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7th Grade Curriculum DocumentOriginal Development: Summer 2013

Grade 7 Pacing Guide

Unit Title Pacing Standards

1. Operating with Rational Numbers (add/sub) 4 weeks 7.NS.1 7.MP.2 7.MP.77.NS.3 7.MP.3 7.MP.8

2. Operating with Rational Numbers (mult/div) 4 weeks

7.NS.2 7.MP.27.NS.3 7.MP.37.EE.2 7.MP.77.EE.3 7.MP.8

3. Two and Three Dimensional Geometry 4 weeks

7.G.2 7.MP.17.G.3 7.MP.47.G.4 7.MP.57.G.5 7.MP.67.G.6 7.MP.7

4. Proportional Relationships 5 weeks

7.RP.1 7.MP.1 7.MP.67.RP.2 7.MP.27.RP.3 7.MP.37.G.1 7.MP.4

5. Algebraic Reasoning II 4 weeks7.EE.1 7.MP.1 7.MP.47.EE.2 7.MP.2 7.MP.77.EE.4 7.MP.3

6. Inferences about Populations 3 weeks

7.SP.1 7.MP.17.SP.2 7.MP.37.SP.3 7.MP.47.SP.4

7. Probability 3 weeks

7.SP.5 7.MP.17.SP.6 7.MP.47.SP.7 7.MP.77.SP.8

Grade Seven Standards for Mathematical Practicedocument.docx Page 1

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 Explanations and ExamplesStudents are expected to:1. Make sense of problems and persevere in solving them.

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?”

Students are expected to:.2. Reason abstractly and quantitatively.

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.

Students are expected to:3. Construct viable arguments and critique the reasoning of others.

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.

Students are expected to:4. Model with mathematics.

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 are expected to:5. Use appropriate tools strategically.

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.

Students are expected to:6. Attend to precision.

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 are expected to:7. Look for and make use of structure.

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 three-dimensional 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.

Students are expected to:8. Look for and express regularity in repeated reasoning.

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.

document.docx Page 2

Curriculum DocumentOriginal Development: Spring 2013

Unit: 1 - Operations with Rational Numbers (Addition/Subtraction)

Subject/Course: General Math

Grade Level: 7th

School Year: 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 StandardsContent Standard:including CODE + (Rigor)

Domain: Number SystemCluster: Apply and extend previous understandings of operations with fractions to add, subtract, 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 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.)

Integration of Reading &Writing Anchor and/orMathematical Practicesincluding CODE

College and Career Readiness Anchor Standards for ReadingCraft 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 WritingRange 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.

TechnologyStandard:including CODE

ET07-S6C2-03: Enter/Edit data using simple formulas while using spreadsheet(s) to perform calculations.

ELP Standard:including CODE

Completed by SEI/ELP teachers (later)

Clarifications of Content StandardAcademic 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 inverseso Number line

Absolute valueo 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)

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?


AssessmentsProvide 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) 1p

b) 1q 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 & InstructionPrimary 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

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 solarsystem using an Excel spreadsheet.

o Using An Excel Spreadsheet

Integration of ELP Strategies: (Language, Grammar, etc)Completed by SEI/ELP teachers (later)document.docx Page 5

Exemplary Learning Activities (Optional): List one exemplary strategy per box.

Exemplary Scaffolding Strategy (Optional): List one exemplary strategy per box.



Unit: 2 - Operations with Rational Number (Multiply/Divide)


Grade Level: 7th



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.


Domain: Number SystemCluster: Apply and extend previous understandings of operations with fractions to add, subtract, 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 EquationsCluster: 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 EquationsCluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equationsStandard Code: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. (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.






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.


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.



Clarifications of Content StandardAcademic Vocabulary: What academic vocabulary does the student need to know?Terminating Decimals, Repeating Decimals


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 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.

AssessmentsProvide 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?



Standards: 7.NS.2 and 7.NS.3

Properties of Numbers, Chapter 1-5, pages 24-27 Integers, Chapter 2-1, pages 72-75 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



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 singlesetting.

o Read or Listen to Shel Silverstein’s poem, Hungry Mungry from Wherethe Sidewalk Ends

Students calculate their age on each of the nine planets in our solarsystem using an Excel spreadsheet.

o Using An Excel Spreadsheet

Integration of ELP Strategies: (Language, Grammar, etc)Completed by SEI/ELP teachers (later)





Unit: 3 - Two and Three Dimensional Geometry


Grade Level: 7th




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.


Domain: GeometryCluster: Draw, construct, and describe geometrical figures and describe the relationships between 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: GeometryCluster: 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)






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.


ET07-S1C1-01: Analyze and evaluate information to generate new ideas, processes or products.



Clarifications of Content StandardAcademic Vocabulary: What academic vocabulary does the student need to know?Area, Quadrilaterals, Parallelogram, Complementary Angles , Supplementary Angles, Volume, Surface Area


Formulaso Area of circleo 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 Supplementaryo Complementaryo Verticalo Adjacent

Areao Triangleso Quadrilateralso Polygons

Volumeo Cubeso Right prisms

Surface Areao Cubeso Right prisms


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)

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.

