Math 7 - Santa Ana Unified School District · SAUSD Curriculum Map 2015-2016: Math 7 (Last updated May 18, 2015) 3 4. Model with mathematics Mathematically proficient students can

SAUSD Curriculum Map 2015-2016: Math 7

(Last updated May 18, 2015) 1

Math 7 These curriculum maps are designed to address CCSS Mathematics and Literacy outcomes. The overarching focus for all curriculum maps is building student’s content knowledge and literacy skills as they develop knowledge about the world. Each unit provides several weeks of instruction. Each unit also includes various assessments. Taken as a whole, this curriculum map is designed to give teachers recommendations and some concrete strategies to address the shifts required by CCSS.

Instructional Shifts in Mathematics

Focus:

Focus strongly where the

Standards focus

Focus requires that we significantly narrow and deepen the scope of content in each grade so that students experience concepts at a deeper level.

Instruction engages students through cross-curricular concepts and application. Each unit focuses on implementation of the Math Practices in conjunction with math content.

Effective instruction is framed by performance tasks that engage students and promote inquiry. The tasks are sequenced around a topic leading to the big idea and essential questions in order to provide a clear and explicit purpose for instruction.

Coherence:

Think across grades, and link to major topics within grades

Coherence in our instruction supports students to make connections within and across grade levels.

Problems and activities connect clusters and domains through the art of questioning. A purposeful sequence of lessons build meaning by moving from concrete to abstract,

with new learning built upon prior knowledge and connections made to previous learning.

Coherence promotes mathematical sense making. It is critical to think across grades and examine the progressions in the standards to ensure the development of major topics over time. The emphasis on problem solving, reasoning and proof, communication, representation, and connections require students to build comprehension of mathematical concepts, procedural fluency, and productive disposition.

Rigor:

In major topics, pursue

conceptual understanding,

procedural skills and fluency, and

application

Rigor helps students to read various depths of knowledge by balancing conceptual understanding, procedural skills and fluency, and real-world applications with equal intensity.

Conceptual understanding underpins fluency; fluency is practiced in contextual applications; and applications build conceptual understanding.

These elements may be explicitly addressed separately or at other times combined. Students demonstrate deep conceptual understanding of core math concepts by applying them in new situations, as well as writing and speaking about their understanding. Students will make meaning of content outside of math by applying math concepts to real-world situations.

Each unit contains a balance of challenging, multiple-step problems to teach new mathematics, and exercises to practice mathematical skills



8 Standards for Mathematical Practice

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. They describe how students should learn the content standards, helping them to build agency in math and become college and career ready. The Standards for Mathematical Practice are interwoven into every unit. Individual lessons may focus on one or more of the Math Practices, but every unit must include all eight:

1. Make sense of problems and persevere in solving them

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

2. Reason Abstractly and quantitatively

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

3. Construct viable arguments and critique the reasoning of others

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.



4. Model with mathematics

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

5. Use appropriate tools strategically

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.

6. Attend to precision

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.

7. Look for and make use of structure

Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3(x - y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.

8. Look for and express regularity in repeated reasoning

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y - 2)/(x - 1) = 3. Noticing the regularity in the way terms cancel when expanding (x - 1)(x + 1), (x - 1)(x2 + x + 1), and (x - 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.



English Language Development Standards

The California English Language Development Standards (CA ELD Standards) describe the key knowledge, skills, and abilities in core areas of English language development that students learning English as a new language need in order to access, engage with, and achieve in grade‐level academic content, with particular alignment to the key knowledge, skills, and abilities for achieving college‐ and career‐readiness. ELs must have full access to high quality English language arts, mathematics, science, and social studies content, as well as other subjects, at the same time as they are progressing through the ELD level continuum. The CA ELD Standards are intended to support this dual endeavor by providing fewer, clearer, and higher standards. The ELD Standards are interwoven into every unit.

Interacting in Meaningful Ways

A. Collaborative (engagement in dialogue with others)

1. Exchanging information/ideas via oral communication and conversations

B. Interpretive (comprehension and analysis of written and spoken texts)

5. Listening actively and asking/answering questions about what was heard

8. Analyzing how writers use vocabulary and other language resources

C. Productive (creation of oral presentations and written texts)

9. Expressing information and ideas in oral presentations

11. Supporting opinions or justifying arguments and evaluating others’ opinions or arguments



How to Read this Document

The purpose of this document is to provide an overview of the progression of units of study within a

particular grade level and subject describing what students will achieve by the end of the year. The work of Big Ideas and Essential Questions is to provide an overarching understanding of the mathematics structure that builds a foundation to support the rigor of subsequent grade levels. The Performance Task will assess student learning via complex mathematical situations. Each unit incorporates components of the SAUSD Theoretical Framework and the philosophy of Quality Teaching for English Learners (QTEL). Each of the math units of study highlights the Common Core instructional shifts for mathematics of focus, coherence, and rigor.

The 8 Standards for Mathematical Practice are the key shifts in the pedagogy of the classroom.

These 8 practices are to be interwoven throughout every lesson and taken into consideration during planning. These, along with the ELD Standards, are to be foundational to daily practice.

First, read the Framework Description/Rationale paragraph, as well as the Common Core State Standards. This describes the purpose for the unit and the connections with previous and subsequent units.

The units show the progression of units drawn from various domains.

The timeline tells the length of each unit and when each unit should begin and end.



SAUSD Scope and Sequence for Math 7

Unit 1 Unit 2 Unit 3 Unit 4A

9/01/15 -10/09/15 6 weeks

10/12/15 -11/20/15 6 Weeks

11/30/15-12/18/15

3 Week

01/04/16 – 01/22/16 3 Weeks

Operations with Rational Numbers

Rates, Ratios, and

Proportional Reasoning

Part A

Percent Applications

Expressions, Equations, & Inequalities

****SEMESTER****

Unit 4B Unit 5 Unit 6 Unit 7 Unit 8

02/01/16 – 02/19/16 3 Weeks

02/22/16 – 04/01/16 6 Weeks

04/11/16-04/29/16 3 Weeks

05/02/16 - 05/20/16 3 Weeks

05/23/16 – 6/16/16 4 Weeks

Expressions, Equations, & Inequalities

Geometry Probability

Statistics Enrichment



Math 7 Overview:

As students enter seventh grade, they have an understanding of variables and how to apply properties of operations to write and solve simple one-step equations. They are fluent in all positive rational number operations. Students have been introduced to ratio concepts and applications, concepts of negative rational numbers, absolute value, and all four quadrants of the coordinate plane. Students have a solid foundation for understanding area, surface area, and volume of geometric figures and have been introduced to statistical variability and distributions (Adapted from The Charles A. Dana 9 Center Mathematics Common Core Toolbox 2012). In grade seven instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships, including percentages; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples. (CCSSO 2010, Grade 7 Introduction). Students also work towards fluently solving equations of the form 𝑝𝑥 + 𝑞=𝑟 and (𝑥 + 𝑞)=𝑟.

