2015)
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SAUSD Curriculum Map 2015-2016: Math 7
How to Read this Document

The purpose of this document is to provide an overview of the progression of units of study within a
particular grade level and subject describing what students will achieve by the end of the year. The
work of Big Ideas and Essential Questions is to provide an overarching understanding of the
mathematics structure that builds a foundation to support the rigor of subsequent grade levels. The
Performance Task will assess student learning via complex mathematical situations. Each unit
incorporates components of the SAUSD Theoretical Framework and the philosophy of Quality
Teaching for English Learners (QTEL). Each of the math units of study highlights the Common Core
instructional shifts for mathematics of focus, coherence, and rigor.

The 8 Standards for Mathematical Practice are the key shifts in the pedagogy of the classroom.
These 8 practices are to be interwoven throughout every lesson and taken into consideration during
planning. These, along with the ELD Standards, are to be foundational to daily practice.

First, read the Framework Description/Rationale paragraph, as well as the Common Core State
Standards. This describes the purpose for the unit and the connections with previous and subsequent
units.

The units show the progression of units drawn from various domains.

The timeline tells the length of each unit and when each unit should begin and end.
(Last updated May 18, 2015)
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SAUSD Curriculum Map 2015-2016: Math 7
SAUSD Scope and Sequence for Math 7
Unit 1
9/01/15 10/09/15
6 weeks
Operations with
Rational
Numbers
Unit 2
10/12/15 11/20/15
6 Weeks
Rates, Ratios,
and
Proportional
Reasoning
Part A
Unit 3
11/30/1512/18/15
3 Week
Percent
Applications
Unit 4A
01/04/16 –
01/22/16
3 Weeks
Expressions,
Equations, &
Inequalities
****SEMESTER****
Unit 4B
02/01/16 –
02/19/16
3 Weeks
Expressions,
Equations, &
Inequalities
Unit 5
02/22/16 –
04/01/16
6 Weeks
Geometry
Unit 6
04/11/1604/29/16
3 Weeks
Probability
Unit 7
05/02/16 05/20/16
3 Weeks
Statistics
Unit 8
05/23/16 –
6/16/16
4 Weeks
Enrichment
(Last updated May 18, 2015)
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SAUSD Curriculum Map 2015-2016: Math 7
Math 7 Overview:
As students enter seventh grade, they have an understanding of variables and how to apply
properties of operations to write and solve simple one-step equations. They are fluent in all positive
rational number operations. Students have been introduced to ratio concepts and applications,
concepts of negative rational numbers, absolute value, and all four quadrants of the coordinate
plane. Students have a solid foundation for understanding area, surface area, and volume of
geometric figures and have been introduced to statistical variability and distributions (Adapted
from The Charles A. Dana 9 Center Mathematics Common Core Toolbox 2012).
In grade seven instructional time should focus on four critical areas: (1) developing understanding
of and applying proportional relationships, including percentages; (2) developing understanding of
operations with rational numbers and working with expressions and linear equations; (3) solving
problems involving scale drawings and informal geometric constructions and working with twoand three-dimensional shapes to solve problems involving area, surface area, and volume; and (4)
drawing inferences about populations based on samples. (CCSSO 2010, Grade 7 Introduction).
Students also work towards fluently solving equations of the form 𝑝𝑥 + 𝑞=𝑟 and (𝑥 + 𝑞)=𝑟.
(From the CA Mathematics Framework for Math 7)
(Last updated May 18, 2015)
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SAUSD Curriculum Map 2015-2016: Math 7
Unit 1: Operations with Rational Numbers
(6 weeks 9/01-10/09)
Big Idea
For a given set of numbers there are relationships that are always true, and
these are the rules that govern arithmetic and algebra.
Essential Questions
Performance Task
Problem of the
Month


How can operations with integers be
illustrated in multiple ways? (Models,
verbally, and symbolically)
What’s the difference between the
opposite and the absolute value of a
number?
Unit Topics/Concepts
Introduction to Addition &
Subtraction of Rational
Numbers (including
fractions and decimals)
1. Understand “Opposite
quantities combine to make
zero.” Additive Inverse
2. Identify the absolute Value as
the distance between two
numbers on a number line
3. Apply the properties of
operations to adding and
subtracting rational numbers
and represent the information
on a number line
 Commutative Property
 Associative Property
Interpret sums of rational
numbers by describing realworld contexts.
Understand subtraction
of rational numbers as adding
the additive inverse and
apply this to real world
situations
Introduction to Multiplication
& Division of rational numbers
(including fractions and
decimals)
1. Apply properties of
operations to multiply and
divide rational numbers
 Commutative Property
 Associative Property







Division [6th Grade 2007] p.35
Fractions [6th Grade 2010] p.4
Fraction Match [6th Grade 2012] p.5-6
Ribbons and Bows [6th Grade 2013] p.8-9
Brenda’s Brownies [6th Grade 2014] p.2-3
Yogurt [7th Grade 2003] p.59-60
Cat Food [7th Grade 2009] p.74
Content Standards
 Got Your Number
POM and
Teacher’s Notes
Resources
7.NS Apply and extend previous understandings of
operations with fractions to add, subtract, multiply,
and divide rational numbers.
7.NS.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
context.
d. The Apply properties of operations as strategies to
add and subtract rational numbers.
7.NS.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
Essential Resources:
7th Grade Framework
(pgs 19-22)
University of Arizona
Progressions
(Documents for the
Common Core Math
Standards:
Draft 6-7 Progression
on The Number System
pg. 9)
Instructional
Resources:
Adopted Text CGP:
231 – +/- Integers &
Decimals 232 – x /
Integers
113 – Distributive
Property
114 – Identity & Inverse
properties
221 – Absolute Value
IMP: Discovering
Properties (4.0-4.2)
http://sausdmath.pbwor
ks.com/w/file/28887951
/Discovering%20Propert
ies.pdf
Dan Meyer 3-act videos
(list and interactive link
to Dan Meyer's videos by
standard)
(Last updated May 18, 2015)
8
SAUSD Curriculum Map 2015-2016: Math 7
 Distributive Property
 Multiplicative Inverse
2. Interpret products of rational
numbers by describing realworld situations and
understand that
multiplication of rational
numbers satisfies properties
of operations
Expanding understandings of
rational numbers
1. Convert between fractions
and decimals (terminating
and repeating)
 Use equivalent fractions
 Use long division
2. Assess the reasonableness of
answers using mental
computation and estimation.
 Rounding
 Front-end
3. Understand that a rational
number is the quotient of
two integers (without a zero
denominator)
4. Interpret products and
quotients by describing in
real-world contexts
rules for multiplying signed numbers. Interpret
products of rational numbers by describing realworld 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.
7.NS.3 Solve real-world and mathematical problems
involving the four operations with rational numbers.
7.EE.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.
MAP Lessons:
http://map.mathshell.org
/materials/lessons.php
 Using Positive and
Negative Numbers in
Context – 7th Grade
Formative Assessment
Lesson
MARS- Number System
tasks
http://map.mathshell.org
/materials/stds.php?id=1
559#standard1569
● Division
● A Day Out
● Taxi Cabs
 SERP Problem:
http://math.serpmedi
a.org/diagnostic_teach
ing/poster-problems
Walking the Line
 SERP Problem:
http://math.serpmedi
a.org/diagnostic_teach
ing/poster-problems
Seeing Sums
Additional Resources:
Video: Discovery
Streaming- Introduction
to integers.mov (see site
for more)
Integer War (Cards or
dice)
(to be developed)
Algebra/ 2-color tiles for
review
(Last updated May 18, 2015)
9
SAUSD Curriculum Map 2015-2016: Math 7
Unit 1: Operations with Rational Numbers
(Support & Strategies)
Framework Description/Rationale
Rationale:
This is placed as the second unit to provide a foundation of skills for the work that follows in units 3-7,
specifically working with rational numbers with all four operations. This should lead nicely into unit 3 work
with expressions and equations and decimal & fractional representations in unit 4 (Percent Applications).
Framework Description:

