Download Math 7

SAUSD Curriculum Map 2014-2015: 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
Under Revision (Last updated July 21, 2014)
1
SAUSD Curriculum Map 2014-2015: 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.
Under Revision (Last updated July 21, 2014)
2
SAUSD Curriculum Map 2014-2015: 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.
Under Revision (Last updated July 21, 2014)
3
SAUSD Curriculum Map 2014-2015: 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
Under Revision (Last updated July 21, 2014)
4
SAUSD Curriculum Map 2014-2015: 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.
Under Revision (Last updated July 21, 2014)
5
SAUSD Curriculum Map 2014-2015: Math 7
SAUSD Scope and Sequence for Math 7:
Unit 1
Unit 2
Unit 3
Unit 4
09/03 -10/10
10/13 - 11/7
11/12 - 01/09
01/12 - 01/30
28 days
5 Weeks
20 days
4 Weeks
28 days
5 Weeks
14 days
3 Weeks
Ratios and
Proportional
Reasoning
Operations with
Rational Numbers
Expressions,
Equations, &
Inequalities
Percent
Applications
****SEMESTER****
Unit 5
Unit 6
Unit 7
Unit 8
02/02 -03/13
03/16 - 04/17
04/20 - 05/15
28 days
5 Weeks
20 days
4 Weeks
20 days
4 Weeks
5/18 – 6/12
4 weeks
Geometry
Probability
Statistics
Enrichment
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)
Under Revision (Last updated July 21, 2014)
6
SAUSD Curriculum Map 2014-2015: Math 7
Unit 1: Ratios and Proportional Relationships (5 weeks; 09/03-10/10)
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?
 The Poster [7th Grade 2001]
 POM: “First
Rate” First Rate
How can two quantities be identified as
 Leaky Faucet [7th Grade 2002]
(Teacher Notes)
 Mixing Paints [7th Grade 2003]
proportional or non-proportional?
 Level A
 Rate Concentrate [6th Grade 2012]
How can the constant of proportionality
th
 Level B
 Cereal [7 Grade 2004]
(unit rate) be determined given a table?
 Level C
 Lawn Mowing [7th Grade 2005]
Graph? Equation? Diagram? Verbal
th
 Level D
 Breakfast of Champions [7 Grade 2012]
description?
th
 Level E
 Roxie’s Photo [7 Grade 2013]
What does a specific point on a graph (x,y)  Truffles [6th Grade 2009]
represent?
 Is it Proportional? [7th Grade 2014]
 Journey [7th Grade 2007]
 Buses [7th Grade 2009]
 European Trip [7th Grade 2010]
(See the end of this document for Performance
Task descriptions)
*Please read SVMI’s document security
information:
 http://www.svmimac.org/memberresources.html
Unit Topics/Concepts
Unit Rate
● Compute unit rates
● Include complex fractions
● Best deal
Recognize and represent
proportional relationships
1. Determine if two quantities are
proportional or nonproportional.
a. Prove in a table.
b. Graph on a coordinate plane.
(Quadrant I only)
c. Identify ratios as
proportional if two
conditions are met:
 Linear
 Starts at the origin
2. Identify the constant of
proportionality (unit rate)
a. In a table
b. Graphs
c. Equations
d. Diagrams
e. Verbal description
3. Write equations that represents
proportional relationships. y=kx
(k = constant of proportionality)
Content Standards
7.RP Analyze proportional relationships and use them to
solve real-world and mathematical problems.
7.RP.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 ½ 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.
7.RP.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.
7.EE.3 Solve multi-step real-life and mathematical problems
Resources
Essential Resources:
CCSS 7th Grade
Framework (pgs. 6-13 and
33-36)
University of Arizona
Progressions
(Documents for the
Common Core Math
Standards:
Draft 6-7 Progression on
Ratios and Proportional
Relationships)
Instructional Resources:
• Engage NY – Adapted
• IMP Unit Plan: Unit 8
 Susan Mercer: 7th
Proportion Rates
• 7th Proportions, Rates
(Carr 11-12)
• Illustrative
Mathematics
Track Practice
Adopted Text CGP
421 – Ratios & Rates
422 –Graphing Ratios &
Rates
423 –Speed, Distance & Time
424 –Direct Variation
431 –Converting Measures
432 –Converting between
Under Revision (Last updated July 21, 2014)
7
SAUSD Curriculum Map 2014-2015: Math 7
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
Scale Drawings
* Avoid using the word “similar,”
rather use “scale drawing of
each other.”
1. Blow-up or shrink pictures on
grid paper.
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 not to scale.
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.
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)
Unit Systems
433 – Dimensional Analysis
MAP Lessons:
http://map.mathshell.org/m
aterials/lessons.php
 Developing a Sense of Scale
– 7th Grade Formative
Assessment Lesson
 Proportion and NonProportion 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.or
g/materials/stds.php?id
=1559#standard1569
 SERP Problem:
http://math.serpmedia.or
g/diagnostic_teaching/pos
ter-problems
Drag Racer Dragon Fly
● Buses
● Sale
● T-Shirt Sale
● A golden Crown?
Under Revision (Last updated July 21, 2014)
8
SAUSD Curriculum Map 2014-2015: Math 7
Unit 1: 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 6 th grade. In 7th grade students will find unit rates in ratios involving fractional
quantities, for example,

