Download Grade Level

7th Grade Curriculum Document
Original Development: Summer 2013
Grade 7 Pacing Guide
Unit Title
1. Operating with Rational Numbers (add/sub)
2. Operating with Rational Numbers (mult/div)
Pacing
Standards
4 weeks
7.NS.1 7.MP.2 7.MP.7
7.NS.3 7.MP.3 7.MP.8
4 weeks
7.NS.2
7.NS.3
7.EE.2
7.EE.3
7.MP.2
7.MP.3
7.MP.7
7.MP.8
7.G.2
7.G.3
7.G.4
7.G.5
7.G.6
7.RP.1
7.RP.2
7.RP.3
7.G.1
7.MP.1
7.MP.4
7.MP.5
7.MP.6
7.MP.7
7.MP.1 7.MP.6
7.MP.2
7.MP.3
7.MP.4
3. Two and Three Dimensional Geometry
4 weeks
4. Proportional Relationships
5 weeks
5. Algebraic Reasoning II
4 weeks
7.EE.1 7.MP.1 7.MP.4
7.EE.2 7.MP.2 7.MP.7
7.EE.4 7.MP.3
3 weeks
7.SP.1 7.MP.1
7.SP.2 7.MP.3
7.SP.3 7.MP.4
7.SP.4
3 weeks
7.SP.5 7.MP.1
7.SP.6 7.MP.4
7.SP.7 7.MP.7
7.SP.8
6. Inferences about Populations
7. Probability
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Grade Seven Standards for Mathematical Practice
The K-12 Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in
their students. This page gives examples of what the practice standards look like at the specified grade level.
Standards
Students are expected to:
1. Make sense of problems and
persevere in solving them.
Students are expected to:.
2. Reason abstractly and
quantitatively.
Students are expected to:
3. Construct viable arguments and
critique the reasoning of others.
Students are expected to:
4. Model with mathematics.
Students are expected to:
5. Use appropriate tools
strategically.
Students are expected to:
6. Attend to precision.
Students are expected to:
7. Look for and make use of
structure.
Students are expected to:
8. Look for and express regularity
in repeated reasoning.
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Explanations and Examples
In grade 7, students solve problems involving ratios and rates and discuss how they solved them.
Students solve real world problems through the application of algebraic and geometric concepts.
Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may
check their thinking by asking themselves, “What is the most efficient way to solve the problem?”, “Does
this make sense?”, and “Can I solve the problem in a different way?”
In grade 7, students represent a wide variety of real world contexts through the use of real numbers and
variables in mathematical expressions, equations, and inequalities. Students contextualize to understand
the meaning of the number or variable as related to the problem and decontextualize to manipulate
symbolic representations by applying properties of operations.
In grade 7, students construct arguments using verbal or written explanations accompanied by
expressions, equations, inequalities, models, and graphs, tables, and other data displays (i.e. box plots,
dot plots, histograms, etc.). They further refine their mathematical communication skills through
mathematical discussions in which they critically evaluate their own thinking and the thinking of other
students. They pose questions like “How did you get that?”, “Why is that true?” “Does that always work?”
They explain their thinking to others and respond to others’ thinking.
In grade 7, students model problem situations symbolically, graphically, tabularly, and contextually.
Students form expressions, equations, or inequalities from real world contexts and connect symbolic and
graphical representations. Students explore covariance and represent two quantities simultaneously.
They use measures of center and variability and data displays (i.e. box plots and histograms) to draw
inferences, make comparisons and formulate predictions. Students use experiments or simulations to
generate data sets and create probability models. Students need many opportunities to connect and
explain the connections between the different representations. They should be able to use all of these
representations as appropriate to a problem context.
Students consider available tools (including estimation and technology) when solving a mathematical
problem and decide when certain tools might be helpful. For instance, students in grade 7 may decide to
represent similar data sets using dot plots with the same scale to visually compare the center and
variability of the data. Students might use physical objects or applets to generate probability data and use
graphing calculators or spreadsheets to manage and represent data in different forms.
In grade 7, students continue to refine their mathematical communication skills by using clear and precise
language in their discussions with others and in their own reasoning. Students define variables, specify
units of measure, and label axes accurately. Students use appropriate terminology when referring to rates,
ratios, probability models, geometric figures, data displays, and components of expressions, equations or
inequalities.
Students routinely seek patterns or structures to model and solve problems. For instance, students
recognize patterns that exist in ratio tables making connections between the constant of proportionality in
a table with the slope of a graph. Students apply properties to generate equivalent expressions (i.e. 6 + 2x
= 3 (2 + x) by distributive property) and solve equations (i.e. 2c + 3 = 15, 2c = 12 by subtraction property of
equality), c=6 by division property of equality). Students compose and decompose two- and threedimensional figures to solve real world problems involving scale drawings, surface area, and volume.
Students examine tree diagrams or systematic lists to determine the sample space for compound events
and verify that they have listed all possibilities.
In grade 7, students use repeated reasoning to understand algorithms and make generalizations about
patterns. During multiple opportunities to solve and model problems, they may notice that a/b ÷ c/d =
ad/bc and construct other examples and models that confirm their generalization. They extend their
thinking to include complex fractions and rational numbers. Students formally begin to make connections
between covariance, rates, and representations showing the relationships between quantities. They
create, explain, evaluate, and modify probability models to describe simple and compound events.
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Curriculum Document
Original Development: Spring 2013
Unit:
Subject/Course:
Grade Level:
School Year:
1 - Operations with Rational Numbers (Addition/Subtraction)
General Math
7th
2013-2014
This section completed once per whole unit. (Its purpose is to clarify the unit’s big idea and connecting standards.)
Big Ideas: Why is this learning important?
What generalization or principle do you want to know/do?
The big idea resides at the heart of the discipline, and has value beyond classroom. These may come from the cluster deconstructing process.