In grade 6, students learn the concept of a negative number and work with absolute value, opposites, and
making “0.” In grade 7, students will experience for the first time performing operations with negative
numbers. Using the number line and other tools, students will perform operations with integers, fractions, and
decimals.
 Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide
rational numbers.
 Use properties of operations to generate equivalent expressions.
(See CCSS CA 7th Grade Framework pgs. 19-22 for more details)
Academic Language
Support
Key Vocabulary for Word
Bank:
 Integers
 Signed Numbers
 Positive
 Negative
 Rational Numbers
 Sum/Difference
 Deposit/Withdraw/
Overdraft
 Credit/Debit
 Profit/Loss
 Product/Quotient
 Absolute Value
 Opposites
 Additive Inverse
 Multiplicative Inverse
 Identity Properties
 Commutative Property
 Associative Property
 Distributive Property
 Terminating Decimals
 Repeating Decimals
Instructional Tool/Strategy Examples








Number Line Model (Vector Model)
Colored Chip Model (mainly for integers)
Money Account Models
Class Discussion on the meaning of
operations
Pattern Tables
Model with Equation
Area Models
Estimation Strategies:
 Front-end estimation with adjusting
(using the highest place value and
estimating from the front end making
adjustments to the estimate by taking
into account the remaining amounts),
 Rounding and adjusting (students
round down or round up and then
adjust their estimate depending on
how much the rounding affected the
original values)
Preparing the Learner
Fractions (prior knowledge)
5th grade
- unit fractions
- adding unlike
denominators
6th grade
- dividing a fraction by a
fraction
- concepts of negative
numbers
- negative fractions on a
number line
By end of 6th grade,
students have used every
operation with fractions

Activity: Above & Below
Sea Level (7.NS.1.c)
Teacher Notes:
(Last updated May 18, 2015)
10
SAUSD Curriculum Map 2015-2016: Math 7
Unit 2: Rates, Ratios, and Proportional Relationships
(6 weeks 10/12-11/20)
Big Idea
If two quantities vary proportionally, that relationship can be represented in
multiple ways.
Essential Questions
Performance Task
Problem of the
Month




What is the constant of
proportionality?
How can two quantities be
identified as proportional or nonproportional?
How can the constant of
proportionality (unit rate) be
determined given a table? Graph?
Equation? Diagram? Verbal
description?
What does a specific point on a
graph (x,y) represent?
Unit Topics/Concepts
Unit Rate
● Compute unit rates
● Include complex
fractions
 Leaky Faucet [7th Grade 2002] p.9
 Mixing Paints [7th Grade 2003] p.4
 Cereal [7th Grade 2004] p.17
 Lawn Mowing [7th Grade 2005] p.3
 Breakfast of Champions [7th Grade 2012] p.8-9
 Is it Proportional? [7th Grade 2014] p.6-7
(See the end of this document for Performance Task
descriptions)
*Please read SVMI’s document security
information:
 http://www.svmimac.org/memberresources.htm
l
Content Standards
 POM: “First
Rate” First Rate
(Teacher Notes)
 Level A
 Level B
 Level C
 Level D
 Level E
Resources
7.RP Analyze proportional relationships and use
them to solve real-world and mathematical
problems.
7.RP.1 Compute unit rates associated with ratios
Recognize and represent
of fractions, including ratios of lengths, areas and
proportional relationships other quantities measured in like or different
1. Determine if two
units.
quantities are
proportional or nonFor example, if a person walks ½ mile in each 1/4
proportional.
hour, compute the unit rate as the complex fraction
a. Prove in a table.
1/2/1/4 miles per hour, equivalently 2 miles per
b. Graph on a
hour.
coordinate plane.
(Quadrant I only)
7.RP.2 Recognize and represent proportional
c. Identify ratios as
relationships between quantities.
proportional if two
a. Decide whether two quantities are in a
conditions are met:
proportional relationship, e.g., by testing for
equivalent ratios in a table or graphing on a
 Linear
coordinate plane and observing whether the
 Starts at the
graph is a straight line through the origin.
origin
b. Identify the constant of proportionality (unit
rate) in tables, graphs, equations, diagrams,
2. Identify the constant of
and verbal descriptions of proportional
proportionality (unit
relationships.
rate)
c. Represent proportional relationships by
a. In a table
equations. For example, if total cost t is
b. Graphs
proportional to the number n of items
c. Equations
purchased at a constant price p, the
d. Diagrams
relationship between the total cost and the
e. Verbal description
number of items can be expressed as t = pn.
d.
Explain what a point (x, y) on the graph of a
3. Write equations that
proportional relationship means in terms of
Essential Resources:
CCSS 7th Grade Framework
(pgs. 6-11)
University of Arizona
Progressions
(Documents for the Common
Core Math Standards:
Draft 6-7 Progression on Ratios
and Proportional
Relationships)
Instructional Resources:
• Ratios & Proportional
Reasoning Unit
• Engage NY – Adapted
• IMP Unit Plan: Unit 8
 Susan Mercer: 7th
Proportion Rates
• 7th Proportions, Rates (Carr
11-12)
• Illustrative Mathematics
Track Practice
 Dan Meyer 3-act videos (list
and interactive link to Dan
Meyer's videos by standard)
 YouTube Video about Double
Number Lines and Tape
Diagrams
Adopted Text CGP
421 – Ratios & Rates
422 –Graphing Ratios & Rates
(Last updated May 18, 2015)
11
SAUSD Curriculum Map 2015-2016: Math 7
represents proportional
relationships. y=kx
(k = constant of
proportionality)
4. Explain what a point
(x,y) means on a graph.
a. Focus on the points
(0,0) and (1,r) in the
context of the
problem where r is
the unit rate
the situation, with special attention to the
points (0, 0) and (1, r) where r is the unit rate.
7.EE.3 Solve multi-step real-life and mathematical
problems posed with positive 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.
423 –Speed, Distance & Time
424 –Direct Variation
431 –Converting Measures
432 –Converting between Unit
Systems
433 – Dimensional Analysis
MAP Lessons:
 Developing a Sense of Scale –
7th Grade Formative
Assessment Lesson
 Proportion and Non-Proportion
Situations– 6th Grade
Formative Assessment Lesson
 Modeling: A Race– 7th Grade
Formative Assessment Lesson
 Drawing to Scale: Designing a
Garden – 7th Grade Formative
Assessment Lesson
 MARS - Ratios and
proportional Relationships
http://map.mathshell.org/m
aterials/stds.php?id=1559#s
tandard1569
● Buses
● Sale
● T-Shirt Sale
● A golden Crown?
 SERP Problem:
http://math.serpmedia.org/di
agnostic_teaching/posterproblems
Drag Racer Dragon Fly
(Last updated May 18, 2015)
12
SAUSD Curriculum Map 2015-2016: Math 7
Unit 2: Rates, Ratios, and Proportional Relationships
(Support & Strategies)
Framework Description/Rationale
Rationale:
Ratios and Proportional Relationships is the first unit because it is the primary theme of 7th grade. This type of reasoning
should be at the foundation of units that follow. Negative values will not be used in this unit and algorithmic equation strategies
should not be the focus. Percents will be the focus of a later unit.
Framework Description:
In addition, standard 7.EE.3, “assess the reasonableness of answers using mental computation and estimation strategies,“ is a
recurring focus in each unit.
Unit Rate
 Students further their understanding of unit rate from 6th grade. In 7th grade students will find unit rates in ratios involving
fractional quantities, for example,