Students will set up an equation with equivalent fractions and use reasoning about equivalent fractions to solve them, for example,
(See 7th Grade Framework for more details pages (6-13)
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 6-13)
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 33-36)
Academic Language Support
Key Terms:
● Identify
● Determine
● Equivalent
● Quantities
● Ratio
● Ratio Table
● Unit Rate (r/1)
● Constant
● Coordinate Plane
● Constant of Proportionality (k)
● Proportional Relationships
● Scale Drawing
● Scale Factor
Instructional Tool/Strategy Examples
Instructional Tools:

Strategies:

Pre-Unit: Preparing the
Learner
(number of days)
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:
Under Revision (Last updated July 21, 2014)
9
SAUSD Curriculum Map 2014-2015: Math 7
Unit 2: Operations with Rational Numbers (4 weeks; 10/13-11/7)
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
 Division [6th Grade 2007]
 Got Your
illustrated in multiple ways? (Models,
 Fractions [6th Grade 2010]
Number POM
verbally, and symbolically)
 Fraction Match [6th Grade]
and Teacher’s
 Ribbons and Bows [6th Grade 2013]
Notes
What’s the difference between the opposite
 Brenda’s Brownies [6th Grade 2014]
and the absolute value of a number?
 Yogurt [7th Grade 2003]
 Cat Food [7th Grade 2009]
 Breakfast of Champions [7th Grade 2012]
 Hotel Elevator [6th Grade 2014]
 Freezing in Fargo [6th Grade 2012]
Unit Topics/Concepts
Content Standards
Resources
Introduction to Addition &
Subtraction of Rational
Numbers (including
fractions and decimals)
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. Apply properties of operations as strategies to add and
subtract rational numbers.
1. “Opposite quantities combine
to make zero.” Additive
Inverse
2. Absolute Value as the
distance between two
numbers on a number line
3. Apply the properties of
Operations to adding and
subtracting rational numbers
 Commutative Property
 Associative Property
Interpret sums of rational
numbers by describing realworld contexts.
7.NS.2 Apply and extend previous understandings of multiplication
Understand subtraction
and division and of fractions to multiply and divide rational
of rational numbers as adding numbers.
the additive inverse and
a. Understand that multiplication is extended from fractions to
apply this to real world
rational numbers by requiring that operations continue to
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
b.
c.
d.
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.
Understand that integers can be divided, provided that the
divisor is not zero, and every quotient of integers (with nonzero 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.
Apply properties of operations as strategies to multiply and
divide rational numbers.
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.
Essential Resources:
7th Grade Framework
(pgs 19-28)
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.pbworks.com
/w/file/28887951/Discovering
%20Properties.pdf
MAP Lessons:
http://map.mathshell.org/mate
rials/lessons.php
 Using Positive and Negative
Numbers in Context – 7th
Grade Formative
Assessment Lesson
MARS- Number System tasks
http://map.mathshell.org/mate
rials/stds.php?id=1559#standa
rd1569
● Division
● A Day Out
● Taxi Cabs