Add and subtract rational numbers.
Represent addition and subtraction on a horizontal or vertical number line diagram
Common Core Standards / State Standards
Domain: Number System
Content Standard:
Cluster: Apply and extend previous understandings of operations with fractions to add, subtract,
including CODE + (Rigor)
multiply, and divide rational numbers.
Standard Code:
 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. (Apply/DOK 3)
a) Describe situations in which opposite quantities combine to make 0. For
example, a hydrogen atom has 0 charge because its two constituents are
oppositely charged.
b) Understand p + q as the number located a distance |q| from p, in the positive
or negative direction depending on whether q is positive or negative. Show
that a number and its opposite have a sum of 0 (are additive inverses).
Interpret sums of rational numbers by describing real-world contexts.
c) Understand subtraction of rational numbers as adding the additive inverse, p
– q = p + (–q). Show that the distance between two rational numbers on the
number line is the absolute value of their difference, and apply this principle in
real-world contexts.
d) Apply properties of operations as strategies to add and subtract rational

Integration of Reading &
Writing Anchor and/or
Mathematical Practices
including CODE
numbers.
7.NS.3 Solve real-world and mathematical problems involving the four operations with
rational numbers. (Computations with rational numbers extend the rules for manipulating
fractions to complex fractions.)
College and Career Readiness Anchor Standards for Reading
Craft and Structure
4. Interpret words and phrases as they are used in a text, including determining technical,
connotative, and figurative meanings, and analyze how specific word choices shape meaning
or tone.
College and Career Readiness Anchor Standards for Writing
Range of Writing
10. Write routinely over extended time frames(time for research, reflection, and revision) and
shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and
audiences.
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Mathematical Practices (MP) (boldface correlation to unit focus standards)
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.
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.
Technology
Standard:
ET07-S6C2-03: Enter/Edit data using simple formulas while using spreadsheet(s) to perform
calculations.
including CODE
ELP Standard:
Completed by SEI/ELP teachers (later)
including CODE
Clarifications of Content Standard
Academic Vocabulary: What academic vocabulary does the student need to know?
Additive Inverse, Absolute Value, Number Line, Integers
Declarative Knowledge: What concepts (facts, ideas, cause/effect) does the student need to KNOW?
Students will need to know:
 Addition and subtraction of positive and negative numbers (begin with integers and extend to rational number)
o Number line
 Equivalent forms
 Opposite quantities
o Additive inverses
o Number line
 Absolute value
o Number line
 Properties of operations
 Mental computation strategies
 Estimation strategies
Procedural Skill: What procedures (steps, algorithms, tactics) does the student need to know HOW to DO?
Students will:
 ADD and SUBTRACT (rational numbers)
 DESCRIBE (opposites quantities)
 UNDERSTAND (positive or negative direction)
 SHOW (additive inverses)
 INTERPRET (sums in context)
 UNDERSTAND (subtraction as additive inverses)
 SHOW (absolute value)
 APPLY (absolute value principle in context)
 APPLY (properties of operations as strategies)
 SOLVE (with and without context)
o APPLY (properties of operations to calculate)
o CONVERT (between equivalent forms)
o ASSESS (reasonableness of answers)
 USE (mental computation and estimation strategies)
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Prerequisites: What concepts does the student need prior to engaging in this standard?
6.NS.1: Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions, e.g., by using
visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual
fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because ¾
of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share ½ lb of chocolate equally?
How many ¾-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length ¾ mi and area ½ square mi?
Assessments
Provide one assessment item for each content standard (one standard per box). For each assessment include: 1) standard + descriptive title + (Rigor)
2) an actual assessment item or quality description of the assessment 3) connection to Rdg, Wrtg, or Math Practice (if appropriate)
7.NS.1 (Analyze DOK 3)
Descriptive title: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational
numbers.
If m, n, p and q are four numbers on the number line below, which of the following numbers is
negative and greater than -1?
a)
1
p
b)
1
q
c)
1
m
d)
1
n
This section completed per whole unit. (Its purpose is to focus on integrating the standards through resources & instructional strategies that focus on unit big ideas.)
UNIT Resources & Instruction
Primary text connections: List chapters, pages, etc.
Holt McDougal Mathematics Course 2:







Properties of Numbers, Chapter 1-5, pages 24-27
Integers, Chapter 2-1, pages 72-75
Adding Integers, Chapter 2-2, pages 80-85
Subtracting Integers, Chapter 2-3, pages 84-89
Adding and Subtracting Decimals, Chapter 3-2, pages 148-151
Adding and Subtracting Fractions, Chapter 3-7, pages 174-179
Adding and Subtracting Mixed Numbers, Chapter 3-8, pages 180-183
Supplemental Text Connections: List other school-purchased curriculum resources.
Other materials available: List other useful resources, teacher-created, online, etc.
Teacher Instructional Strategies: Research-based strategies that “fit.”
Grouping, Questioning, Visual Aids, Setting High Expectations, Technology, Assessments
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Integration of Technology: Specific examples that apply the technology standards in the content.
 Calculate and compare the number of servings Mungry ate in a single
setting.
o Read or Listen to Shel Silverstein’s poem, Hungry Mungry from Where
the Sidewalk Ends
 Students calculate their age on each of the nine planets in our solar
system using an Excel spreadsheet.
o Using An Excel Spreadsheet
Integration of ELP Strategies: (Language, Grammar, etc)
Completed by SEI/ELP teachers (later)
Exemplary Learning Activities (Optional): List one exemplary strategy per box.
Exemplary Scaffolding Strategy (Optional): List one exemplary strategy per box.
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Curriculum Document
Original Development: Spring 2013
Unit:
Subject/Course:
Grade Level:
School Year:
2 - Operations with Rational Number (Multiply/Divide)
General Math
7th
2013-2014
This section completed once per whole unit. (Its purpose is to clarify the unit’s big idea and connecting standards.)
Big Ideas: Why is this learning important?
What generalization or principle do you want to know/do?
The big idea resides at the heart of the discipline, and has value beyond classroom. These may come from the cluster deconstructing process.
Number System
 Multiply and divide rational numbers.
Expressions and Equations
 Solve multi-step real-life and mathematical problems that includes positive and negative rational numbers.
Common Core Standards / State Standards
Domain: Number System
Content Standard:
Cluster: Apply and extend previous understandings of operations with fractions to add, subtract,
including CODE + (Rigor)
multiply, and divide rational numbers.
Standard Code:
 7.NS.2. Apply and extend previous understandings of multiplication and division
and of fractions to multiply and divide rational numbers. (Apply/DOK 3)
a) Understand that multiplication is extended from fractions to rational numbers
by requiring that operations continue to satisfy the properties of operations,
particularly the distributive property, leading to products such as (–1)(–1) = 1
and the rules for multiplying signed numbers. Interpret products of rational
numbers by describing real- world contexts.
b) Understand that integers can be divided, provided that the divisor is not zero,
and every quotient of integers (with non-zero divisor) is a rational number. If p
and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational
numbers by describing real-world contexts.
c) Apply properties of operations as strategies to multiply and divide rational
numbers.
d) Convert a rational number to a decimal using long division; know that the
decimal form of a rational number terminates in 0s or eventually repeats.
 7.NS.3. Solve real-world and mathematical problems involving the four operations with
rational numbers. (Computations with rational numbers extend the rules for
manipulating fractions to complex fractions.)
Domain: Expressions and Equations
Cluster: Use properties of operations to generate equivalent expressions.
Standard Code:
 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. For example, a +
0.05a = 1.05a means that “increase by 5 percent” is the same as “multiply by 1.05.”
Domain: Expressions and Equations
Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions
and equations
Standard Code:
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7.EE.3.