AssessmentsProvide 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)document.docx Page 12

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 area2) Volume



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

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



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 multiplieddimensions. Students will then compare the surface area and volume of theoriginal object and the enlarged model.

o Scaling Away


Students gather information about aluminum can usage and graph theirfindings in a line plot.

o Aluminum Cans






Unit: 4 - Proportional Reasoning


Grade Level: 7th




Recognize and represent proportional relationships between quantities. Solve multistep ratio and percent problems by using proportional relationships.


Domain: Ratio and Proportional RelationshipsCluster: Analyze proportional relationships and use them to solve real-world and mathematical 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: GeometryCluster: 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.



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.





ET07-S1C2-02: Analyze system processes and outcomes using models or simulations.



Clarifications of Content StandardAcademic 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 tableo Straight line through the origin when graphing on a coordinate planeo Equation

Constant of proportionality (unit rate)o Tableso Graphso Equationso Diagramso Verbal descriptions

Point (x,y) in terms of situationo (0, 0)o (1, r) where r is the unit rate

Multi-step problemso Ratioo Percent

Scale drawingso Scaleo Actual lengths and areas

Procedural Skill: What procedures (steps, algorithms, tactics) does the student need to know HOW to DO? RECOGNIZE (proportional relationships) 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.

AssessmentsProvide 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.

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 $ ______. document.docx Page 17

(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.



Standards: 7.RP.1, 7.RP.2 and 7.RP.3

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



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 arechallenged to consider graphs where no movements are possible tocreate 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





Unit: 5 - Algebraic Reasoning II


Grade Level: 7th



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.


Domain: Expressions and EquationsCluster: Use properties of operations to generate equivalent expressions.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 EquationsCluster: 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.








Not applicable

ELP Standard: Completed by SEI/ELP teachers (later)document.docx Page 20

including CODE

Clarifications of Content StandardAcademic Vocabulary: What academic vocabulary does the student need to know?Algebraic Solutions, Arithmetic Solutions, Inequalities, Equation, Expression, CoefficientsDeclarative 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


USE (variables) CONSTRUCT (simple equations and inequalities) SOLVE (problems in context)

o Simple equationso 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) 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.

AssessmentsProvide 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




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



Integration of Technology: Specific examples that apply the technology standards in the content.Not applicable






Unit: 6 - Inferences about Populations


Grade Level: 7th Grade



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.


Domain: Statistics and ProbabilityCluster: Use random sampling to draw inferences about a population. 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 ProbabilityCluster: 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.


College and Career Readiness Anchor Standards for ReadingIntegration 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 WritingResearch to Build and Present Knowledge

9. Draw evidence from literary or informational texts to support analysis, reflection, and research.




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.



Clarifications of Content StandardAcademic Vocabulary: What academic vocabulary does the student need to know?Population, Sample, Mean, Median, Mode, Range, Measures of Central Tendency


Statistics Population

o Representative Sample

o Representative/valido Random

Measures of center Measures of variability Inferences

o Informal comparative Data Variation Data distribution

o Variabilityo Centero Mean absolute deviation


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) 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?document.docx Page 24

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.

AssessmentsProvide 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?



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 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




Integration of Technology: Specific examples that apply the technology standards in the content. Sales forecast Stock Market Probability, statistics, data analysis Six Thinking Hats: Looking at Decisions from All Points of View

Mind Tools Links for planningo Survey Basicso Science Buddies

Students plan and create an online survey using free survey resource.o Googleo Survey Monkey

Tools for online communication:o Where students can safely connect, collaborate and learn usingo protected email and blogs.o EPalso Live workspace (Google Docs, Windows Live)o Wikiso Blogso Emailo Video conferencingo Chain story (might want to explain what this is and how it can be doneo with technology)o Textingo Student response clickerso Classroom presentationso Web publishing

Students use spreadsheet program (i.e. Excel, Numbers) to compare datasets.(a)Students input two different sets of data, using the formula for calculatingmean.(b)Then compare results for difference between the central measures of thedata.(c)Also use spreadsheet data to make comparative inferences about twopopulations.






Unit: 7 - Probability


Grade Level: 7th




Develop and use probability models. Compare probabilities from a model to observed frequencies.


Domain: Statistics and ProbabilityCluster: Investigate chance processes and develop, use, and evaluate probability models. 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?

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 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 & College and Career Readiness Anchor Standards for Readingdocument.docx Page 27

Writing Anchor and/orMathematical Practicesincluding CODE

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 WritingResearch to Build and Present Knowledge

9. Draw evidence from literary or informational texts to support analysis, reflection, and research.



Not applicable



Clarifications of Content StandardAcademic Vocabulary: What academic vocabulary does the student need to know?Theoretical Probability, Experimental Probability, Sample Space, Compound Event, Tree Diagram


Probability modelo Uniformo Not uniform

Probabilities Events

o Compound Frequencies Outcomes Data Chance o Processo Event Probability of a chance event Relative frequency Organized list Tables Tree diagram Simulation Sample space


DEVELOP/USE o (a uniform probability model)o (a probability model which may not be uniform)

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

AssessmentsProvide 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. What proportion of the time would you expect to roll at least one six?




Standards: 7.SP.5, 7.SP.6, 7.SP.7 and 7.SP.8

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



Integration of Technology: Specific examples that apply the technology standards in the content.Not applicable





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