(From the CA Mathematics Framework for Math 7)

http://www.cde.ca.gov/ci/ma/cf/documents/mathfwgrade7.pdf



Unit 1: Operations with Rational Numbers

(6 weeks 9/01-10/09) Big Idea For a given set of numbers there are relationships that are always true, and

these are the rules that govern arithmetic and algebra. Essential Questions Performance Task Problem of the

Month How can operations with integers be

illustrated in multiple ways? (Models, verbally, and symbolically)

What’s the difference between the opposite and the absolute value of a number?

Division [6th Grade 2007] p.35 Fractions [6th Grade 2010] p.4 Fraction Match [6th Grade 2012] p.5-6 Ribbons and Bows [6th Grade 2013] p.8-9 Brenda’s Brownies [6th Grade 2014] p.2-3 Yogurt [7th Grade 2003] p.59-60 Cat Food [7th Grade 2009] p.74

Got Your Number

POM and

Teacher’s Notes

Unit Topics/Concepts Content Standards Resources

Introduction to Addition & Subtraction of Rational Numbers (including fractions and decimals) 1. Understand “Opposite

quantities combine to make zero.” Additive Inverse

2. Identify the absolute Value as the distance between two numbers on a number line

3. Apply the properties of operations to adding and subtracting rational numbers and represent the information on a number line Commutative Property Associative Property

Interpret sums of rational numbers by describing real-world contexts. Understand subtraction of rational numbers as adding the additive inverse and apply this to real world situations

Introduction to Multiplication & Division of rational numbers (including fractions and decimals) 1. Apply properties of

operations to multiply and divide rational numbers Commutative Property Associative Property

7.NS Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. 7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. a. Describe situations in which opposite quantities

combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (– q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world context.

d. The Apply properties of operations as strategies to add and subtract rational numbers.

7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. a. Understand that multiplication is extended from

fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the

Essential Resources: 7th Grade Framework (pgs 19-22) University of Arizona Progressions (Documents for the Common Core Math Standards: Draft 6-7 Progression on The Number System pg. 9) Instructional Resources: Adopted Text CGP: 231 – +/- Integers & Decimals 232 – x / Integers 113 – Distributive Property 114 – Identity & Inverse

properties 221 – Absolute Value IMP: Discovering Properties (4.0-4.2) http://sausdmath.pbworks.com/w/file/28887951/Discovering%20Properties.pdf Dan Meyer 3-act videos (list and interactive link to Dan Meyer's videos by standard)

http://www.svmimac.org/images/MARS2010-06.pdf

http://noycefdn.org/documents/math/MARS/MARS2003/tft2003gr7.pdf#page=58

http://www.scoe.org/files/mars-grade7.pdf

http://www.insidemathematics.org/assets/problems-of-the-month/got%20your%20number.pdf

http://www.insidemathematics.org/assets/problems-of-the-month/got%20your%20number.pdf

http://www.svmimac.org/images/POM-GotYourNumber-TN.pdf



http://commoncoretools.me/wp-content/uploads/2013/07/ccssm_progression_NS+Number_2013-07-09.pdf

http://commoncoretools.me/wp-content/uploads/2013/07/ccssm_progression_NS+Number_2013-07-09.pdf

http://ime.math.arizona.edu/progressions/



http://sausdmath.pbworks.com/w/file/28887951/Discovering%20Properties.pdf






https://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0



Distributive Property Multiplicative Inverse

2. Interpret products of rational

numbers by describing real-

world situations and

understand that

multiplication of rational

numbers satisfies properties

of operations

Expanding understandings of rational numbers 1. Convert between fractions

and decimals (terminating and repeating) Use equivalent fractions

Use long division

2. Assess the reasonableness of answers using mental computation and estimation. Rounding Front-end

3. Understand that a rational

number is the quotient of

two integers (without a zero

denominator)

4. Interpret products and

quotients by describing in

real-world contexts

rules for multiplying signed numbers. Interpret products of rational numbers by describing 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. 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

MAP Lessons: http://map.mathshell.org/materials/lessons.php Using Positive and

Negative Numbers in Context – 7th Grade Formative Assessment Lesson

MARS- Number System tasks http://map.mathshell.org/materials/stds.php?id=1559#standard1569 ● Division ● A Day Out ● Taxi Cabs

SERP Problem:

http://math.serpmedia.org/diagnostic_teaching/poster-problems

Walking the Line SERP Problem:


Seeing Sums Additional Resources: Video: Discovery Streaming- Introduction to integers.mov (see site for more) Integer War (Cards or dice) (to be developed) Algebra/ 2-color tiles for review

http://map.mathshell.org/materials/lessons.php


http://map.mathshell.org/materials/stds.php?id=1559#standard1569












Unit 1: Operations with Rational Numbers

(Support & Strategies) Framework Description/Rationale

Rationale: This is placed as the second unit to provide a foundation of skills for the work that follows in units 3-7, specifically working with rational numbers with all four operations. This should lead nicely into unit 3 work with expressions and equations and decimal & fractional representations in unit 4 (Percent Applications). Framework Description:

In grade 6, students learn the concept of a negative number and work with absolute value, opposites, and making “0.” In grade 7, students will experience for the first time performing operations with negative numbers. Using the number line and other tools, students will perform operations with integers, fractions, and decimals.

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Use properties of operations to generate equivalent expressions. (See CCSS CA 7th Grade Framework pgs. 19-22 for more details)

Academic Language Support

Instructional Tool/Strategy Examples

Preparing the Learner

Key Vocabulary for Word Bank: Integers Signed Numbers

Positive Negative

Rational Numbers Sum/Difference Deposit/Withdraw/

Overdraft Credit/Debit Profit/Loss Product/Quotient Absolute Value Opposites Additive Inverse Multiplicative Inverse Identity Properties Commutative Property Associative Property Distributive Property Terminating Decimals

Repeating Decimals

Number Line Model (Vector Model) Colored Chip Model (mainly for integers) Money Account Models Class Discussion on the meaning of

operations Pattern Tables Model with Equation Area Models Estimation Strategies:

Front-end estimation with adjusting (using the highest place value and estimating from the front end making adjustments to the estimate by taking into account the remaining amounts),

Rounding and adjusting (students round down or round up and then adjust their estimate depending on how much the rounding affected the original values)

Fractions (prior knowledge) 5th grade - unit fractions - adding unlike

denominators 6th grade - dividing a fraction by a

fraction - concepts of negative

numbers - negative fractions on a

number line By end of 6th grade, students have used every operation with fractions

Activity: Above & Below

Sea Level (7.NS.1.c)

Teacher Notes:





Unit 2: Rates, Ratios, and Proportional Relationships (6 weeks 10/12-11/20)

Big Idea If two quantities vary proportionally, that relationship can be represented in multiple ways.