Integration of Reading &
Writing Anchor and/or
Mathematical Practices
including CODE
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.
(Analyze/DOK 3)
o For example: If a woman making $25 an hour gets a 10percent raise, she will
make an additional 1/10 of her salary an hour, or $2.50, for a new salary of
$27.50. If you want to place a towel bar 9 3/4 inches long in the center of a
door that is 27 1/2 inches wide, you will need to place the bar about 9 inches
from each edge; this estimate can be used as a check on the exact
computation.
College and Career Readiness Anchor Standards for Reading
Craft and Structure
4. Interpret words and phrases as they are used in a text, including determining technical,
connotative, and figurative meanings, and analyze how specific word choices shape meaning
or tone.
College and Career Readiness Anchor Standards for Writing
Range of Writing
10. Write routinely over extended time frames(time for research, reflection, and revision) and
shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and
audiences.
Mathematical Practices (MP) (boldface correlation to unit focus standards)
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.
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.
Technology
Standard:
including CODE
ELP Standard:
ET07-S1C4-02: Use digital collaborative tools to synthesize information, produce original works,
and express ideas.
ET07-S6C2-03: Enter/Edit data using simple formulas while using spreadsheet(s) to perform
calculations.
Completed by SEI/ELP teachers (later)
including CODE
Clarifications of Content Standard
Academic Vocabulary: What academic vocabulary does the student need to know?
Terminating Decimals, Repeating Decimals
Declarative Knowledge: What concepts (facts, ideas, cause/effect) does the student need to KNOW?
Students will need to know:
 Multiplication of positive and negative numbers (begin with integers and extend to rational numbers)
 Division of positive and negative numbers (begin with integers and extend to rational numbers)
 Equivalent forms of rational numbers
 Equivalent forms of expressions
 Properties of operations
o Distributive property
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


Terminating and repeating decimals
Mental computation strategies
Estimation strategies
Procedural Skill: What procedures (steps, algorithms, tactics) does the student need to know HOW to DO?
Students will:
 MULTIPLY and DIVIDE (rational numbers)
 UNDERSTAND/DEVELOP (rules for multiplying signed numbers)
 UNDERSTAND (every quotient of integers (with non-zero divisor) is a rational number)
 INTERPRET (products & quotients in context)
 APPLY (properties of operations as strategies)
 SOLVE (multi-step problems in context)
o APPLY (properties of operations to calculate)
o CONVERT (between equivalent forms of rational numbers)
o UNDERSTAND (the relationship between equivalent forms of an expression)
o ASSESS (reasonableness of answers)
 USE (mental computation and estimation strategies)
Prerequisites: What concepts does the student need prior to engaging in this standard?
6.NS.2: Fluently divide multi-digit numbers using the standard algorithm.
6.EE.3: Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the
expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce
the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
Assessments
Provide one assessment item for each content standard (one standard per box). For each assessment include: 1) standard + descriptive title + (Rigor)
2) an actual assessment item or quality description of the assessment 3) connection to Rdg, Wrtg, or Math Practice (if appropriate)
7.NS.2 (Apply DOK 3)
Descriptive title: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational
numbers.
24lb of flour are divided into 1/3lb portions. The number of 1/3lb portions is:
a)
48
b)
50
c)
64
d)
72
7.EE.3 (Analyze DOK 3)
Descriptive title: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
The price of a share of a company is $20 before the trading open on Monday. The price raises
10% on Monday and falls 10% on Tuesday. How much is the share price at the end of Tuesday?
This section completed per whole unit. (Its purpose is to focus on integrating the standards through resources & instructional strategies that focus on unit big ideas.)
UNIT Resources & Instruction
Primary text connections: List chapters, pages, etc.
Holt McDougal Mathematics Course 2:
Standards: 7.NS.2 and 7.NS.3
 Properties of Numbers, Chapter 1-5, pages 24-27
 Integers, Chapter 2-1, pages 72-75
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






Multiplying and Dividing Integers, Chapter 2-4, pages
Equivalent Fractions and Mixed Numbers, Chapter 2-9, pages 118-121
Equivalent Fractions and Decimals, Chapter 2-10, pages 122-125
Multiplying Decimals, Chapter 3-3, pages
Dividing Decimals, Chapter 3-4, pages
Multiplying Fractions and Mixed Numbers, Chapters 3-9, pages
Dividing Fractions and Mixed Numbers, Chapters 3-10, pages
Standards: 7.EE.2 and 7.EE.3














Variables and Algebraic Expressions, Chapter 1-6, pages 30-33
Translating Words into Math, Chapter 1-7, pages 34-37
Simplifying Algebraic Expressions, Chapter 1-8, pages 38-41
Equations and Their Solutions, Chapter 1-9, pages 42-47
Solving Equations by Adding or Subtracting, Chapter 1-10, pages 48-51
Solving Equations by Multiplying or Dividing, Chapter 1-11, pages 52-55
Solving Equations Containing Integers, Chapter 2-5, pages 96-101
Estimating with Decimals, Chapter 3-1, pages 144-147
Solving Equations Containing Decimals, Chapter 3-5, pages 164-167
Estimating with Fractions, Chapter 3-6, pages 170-173
Solving Equations Containing Fractions, Chapter 3-11, pages 194-197
Solving Two-Step Equations, Chapter 12-1, pages 694-699
Solving Multi-Step Equations, Chapter 12-2, pages 700-703
Solving Equations with Variables on Both Sides, Chapter 12-3, pages 704-707
Supplemental Text Connections: List other school-purchased curriculum resources.
Other materials available: List other useful resources, teacher-created, online, etc.
Teacher Instructional Strategies: Research-based strategies that “fit.”
Grouping, Questioning, Visual Aids, Setting High Expectations, Technology, Assessments
Integration of Technology: Specific examples that apply the technology standards in the content.
 Students create a table and graph using Excel or other spreadsheet
program.
o Printing Books
 Calculate and compare the number of servings Mungry ate in a single
setting.
o Read or Listen to Shel Silverstein’s poem, Hungry Mungry from Where
the Sidewalk Ends
 Students calculate their age on each of the nine planets in our solar
system using an Excel spreadsheet.
o Using An Excel Spreadsheet
Integration of ELP Strategies: (Language, Grammar, etc)
Completed by SEI/ELP teachers (later)
Exemplary Learning Activities (Optional): List one exemplary strategy per box.
Exemplary Scaffolding Strategy (Optional): List one exemplary strategy per box.
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Curriculum Document
Original Development: Spring 2013
Unit:
Subject/Course:
Grade Level:
School Year:
3 - Two and Three Dimensional Geometry
General Math
7th
2013-2014
This section completed once per whole unit. (Its purpose is to clarify the unit’s big idea and connecting standards.)
Big Ideas: Why is this learning important?
What generalization or principle do you want to know/do?
The big idea resides at the heart of the discipline, and has value beyond classroom. These may come from the cluster deconstructing process.