SERP Problem:
http://math.serpmedia.org/
diagnostic_teaching/posterproblems
Under Revision (Last updated July 21, 2014)
10
SAUSD Curriculum Map 2014-2015: Math 7
 Distributive Property
 Multiplicative Inverse
2. Interpret products of rational
numbers by describing realworld situations
Expanding understandings of
rational numbers
1. Converting between fractions
and decimals (terminating
and repeating)
 Using equivalent fractions
 Using long division
2. Assess the reasonableness of
answers using mental
computation and estimation.
 Rounding
 Front-end
Walking the Line
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.

SERP Problem:
http://math.serpmedia.org/
diagnostic_teaching/posterproblems
Seeing Sums
Additional Resources:
Video: Discovery StreamingIntroduction to integers.mov
(see site for more)
Integer War (Cards or dice)
(to be developed)
Algebra/ 2-color tiles for review
Under Revision (Last updated July 21, 2014)
11
SAUSD Curriculum Map 2014-2015: Math 7
Unit 2: 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. 19-28 for more details)
Academic Language Support
Instructional Tool/Strategy Examples
Pre-Unit: Preparing the
Learner
Key Terms:
Estimation Strategies:
Fractions (prior knowledge)
● Front-end estimation with adjusting (using the highest
 Integers
place value and estimating from the front end making
 Signed Numbers
5th grade
adjustments to the estimate by taking into account the
 Positive
- unit fractions
remaining amounts),
 Negative
- adding unlike
● Rounding and adjusting (students round down or round
 Rational Numbers
up and then adjust their estimate depending on how
denominators
 Sum/Difference
much the rounding affected the original values)
6th grade
 Deposit/Withdraw/
- dividing a fraction by a
Overdraft
fraction
 Credit/Debit
- concepts of negative
 Profit/Loss
numbers
 Product/Quotient
negative fractions on a
 Absolute Value
number line
 Opposites
 Additive Inverse
By end of 6th grade, students
 Multiplicative Inverse
have used every operation with
 Identity Properties
fractions
 Commutative Property
 Associative Property
 Activity: Above & Below
 Distributive Property
Sea Level (7.NS.1.c)
 Terminating Decimals
 Repeating Decimals
Teacher Notes:
Under Revision (Last updated July 21, 2014)
12
SAUSD Curriculum Map 2014-2015: Math 7
Unit 3: Expressions, Equations, and Inequalities (5 weeks; 11/12-01/9)
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
th Grade

The
Number
Cruncher
[6
How can estimation be used to test the
 Tri-Triangles
2001]
reasonableness of a solution?
POM and
Teacher’s
How can the properties of rational numbers be used  Festival Lights [6th Grade 2011]
th Grade 2012]
Notes

Lattice
Fence
[6
to create equivalent expressions and equations?
th
 Facts in Fruit [7 Grade 2012]
 Playing with Blocks [7th Grade 2013]
 Banquet Tables [7th Grade 2014]
Unit Topics/Concepts
Content Standards
Resources
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
2. Create equivalent expressions.
● Combine like terms
● Use properties of rational numbers
● Distributive Property
(forwards & backwards)
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?
Equations with rational numbers and a
single variable “fluently.”
1. Create an equation for a given situation
using rational numbers and variables
● Visual model
● Verbal equation
● Numeric/ algebraic equation
2. Solve multi-step real-life and
mathematical problems posed with
positive and negative rational numbers
in any form.
● One-step equations
7.EE Use properties of operations to generate
equivalent expressions.
7.EE.1 Apply properties of operations as strategies to
add, subtract, factor, and expand linear expressions
with rational coefficients.
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.
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.
7.EE.4 Use variables to represent quantities in a realworld 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 + 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.
Essential Resources:
7th Grade Framebook (pgs 2833)
University of Arizona
Progressions
(Documents for the Common
Core Math Standards:
Draft 6-7 Progression on
Expressions and Equations
pg. 8)
Instructional Resources
SAUSD Unit of Study:
Expressions (this unit of study
covers part of this unit)
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
(1.0-1.2)
● 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
SAM:
http://sausdmath.pbworks.com
/w/browse/#view=ViewFolder
&param=Unit%202%20Activiti
es
Cockroach Condos Activity
The Crowded Skies (Marc
Petrie)
Under Revision (Last updated July 21, 2014)
13
SAUSD Curriculum Map 2014-2015: Math 7
●
●
●
●
Two-step equations
Multi-step equations
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
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
Susan Mercer: Variables with
Food
MAP Lesson:
http://map.mathshell.org/mate
rials/lessons.php
 Steps to Solving Equations –
7th Grade Formative
Assessment Lesson