1
1
2
3
=
3
6
Students will set up an equation with equivalent fractions and use reasoning about equivalent fractions to solve them, for
1
1
𝑥
example, 2 =
(See 7th Grade Framework for more details pages (6-11)
3
12
Recognize and Represent Proportional Relationships
 In this sections students will determine if two quantities are proportional by using tables, equations, and graphs. The
shortcut of “cross products” should be examined later as students begin to recognize patterns and why the shortcut
works. Students should not be using “cross products” as the first Students will need to identify the unit rate given a
table, graph, equation, diagrams, and a verbal description. Knowing the constant of proportionality (unit rate) students
will be able to write equations in the form y=kx (See 7th Grade Framework for more details pages 6-11)
Academic
Instructional Tool/Strategy Examples
Language Support
Key Vocabulary for  Manipulatives and picture representations.
 Double Sided Number Lines
Word Bank:
●
●
●
●
●
●
●
●
●
●
●
●
●
Identify
Determine
Equivalent
Quantities
Ratio
Ratio Table
Unit Rate (r/1)
Constant
Coordinate Plane
Constant of
Proportionality
(k)
Proportional
Relationships
Scale Drawing
Scale Factor





Tape Diagram
Graphs
Equations
Verbal Descriptions focusing on the numerical value.
Graph showing the increase of y to x in a” Unit Rate
Triangle”. Translate the graph to an equation in the form of
y=kx.
 Create a table, graph data and derive that x and y are values that
form a ray with an end point at the origin
 Record measurements of shapes, determine ratios between two
figures and ratios within a single figure, notice that ratios are
equal, and use these relationships to create scale drawings using
grid paper. Students should also be able to explain why two
figures are not scale drawings of one another using their
understanding of ratios.
 Example: Students can blow-up or shrink pictures on grid paper
(foundation for “dilations”). Students can recreate an image
using 2 units of length for every 1 unit on the original picture.
Preparing the
Learner
Topics:
 Equivalent
fractions
 Plotting points on a
coordinate grid
(Quadrant 1)
6th grade
 Concept of a ratio
 Equivalent ratios
 Constant speed
 Unit rate
Teacher Notes:
(Last updated May 18, 2015)
13
SAUSD Curriculum Map 2015-2016: Math 7
Unit 3: Percent Applications
(3 weeks 11/30 - 12/18)
Big Idea
Proportional relationships can be used to solve real-world problems.
Essential Questions


Performance Task
How can proportions be used to
solve real-world problems
involving percents? (Mark-up,
Discounts, tips, tax commission)
How can estimation be used to test
the reasonableness of a solution?
Unit Topics/Concepts
Solve multi-step real-life and
mathematical problems
1. Tax
2. Tip
3. Mark-up
4. Discount/Sale price
5. Commission
6. Simple interest
7. Percent error
Use multiple strategies
● Double-sided number line
● Tape diagram
● Visual model
● Equations
● Proportions
● Use estimation strategies to
test the reasonableness of a
solution







[6th
Problem of the Month
Sewing
Grade 2009] p.61
Work [7th Grade 2007] p.36
Sales [7th Grade 1999] p.2
Special Offer [7th Grade 2004] p.34
Buying a Camera [7th Grade 2006] p.29-30
Sale [7th Grade 2008] p. 60
Shopper’s Corner [7th Grade 2013] p.10-11
Content Standards
7.RP Analyze proportional
relationships and use them to
solve real-world and mathematical
problems.
7.RP.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.
7.EE.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.
● POM: “Measuring Up”
Measuring Up
Teacher Notes
● Level A
● Level B
● Level C
● Level D
● Level E
Resources
Essential Resources:
CCSS 7th Grade Framework
(pgs. 12-13)
Instructional Resources
 IMP Unit Plan: Percent
• Percent 1.0 – 1.2
• Percent 6.0 – 6.2
• Percent 3.0 – 3.1
• Percent 7.0 – 7.3
• Percent 4.0 – 4.2
• Percent 8.0 – 8.2
• Percent 5.0 – 5.3
 EngageNY: Module 4
 Dan Meyer 3-act videos (list and interactive
link to Dan Meyer's videos by standard)
 MAP Lessons:
 Estimation and Approximation: The
Money Munchers – 7th Grade Formative
Assessment Lesson
 Increasing and Decreasing Quantities by
a Percent – 7th Grade Formative
Assessment Lesson
 Georgia Dept. of Ed: Unit 3 (begin on pg.
27)
Adopted Text: CGP
434 – Converting Between Units of Speed
811 – Percents
812 – Changing Fraction & Decimals to
Percents
813 – Percent Increases & Decreases
821 – Discounts & Markups
822 – Tips, Tax & Commission
823 - Profit
824 – Simple Interest
(Last updated May 18, 2015)
14
SAUSD Curriculum Map 2015-2016: Math 7
Unit 3: Percent Applications
(Instructional Support & Strategies)
Framework Description/Rationale
Rationale:
Percents are brought in as the fourth unit to both review and continue the most significant theme of the year (ratios
and proportional reasoning) and following skill development in working with rational numbers, expressions, and
equations.
Framework Description:
Multi-step percent problems involving percent increase and decrease--Building on Proportional understanding from
previous unit using various representations
(see 7th Grade Framework pgs. 12-13 for further explanation, examples, and ways to model problems).
Academic Language
Support
Instructional Tool/Strategy Examples
Preparing the Learner
Key Vocabulary Word Bank:
● Percent
● Percentage
● Percent Increase
● Percent Decrease
● Enlargement
● Reduction
● Tax
● Tip/Gratuity
● Markup/Markdown
● Discount
● Sale Price
● Commission
● Fees
● Simple Interest
● Percent Error
Use multiple strategies to work with percents
● double-sided number line
● tape diagram
Example: Gas prices are projected to
increase 124% by April 2015. A gallon of gas
currently costs $4.17. What is the projected
cost of a gallon of gas for April 2015?
From 6th Grade:
● Fluently add, subtract,
multiply, and divide multidigit decimals using the
standard algorithm for
each operation.
● Find a percent of a quantity
as a rate per 100 (e.g., 30%
of a quantity means
30/100 times the
quantity); solve problems
involving finding the
whole, given a part and the
percent.
● Use ratio reasoning to
convert measurement
units; manipulate and
transform units
appropriately when
multiplying or dividing
quantities.
●
●
●
●
●
●
visual model
Example: A sweater is marked down 33%. Its
original price was $37.50. What is the price of
the sweater before sales tax?
Equations
Ex: Sale Price = 0.67 x Original Price
Proportions
Use estimation strategies to test the
reasonableness of a solution
Equivalent fractions
T-tables
Teacher Notes:
(Last updated May 18, 2015)
15
SAUSD Curriculum Map 2015-2016: Math 7
Unit 4A and 4B: Expressions, Equations, and Inequalities
(6 weeks 1/04-02/19)
Big Idea
Any number, measure, numerical expression, algebraic expression, or equation
can be represented in an infinite number of ways that have the same value.
Essential Questions
Performance Task
Problem of the
Month