Solve problems for area and circumference of a circle.
Understand the relationship between the circumference and area of a circle.
Solve real-world and mathematical problems involving area, volume, and surface area.
Common Core Standards / State Standards
Domain: Geometry
Content Standard:
Cluster: Draw, construct, and describe geometrical figures and describe the relationships between
including CODE + (Rigor)
them.
Standard Code:
 7.G.2. Draw (freehand, with ruler and protractor, and with technology) geometric shapes
with given conditions. Focus on constructing triangles from three measures of angles or
sides, noticing when the conditions determine a unique triangle, more than one triangle or
no triangle.
 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.
Domain: Geometry
Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area,
and volume.
Standard Code:
 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. (Analyze/DOK 3)
 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. (Apply/DOK 2)
Integration of Reading &
Writing Anchor and/or
Mathematical Practices
including CODE
College and Career Readiness Anchor Standards for Reading
Craft and Structure
4. Interpret words and phrases as they are used in a text, including determining technical,
connotative, and figurative meanings, and analyze how specific word choices shape meaning
or tone.
College and Career Readiness Anchor Standards for Writing
Range of Writing
10. Write routinely over extended time frames(time for research, reflection, and revision) and
shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and
audiences.
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Mathematical Practices (MP) (boldface correlation to unit focus standards)
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.
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.
Technology
Standard:
ET07-S1C1-01: Analyze and evaluate information to generate new ideas, processes or products.
including CODE
ELP Standard:
Completed by SEI/ELP teachers (later)
including CODE
Clarifications of Content Standard
Academic Vocabulary: What academic vocabulary does the student need to know?
Area, Quadrilaterals, Parallelogram, Complementary Angles , Supplementary Angles, Volume, Surface Area
Declarative Knowledge: What concepts (facts, ideas, cause/effect) does the student need to KNOW?
Students will need to know:
 Formulas
o Area of circle
o Circumference of circle
 Relationship between circumference and area of a circle
 Geometric conditions (points, line segments, angles, parallelism, congruence, and perpendicularity.)
 Plane sections of three-dimensional figures
 Angle relationships
o Supplementary
o Complementary
o Vertical
o Adjacent
 Area
o Triangles
o Quadrilaterals
o Polygons
 Volume
o Cubes
o Right prisms
 Surface Area
o Cubes
o Right prisms
Procedural Skill: What procedures (steps, algorithms, tactics) does the student need to know HOW to DO?
Students will:
 KNOW/DEVELOP (formulas)
 SOLVE (problems using formulas)
 GIVE/DERIVE (informally the relationship between circumference and area of a circle)
 SOLVE (with and without context)
 DRAW/CONSTRUCT (geometric shapes with given conditions)
 USE (ruler, protractor, technology)
 DESCRIBE (two-dimensional figures that result from plane sections of three-dimensional figures)
 WRITE/SOLVE (problems using equations to find an unknown angle in a figure)
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Prerequisites: What concepts does the student need prior to engaging in this standard?
6.G.4: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of
these figures. Apply these techniques in the context of solving real-world and mathematical problems.
Assessments
Provide one assessment item for each content standard (one standard per box). For each assessment include: 1) standard + descriptive title + (Rigor)
2) an actual assessment item or quality description of the assessment 3) connection to Rdg, Wrtg, or Math Practice (if appropriate)
7.G.4 (Analyze DOK 3)
Descriptive title: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Which of the following numbers is closer to the area of a circle with a radius of 2.1?
a) 10.25
b)
11.33
c) 13.85
d)
14.2
7.G.6 (Apply DOK 2)
Descriptive title: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Using a cereal box, which is a rectangular prism, find the following:
1) Surface area
2) Volume
This section completed per whole unit. (Its purpose is to focus on integrating the standards through resources & instructional strategies that focus on unit big ideas.)
UNIT Resources & Instruction
Primary text connections: List chapters, pages, etc.
Holt McDougal Mathematics Course 2:
Standards: 7.G.2 and 7.G.3




Classifying Angles, Chapter 8-2, pages 454-457
Classifying Triangles, Chapter 8-6, pages 478-481
Angles in Polygons, Chapter 8-8, pages 486-489
Congruent Figures, Chapter 8-9, pages 492-495
Standards: 7.G.4, 7.G.5 and 7.G.6

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









Classifying Angles, Chapter 8-2, pages 454-457
Line and Angle Relationships, Chapter 8-3, pages 458-463
Perimeter and Circumference, Chapter 9-2, pages 528-533
Area of Parallelograms, Chapter 9-3, pages 534-539
Area of Triangles and Trapezoids, Chapter 9-4, pages 540-543
Area of Circles, Chapter 9-5, pages 546-549
Area of Irregular Figures, Chapter 9-6, pages 550-553
Introduction to Three-Dimensional Figures, Chapter 10-1, pages 588-593
Volume of Prisms and Cylinders, Chapter 10-2, pages 594-599
Volume of Pyramids and Cones, Chapter 10-3, pages 600-603
Surface Area of Prisms and Cylinders, Chapter 10-4, pages 606-611
Surface Area of Pyramids and Cones, Chapter 10-5, pages 612-617
Supplemental Text Connections: List other school-purchased curriculum resources.
Other materials available: List other useful resources, teacher-created, online, etc.
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Page 14
Teacher Instructional Strategies: Research-based strategies that “fit.”
Grouping, Questioning, Visual Aids, Setting High Expectations, Technology, Assessments
Integration of Technology: Specific examples that apply the technology standards in the content.
 Students will measure the dimensions of a common object, multiply each
dimension by a scale factor, and examine a model using the multiplied
dimensions. Students will then compare the surface area and volume of the
original object and the enlarged model.
o Scaling Away
 Students gather information about aluminum can usage and graph their
findings in a line plot.
o Aluminum Cans
Integration of ELP Strategies: (Language, Grammar, etc)
Completed by SEI/ELP teachers (later)
Exemplary Learning Activities (Optional): List one exemplary strategy per box.
Exemplary Scaffolding Strategy (Optional): List one exemplary strategy per box.
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Curriculum Document
Original Development: Spring 2013
Unit:
Subject/Course:
Grade Level:
School Year:
4 - Proportional Reasoning
General Math
7th
2013-2014
This section completed once per whole unit. (Its purpose is to clarify the unit’s big idea and connecting standards.)
Big Ideas: Why is this learning important?
What generalization or principle do you want to know/do?
The big idea resides at the heart of the discipline, and has value beyond classroom. These may come from the cluster deconstructing process.