Essential Questions Performance Task Problem of the Month

What is the constant of proportionality?

How can two quantities be identified as proportional or non-proportional?

How can the constant of proportionality (unit rate) be determined given a table? Graph? Equation? Diagram? Verbal description?

What does a specific point on a graph (x,y) represent?

Leaky Faucet [7th Grade 2002] p.9 Mixing Paints [7th Grade 2003] p.4 Cereal [7th Grade 2004] p.17 Lawn Mowing [7th Grade 2005] p.3 Breakfast of Champions [7th Grade 2012] p.8-9 Is it Proportional? [7th Grade 2014] p.6-7 (See the end of this document for Performance Task descriptions) *Please read SVMI’s document security information: http://www.svmimac.org/memberresources.htm

l

POM: “First Rate” First Rate

(Teacher Notes) Level A Level B Level C Level D Level E

Unit Topics/Concepts Content Standards Resources Unit Rate ● Compute unit rates ● Include complex

fractions Recognize and represent proportional relationships 1. Determine if two

quantities are proportional or non-proportional. a. Prove in a table. b. Graph on a

coordinate plane. (Quadrant I only)

c. Identify ratios as proportional if two conditions are met: Linear Starts at the

origin

2. Identify the constant of proportionality (unit rate) a. In a table b. Graphs c. Equations d. Diagrams e. Verbal description

3. Write equations that

7.RP Analyze proportional relationships and use them to solve real-world and mathematical problems. 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks ½ mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. 7.RP.2 Recognize and represent proportional relationships between quantities. a. Decide whether two quantities are in a

proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of

Essential Resources: CCSS 7th Grade Framework (pgs. 6-11) University of Arizona Progressions (Documents for the Common Core Math Standards: Draft 6-7 Progression on Ratios and Proportional Relationships) Instructional Resources: • Ratios & Proportional

Reasoning Unit • Engage NY – Adapted • IMP Unit Plan: Unit 8 Susan Mercer: 7th

Proportion Rates • 7th Proportions, Rates (Carr

11-12) • Illustrative Mathematics

Track Practice Dan Meyer 3-act videos (list

and interactive link to Dan Meyer's videos by standard)

YouTube Video about Double Number Lines and Tape Diagrams

Adopted Text CGP 421 – Ratios & Rates 422 –Graphing Ratios & Rates

http://www.svmimac.org/images/MARS2002_7A.pdf





http://www.svmimac.org/images/MAC2014-07.pdf

http://www.svmimac.org/memberresources.html

http://www.svmimac.org/memberresources.html

http://www.insidemathematics.org/assets/problems-of-the-month/first%20rate.pdf

http://www.insidemathematics.org/assets/problems-of-the-month/first%20rate.pdf

http://www.svmimac.org/images/POM-FirstRate-TN.pdf


http://commoncoretools.files.wordpress.com/2011/12/ccss_progression_sp_68_2011_12_26_bis.pdf




http://www.engageny.org/resource/grade-7-mathematics-module-1

http://s3.amazonaws.com/illustrativemathematics/illustration_pdfs/000/000/082/original/illustrative_mathematics_82.pdf?1372633563


https://www.youtube.com/watch?v=TGhA9lalIGQ&feature=youtu.be





represents proportional relationships. y=kx

(k = constant of proportionality) 4. Explain what a point

(x,y) means on a graph. a. Focus on the points

(0,0) and (1,r) in the context of the problem where r is the unit rate

the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

7.EE.3 Solve multi-step real-life and mathematical problems posed with positive rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

423 –Speed, Distance & Time 424 –Direct Variation 431 –Converting Measures 432 –Converting between Unit Systems 433 – Dimensional Analysis MAP Lessons: Developing a Sense of Scale –

7th Grade Formative

Assessment Lesson

Proportion and Non-Proportion Situations– 6th Grade Formative Assessment Lesson

Modeling: A Race– 7th Grade Formative Assessment Lesson

Drawing to Scale: Designing a Garden – 7th Grade Formative Assessment Lesson

MARS - Ratios and proportional Relationships http://map.mathshell.org/materials/stds.php?id=1559#standard1569 ● Buses ● Sale ● T-Shirt Sale ● A golden Crown?

SERP Problem: http://math.serpmedia.org/diagnostic_teaching/poster-problems

Drag Racer Dragon Fly











Unit 2: Rates, Ratios, and Proportional Relationships


Rationale: Ratios and Proportional Relationships is the first unit because it is the primary theme of 7th grade. This type of reasoning should be at the foundation of units that follow. Negative values will not be used in this unit and algorithmic equation strategies should not be the focus. Percents will be the focus of a later unit. Framework Description: In addition, standard 7.EE.3, “assess the reasonableness of answers using mental computation and estimation strategies,“ is a recurring focus in each unit. Unit Rate Students further their understanding of unit rate from 6th grade. In 7th grade students will find unit rates in ratios involving

fractional quantities, for example, 11

2

3=

3

6

Students will set up an equation with equivalent fractions and use reasoning about equivalent fractions to solve them, for

example, 11

2

3=

𝑥

12 (See 7th Grade Framework for more details pages (6-11)

Recognize and Represent Proportional Relationships In this sections students will determine if two quantities are proportional by using tables, equations, and graphs. The

shortcut of “cross products” should be examined later as students begin to recognize patterns and why the shortcut works. Students should not be using “cross products” as the first Students will need to identify the unit rate given a table, graph, equation, diagrams, and a verbal description. Knowing the constant of proportionality (unit rate) students will be able to write equations in the form y=kx (See 7th Grade Framework for more details pages 6-11)




Key Vocabulary for Word Bank: ● Identify ● Determine ● Equivalent ● Quantities ● Ratio ● Ratio Table ● Unit Rate (r/1) ● Constant ● Coordinate Plane ● Constant of

Proportionality (k)

● Proportional Relationships

● Scale Drawing ● Scale Factor

Manipulatives and picture representations. Double Sided Number Lines Tape Diagram Graphs Equations Verbal Descriptions focusing on the numerical value. Graph showing the increase of y to x in a” Unit Rate

Triangle”. Translate the graph to an equation in the form of y=kx.

Create a table, graph data and derive that x and y are values that form a ray with an end point at the origin

Record measurements of shapes, determine ratios between two figures and ratios within a single figure, notice that ratios are equal, and use these relationships to create scale drawings using grid paper. Students should also be able to explain why two figures are not scale drawings of one another using their understanding of ratios.

Example: Students can blow-up or shrink pictures on grid paper (foundation for “dilations”). Students can recreate an image using 2 units of length for every 1 unit on the original picture.

Topics:

Equivalent

fractions

Plotting points on a

coordinate grid

(Quadrant 1)

6th grade Concept of a ratio Equivalent ratios Constant speed Unit rate

Teacher Notes:

http://www.cde.ca.gov/ci/ma/cf/documents/aug2013gradeseven.pdf






Unit 3: Percent Applications

(3 weeks 11/30 - 12/18) Big Idea Proportional relationships can be used to solve real-world problems.