SERP Problem:
http://math.serpmedia.org/
diagnostic_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
Under Revision (Last updated July 21, 2014)
14
SAUSD Curriculum Map 2014-2015: Math 7
Unit 3: 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. 28-33 for more details)
Academic Language
Instructional Tool/Strategy Examples
Support
Instructional Tools:
Key Terms:
















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
Strategy:
Tree Map: Operation
Vocabulary
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.
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)
Pre-Unit: Preparing the
Learner
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.
Teacher Notes:
Under Revision (Last updated July 21, 2014)
15
SAUSD Curriculum Map 2014-2015: Math 7
Unit 4: Percent Applications (3 weeks; 01/12-1/30)
Big Idea
Proportional relationships can be used to solve real-world problems.
Essential Questions


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










Performance Task
Sewing [6th Grade 2009]
Work [7th Grade 2007]
Sales [7th Grade 1999]
Special Offer [7th Grade 2004]
Sneakers [7th Grade 2007]
Buying a Camera [7th Grade 2006]
Sale [7th Grade 2008]
Shopper’s Corner [7th Grade 2013]
To Buy or not To Buy [7th Grade 2012]
Duplicating Dollars [7th Grade 2014]
Content Standards
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
7.RP Analyze proportional relationships and
use them to solve real-world and mathematical
problems.
Use multiple strategies
● Double-sided number line
● Tape diagram
● Visual model
● Equations
● Proportions
● Use estimation strategies to
test the reasonableness of a
solution
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.
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.
Problem of the Month
● 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. 14-17)
Instructional Resources
IMP Unit Plan: Percent
http://sausdmath.pbworks.com/w/browse/#vie
w=ViewFolder&param=Unit%2010%20Activities
• 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
http://www.engageny.org/resource/grade-7mathematics-module-4
MAP Lessons:
http://map.mathshell.org/materials/lessons.php
 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)
https://www.georgiastandards.org/CommonCore/Pages/Math-6-8.aspx
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
Under Revision (Last updated July 21, 2014)
16
SAUSD Curriculum Map 2014-2015: Math 7
Unit 4: 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. 14-17 for further explanation, examples, and ways to model problems).
Academic Language
Support
Key Terms:
● Percent
● Percentage
● Percent Increase
● Percent Decrease
● Enlargement
● Reduction
● Tax
● Tip/Gratuity
● Markup/Markdown
● Discount
● Sale Price
● Commission
● Fees
● Simple Interest
● Percent Error
Instructional Tool/Strategy Examples
Pre-Unit: Preparing the
Learner
Use multiple strategies
● 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 multi-digit 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
Teacher Notes:
Under Revision (Last updated July 21, 2014)
17
SAUSD Curriculum Map 2014-2015: Math 7
Unit 5: Geometry (5 weeks; 02/02-03/13)
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,
and with technology
2. Determine what conditions
Performance Task