How can estimation be used to test the
reasonableness of a solution?
How can the properties of rational
numbers be used to create equivalent
expressions and equations?
Unit Topics/Concepts
Expressions with rational numbers
and variables (including fractions and
decimals)
1. Create an expression for a given
situation using rational numbers.
● Visual model
● Verbal expression
● Numeric/ algebraic expression




The Number Cruncher [6th Grade 2001] p.3-4
Festival Lights [6th Grade 2011] p.4-5
Lattice Fence [6th Grade 2012] p.7-8
Facts in Fruit [7th Grade 2012] p.6-7
 Tri-Triangles
POM and
Teacher’s
Notes
Content Standards
Resources
7.EE Use properties of operations to
generate equivalent expressions.
Essential Resources:
7th Grade Framework (pgs. 22-27)
University of Arizona
Progressions
(Documents for the Common Core
Math Standards:
Draft 6-7 Progression on
Expressions and Equations pg. 8)
7.EE.1 Apply properties of
operations as strategies to add,
subtract, factor, and expand linear
expressions with rational
coefficients.
2. Create equivalent expressions.
● Combine like terms
● Use properties of rational
numbers
● Distributive Property
(forwards & backwards)
 Factoring a coefficient
12x + 20 = 4(3x+5)
7.EE.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. 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.
Students may create several different
expressions depending upon how they
group the quantities in the problem.
- Example: Jamie and Ted both get paid
an equal hourly wage of $9 per hour. This
week, Ted made an additional $27 dollars
in overtime. Write an expression that
represents the weekly wages of both if J =
the number of hours that Jamie worked
this week and T = the number of hours
Ted worked this week? Can you write the
expression in another way?
7.EE.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.
Equations with rational numbers and
a single variable “fluently.”
1. Create an equation for a given
situation using rational numbers and
variables
● Visual model
7.EE.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.
Instructional Resources
SAUSD Unit of Study: Expressions
(this unit of study covers Expressions
part of this unit only and does not
cover Equations or Inequalities)
IMP- Guess & Check Tables - Solve
word problems leading to equations
IMP:
http://sausdmath.pbworks.com/w/
browse/#view=ViewFolder&param
=Grade%207
● Word Problem Expressions
(2.1)
● Evaluating Expressions with
Tiles (1.2)
● Solving Linear Equations (1.01.2)
● Solve my problems (2.2)
● Day3-5 Solving Linear
● Equations
● Toothpicks 2.2
IMP: Word Wall 2.3
Instructional Resources
Brad Fulton: Patterns and
Function Connection book
Linear Functions (Carr Packet)
Susan Mercer Unit
Y=mx+b Word Problems
(Last updated May 18, 2015)
16
SAUSD Curriculum Map 2015-2016: Math 7
●
●
Verbal equation
Numeric/ algebraic equation
2. Solve multi-step real-life and
mathematical problems posed with
positive and negative rational
numbers in any form.
● Multi-step equations (previously
referred to as one, two, and
multi-step equations—note: this
is students’ first year seeing
equations solved formally using
new knowledge of inverse
operations)
● Define the variable and use
appropriate units.
● d=rt
3. Create equivalent equations.
● Combine like terms.
● Using Properties of Rational
Numbers.
● Distributive Property
(forwards & backwards)
● Apply inverse operations to
solve equations.
● Check solutions by substitution.
● Solve word problems leading to
equations. (See “strategies”)
Inequalities with rational numbers
and variables
1. Create an inequality for a given
situation using rational numbers.
2. Solve word problems leading to
inequalities.
3. Apply inverse operations to solve
inequalities.
4. Graph the solution for an
inequality
5. Interpret the solution.
Estimation strategies for calculations
with fractions and decimals (assessing
reasonableness of answers)
Extend from students’ work with whole
number operations. (see “strategies”)
● Front-end estimation
● Clustering around an average
● Rounding and adjusting
● Using friendly or compatible numbers
such as factors
● Using benchmark numbers that are
easy to compute
a. Solve word problems leading to
equations of the form px + pq = 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.
b. 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.
Graph the solution set of the
inequality and interpret it in the
context of the problem.
SAM:
http://sausdmath.pbworks.com/w/
browse/#view=ViewFolder&param
=Unit%202%20Activities
Cockroach Condos Activity
The Crowded Skies (Marc Petrie)
Susan Mercer: Variables with Food
Dan Meyer 3-act videos (list and
interactive link to Dan Meyer's
videos by standard)
MAP Lesson:
http://map.mathshell.org/material
s/lessons.php
 Steps to Solving Equations – 7th
Grade Formative Assessment
Lesson
 SERP Problem:
http://math.serpmedia.org/diag
nostic_teaching/posterproblems
On the Download
Adopted Text CGP
111 – Variables and Expressions
112 –Simplifying Expressions
121 – Writing Expressions
115 – Associative &
Commutative Props.
411 – Graphing equations
413 – Slope Key
123 Solving One-Step Equations
124 – Solving Two-Step Equations
125 –More two-step Equations
126 –Applications of Equations
127 –Understanding Problems
Additional Resources:
Interactive Algebra Tiles From the
Illuminations website (NCTM).
Click on the orange “Expand” tab to
find tile activities focusing on the
Distributive Property. Click on the
blue “Solve” tab to find tile activities
focusing on solving equations. Click
on the purple “Substitute” tab to
find tile activities
YouTube Video on Bar Models
(Last updated May 18, 2015)
17
SAUSD Curriculum Map 2015-2016: Math 7
Unit 4: Expressions, Equations, and Inequalities
(Support & Strategies)
Framework Description/Rationale
Expressions and equations fall after unit 2 (rational numbers) to build on the understanding of operations
with negative numbers. This unit is also to support students to prepare for units 4-7 (percents, geometry,
probability, and statistics).
(See CCSS CA 7th Grade Framework pgs. 22-27 for more details)
Academic Language
Support
Instructional Tool/Strategy Examples
Preparing the
Learner
Key Vocabulary for Word
Bank:
 Expression
 Equation
 Variable
 Variable Expression
 Numeric Expression
 Like/Unlike Terms
 Evaluate
 Simplify
 Constant
 Coefficient
 Distributive Property
 Inverse Operations
 Operations Models
 Inequality
 Is Greater Than
 Is Less Than
 Equal To
 Modeling with tiles
 Word walls
• color coding like terms
• graph inequalities on the number line
• drawing a model/diagram
• guess and check tables
• Tiles
• number lines
• tape diagram
• introduce symbols of inequalities estimating
• Solve word problems leading to equations:
Example: The youth group is going on a trip to the state fair. The trip
costs $52. Included in that price is $11 for a concert ticket and the cost
of 2 passes, one for the rides and one for the game booths. Each of the
passes cost the same price. Write an equation representing the cost of
the trip and determine the price of one pass.
From 6th Grade:
● Understand
solving an
equation or
inequality as a
process of
answering a
question: which
values from a
specified set, if
any, make the
equation or
inequality true?
● Use substitution
to determine
whether a given
number in a
specified set
makes an
equation or
inequality true.
Strategy:
Tree Map: Operation
Vocabulary
Estimation Strategies:
● Front-end estimation with adjusting (using the highest place value
and estimating from the front end making adjustments to the
estimate by taking into account the remaining amounts),
● Clustering around an average (when the values are close together
an average value is selected and multiplied by the number of values
to determine an estimate)
● Rounding and adjusting (students round down or round up and
then adjust their estimate depending on how much the rounding
affected the original values)
● Using friendly or compatible numbers such as factors (students seek
to fit numbers together - i.e., rounding to factors and grouping
numbers together that have round sums like 100 or 1000)
● Using benchmark numbers that are easy to compute (students
select close whole numbers for fractions or decimals to determine
an estimate)
Teacher Notes:
(Last updated May 18, 2015)
18
SAUSD Curriculum Map 2015-2016: Math 7
Unit 5: Geometry
(6 weeks 02/22-04/01)
Big Idea
Geometric figures can be compared by their relative values.
Essential Questions
 What is the relationship between the area
and circumference of a circle?
 How can we solve for an unknown angle?
 How is the area of a 2-dimensional figure
related to the volume of a 3-dimensional
figure?
 What are some real-world applications
involving area and volume?
 How can we determine whether 3 side
lengths will make a triangle?
Unit Topics/Concepts
Circles
1. Determine the constants of
proportionality for circle
measures. (d=2r, c=πd)
2. Discover π as a proportional
relationship between
diameter and circumference.
3. Construct circles for specific
radii and diameters.
4. Derive the formulas for
circumference and area.
5. Use the formulas to solve
real-world problems
involving circumference and
area
6. Given the area or
circumference, find the other.
Angles
1. Classify angles
● Supplementary
● Complementary
2. Solve for an unknown angle
using multi-step equations
involving:
● Supplementary
● Complementary
● Vertical
● Adjacent
Triangles
1. Construct triangles (focus on
measures of angles- freehand,
with ruler and protractor,
Performance Task
Problem of the
Month
Which is Bigger? [7th Grade 2004] p.61
Pizza Crusts [7th Grade 2006] p.26-27
Winter Hat [7th Grade 2008] p.58
Sequoia [7th Grade 2009] p.68-69
Merritt Bakery [8th Grade 2004] p.4
Wallpaper [7th Grade 2011] p.3-4
The Poster [7th Grade 2001] p.9 scale
drawing
 Roxie’s Photo [7th Grade 2013] p.8-9 Geo
 Circular
Reasoning POM
and Teacher’s
Notes
 Piece it Together
POM and
Teacher’s Notes