Essential Questions Performance Task Problem of the Month How can proportions be used to

solve real-world problems involving percents? (Mark-up, Discounts, tips, tax commission)

How can estimation be used to test the reasonableness of a solution?

Sewing [6th Grade 2009] p.61 Work [7th Grade 2007] p.36 Sales [7th Grade 1999] p.2 Special Offer [7th Grade 2004] p.34 Buying a Camera [7th Grade 2006] p.29-30 Sale [7th Grade 2008] p. 60 Shopper’s Corner [7th Grade 2013] p.10-11

● POM: “Measuring Up” Measuring Up Teacher Notes

● Level A ● Level B ● Level C ● Level D ● Level E


Solve multi-step real-life and mathematical problems

1. Tax 2. Tip 3. Mark-up 4. Discount/Sale price 5. Commission 6. Simple interest 7. Percent error

Use multiple strategies ● Double-sided number line ● Tape diagram ● Visual model ● Equations ● Proportions ● Use estimation strategies to

test the reasonableness of a solution

7.RP Analyze proportional relationships and use them to solve real-world and mathematical problems. 7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

Essential Resources: CCSS 7th Grade Framework (pgs. 12-13) Instructional Resources IMP Unit Plan: Percent

• Percent 1.0 – 1.2 • Percent 6.0 – 6.2 • Percent 3.0 – 3.1 • Percent 7.0 – 7.3 • Percent 4.0 – 4.2 • Percent 8.0 – 8.2 • Percent 5.0 – 5.3

EngageNY: Module 4 Dan Meyer 3-act videos (list and interactive

link to Dan Meyer's videos by standard) MAP Lessons:

Estimation and Approximation: The Money Munchers – 7th Grade Formative Assessment Lesson

Increasing and Decreasing Quantities by a Percent – 7th Grade Formative Assessment Lesson

Georgia Dept. of Ed: Unit 3 (begin on pg. 27)

Adopted Text: CGP 434 – Converting Between Units of Speed 811 – Percents 812 – Changing Fraction & Decimals to Percents 813 – Percent Increases & Decreases 821 – Discounts & Markups 822 – Tips, Tax & Commission 823 - Profit 824 – Simple Interest








http://www.insidemathematics.org/assets/problems-of-the-month/measuring%20up.pdf

http://www.svmimac.org/images/POM-MeasuringUp-TN.pdf


http://sausdmath.pbworks.com/w/browse/#view=ViewFolder&param=Unit%2010%20Activities

http://www.engageny.org/resource/grade-7-mathematics-module-4



https://www.georgiastandards.org/Common-Core/Pages/Math-6-8.aspx

https://www.georgiastandards.org/Common-Core/Pages/Math-6-8.aspx




(Instructional Support & Strategies) Framework Description/Rationale

Rationale: Percents are brought in as the fourth unit to both review and continue the most significant theme of the year (ratios and proportional reasoning) and following skill development in working with rational numbers, expressions, and equations. Framework Description: Multi-step percent problems involving percent increase and decrease--Building on Proportional understanding from previous unit using various representations (see 7th Grade Framework pgs. 12-13 for further explanation, examples, and ways to model problems).




Key Vocabulary Word Bank: ● Percent ● Percentage ● Percent Increase ● Percent Decrease ● Enlargement ● Reduction ● Tax ● Tip/Gratuity ● Markup/Markdown ● Discount ● Sale Price ● Commission ● Fees ● Simple Interest ● Percent Error

Use multiple strategies to work with percents ● double-sided number line ● tape diagram

Example: Gas prices are projected to increase 124% by April 2015. A gallon of gas currently costs $4.17. What is the projected cost of a gallon of gas for April 2015?

● visual model

Example: A sweater is marked down 33%. Its original price was $37.50. What is the price of the sweater before sales tax?

● Equations

Ex: Sale Price = 0.67 x Original Price ● Proportions ● Use estimation strategies to test the

reasonableness of a solution ● Equivalent fractions ● T-tables

From 6th Grade: ● Fluently add, subtract,

multiply, and divide multi-digit decimals using the standard algorithm for each operation.

● Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

● Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Teacher Notes:







Unit 4A and 4B: Expressions, Equations, and Inequalities

(6 weeks 1/04-02/19) Big Idea Any number, measure, numerical expression, algebraic expression, or equation

can be represented in an infinite number of ways that have the same value. Essential Questions Performance Task Problem of the

Month

How can estimation be used to test the reasonableness of a solution?

How can the properties of rational numbers be used to create equivalent expressions and equations?

The Number Cruncher [6th Grade 2001] p.3-4 Festival Lights [6th Grade 2011] p.4-5 Lattice Fence [6th Grade 2012] p.7-8 Facts in Fruit [7th Grade 2012] p.6-7

Tri-Triangles POM and Teacher’s Notes


Expressions with rational numbers and variables (including fractions and decimals) 1. Create an expression for a given

situation using rational numbers. ● Visual model ● Verbal expression ● Numeric/ algebraic expression

2. Create equivalent expressions.

● Combine like terms ● Use properties of rational

numbers ● Distributive Property

(forwards & backwards) Factoring a coefficient

12x + 20 = 4(3x+5) Students may create several different expressions depending upon how they group the quantities in the problem. - Example: Jamie and Ted both get paid an equal hourly wage of $9 per hour. This week, Ted made an additional $27 dollars in overtime. Write an expression that represents the weekly wages of both if J = the number of hours that Jamie worked this week and T = the number of hours Ted worked this week? Can you write the expression in another way? Equations with rational numbers and a single variable “fluently.” 1. Create an equation for a given

situation using rational numbers and variables ● Visual model

7.EE Use properties of operations to generate equivalent expressions. 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. 7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Essential Resources: 7th Grade Framework (pgs. 22-27) University of Arizona Progressions (Documents for the Common Core Math Standards: Draft 6-7 Progression on Expressions and Equations pg. 8) Instructional Resources SAUSD Unit of Study: Expressions (this unit of study covers Expressions part of this unit only and does not cover Equations or Inequalities) IMP- Guess & Check Tables - Solve word problems leading to equations IMP: http://sausdmath.pbworks.com/w/browse/#view=ViewFolder&param=Grade%207 ● Word Problem Expressions

(2.1) ● Evaluating Expressions with

Tiles (1.2) ● Solving Linear Equations (1.0-

1.2) ● Solve my problems (2.2) ● Day3-5 Solving Linear ● Equations ● Toothpicks 2.2