Which is Bigger? [7th Grade 2004]
Pizza Crusts [7th Grade 2006]
Winter Hat [7th Grade 2008]
Sequoia [7th Grade 2009]
Merritt Bakery [8th Grade 2004]
Wallpaper [7th Grade 2011]
Boxes [7th Grade 2011]
What’s Mu Angle? [7th Grade 2013]
A Drink Carton [7th Grade 2014]
Content Standards
Problem of the
Month
 Circular
Reasoning POM
and Teacher’s
Notes
 Piece it Together
POM and
Teacher’s Notes
Resources
7.G Draw, construct, and describe geometrical figures
and describe the relationships between them.
Essential Resources:
7th Grade Framework (pgs. 33-38)
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
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.
Adopted Text CGP
721 –Volumes
312 – Area of Polygons
314 –Area of Irregular Shape
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 right prisms.
MAP Lessons:
http://map.mathshell.org/materials/
lessons.php
 Possible Triangle Constructions –
7th Grade Formative Assessment
Lesson
 Applying Angle Theorems– 7th
Grade Formative Assessment
Lesson
 The Area of a Circle – 7th Grade
Formative Assessment Lesson
 Using Dimensions: Designing a
Sports Bag – 7th Grade Formative
Assessment Lesson
 MARS - Geometry
http://map.mathshell.org/materials/
stds.php?id=1559#standard1598

SERP Problem:
http://math.serpmedia.org/diag
nostic_teaching/poster-problems
Triangles to Order
Additional Resources
 Slicing 3-D video
 Isometric Drawing
 GeoGebra (free downloadable
Under Revision (Last updated July 21, 2014)
18
SAUSD Curriculum Map 2014-2015: Math 7
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

resource)
Examples of understanding
circle formulas:
http://www.illustrativemathema
tics.org/illustrations/1553
Slicing
Describe the 2-dimensional
figures that result from slicing 3dimensional figures
● Right rectangular prisms
● Right rectangular
pyramids.
Under Revision (Last updated July 21, 2014)
19
SAUSD Curriculum Map 2014-2015: 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: (Framework, pages 33-38)
 In this section, students work towards developing an understanding of several concepts:
 Draw and constructing shapes-- (see 7th Grade Framework pg. 36 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. 36-38 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. 38 for an example).
Academic Language
Instructional Tool/Strategy Examples
Pre-Unit: Preparing the
Support
Learner
Earlier Grade:
Key Terms:
Activities:
Acute
- “Discovering Pi”
● Pi
Circumference
Area
Compass
Protractor
Complementary
Supplementary
Vertical
Adjacent
Surface Area
Volume
2-Dimensional (2-D)
3-Dimensional (3-D)
Slicing
● Polygons, triangles,
quadrilaterals, cubes,
right prisms, right
rectangular pyramids
●
●
●
●
●
●
●
●
●
●
●
●
●
Obtuse
From 6th Grade:
Area of right triangles, other triangles,
special quadrilaterals, and polygons by
composing into rectangles or
decomposing into triangles, rectangles,
and other shapes
Teacher Notes:
Under Revision (Last updated July 21, 2014)
20
SAUSD Curriculum Map 2014-2015: Math 7
Unit 6: Probability (4 weeks; 03/16-04/17)
Big Idea
Collecting and analyzing data can answer questions, and determine further data
collection.
Essential Questions
Performance Task
Problem of the
Month
th Grade 2008]
POM:
“Fair
Game”

Will
it
Happen?
[7
 How can a model be used to predict
th
●
Level
A
the probability of an event occurring?  Flora, Freddy, and the Future [8 Grade
● Level B
2008]
 How can you determine if a game of
th Grade 2001]
● Level C