Recognize and represent proportional relationships between quantities.
Solve multistep ratio and percent problems by using proportional relationships.
Common Core Standards / State Standards
Domain: Ratio and Proportional Relationships
Content Standard:
Cluster: Analyze proportional relationships and use them to solve real-world and mathematical
including CODE + (Rigor)
problems.
Standard Code:
 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 ¼ hour, compute the unit rate as the complex fraction ½ to ¼ miles
per hour, equivalently 2 miles per hour.
 7.RP.2. Recognize and represent proportional relationships between quantities.
(Analyze/DOK 3)
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.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. (Apply/DOK 2)
Domain: Geometry
Cluster: Draw, construct, and describe geometrical figures and describe the relationships between
them.
Standard Code:
 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.
Integration of Reading &
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College and Career Readiness Anchor Standards for Reading
Page 16
Writing Anchor and/or
Mathematical Practices
including CODE
Craft and Structure
4. Interpret words and phrases as they are used in a text, including determining technical,
connotative, and figurative meanings, and analyze how specific word choices shape meaning
or tone.
College and Career Readiness Anchor Standards for Writing
Range of Writing
10. Write routinely over extended time frames(time for research, reflection, and revision) and
shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and
audiences.
Mathematical Practices (MP) (boldface correlation to unit focus standards)
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.
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.
Technology
Standard:
ET07-S1C2-02: Analyze system processes and outcomes using models or simulations.
including CODE
ELP Standard:
Completed by SEI/ELP teachers (later)
including CODE
Clarifications of Content Standard
Academic Vocabulary: What academic vocabulary does the student need to know?
Ratio, Proportions, Percent, Scale
Declarative Knowledge: What concepts (facts, ideas, cause/effect) does the student need to KNOW?






Proportional relationships
Equivalent ratios
o In a table
o Straight line through the origin when graphing on a coordinate plane
o Equation
Constant of proportionality (unit rate)
o Tables
o Graphs
o Equations
o Diagrams
o Verbal descriptions
Point (x,y) in terms of situation
o (0, 0)
o (1, r) where r is the unit rate
Multi-step problems
o Ratio
o Percent
Scale drawings
o Scale
o Actual lengths and areas
Procedural Skill: What procedures (steps, algorithms, tactics) does the student need to know HOW to DO?

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RECOGNIZE (proportional relationships)
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







REPRESENT (proportional relationships in a variety of ways)
DECIDE (proportional relationship)
o TEST (equivalent ratios)
o OBSERVE (graph)
IDENTIFY (constant of proportionality)
EXPLAIN [point (x,y)]
SOLVE (multi-step problems)
COMPUTE (unit rates)
COMPUTE (actual lengths/areas from scale drawings)
REPRODUCE (a scale drawing at a different scale)
Prerequisites: What concepts does the student need prior to engaging in this standard?
6.RP.2: Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio
relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is ¾ cup of flour for each cup of sugar.”
“We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Note: Expectations for unit rates in this grade are limited to
non-complex fractions.)
6.RP.3: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent
ratios, tape diagrams, double number line diagrams, or equations.
a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables,
and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
b. Solve unit rate problems including those involving unit pricing and constant speed. For example, it took 7 hours to mow 4
lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
c. 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.
d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or
dividing quantities.
Assessments
Provide one assessment item for each content standard (one standard per box). For each assessment include: 1) standard + descriptive title + (Rigor)
2) an actual assessment item or quality description of the assessment 3) connection to Rdg, Wrtg, or Math Practice (if appropriate)
7.RP.2 (Analyze DOK 3)
Descriptive title: Analyze proportional relationships and use them to solve real-world and mathematical problems.
Question 3: Line v in the coordinate graph below represents the distance in time travelled by a
vehicle. What is the distance travelled after 75 minutes?
a)
50 miles
b)
60 miles
c)
70 miles
d)
75 miles
7.RP.3 (Apply DOK 2)
Descriptive title: Analyze proportional relationships and use them to solve real-world and mathematical problems.
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A store is advertising a sale with 10% off all items in the store. Sales tax is 5%.
(a) A 32-inch television is regularly priced at $295.00. What is the total price of the television,
including sales tax, if it was purchased on sale? Fill in the blank to complete the sentence. Round
your answer to the nearest cent.
The total cost of the television is $ ______.
(b) Adam and Brandi are customers discussing how the discount and tax will be calculated.
Here is Adam's process for finding the total cost for any item in the store.
· Take 10% off the original price.
· Then, add the sales tax to the discounted price.
Adam represents his process as:
Here is Brandi's process for finding the total cost for any item in the store.
· Determine the original price of the item, including sales tax.
· Then, take 10% off.
Brandi represents her process as:
In both equations, T represents the total cost of the television and p represents the regular price.
Are they both correct? Use the properties of operations to justify your answer.
This section completed per whole unit. (Its purpose is to focus on integrating the standards through resources & instructional strategies that focus on unit big ideas.)
UNIT Resources & Instruction
Primary text connections: List chapters, pages, etc.
Holt McDougal Mathematics Course 2:
Standards: 7.RP.1, 7.RP.2 and 7.RP.3
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
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








Ratios, Chapter 4-1, pgs 214-217
Rates, Chapter 4-2, pgs 218-221
Identifying and Writing Proportions, Chapter 4-3, pgs 222-225
Solving Proportions, Chapter 4-4, pgs 226-229
Customary Measurements, Chapters 4-5, pgs 232-235
Metric Measurements, Chapter 4-6, pgs 236-239
Dimensional Analysis, Chapter 4-7, pgs 240-243
Similar Figures and Proportions, Chapter 4-8, pgs 248-251
Using Similar Figures, Chapter 4-9, pgs 252-255
Functions, Tables, and Graphs, Chapter 5-3, pgs 284-287
Graphing Linear Functions, Chapter 5-5, pgs 296-299
Slope and Rates of Change, Chapter 5-6, pgs 302-306
Percents, Chapter 6-1, pgs 336-339
Estimating with Percents, Chapter 6-3, pgs 344-347
Percent of a Number, Chapter 6-4, pgs 348-351
Solving Percent Problems, Chapter 6-5, pgs 352-355
Simple Interest, Chapter 6-7, pgs 362-365
Standards: 7.G.1
 Scale Drawings and Scale Models, Chapter 4-10, pgs 256-259
Supplemental Text Connections: List other school-purchased curriculum resources.
Other materials available: List other useful resources, teacher-created, online, etc.
Teacher Instructional Strategies: Research-based strategies that “fit.”
Grouping, Questioning, Visual Aids, Setting High Expectations, Technology, Assessments
Integration of Technology: Specific examples that apply the technology standards in the content.
 Students use motion detectors to understand graphs and equations.
Students experience constant and variable rates of change and are
challenged to consider graphs where no movements are possible to
create them.
o Movement with Functions ‐ How Should I Move?
 Students use remote‐controlled cars to create a system of equations.
o Movement with Functions Road Rage
Integration of ELP Strategies: (Language, Grammar, etc)
Completed by SEI/ELP teachers (later)
Exemplary Learning Activities (Optional): List one exemplary strategy per box.
Exemplary Scaffolding Strategy (Optional): List one exemplary strategy per box.
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Curriculum Document
Original Development: Spring 2013
Unit:
Subject/Course:
Grade Level:
School Year:
5 - Algebraic Reasoning II
General Math
7th
2013-2014
This section completed once per whole unit. (Its purpose is to clarify the unit’s big idea and connecting standards.)
Big Ideas: Why is this learning important?
What generalization or principle do you want to know/do?
The big idea resides at the heart of the discipline, and has value beyond classroom. These may come from the cluster deconstructing process.