Content Standards
Resources
7.G Draw, construct, and describe geometrical
figures and describe the relationships between
them.
Essential Resources:
7th Grade Framework (pgs.
28-31)
7.G.2 Draw geometric shapes with given
conditions (freehand, with ruler and protractor,
and with technology). 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.
Instructional Resources
 IMP Geometry Activities
IMP: GBB Geonets
IMP: Good, Better, Best
Container
 EngageNY: Module 6
 Georgia Dept. of Ed: Unit
5
 Dan Meyer 3-act videos
(list and interactive link
to Dan Meyer's videos by
standard)
7.G.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.
7.G.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.
7.G.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.
7.G.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
Adopted Text CGP
721 –Volumes
312 – Area of Polygons
314 –Area of Irregular
Shape
MAP Lessons:
 Possible Triangle
Constructions – 7th Grade
Formative Assessment
Lesson
 Applying Angle
Theorems– 7th Grade
Formative Assessment
Lesson
 The Area of a Circle – 7th
Grade Formative
(Last updated May 18, 2015)
19
SAUSD Curriculum Map 2015-2016: Math 7
and with technology
2. Determine what conditions
are needed for a unique
triangle or no triangle
Area, volume, surface area
1. Write expressions and
equations to solve for area,
volume, surface area of 2-D
and 3-dimensional figures
● Triangles, quadrilaterals,
polygons, cubes and right
prisms
Slicing
Describe the 2-dimensional
figures that result from slicing 3dimensional figures
● Right rectangular prisms
● Right rectangular
pyramids.
Scale Drawings
* Avoid using the word
“similar,” rather use “scale
drawing of each other.” The
term “similar” will be defined
in Math 8
1. Blow-up or shrink
pictures on grid paper
(“dilations”)
2. Compute actual side
lengths and new areas.
3. Identify the ratios
between side lengths of
two figures.
4. Identify the ratio of side
lengths within a single
figure.
5. Use the ratio of side
lengths to determine the
dimensions of scaled
figures.
6. Justify mathematically
when drawings are to
scale and not to scale.
right prisms.
7.G. Draw, construct, and describe geometrical
figures and describe the relationships between
them.
7.G.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.
(Note: Refrain from using term similar here)
Assessment Lesson
 Using Dimensions:
Designing a Sports Bag –
7th Grade Formative
Assessment Lesson
 MARS - Geometry
http://map.mathshell.org/m
aterials/stds.php?id=1559#s
tandard1598
 SERP Problem:
http://math.serpmedia.o
rg/diagnostic_teaching/p
oster-problems
Triangles to Order
Additional Resources
Slicing 3-D YouTube video:
https://www.youtube.com/
watch?v=hlD_j3AtxGs&nored
irect=1
 Isometric Drawing
 GeoGebra (free
downloadable resource)
 Examples of
understanding circle
formulas:
http://www.illustrativem
athematics.org/illustratio
ns/1553
(Last updated May 18, 2015)
20
SAUSD Curriculum Map 2015-2016: Math 7
Unit 5: Geometry (Instructional Support & Strategies)
Framework Description/Rationale
Rationale:
Geometry was placed ahead of probability and statistics to ensure its completion by the end of the school year. This
also provides further opportunities for practice and extension working with proportional reasoning and working
with rational numbers.
Framework Description: (7th Grade Framework, pages 28-31)
 In this section, students work towards developing an understanding of several concepts:
 Draw and constructing shapes-- (see 7th Grade Framework pg. 29 for brief details)
 Cross-sections of 3-D shapes
 Area and Circumference of Circles –focusing on understanding of the formulas and why they work (see 7th Grade
Framework pgs. 30-31 for further explanation and examples). The focus should not be on memorization of
formulas. Students focus on applying those formulas to other problems.
 Using facts about angles to find unknown angle measurements
 Dimensions of shapes --find the area, surface area, and volume of 2-D shapes and 3-D shapes composed of other
shapes (see 7th Grade Framework pg. 31 for an example).
 Scale Drawings--Students solve problems involving scale drawing by applying their understanding of ratios and
proportions. Compute actual lengths and areas and reproduced a scale drawing at a different scale. Students
need to be able to determine that there are two important ratios with scale drawings: the ratios between two
figures and the ratios within a single figure. Avoid using or defining similar shapes this will be done in 8th grade.
(See 7th Grade Framework for more details pages 28-29)
Academic
Language
Support
Instructional Tool/Strategy Examples
Preparing
the Learner
Key Vocabulary
for Word Bank:
 Model the use of rulers, protractors, compass, and technology.
 Use strings to construct and name the figure. Double the strings size and construct the
figure. Compare/calculate the ratios.
 Use the free software called GeoGebra
 Example: Draw an equilateral triangle with a side of 3 units using a compass and a
straight edge.
 Use play-dough to create 3D shape and fishing line to cut into 2D shapes. Examine the
cross-sections that result when 3D figures are split. Students describe how two or
more objects are related in space (skew line)
 Activities: “Discovering Pi”: Students should “know” the formulas for area and
circumference by being able to explain why the formula works and how the formula
relates to area and circumference. Teachers should not give students any formulas or
even the value of π until students discover it (see examples below). After students
know the formulas, they should be able to apply their knowledge to solve problems:
 Students can also understand the relationship between circumference and area by
tracing the circumference of a cylindrical can on patty paper, then measuring the
diameter after folding the paper appropriately. Then, students can measure a string the
same length as the diameter to realize that the string can go around the circumference
approximately three and one-sixth times. This will lead them to understand that c=πd.
Therefore, students discover π and the formula for circumference on their own.
 Students can cut circles into finer pie pieces (sectors) and arrange them side by side to
create a parallelogram, which will create a length that is approximately πr and a height
that is approximately r. This will give students the opportunity to come to the
conclusion that the approximate area of this shape is πr2
 Color and then cut out the angles of the triangles and put them together to see the
relationship. Use patty paper to copy one of the vertical angles and apply it over the
other angle to compare.
 Use 3D geometric shapes that students can hold and see the different shapes that
compose a 3D figure. The use of graph paper and nets. For example, bring in realworld objects that students can use to solve for the area, volume, and or surface area
(eg cereal boxes, shoe boxes, or cell phones)
Earlier Grade:
Acute
Obtuse
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
Pi
Circumference
Area
Compass
Protractor
Complementar
y
Supplementary
Vertical
Adjacent
Surface Area
Volume
2-Dimensional
(2-D)
3-Dimensional
(3-D)
Slicing
Polygons,
triangles,
quadrilaterals,
cubes, right
prisms, right
rectangular
pyramids
(Last updated May 18, 2015)
From 6th
Grade:
Area of right
triangles,
other
triangles,
special
quadrilateral
s, and
polygons by
composing
into
rectangles or
decomposing
into triangles,
rectangles,
and other
shapes
21
SAUSD Curriculum Map 2015-2016: Math 7
Unit 6: Probability
(3 weeks 04/11-04/29)
Big Idea
Essential Questions