IMP: Word Wall 2.3 Instructional Resources Brad Fulton: Patterns and Function Connection book Linear Functions (Carr Packet) Susan Mercer Unit Y=mx+b Word Problems





http://www.insidemathematics.org/assets/problems-of-the-month/tri-triangles.pdf

http://www.insidemathematics.org/assets/problems-of-the-month/tri-triangles.pdf

http://www.svmimac.org/images/POM-Tri-Triangles-TN.pdf

http://www.svmimac.org/images/POM-Tri-Triangles-TN.pdf

http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/7th.pdf#page=18

http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/7th.pdf#page=18

http://www.google.com/url?q=http%3A%2F%2Fwww.cde.ca.gov%2Fci%2Fma%2Fcf%2Fdocuments%2Faug2013gradeseven.pdf&sa=D&sntz=1&usg=AFQjCNF3mIFS3FS4a57tHrq0q3KdQR0xzg&surl=1&safe=active

http://commoncoretools.files.wordpress.com/2011/04/ccss_progression_ee_2011_04_25.pdf

http://commoncoretools.files.wordpress.com/2011/04/ccss_progression_ee_2011_04_25.pdf



http://sausdmath.pbworks.com/w/browse/#view=ViewAllObjects

http://sausdmath.pbworks.com/w/browse/#view=ViewFolder&param=Grade%207






● Verbal equation ● Numeric/ algebraic equation

2. Solve multi-step real-life and

mathematical problems posed with positive and negative rational numbers in any form. ● Multi-step equations (previously

referred to as one, two, and multi-step equations—note: this is students’ first year seeing equations solved formally using new knowledge of inverse operations)

● Define the variable and use appropriate units.

● d=rt 3. Create equivalent equations.

● Combine like terms. ● Using Properties of Rational

Numbers. ● Distributive Property

(forwards & backwards) ● Apply inverse operations to

solve equations. ● Check solutions by substitution. ● Solve word problems leading to

equations. (See “strategies”) Inequalities with rational numbers and variables

1. Create an inequality for a given situation using rational numbers.

2. Solve word problems leading to inequalities.

3. Apply inverse operations to solve inequalities.

4. Graph the solution for an inequality

5. Interpret the solution. Estimation strategies for calculations with fractions and decimals (assessing reasonableness of answers) Extend from students’ work with whole number operations. (see “strategies”) ● Front-end estimation ● Clustering around an average ● Rounding and adjusting ● Using friendly or compatible numbers

such as factors ● Using benchmark numbers that are

easy to compute

a. Solve word problems leading to

equations of the form px + pq = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

SAM: http://sausdmath.pbworks.com/w/browse/#view=ViewFolder&param=Unit%202%20Activities Cockroach Condos Activity The Crowded Skies (Marc Petrie) Susan Mercer: Variables with Food Dan Meyer 3-act videos (list and interactive link to Dan Meyer's videos by standard) MAP Lesson: http://map.mathshell.org/materials/lessons.php Steps to Solving Equations – 7th

Grade Formative Assessment Lesson

SERP Problem: http://math.serpmedia.org/diagnostic_teaching/poster-problems

On the Download Adopted Text CGP 111 – Variables and Expressions 112 –Simplifying Expressions 121 – Writing Expressions 115 – Associative & Commutative Props. 411 – Graphing equations 413 – Slope Key 123 Solving One-Step Equations 124 – Solving Two-Step Equations 125 –More two-step Equations 126 –Applications of Equations 127 –Understanding Problems Additional Resources: Interactive Algebra Tiles From the Illuminations website (NCTM). Click on the orange “Expand” tab to find tile activities focusing on the Distributive Property. Click on the blue “Solve” tab to find tile activities focusing on solving equations. Click on the purple “Substitute” tab to find tile activities YouTube Video on Bar Models











http://illuminations.nctm.org/Activity.aspx?id=3482

https://www.youtube.com/watch?v=TbayTZvS_bc&sns=em&noredirect=1



Unit 4: Expressions, Equations, and Inequalities


Expressions and equations fall after unit 2 (rational numbers) to build on the understanding of operations

with negative numbers. This unit is also to support students to prepare for units 4-7 (percents, geometry,

probability, and statistics).

(See CCSS CA 7th Grade Framework pgs. 22-27 for more details)




Key Vocabulary for Word Bank: Expression Equation Variable Variable Expression Numeric Expression Like/Unlike Terms Evaluate Simplify Constant Coefficient Distributive Property Inverse Operations Operations Models Inequality Is Greater Than Is Less Than Equal To Strategy: Tree Map: Operation Vocabulary

Modeling with tiles Word walls • color coding like terms • graph inequalities on the number line • drawing a model/diagram • guess and check tables • Tiles • number lines • tape diagram • introduce symbols of inequalities estimating • Solve word problems leading to equations:

Example: The youth group is going on a trip to the state fair. The trip costs $52. Included in that price is $11 for a concert ticket and the cost of 2 passes, one for the rides and one for the game booths. Each of the passes cost the same price. Write an equation representing the cost of the trip and determine the price of one pass.

Estimation Strategies: ● Front-end estimation with adjusting (using the highest place value

and estimating from the front end making adjustments to the estimate by taking into account the remaining amounts),

● Clustering around an average (when the values are close together an average value is selected and multiplied by the number of values to determine an estimate)

● Rounding and adjusting (students round down or round up and then adjust their estimate depending on how much the rounding affected the original values)

● Using friendly or compatible numbers such as factors (students seek to fit numbers together - i.e., rounding to factors and grouping numbers together that have round sums like 100 or 1000)

● Using benchmark numbers that are easy to compute (students select close whole numbers for fractions or decimals to determine an estimate)

From 6th Grade: ● Understand

solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true?

● Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

Teacher Notes:






Unit 5: Geometry

(6 weeks 02/22-04/01) Big Idea Geometric figures can be compared by their relative values.

Essential Questions Performance Task Problem of the Month

What is the relationship between the area and circumference of a circle?

How can we solve for an unknown angle? How is the area of a 2-dimensional figure

related to the volume of a 3-dimensional figure?

What are some real-world applications involving area and volume?

How can we determine whether 3 side lengths will make a triangle?