Duck
Game
[7
chance is fair?
th
● Level D
 Dice Game [7 Grade 2002]
● Level E
th
 Fair Game? [7 Grade 2003]
Diminishing
Return
 Counters [7th Grade 2004]
POM and Teacher’s
 How I Roll [7th Grade 2012]
Notes
 Designing a Spinner [7th grade 2013]
 Playoff Party [7th Grade 2014]
Unit Topics/Concepts
Content Standards
Resources
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.
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.
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
 Simulation
2. Develop a uniform
probability model by
assigning equal
probability to all
outcomes. (dice)
3. Develop a probability
model by observing
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 longrun 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 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
Essential Resources:
7th Grade Framework (pgs. 42-45)
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
MAP Lessons:
http://map.mathshell.org/material
s/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.org/mat
erials/stds.php?id=1559#stan
dard1598
 SERP Problem:
http://math.serpmedia.org/di
agnostic_teaching/posterproblems
Try, Try Again
IMP:
http://sausdmath.pbworks.com/w
/browse/#view=ViewFolder&para
m=Unit%20Plan%3A%20Probabili
ty
● Unit Plan: Probability
● Building A Winning Die
● Choosing Pair of Dice
● I’m on a Roll
● Spinner Mania
Under Revision (Last updated July 21, 2014)
21
SAUSD Curriculum Map 2014-2015: Math 7
frequencies in data
generated from a
chance process.
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.
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.
Under Revision (Last updated July 21, 2014)
22
SAUSD Curriculum Map 2014-2015: 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. 42-45 for details and examples)
Academic Language
Support
Key Terms:












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
Instructional Tools:

Strategies:
Pre-Unit: Preparing the
Learner
Topics:
(information necessary to
support students with accessing
the unit)


Resources:

Teacher Notes:
Under Revision (Last updated July 21, 2014)
23
SAUSD Curriculum Map 2014-2015: Math 7
Unit 7: Statistics (4 weeks; 04/20-05/15)
Big Idea
Collecting and analyzing data can answer questions, and determine further data
collection.
Essential Questions
Performance Task
Problem of the Month
POM: Sorting the Mix
 How can random sampling be used  Basketball [6th Grade 2002]
Teacher Notes
 Basketball Players [6th Grade 2003]
to draw inferences about a
th
POM: “Through the Grapevine“
population?
 Money [6 Grade 2005]
(Student)
 Supermarket [7th Grade 2000]
 How can data sets be used to
http://svmimac.org/images/PO
th
 TV Hours [7 Grade 2002]
predict future events?
M-ThroughTheGrapevine.pdf
th
 Ducklings [7 Grade 2005]
(Teacher Notes)
 Suzi’s Company [7th Grade 2007]
● Level A
 Archery [7th Grade 2009]
● Level B
 Population [7th Grade 2011]
● Level C
 Animals [Grade 8 2004]
● Level D
 Temperatures [8th Grade 2006]
● Level E
 A New Car [8th Grade 2011]
Unit Topics/Concepts
Content Standards
Resources
1. Understand that statistics can
7.SP Use random sampling to draw inferences about a
population.
2.
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.
3.
4.
5.
be used to gain information
about a population by
examining a sample of the
population
Understand that
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.
Use data from a random
sample to draw inferences
about a population with an
unknown characteristic of
interest.
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.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 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.
Essential Resources:
7th Grade Framework
(pgs. 38-42)
University of Arizona
Progressions
(Documents for the Common
Core Math Standards:
Draft 6-7 Progression on
Probability and Statistics pg. 7)
Instructional Resources:
MAP Lessons:
http://map.mathshell.org/material
s/lessons.php
 Estimating: Counting Trees –
7th Grade Formative
Assessment Lesson
 Relative Frequency 7th Grade
Formative Assessment Lesson
 Comparing Data – 7th Grade
Formative Assessment Lesson
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.illustrativemathemat
ics.org/7
Sampling for a Rock Concert
Under Revision (Last updated July 21, 2014)
24
SAUSD Curriculum Map 2014-2015: 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. 38-40 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. 40-42 for further explanation).
Academic Language
Support
Key Terms:
● 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
Pre-Unit: Preparing the
Learner
Instructional Tools:
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.