How can a model be
used to predict the
probability of an event
occurring?
How can you determine
if a game of chance is
fair?
Unit Topics/Concepts
The probability of a
chance event occurring is
between 0 and 1.
1. Understand that the
probability of an event
occurring can be
represented as a
fraction and understand
the range in the
probability relates to
likelihood (closer to 1-more likely; closer to 0-less likely, and ½-neither likely or
unlikely).
2. Collect data and
approximate the
probability of a chance
event occurring.
3. Predict the relative
frequency of an event
based on a given
probability.
4. Investigate both
empirical and
theoretical probability.
Probability models can be
used to find probabilities
of events.
1. Develop and represent
probability models and
sample spaces for single
and compound events.
 Tree Diagram
 Table
 Organized List
Collecting and analyzing data can answer questions, and determine further
data collection.
Performance Task
Problem of the Month
 Will it Happen? [7th Grade 2008] p.50
 Flora, Freddy, and the Future [8th Grade 2008] p.6061
 Duck Game [7th Grade 2001] p.5-6
 Dice Game [7th Grade 2002] p.2
 Fair Game? [7th Grade 2003] p.48-49
 Counters [7th Grade 2004] p.46-47
Content Standards
POM: “Fair Game”
● Level A
● Level B
● Level C
● Level D
● Level E
And Teacher’s Notes
Diminishing Return
POM and Teacher’s Notes
Resources
7.SP Investigate chance processes and develop, use,
and evaluate probability models.
7.SP.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.
7.SP.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.SP.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
Essential Resources:
7th Grade Framework
(pgs. 35-37)
University of Arizona
Progressions
(Documents for the
Common Core Math
Standards:
Draft 6-7 Progression
on Probability and
Statistics pg. 7)
Instructional
Resources:
SAUSD Unit of Study:
Probability
Dan Meyer 3-act videos
(list and interactive link
to Dan Meyer's videos by
standard)
MAP Lessons:
http://map.mathshell.org
/materials/lessons.php
 Probability Games
Constructions – 7th
Grade Formative
Assessment Lesson
 Evaluating Statements
about Probability – 7th
Grade Formative
Assessment Lesson
 MARS - Statistics and
Probability
http://map.mathshell
(Last updated May 18, 2015)
22
SAUSD Curriculum Map 2015-2016: Math 7
 Simulation
2. Develop a uniform
probability model by
assigning equal
probability to all
outcomes. (dice)
3. Develop a probability
model by observing
frequencies in data
generated from a
chance process.
on the observed frequencies?
7.SP.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.
7.EE.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.
.org/materials/stds.p
hp?id=1559#standar
d1598
 SERP Problem:
http://math.serpmedi
a.org/diagnostic_teac
hing/posterproblems
Try, Try Again
IMP:
http://sausdmath.pbwor
ks.com/w/browse/#view
=ViewFolder&param=Uni
t%20Plan%3A%20Proba
bility
● Unit Plan: Probability
● Building A Winning
Die
● Choosing Pair of Dice
● I’m on a Roll
● Spinner Mania
Probability Tree Map
Inside Math: Fair Game
Additional Resources:
Science Net Links Marble
Mania
Activity for definition
incorporate: The chance
of an event occurring can
be described numerically
by a number between 0
and 1 inclusive and used
to make predictions
about other events.
(Last updated May 18, 2015)
23
SAUSD Curriculum Map 2015-2016: Math 7
Unit 6: Probability
(Instructional Support & Strategies)
Framework Description/Rationale
Rationale:
Probability is brought into the map at this time of year as an important life skill that utilizes proportional reasoning
and which commonly includes very engaging hands-on lesson activities and can involve high-stakes real world
scenarios.
Framework Description:
Probability Models and Simulations (simple and compound)
(see 7th Grade Framework pg. 35-37 for details and examples)
Academic Language
Support
Key Vocabulary for Word
Bank:
 Probability
 Theoretical probability
 Empirical
(Experimental
probability)
 Simple events
 Compound events
 Certain event
 Impossible event
 Equally likely events
 Sample Space
 Probability model
 Relative frequency of
outcomes
 Simulation
Instructional Tool/Strategy Examples
Preparing the
Learner