Which is Bigger? [7th Grade 2004] p.61 Pizza Crusts [7th Grade 2006] p.26-27 Winter Hat [7th Grade 2008] p.58 Sequoia [7th Grade 2009] p.68-69 Merritt Bakery [8th Grade 2004] p.4 Wallpaper [7th Grade 2011] p.3-4 The Poster [7th Grade 2001] p.9 scale

drawing Roxie’s Photo [7th Grade 2013] p.8-9 Geo

Circular Reasoning POM and Teacher’s Notes

Piece it Together POM and Teacher’s Notes


Circles 1. Determine the constants of

proportionality for circle measures. (d=2r, c=πd)

2. Discover π as a proportional relationship between diameter and circumference.

3. Construct circles for specific radii and diameters.

4. Derive the formulas for circumference and area.

5. Use the formulas to solve real-world problems involving circumference and area

6. Given the area or circumference, find the other.

Angles 1. Classify angles

● Supplementary ● Complementary

2. Solve for an unknown angle using multi-step equations involving: ● Supplementary ● Complementary ● Vertical ● Adjacent

Triangles 1. Construct triangles (focus on

measures of angles- freehand, with ruler and protractor,

7.G Draw, construct, and describe geometrical figures and describe the relationships between them. 7.G.2 Draw geometric shapes with given conditions (freehand, with ruler and protractor, and with technology). Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. 7.G.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. 7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. 7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and

Essential Resources: 7th Grade Framework (pgs. 28-31) Instructional Resources IMP Geometry Activities

IMP: GBB Geonets IMP: Good, Better, Best Container

EngageNY: Module 6 Georgia Dept. of Ed: Unit

5 Dan Meyer 3-act videos

(list and interactive link to Dan Meyer's videos by standard)

Adopted Text CGP

721 –Volumes 312 – Area of Polygons 314 –Area of Irregular Shape

MAP Lessons: Possible Triangle

Constructions – 7th Grade Formative Assessment Lesson

Applying Angle Theorems– 7th Grade Formative Assessment Lesson

The Area of a Circle – 7th Grade Formative









http://www.insidemathematics.org/assets/problems-of-the-month/circular%20reasoning.pdf

http://www.insidemathematics.org/assets/problems-of-the-month/circular%20reasoning.pdf

http://www.svmimac.org/images/POM-CircularReasoning-TN.pdf

http://www.svmimac.org/images/POM-CircularReasoning-TN.pdf

http://www.insidemathematics.org/assets/problems-of-the-month/piece%20it%20together.pdf

http://www.svmimac.org/images/POM-PieceItTogether-TN.pdf





http://www.engageny.org/sites/default/files/resource/attachments/math-g7-m6-student-materials.pdf

http://www.engageny.org/sites/default/files/resource/attachments/math-g7-m6-student-materials.pdf

https://www.georgiastandards.org/Common-Core/Common%20Core%20Frameworks/CCGPS_Math_7_7thGrade_Unit5SE.pdf







and with technology 2. Determine what conditions

are needed for a unique triangle or no triangle

Area, volume, surface area 1. Write expressions and

equations to solve for area, volume, surface area of 2-D and 3-dimensional figures ● Triangles, quadrilaterals,

polygons, cubes and right prisms

Slicing Describe the 2-dimensional figures that result from slicing 3-dimensional figures

● Right rectangular prisms ● Right rectangular

pyramids. Scale Drawings

* Avoid using the word “similar,” rather use “scale drawing of each other.” The term “similar” will be defined in Math 8 1. Blow-up or shrink pictures on grid paper (“dilations”) 2. Compute actual side

lengths and new areas. 3. Identify the ratios

between side lengths of two figures.

4. Identify the ratio of side lengths within a single figure.

5. Use the ratio of side lengths to determine the dimensions of scaled figures.

6. Justify mathematically when drawings are to scale and not to scale.

right prisms.

7.G. Draw, construct, and describe geometrical figures and describe the relationships between them.

7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. (Note: Refrain from using term similar here)

Assessment Lesson Using Dimensions:

Designing a Sports Bag – 7th Grade Formative Assessment Lesson

MARS - Geometry http://map.mathshell.org/materials/stds.php?id=1559#standard1598 SERP Problem:


Triangles to Order

Additional Resources Slicing 3-D YouTube video: https://www.youtube.com/watch?v=hlD_j3AtxGs&noredirect=1 Isometric Drawing GeoGebra (free

downloadable resource) Examples of

understanding circle formulas: http://www.illustrativemathematics.org/illustrations/1553








https://www.youtube.com/watch?v=hlD_j3AtxGs&noredirect=1



http://www.geogebra.org/cms/en/

http://www.illustrativemathematics.org/illustrations/1553





Unit 5: Geometry (Instructional Support & Strategies) Framework Description/Rationale

Rationale: Geometry was placed ahead of probability and statistics to ensure its completion by the end of the school year. This also provides further opportunities for practice and extension working with proportional reasoning and working with rational numbers. Framework Description: (7th Grade Framework, pages 28-31) In this section, students work towards developing an understanding of several concepts: Draw and constructing shapes-- (see 7th Grade Framework pg. 29 for brief details) Cross-sections of 3-D shapes Area and Circumference of Circles –focusing on understanding of the formulas and why they work (see 7th Grade

Framework pgs. 30-31 for further explanation and examples). The focus should not be on memorization of formulas. Students focus on applying those formulas to other problems.

Using facts about angles to find unknown angle measurements Dimensions of shapes --find the area, surface area, and volume of 2-D shapes and 3-D shapes composed of other

shapes (see 7th Grade Framework pg. 31 for an example). Scale Drawings--Students solve problems involving scale drawing by applying their understanding of ratios and

proportions. Compute actual lengths and areas and reproduced a scale drawing at a different scale. Students need to be able to determine that there are two important ratios with scale drawings: the ratios between two figures and the ratios within a single figure. Avoid using or defining similar shapes this will be done in 8th grade. (See 7th Grade Framework for more details pages 28-29)




Key Vocabulary for Word Bank: ● Pi ● Circumference ● Area ● Compass ● Protractor ● Complementar

y ● Supplementary ● Vertical ● Adjacent ● Surface Area ● Volume ● 2-Dimensional

(2-D) ● 3-Dimensional

(3-D) ● Slicing

● Polygons, triangles, quadrilaterals, cubes, right prisms, right rectangular pyramids

Model the use of rulers, protractors, compass, and technology. Use strings to construct and name the figure. Double the strings size and construct the

figure. Compare/calculate the ratios. Use the free software called GeoGebra Example: Draw an equilateral triangle with a side of 3 units using a compass and a

straight edge. Use play-dough to create 3D shape and fishing line to cut into 2D shapes. Examine the

cross-sections that result when 3D figures are split. Students describe how two or more objects are related in space (skew line)

Activities: “Discovering Pi”: Students should “know” the formulas for area and circumference by being able to explain why the formula works and how the formula relates to area and circumference. Teachers should not give students any formulas or even the value of π until students discover it (see examples below). After students know the formulas, they should be able to apply their knowledge to solve problems:

Students can also understand the relationship between circumference and area by tracing the circumference of a cylindrical can on patty paper, then measuring the diameter after folding the paper appropriately. Then, students can measure a string the same length as the diameter to realize that the string can go around the circumference approximately three and one-sixth times. This will lead them to understand that c=πd. Therefore, students discover π and the formula for circumference on their own.

Students can cut circles into finer pie pieces (sectors) and arrange them side by side to create a parallelogram, which will create a length that is approximately πr and a height that is approximately r. This will give students the opportunity to come to the conclusion that the approximate area of this shape is πr2

Color and then cut out the angles of the triangles and put them together to see the relationship. Use patty paper to copy one of the vertical angles and apply it over the other angle to compare.