Represent quantities using variables.
Construct simple equations and inequalities.
Common Core Standards / State Standards
Domain: Expressions and Equations
Content Standard:
Cluster: Use properties of operations to generate equivalent expressions.
including CODE + (Rigor)
Standard Code:
 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. For example, a +
0.05a = 1.05a means that “increase by 5 percent” is the same as “multiply by 1.05.”
Domain: Expressions and Equations
Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions
and equations.
Standard Code:
 7.EE.4 (emphasis on a) 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. (Create/DOK 3)
a) Solve word problems leading to equations of the form px + q = r and p(x + q) =
r, where p, q, and r are specific rational numbers. Solve equations of these
forms fluently. Compare an algebraic solution to an arithmetic solution,
identifying the sequence of the operations used in each approach. For
example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
b) Solve word problems leading to equations 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. For example: As a
salesperson, you are paid $50 per week plus $3 per sale. This week you want your
pay to be at least $100. Write an inequality for the number of sales you need to
make and describe the solutions.
Integration of Reading &
Writing Anchor and/or
Mathematical Practices
including CODE
College and Career Readiness Anchor Standards for Reading
Craft and Structure
4. Interpret words and phrases as they are used in a text, including determining technical,
connotative, and figurative meanings, and analyze how specific word choices shape meaning
or tone.
College and Career Readiness Anchor Standards for Writing
Range of Writing
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Page 21
10. Write routinely over extended time frames(time for research, reflection, and revision) and
shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and
audiences.
Mathematical Practices (MP) (boldface correlation to unit focus standards)
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.
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.
Technology
Standard:
Not applicable
including CODE
ELP Standard:
Completed by SEI/ELP teachers (later)
including CODE
Clarifications of Content Standard
Academic Vocabulary: What academic vocabulary does the student need to know?
Algebraic Solutions, Arithmetic Solutions, Inequalities, Equation, Expression, Coefficients
Declarative Knowledge: What concepts (facts, ideas, cause/effect) does the student need to KNOW?
Students will need to know:
 Variables
 Simple equations
o form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers
 Simple inequalities
o form px + q > r or px + q < r, where p, q, and r are specific rational numbers.
 Algebraic solution
 Arithmetic solution
 Solution set of an inequality
 Properties of operations
 Linear expressions
 Rational coefficients
 Expressions in different forms
 Quantities in a problem are related
Procedural Skill: What procedures (steps, algorithms, tactics) does the student need to know HOW to DO?
Students will:
 USE (variables)
 CONSTRUCT (simple equations and inequalities)
 SOLVE (problems in context)
o Simple equations
o Simple inequalities
 REASON (about quantities)
 COMPARE (solutions)
 GRAPH (inequality)
 INTERPRET (inequality)
 APPLY (properties of operations)
 FACTOR (Linear expressions with rational coefficients)
 EXPAND (Linear expressions with rational coefficients)
 WRITE (an expression in different forms)
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
UNDERSTAND (how rewriting an expression in different forms can show how the quantities in a problem are related)
Prerequisites: What concepts does the student need prior to engaging in this standard?
6.EE.4: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value
is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number
regardless of which number y stands for.
Assessments
Provide one assessment item for each content standard (one standard per box). For each assessment include: 1) standard + descriptive title + (Rigor)
2) an actual assessment item or quality description of the assessment 3) connection to Rdg, Wrtg, or Math Practice (if appropriate)
7.EE.4 (Create DOK 3)
Descriptive title: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
This is the call plan for Minna’s cell phone:
$15 a month plus $0.20 per minute of call time. Free texting.
Minna made 30 minutes of calls this month, and sent 110 texts.
Write an equation for the total cost that Minna has to pay the phone company.
How much does she have to pay the phone company?
Explain how you figure this out
This section completed per whole unit. (Its purpose is to focus on integrating the standards through resources & instructional strategies that focus on unit big ideas.)
UNIT Resources & Instruction
Primary text connections: List chapters, pages, etc.
Holt McDougal Mathematics Course 2:
Standards: 7.EE.1, 7.EE.2 and 7.EE.4