Perform experiments: dice, games, spinners, coins,
colored cubes
 Tree diagrams
 Frequency tables
Examples:
Investigate chance processes and develop, use, and
evaluate probability models
Teacher Notes:
(Last updated May 18, 2015)
24
SAUSD Curriculum Map 2015-2016: Math 7
Unit 7: Statistics
(3 weeks 05/02 - 05/20)
Big Idea
Collecting and analyzing data can answer questions, and determine
further data collection.
Performance Task
Problem of the Month
Essential Questions
 How can random sampling
be used to draw inferences
about a population?
 How can data sets be used
to predict future events?









Basketball [6th Grade 2002] p.2
Baseball Players [6th Grade 2003] p.3-4
Money [6th Grade 2005] p.6-7
Supermarket [7th Grade 2000]
TV Hours [7th Grade 2002] p.7-8
Ducklings [7th Grade 2005] p.14-15
Suzi’s Company [7th Grade 2007] p.38-39
Archery [7th Grade 2009] p.71-72
Population [7th Grade 2011] p.8-9
Unit Topics/Concepts
1. Understand that statistics can be
used to gain information about a
population by examining a sample of
the population
2. Understand that generalizations
about a population from a sample
are valid only if the sample is
representative of that population.
3. Understand that random sampling
tends to produce representative
samples and support valid
inferences.
4. Use data from a random sample to
draw inferences about a population
with an unknown characteristic of
interest.
5. Generate multiple samples (of the
same size) to gauge the variation in
estimates or prediction
6. Use measures of center and
measures of variability for numerical
data from random samples to draw
informal comparative inferences
about two populations.
a. Mean
b. Median
c. Mode
d. Range
e. Mid-range
7. Assess the degree of visual overlap
of two numerical data distributions
with similar variability.
8. Compare the mean, median, MAD
POM: Sorting the Mix
Teacher Notes (n/a)
POM: “Through the Grapevine“
(Student)
http://svmimac.org/images/PO
M-ThroughTheGrapevine.pdf
(Teacher Notes)
● Level A
● Level B
● Level C
● Level D
● Level E
Content Standards
Resources
7.SP Use random sampling to draw
inferences about a population.
7.SP.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.
7.SP.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.
7.SP Draw informal comparative inferences
about two populations.
7.SP.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.
7.SP.4 Use measures of center and
measures of variability for numerical data
from random samples to draw informal
comparative inferences about two
Essential Resources:
7th Grade Framework
(pgs. 31-34)
University of Arizona
Progressions
(Documents for the
Common Core Math
Standards:
Draft 6-7 Progression
on Probability and
Statistics pg. 7)
Dan Meyer 3-act videos
(list and interactive link
to Dan Meyer's videos
by standard)
Instructional
Resources:
MAP Lessons:
http://map.mathshell.or
g/materials/lessons.php
 Estimating:
Counting Trees – 7th
Grade Formative
Assessment Lesson
 Relative Frequency
7th Grade Formative
Assessment Lesson
 Comparing Data – 7th
Grade Formative
Assessment Lesson
(Last updated May 18, 2015)
25
SAUSD Curriculum Map 2015-2016: Math 7
(mean absolute deviation), and
interquartile range from two
different sets of data.
9. Measure the differences between the
centers of two populations as a
multiple of a measure of variability
populations.
7.RP Analyze proportional relationships
and use them to solve real-world and
mathematical problems.
7.EE.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.
Adopted Text CGP
611 – Median & Range
612 – Box & Whisker
Plots
614 – Stem & Leaf Plots
621 – Making Scatter
Plots
622 – Shapes of Scatter
Plots
Additional Resources:
Illustrative
Mathematics
https://www.illustrativ
emathematics.org/7
Sampling for a Rock
Concert
(Last updated May 18, 2015)
26
SAUSD Curriculum Map 2015-2016: Math 7
Unit 7: Statistics
(Instructional Support & Strategies)
Framework Description/Rationale
Rationale:
This is the final unit that introduces new content and skills from the 7th grade standards. Students will utilize
proportional reasoning in their use of samples to represent larger populations. The unit should be completed well
before testing, allowing ample time before testing for SBAC prep and review, then enrichment, review, and/or
preparation for the following year, after the SBAC.
Framework Description:
In this section, students work towards developing a deeper understanding of the following:
 Using samples to represent larger populations - applying understanding of proportions to develop this idea
(see 7th Grade Framework Pg. 31-33 for further explanation and examples).
 Using measures of center and variability to compare two populations--building on their understanding of
mean, median, mean, inter-quartile range, and mean absolute deviation students compare data from two
populations (see 7th Grade Framework pgs. 33-34 for further explanation).
Academic Language
Support
Key Vocabulary for Word
Bank:
● Inferences
● Representative Sample
● Biased/Unbiased
● Random Sample
● Population
● Line Plot
● Box Plot
● Measures of Center:
● Mean
● Median
● Mode
● Range
● Maximum
● Minimum
● Outlier
● Upper Quartile
● Lower Quartile
● Mid-range
● Frequency Table
Instructional Tool/Strategy
Examples
Preparing the Learner
● Conduct surveys
 web-based software
 spread sheets
 box plots
 tables
 probability models