Use 3D geometric shapes that students can hold and see the different shapes that compose a 3D figure. The use of graph paper and nets. For example, bring in real-world objects that students can use to solve for the area, volume, and or surface area (eg cereal boxes, shoe boxes, or cell phones)

Earlier Grade: Acute Obtuse From 6th Grade: Area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles, rectangles, and other shapes





















Unit 6: Probability

(3 weeks 04/11-04/29) Big Idea Collecting and analyzing data can answer questions, and determine further

data collection. Essential Questions Performance Task Problem of the Month

How can a model be used to predict the probability of an event occurring?

How can you determine if a game of chance is fair?

Will it Happen? [7th Grade 2008] p.50 Flora, Freddy, and the Future [8th Grade 2008] p.60-

61 Duck Game [7th Grade 2001] p.5-6 Dice Game [7th Grade 2002] p.2 Fair Game? [7th Grade 2003] p.48-49 Counters [7th Grade 2004] p.46-47

POM: “Fair Game” ● Level A ● Level B ● Level C ● Level D ● Level E

And Teacher’s Notes Diminishing Return POM and Teacher’s Notes


The probability of a chance event occurring is between 0 and 1. 1. Understand that the

probability of an event occurring can be represented as a fraction and understand the range in the probability relates to likelihood (closer to 1--more likely; closer to 0--less likely, and ½--neither likely or unlikely).

2. Collect data and approximate the probability of a chance event occurring.

3. Predict the relative frequency of an event based on a given probability.

4. Investigate both empirical and theoretical probability.

Probability models can be used to find probabilities of events. 1. Develop and represent

probability models and sample spaces for single and compound events. Tree Diagram Table Organized List

7.SP Investigate chance processes and develop, use, and evaluate probability models. 7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. 7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. 7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. a. Develop a uniform probability model by assigning

equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based

Essential Resources: 7th Grade Framework (pgs. 35-37) University of Arizona Progressions (Documents for the Common Core Math Standards: Draft 6-7 Progression on Probability and Statistics pg. 7) Instructional Resources: SAUSD Unit of Study: Probability Dan Meyer 3-act videos (list and interactive link to Dan Meyer's videos by standard) MAP Lessons: http://map.mathshell.org/materials/lessons.php Probability Games

Constructions – 7th Grade Formative Assessment Lesson

Evaluating Statements about Probability – 7th Grade Formative Assessment Lesson

MARS - Statistics and Probability http://map.mathshell







http://www.insidemathematics.org/assets/problems-of-the-month/fair%20games.pdf

http://www.svmimac.org/images/POM-FairGames-TN.pdf

http://www.svmimac.org/images/POM-DiminishingReturn.pdf

http://www.svmimac.org/images/POM-DiminishingReturn-TN.pdf

















Simulation 2. Develop a uniform

probability model by assigning equal probability to all outcomes. (dice)

3. Develop a probability model by observing frequencies in data generated from a chance process.

on the observed frequencies? 7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. a. Understand that, just as with simple events, the

probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

c. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood.

7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

.org/materials/stds.php?id=1559#standard1598

SERP Problem: http://math.serpmedia.org/diagnostic_teaching/poster-problems Try, Try Again

IMP: http://sausdmath.pbworks.com/w/browse/#view=ViewFolder&param=Unit%20Plan%3A%20Probability ● Unit Plan: Probability ● Building A Winning

Die ● Choosing Pair of Dice ● I’m on a Roll ● Spinner Mania Probability Tree Map Inside Math: Fair Game Additional Resources: Science Net Links Marble Mania Activity for definition incorporate: The chance of an event occurring can be described numerically by a number between 0 and 1 inclusive and used to make predictions about other events.








http://sausdmath.pbworks.com/w/browse/#view=ViewFolder&param=Unit%20Plan%3A%20Probability








Unit 6: Probability


Rationale: Probability is brought into the map at this time of year as an important life skill that utilizes proportional reasoning and which commonly includes very engaging hands-on lesson activities and can involve high-stakes real world scenarios. Framework Description: Probability Models and Simulations (simple and compound) (see 7th Grade Framework pg. 35-37 for details and examples)




Key Vocabulary for Word Bank: Probability Theoretical probability Empirical

(Experimental probability)

Simple events Compound events Certain event Impossible event Equally likely events Sample Space Probability model Relative frequency of

outcomes Simulation

Perform experiments: dice, games, spinners, coins, colored cubes

Tree diagrams Frequency tables

Examples: Investigate chance processes and develop, use, and evaluate probability models

Teacher Notes:







Unit 7: Statistics

(3 weeks 05/02 - 05/20) Big Idea Collecting and analyzing data can answer questions, and determine

further data collection. Essential Questions Performance Task Problem of the Month

How can random sampling be used to draw inferences about a population?

How can data sets be used to predict future events?

Basketball [6th Grade 2002] p.2 Baseball Players [6th Grade 2003] p.3-4 Money [6th Grade 2005] p.6-7 Supermarket [7th Grade 2000] TV Hours [7th Grade 2002] p.7-8 Ducklings [7th Grade 2005] p.14-15 Suzi’s Company [7th Grade 2007] p.38-39 Archery [7th Grade 2009] p.71-72 Population [7th Grade 2011] p.8-9

POM: Sorting the Mix Teacher Notes (n/a) POM: “Through the Grapevine“ (Student) http://svmimac.org/images/POM-ThroughTheGrapevine.pdf (Teacher Notes)

● Level A ● Level B ● Level C ● Level D ● Level E


1. Understand that statistics can be used to gain information about a population by examining a sample of the population

2. Understand that generalizations about a population from a sample are valid only if the sample is representative of that population.

3. Understand that random sampling tends to produce representative samples and support valid inferences.

4. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest.

5. Generate multiple samples (of the same size) to gauge the variation in estimates or prediction

6. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. a. Mean b. Median c. Mode d. Range e. Mid-range

7. Assess the degree of visual overlap of two numerical data distributions with similar variability.

8. Compare the mean, median, MAD

7.SP Use random sampling to draw inferences about a population. 7.SP.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. 7.SP.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. 7.SP Draw informal comparative inferences about two populations. 7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. 7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two

Essential Resources: 7th Grade Framework (pgs. 31-34) University of Arizona Progressions (Documents for the Common Core Math Standards: Draft 6-7 Progression on Probability and Statistics pg. 7) Dan Meyer 3-act videos (list and interactive link to Dan Meyer's videos by standard) Instructional Resources: MAP Lessons: http://map.mathshell.org/materials/lessons.php Estimating:

Counting Trees – 7th Grade Formative Assessment Lesson

Relative Frequency 7th Grade Formative Assessment Lesson

Comparing Data – 7th Grade Formative Assessment Lesson








http://www.insidemathematics.org/assets/problems-of-the-month/sorting%20the%20mix.pdf

http://svmimac.org/images/POM-ThroughTheGrapevine.pdf



http://svmimac.org/images/POM-ThroughTheGrapevine-TN.pdf














(mean absolute deviation), and interquartile range from two different sets of data.