Strategies:


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:
Under Revision (Last updated July 21, 2014)
25
SAUSD Curriculum Map 2014-2015: Math 7
Performance Task Descriptions by Unit
Unit 1: Ratios and Proportional
Relationships
Unit 2: Operations with Rational
Numbers
Unit 3: Expressions,
Equations, and Inequalities
 The Poster [7th Grade 2001]
(Proportional Reasoning)
 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)
 Rate Concentrate [6th Grade 2012] (Use
rates, find equivalent ratios, compare and
explain the relative size of two rates)
 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)
 Roxie’s Photo [7th Grade 2013] (Work
with ratios and proportional
relationships in the context of enlarging
and reducing a given picture)
 Truffles [6th Grade 2009] (Use
proportional reasoning; interpret a graph
to understand proportionality between
cups of chocolate and cups of cream when
making super truffles)
 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)
 Journey [7th Grade 2007] (Draw and
interpret a graph of speed, distance and
time)
 Buses [7th Grade 2009] (Understand and
decipher a time/distance graph and the
ability to read and interpret scales on the
axes)
 European Trip [7th Grade 2010] (Interpret
and work with travel information; use a
graph to answer questions about
distance, time and rate)
 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)
 Breakfast of Champions [7th Grade 2012]
(Solve problems about rates; determine
unit cost; compare and determine the
larger rate; use division with rational
numbers)
 Hotel Elevator [6th Grade 2014] (Use and
understand positive and negative numbers
in a real life context of an elevator going
between floors below street level in the
basement and 24 floors above street level;
write number sentences with integers to
represent distances traveled)
 Freezing in Fargo [6th Grade 2012] (Use
integer data to answer questions including
finding the average lowest temperature
and comparing two temperatures)
 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)
 Playing with Blocks [7th Grade
2013] (Draw, extend, and
explain how a pattern is
growing; determine the
number of blocks for the 15th
stage; use the inverse
relationship to determine the
stage number when given the
number of blocks)
 Banquet Tables [7th Grade
2014] (Extend and explain
how a pattern is growing;
determine how the
relationship grows between
the number of seats grows as
more tables are added; use
the inverse relationship to
determine the number of
tables needed for 115 guests;
write an equation to
represent the functional rule)
Under Revision (Last updated July 21, 2014)
26
SAUSD Curriculum Map 2014-2015: Math 7
Performance Task Descriptions by Unit
Unit 4: Percent Applications
Unit 5: Geometry
 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)
 Sneakers [7th Grade 2007] (Solve reverse percentage
problems regarding the sale of sneakers)
 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)
 To Buy or not To Buy [7th Grade 2012] (Use percent to
determine mark-up; find a discount; make a conclusion
between the mark-up and the discount)
 Duplicating Dollars [7th Grade 2014] (Use proportional
relationships to solve multi-step ratio and percent
problems involving the reduction of a dollar bill and its
restoration to its original size)
 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)
 Boxes [7th Grade 2011] (Interpret 2D and 3D nets; calculate
surface area and volumes with triangular sections and
compare figures)
 What’s Mu Angle? [7th Grade 2013] (Find a missing angle in
a geometric construction; find the measure of an angle in
three geometric constructions; justify why a given geometric
statement is true or false)
 A Drink Carton [7th Grade 2014] (Find the area of an
isosceles triangle; determine the surface area of a
triangular prism; find the volume of the triangular prism)
Under Revision (Last updated July 21, 2014)
27
SAUSD Curriculum Map 2014-2015: 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)
 How I Roll [7th Grade 2012] (Determine the size of a sample
space; calculate probabilities; compare values in a sample
space)
 Designing a Spinner [7th grade 2013] (Given a description,
draw the spinner; determine the probabilities for different
regions on the spinner; compare the probabilities for
different regions on the spinner)
 Playoff Party [7th Grade 2014] (Determine probabilities of
simple events; understand the sample size; determine the
probability of not winning vs. winning; find the probability of
a compound event)
 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-toback 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 backto-back histograms)
 Animals [Grade 8 2004] (Find the median, mode, and
range of tabulated data in two histograms and make
comparison statements between the two)
 Temperatures [8th Grade 2006] (Compare and interpret
weather data from two cities on a line graph and a box
and whiskers plot)
 A New Car [8th Grade 2011] (Read and interpret
information from two different box and whiskers plots;
determine the min. value, max. value, median, lower
quartile and upper quartile for a given set of data;
draw a box plot of this data)
Under Revision (Last updated July 21, 2014)
28