Topics from 6th grade:
Develop understanding of statistical
variability.
1. Recognize a statistical question as one
that anticipates variability in the data related
to the question
3. Recognize that a measure of center for a
numerical data set summarizes all of its
values with a single number,
4. Display numerical data in plots on a
number line, including dot plots, histograms,
and box plots.
5. Summarize numerical data sets in relation
to their context
c. Giving quantitative measures of center
(median and/or mean) and variability
(interquartile range and/or mean absolute
deviation), as well as describing any overall
pattern and any striking deviations from the
overall pattern with reference to the context
in which the data were gathered.
d. Relating the choice of measures of center
and variability to the shape of the data
distribution and the context in which the data
were gathered.
Teacher Notes:
(Last updated May 18, 2015)
27
SAUSD Curriculum Map 2015-2016: Math 7
Performance Task Descriptions by Unit
Unit 1:Operations with Rational
Numbers







Division [6th Grade 2007] (Relate a
given division calculation to the
appropriate situation)
Fractions [6th Grade 2010] (Given 6
statements to determine if correct
or not; if correct, give another
example and if incorrect, correct
the statement)
Fraction Match [6th Grade] (Order
rational numbers on a number
line; translate between different
rational number representations;
perform operations on rational
numbers and determine an
unknown in rational number
sentences)
Ribbons and Bows [6th Grade 2013]
(Division and multiplication of
fractions by fractions;
understanding of a unit rate and
ratio reasoning)
Brenda’s Brownies [6th Grade 2014]
(Divide a rectangle into 15 equal
sized brownies; determine the
dimensions of just one of these
brownies; interpret and compute
quotients of fractions by using
visual fraction models and
equations to represent problems)
Yogurt [7th Grade 2003] (Use
fractions and percents with
conversion of different units and
percent of decrease)
Cat Food [7th Grade 2009] (Use
rounded numbers appropriately in
the prescribed context; work
flexibly with fractions and
decimals in understanding rates)
Unit 2: Ratios and Proportional
Relationships






Leaky Faucet [7th Grade 2002] (Use
rates, proportional reasoning and
conversions)
Mixing Paints [7th Grade 2003] (Use
ratios and percents to determine
the amount of each color in a
mixture)
Cereal [7th Grade 2004] (Compare
the amount of protein in two
different cereals using
ratios/proportions)
Lawn Mowing [7th Grade 2005]
(Work with ratios and proportional
reasoning)
Breakfast of Champions [7th Grade
2012] (Solve problems with rates;
determine unit cost; compare and
determine the larger rate; use
division with rational numbers)
Is it Proportional? [7th Grade 2014]
(Write an equation to represent a
given math story or graph;
determine if this equation is directly
proportional or not; create and
write a proportional situation)
Unit 3: Percent
Applications
 Sewing [6th Grade 2009] (Use
decimals, fractions, percents
and constraints to determine a
bill of sale for sewing supplies)
 Work [7th Grade 2007] (Match
written phrases with numerical
expressions)
 Sales [7th Grade 1999] (Work
with increase and decrease of
percent changes)
 Special Offer [7th Grade 2004]
(Calculate and compare percent
decreases)
 Buying a Camera [7th Grade
2006] (Work with percentage
increase and decrease)
 Sale [7th Grade 2008] (Compare
sales discount offers and
percents for greatest and
smallest price reductions)
 Shopper’s Corner [7th Grade
2013] (Use proportional
relationships to solve multi-step
percent problems’; markups,
markdowns, and percent of
decrease)
(Last updated May 18, 2015)
28
SAUSD Curriculum Map 2015-2016: Math 7
Performance Task Descriptions by Unit
Unit 4: Expressions, Equations, and
Inequalities




The Number Cruncher [6th Grade 2001] (Relate
simple function rules and pairs of values)
Festival Lights [6th Grade 2011] (Extend a pictorial
pattern and a numeric table for two different
segments of one pattern; determine the inverse
relationship of a proportional function; generalize a
direct variation rule)
Lattice Fence [6th Grade 2012] (Identify polygons in
a geometric growing pattern; extend a linear
pattern; determine the inverse relationship of a
proportional function; generalize a direct variation
rule)
Facts in Fruit [7th Grade 2012] (Use properties of
numbers to find unknowns and solve equations)
Unit 5: Geometry







Which is Bigger? [7th Grade 2004] (Use measurements
from a scale drawing to determine measurements in
real life of a cylindrical vase)
Pizza Crusts [7th Grade 2006] (Find areas and
perimeters of rectangular and circular shapes)
Winter Hat [7th Grade 2008] (Find the surface area of a
shape with circles, rectangles, and trapezoids)
Sequoia [7th Grade 2009] (Understand the relationship
between diameter, radius, and circumference; use
proportion or scale factor)
Merritt Bakery [8th Grade 2004] (Use circle diameter and
circumference relationship; write one variable in terms
of another variable and write a mathematical
explanation of why a given statement is incorrect)
Wallpaper [7th Grade 2011] (Understand how to
determine the number of strips of wallpaper and rolls of
wallpaper needed to cover a wall with given dimensions
for the wall and the wallpaper)
Roxie’s Photo [7th Grade 2013] (Work with ratios and
proportional relationships in the context of enlarging
and reducing a given picture)
(Last updated May 18, 2015)
29
SAUSD Curriculum Map 2015-2016: Math 7
Performance Task Descriptions by Unit
Unit 6: Probability
Unit 7: Statistics
 Will it Happen? [7th Grade 2008] (Describe events as
likely/unlikely; find numerical probability of various
outcomes of rolling a number cube)
 Flora, Freddy, and the Future [8th Grade 2008] (Use terms
“likely” and “unlikely” for events and use numbers 0 to 1 as
measures of likelihood)
 Duck Game [7th Grade 2001] (Find probabilities of a game with
different constraints)
 Dice Game [7th Grade 2002] (Find all possible outcomes in a
table and calculate probabilities)
 Fair Game? [7th Grade 2003] (Use probability to judge the
fairness of a game)
 Counters [7th Grade 2004] (Probability of selecting a
particular color from a bag and then determining the fairness
of attributing $ amounts to the color in a game at the fair)
 Basketball [6th Grade 2002] (Interpret results of a survey;
use mode; use percents)
 Basketball Players [6th Grade 2003] (Work with the
mean)
 Money [6th Grade 2005] (Interpret and compare bar
graphs)
 Supermarket [7th Grade 2000] (Use measures of central
tendency for comparison)
 TV Hours [7th Grade 2002] (Analysis of data from a stem
and leaf plot]
 Ducklings [7th Grade 2005] (Use a frequency table to
determine median and mean of data)
 Suzi’s Company [7th Grade 2007] (Complete a given data
table and interpret the data to determine and interpret
the mean, median, mode)
 Archery [7th Grade 2009] (Use given data, draw a box and
whiskers plot and make interpretations and comparisons
between the two data sets)
 Population [7th Grade 2011] (Interpret two back-to-back
histograms on population data; calculate the percent of
increase in population between 1950 and 2000; calculate
the population in 2050 if this rate continues; describe
differences between the two back-to-back histograms)
(Last updated May 18, 2015)
30