Variables and Algebraic Expressions, Chapter 1-6, pages 30-33
Translating Words into Math, Chapter 1-7, pages 34-37
Properties of Numbers, Chapter 1-5, pages 24-27
Simplifying Algebraic Expressions, Chapter 1-8, pages 38-41
Solving Equations by Adding or Subtracting, Chapter 1-10, pages 48-51
Solving Equations by Multiplying or Dividing, Chapter 1-11, pages 52-55
Solving Two-Step Equations, Chapter 12-1, pages 694-699
Solving Multi-Step Equations, Chapter 12-2, pages 700-703
Inequalities, Chapter 12-4, pages 710-713
Solving Inequalities by Adding or Subtracting, Chapter 12-5, pages 714-717
Solving Inequalities by Multiplying or Dividing, Chapter 12-6, pages 718-721
Solving Multi-Step Inequalities, Chapter 12-7, pages 722-725
Supplemental Text Connections: List other school-purchased curriculum resources.
Other materials available: List other useful resources, teacher-created, online, etc.
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Teacher Instructional Strategies: Research-based strategies that “fit.”
Grouping, Questioning, Visual Aids, Setting High Expectations, Technology, Assessments
Integration of Technology: Specific examples that apply the technology standards in the content.
Not applicable
Integration of ELP Strategies: (Language, Grammar, etc)
Completed by SEI/ELP teachers (later)
Exemplary Learning Activities (Optional): List one exemplary strategy per box.
Exemplary Scaffolding Strategy (Optional): List one exemplary strategy per box.
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Curriculum Document
Original Development: Spring 2013
Unit:
Subject/Course:
Grade Level:
School Year:
6 - Inferences about Populations
General Math
7th Grade
2013-2014
This section completed once per whole unit. (Its purpose is to clarify the unit’s big idea and connecting standards.)
Big Ideas: Why is this learning important?
What generalization or principle do you want to know/do?
The big idea resides at the heart of the discipline, and has value beyond classroom. These may come from the cluster deconstructing process.
Statistics and Probability
 Understand random sampling when drawing inferences about a population.
 Draw informal comparative inferences about two populations.
Common Core Standards / State Standards
Domain: Statistics and Probability
Content Standard:
Cluster: Use random sampling to draw inferences about a population.
including CODE + (Rigor)
Standard Code:
 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. (Understand/DOK 1)
 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. For example, estimate
the mean word length in a book by randomly sampling words from the book; predict the
winner of a school election based on randomly sampled survey data. Gauge how far off
the estimate or prediction might be.
Domain: Statistics and Probability
Cluster: Draw informal comparative inferences about two populations.
Standard Code:
 7.SP.3. Informally assess the degree of visual overlap of two numerical data distributions
with similar variability, measuring the difference between the centers by expressing it as
a multiple of a measure of variability.
o For example, the mean height of players on the basketball team is 10 cm
greater than the mean height of players on the soccer team, about twice the
variability (mean absolute deviation) on either team; on a dot plot, the
separation between the two distributions of heights is noticeable.
 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. (Analyze/DOK 3)
o For example, decide whether the words in a chapter of a seventh-grade
science book are generally longer than the words in a chapter of a fourth-grade
science book.
Integration of Reading &
Writing Anchor and/or
Mathematical Practices
including CODE
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College and Career Readiness Anchor Standards for Reading
Integration of Knowledge and Ideas
8. Delineate and evaluate the argument and specific claims in a text, including the validity of
the reasoning as well as the relevance and sufficiency of the evidence.
Page 25
College and Career Readiness Anchor Standards for Writing
Research to Build and Present Knowledge
9. Draw evidence from literary or informational texts to support analysis, reflection, and
research.
Mathematical Practices (MP) (boldface correlation to unit focus standards)
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.
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.
Technology
Standard:
including CODE
ELP Standard:
ET07-S1C3-01: Identify patterns and trends to forecast possibilities from different perspectives.
ET07-S2C1-01: Collaborate and communicate with peers, experts, or others employing a variety of
digital tools to share findings and/or publish.
ET07-S2C2-01: Communicate and collaborate for the purpose of producing original works or
solving problems.
ET07-S4C2-01: Plan, conduct and manage research using appropriate digital resources to
develop solutions for a question.
Completed by SEI/ELP teachers (later)
including CODE
Clarifications of Content Standard
Academic Vocabulary: What academic vocabulary does the student need to know?
Population, Sample, Mean, Median, Mode, Range, Measures of Central Tendency
Declarative Knowledge: What concepts (facts, ideas, cause/effect) does the student need to KNOW?
Students will need to know:
 Statistics
 Population
o Representative
 Sample
o Representative/valid
o Random
 Measures of center
 Measures of variability
 Inferences
o Informal comparative
 Data
 Variation
 Data distribution
o Variability
o Center
o Mean absolute deviation
Procedural Skill: What procedures (steps, algorithms, tactics) does the student need to know HOW to DO?
Students will:
 UNDERSTAND/USE (statistics)
 EXAMINE (a sample of a population)
 GENERALIZE (information about a population)
o DETERMINE (if a sample is representative/valid)
 USE (measures of center and measures of variability for numerical data from random samples)
o DRAW (informal comparative inferences)
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


USE (data from a random sample)
o DRAW (inferences about a population)
GENERATE (multiple samples of the same size)
o GAUGE (the variation in estimates or predictions)
EXPRESS/CALCULATE (the difference between the centers of two numerical data distributions as a multiple of a measure of
variability – mean absolute deviation)
Prerequisites: What concepts does the student need prior to engaging in this standard?
6.SP.1: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the
answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question
because one anticipates variability in students’ ages.
6.SP.4: Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
Assessments
Provide one assessment item for each content standard (one standard per box). For each assessment include: 1) standard + descriptive title + (Rigor)
2) an actual assessment item or quality description of the assessment 3) connection to Rdg, Wrtg, or Math Practice (if appropriate)
7.SP.1 (Understand DOK 1)
Descriptive title: Use random sampling to draw inferences about a population.
A local newspaper of a New Mexico town intends to find if the mayor of the town is popular with
its adult citizens. Which of the following samples could be used by the newspaper?
a)
a random sample of people from the mayor's political party
b)
a random sample of people selected from all adult citizens of the town
c)
a random sample of people selected from all people registered with a political party
d)
a random sample of people selected from all middle class citizens of the town
7.SP.4 (Analyze DOK 3)
Descriptive title: Draw informal comparative inferences about two populations.
The two data sets below depict the weights of the offensive lineman for two Arizona college football teams, Arizona State University and
University of Arizona.
Arizona State University {277, 265, 292, 303, 320, 300, 313, 267, 288, 311, 280, 302, 335, 310, 307}
University of Arizona {265, 265, 308, 260, 298, 270, 320, 290, 280, 315, 280, 295, 300, 300}
(a) Which team has the larger average weight?
(b) Does one team seem to have greater variability in its weight than the other, or are the two teams similar in that regard?
This section completed per whole unit. (Its purpose is to focus on integrating the standards through resources & instructional strategies that focus on unit big ideas.)
UNIT Resources & Instruction
Primary text connections: List chapters, pages, etc.
Holt McDougal Mathematics Course 2:
Standards: 7.SP.1, 7.SP.2, 7.SP.3 and 7.SP.4
 Frequency Tables, Stem-and-Leaf Plots, and Line Plots, Chapter 7-1, pages 380-384
 Mean, Median, Mode, and Range, Chapter 7-2, pages 385-389
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Bar Graphs and Histograms, Chapter 7-3, pages 390-393
Reading and Interpreting Circle Graphs, Chapter 7-4, pages 394-397
Box-and-Whisker Plots, Chapter 7-5, pages 398-401
Line Graphs, Chapter 7-6, pages 406-409
Populations and Samples, Chapter 7-8, pages 418-421
Scatter Plots, Chapter 7-9, pages 422-425
Supplemental Text Connections: List other school-purchased curriculum resources.
Other materials available: List other useful resources, teacher-created, online, etc.
Teacher Instructional Strategies: Research-based strategies that “fit.”
Grouping, Questioning, Visual Aids, Setting High Expectations, Technology, Assessments
Integration of Technology: Specific examples that apply the technology standards in the content.
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Sales forecast
Stock Market
Probability, statistics, data analysis
Six Thinking Hats: Looking at Decisions from All Points of View
Mind Tools
Links for planning
o Survey Basics
o Science Buddies
Students plan and create an online survey using free survey resource.
o Google
o Survey Monkey
Tools for online communication:
o Where students can safely connect, collaborate and learn using
o protected email and blogs.
o EPals
o Live workspace (Google Docs, Windows Live)
o Wikis
o Blogs
o Email
o Video conferencing
o Chain story (might want to explain what this is and how it can be done
o with technology)
o Texting
o Student response clickers
o Classroom presentations
o Web publishing
Students use spreadsheet program (i.e. Excel, Numbers) to compare data
sets.
(a)Students input two different sets of data, using the formula for calculating
mean.
(b)Then compare results for difference between the central measures of the
data.
(c)Also use spreadsheet data to make comparative inferences about two
populations.
Integration of ELP Strategies: (Language, Grammar, etc)
Completed by SEI/ELP teachers (later)
Exemplary Learning Activities (Optional): List one exemplary strategy per box.
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Exemplary Scaffolding Strategy (Optional): List one exemplary strategy per box.
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Curriculum Document
Original Development: Spring 2013
Unit:
Subject/Course:
Grade Level:
School Year:
7 - Probability
General Math
7th
2013-2014
This section completed once per whole unit. (Its purpose is to clarify the unit’s big idea and connecting standards.)
Big Ideas: Why is this learning important?
What generalization or principle do you want to know/do?
The big idea resides at the heart of the discipline, and has value beyond classroom. These may come from the cluster deconstructing process.
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Develop and use probability models.
Compare probabilities from a model to observed frequencies.
Common Core Standards / State Standards
Domain: Statistics and Probability
Content Standard:
Cluster: Investigate chance processes and develop, use, and evaluate probability models.
including CODE + (Rigor)
Standard Code:
 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. (Create/DOK 3)
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?
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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 events.
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
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question: If 40 percent 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
Integration of Reading &
Writing Anchor and/or
Mathematical Practices
including CODE
College and Career Readiness Anchor Standards for Reading
Integration of Knowledge and Ideas
8. Delineate and evaluate the argument and specific claims in a text, including the validity of
the reasoning as well as the relevance and sufficiency of the evidence.
College and Career Readiness Anchor Standards for Writing
Research to Build and Present Knowledge
9. Draw evidence from literary or informational texts to support analysis, reflection, and
research.
Mathematical Practices (MP) (boldface correlation to unit focus standards)
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.
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.
Technology
Standard:
Not applicable
including CODE
ELP Standard:
Completed by SEI/ELP teachers (later)
including CODE
Clarifications of Content Standard
Academic Vocabulary: What academic vocabulary does the student need to know?
Theoretical Probability, Experimental Probability, Sample Space, Compound Event, Tree Diagram
Declarative Knowledge: What concepts (facts, ideas, cause/effect) does the student need to KNOW?
Students will need to know:
 Probability model
o Uniform
o Not uniform
 Probabilities
 Events
o Compound
 Frequencies
 Outcomes
 Data
 Chance
o Process
o Event
 Probability of a chance event
 Relative frequency
 Organized list
 Tables
 Tree diagram
 Simulation
 Sample space
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Procedural Skill: What procedures (steps, algorithms, tactics) does the student need to know HOW to DO?
Students will:
 DEVELOP/USE
o (a uniform probability model)
o (a probability model which may not be uniform)
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FIND
o (probabilities of simple events)
o (probability of compound events using organized lists, tables, tree diagrams and simulation)
o (frequencies for compound events)
 COMPARE (probabilities from a model to observed frequencies)
 EXPLAIN (possible sources of the discrepancy)
 OBSERVE (frequencies in data)
 UNDERSTAND
o (probability of a chance event is a number between 0 and 1)
o (probability of a compound event is the fraction of outcomes in the sample space)
 PREDICT (approximate relative frequency)
 REPRESENT (sample spaces for compound events using various methods, e.g., organized lists, tables, tree diagrams)
 DESIGN/USE (simulation)
Prerequisites: What concepts does the student need prior to engaging in this standard?
Not applicable
Assessments
Provide one assessment item for each content standard (one standard per box). For each assessment include: 1) standard + descriptive title + (Rigor)
2) an actual assessment item or quality description of the assessment 3) connection to Rdg, Wrtg, or Math Practice (if appropriate)
7.SP.7 (Create DOK 3)
Descriptive title: Investigate chance processes and develop, use, and evaluate probability models.
Roll two dice 10 times. After each roll, note whether any sixes were observed and record your
results in the table below.
(a) What proportion of the 10 rolls resulted in at least one six?
(b) Combine your results with those of your classmates. What proportion of all the rolls in the
class resulted in at least one six?
(c) Make a list of all the different possible outcomes that might be observed when two dice are
rolled. (Hint: There are 36 different possible outcomes.)
(d) What proportion of the 36 possible outcomes result in at least one six?
(e) Suppose you and your classmates were able to roll the two dice many thousands of times.
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What proportion of the time would you expect to roll at least one six?
This section completed per whole unit. (Its purpose is to focus on integrating the standards through resources & instructional strategies that focus on unit big ideas.)
UNIT Resources & Instruction
Primary text connections: List chapters, pages, etc.
Holt McDougal Mathematics Course 2:
Standards: 7.SP.5, 7.SP.6, 7.SP.7 and 7.SP.8
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Probability, Chapter 11-1, pages 640-643
Experimental Probability, Chapter 11-2, pages 644-647
Find Sample Spaces, Chapter 11-3, pages 648-651
Theoretical Probability, Chapter 11-4, pages 652-655
Making Predictions, Chapter 11-5, pages 658-661
Probability of Independent and Dependent Events, Chapter 11-6, pages 666-669
Supplemental Text Connections: List other school-purchased curriculum resources.
Other materials available: List other useful resources, teacher-created, online, etc.
Teacher Instructional Strategies: Research-based strategies that “fit.”
Grouping, Questioning, Visual Aids, Setting High Expectations, Technology, Assessments
Integration of Technology: Specific examples that apply the technology standards in the content.
Not applicable
Integration of ELP Strategies: (Language, Grammar, etc)
Completed by SEI/ELP teachers (later)
Exemplary Learning Activities (Optional): List one exemplary strategy per box.
Exemplary Scaffolding Strategy (Optional): List one exemplary strategy per box.
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