9. Measure the differences between the centers of two populations as a multiple of a measure of variability

populations. 7.RP Analyze proportional relationships and use them to solve real-world and mathematical problems. 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies.

Adopted Text CGP 611 – Median & Range 612 – Box & Whisker Plots 614 – Stem & Leaf Plots 621 – Making Scatter Plots 622 – Shapes of Scatter Plots Additional Resources: Illustrative Mathematics https://www.illustrativemathematics.org/7 Sampling for a Rock Concert

https://www.illustrativemathematics.org/7

https://www.illustrativemathematics.org/7

http://www.nsa.gov/academia/_files/collected_learning/Sampling_for_a_Rock_Concert.pdf

http://www.nsa.gov/academia/_files/collected_learning/Sampling_for_a_Rock_Concert.pdf



Unit 7: Statistics


Rationale: This is the final unit that introduces new content and skills from the 7th grade standards. Students will utilize proportional reasoning in their use of samples to represent larger populations. The unit should be completed well before testing, allowing ample time before testing for SBAC prep and review, then enrichment, review, and/or preparation for the following year, after the SBAC. Framework Description: In this section, students work towards developing a deeper understanding of the following:

Using samples to represent larger populations - applying understanding of proportions to develop this idea (see 7th Grade Framework Pg. 31-33 for further explanation and examples).

Using measures of center and variability to compare two populations--building on their understanding of mean, median, mean, inter-quartile range, and mean absolute deviation students compare data from two populations (see 7th Grade Framework pgs. 33-34 for further explanation).




Key Vocabulary for Word Bank: ● Inferences ● Representative Sample ● Biased/Unbiased ● Random Sample ● Population ● Line Plot ● Box Plot ● Measures of Center:

● Mean ● Median ● Mode ● Range

● Maximum ● Minimum ● Outlier ● Upper Quartile ● Lower Quartile ● Mid-range ● Frequency Table

● Conduct surveys web-based software spread sheets box plots tables probability models

Topics from 6th grade:

Develop understanding of statistical

variability.

1. Recognize a statistical question as one

that anticipates variability in the data related

to the question

3. Recognize that a measure of center for a

numerical data set summarizes all of its

values with a single number,

4. Display numerical data in plots on a

number line, including dot plots, histograms,

and box plots.

5. Summarize numerical data sets in relation

to their context

c. Giving quantitative measures of center

(median and/or mean) and variability

(interquartile range and/or mean absolute

deviation), as well as describing any overall

pattern and any striking deviations from the

overall pattern with reference to the context

in which the data were gathered.

d. Relating the choice of measures of center

and variability to the shape of the data

distribution and the context in which the data

were gathered.

Teacher Notes:









https://education.ohio.gov/getattachment/Topics/Academic-Content-Standards/Mathematics/Resources-Ohio-s-New-Learning-Standards-K-12-Mathe/K-8-Standards-Progressions-2-14-12.pdf.aspx



Performance Task Descriptions by Unit

Unit 1:Operations with Rational Numbers

Unit 2: Ratios and Proportional Relationships


Division [6th Grade 2007] (Relate a

given division calculation to the

appropriate situation)

Fractions [6th Grade 2010] (Given 6

statements to determine if correct

or not; if correct, give another

example and if incorrect, correct

the statement)

Fraction Match [6th Grade] (Order

rational numbers on a number

line; translate between different

rational number representations;

perform operations on rational

numbers and determine an

unknown in rational number

sentences)

Ribbons and Bows [6th Grade 2013]

(Division and multiplication of

fractions by fractions;

understanding of a unit rate and

ratio reasoning)

Brenda’s Brownies [6th Grade 2014]

(Divide a rectangle into 15 equal

sized brownies; determine the

dimensions of just one of these

brownies; interpret and compute

quotients of fractions by using

visual fraction models and

equations to represent problems)

Yogurt [7th Grade 2003] (Use

fractions and percents with

conversion of different units and

percent of decrease)

Cat Food [7th Grade 2009] (Use

rounded numbers appropriately in

the prescribed context; work

flexibly with fractions and

decimals in understanding rates)

Leaky Faucet [7th Grade 2002] (Use

rates, proportional reasoning and

conversions)

Mixing Paints [7th Grade 2003] (Use

ratios and percents to determine

the amount of each color in a

mixture)

Cereal [7th Grade 2004] (Compare

the amount of protein in two

different cereals using

ratios/proportions)

Lawn Mowing [7th Grade 2005]

(Work with ratios and proportional

reasoning)

Breakfast of Champions [7th Grade

2012] (Solve problems with rates;

determine unit cost; compare and

determine the larger rate; use

division with rational numbers)

Is it Proportional? [7th Grade 2014]

(Write an equation to represent a

given math story or graph;

determine if this equation is directly

proportional or not; create and

write a proportional situation)

Sewing [6th Grade 2009] (Use

decimals, fractions, percents

and constraints to determine a

bill of sale for sewing supplies)

Work [7th Grade 2007] (Match

written phrases with numerical

expressions)

Sales [7th Grade 1999] (Work

with increase and decrease of

percent changes)

Special Offer [7th Grade 2004]

(Calculate and compare percent

decreases)

Buying a Camera [7th Grade

2006] (Work with percentage

increase and decrease)

Sale [7th Grade 2008] (Compare

sales discount offers and

percents for greatest and

smallest price reductions)

Shopper’s Corner [7th Grade

2013] (Use proportional

relationships to solve multi-step

percent problems’; markups,

markdowns, and percent of

decrease)




Unit 4: Expressions, Equations, and Inequalities

Unit 5: Geometry

The Number Cruncher [6th Grade 2001] (Relate

simple function rules and pairs of values)

Festival Lights [6th Grade 2011] (Extend a pictorial

pattern and a numeric table for two different

segments of one pattern; determine the inverse

relationship of a proportional function; generalize a

direct variation rule)

Lattice Fence [6th Grade 2012] (Identify polygons in

a geometric growing pattern; extend a linear

pattern; determine the inverse relationship of a

proportional function; generalize a direct variation

rule)

Facts in Fruit [7th Grade 2012] (Use properties of

numbers to find unknowns and solve equations)

Which is Bigger? [7th Grade 2004] (Use measurements

from a scale drawing to determine measurements in

real life of a cylindrical vase)

Pizza Crusts [7th Grade 2006] (Find areas and

perimeters of rectangular and circular shapes)

Winter Hat [7th Grade 2008] (Find the surface area of a

shape with circles, rectangles, and trapezoids)

Sequoia [7th Grade 2009] (Understand the relationship

between diameter, radius, and circumference; use

proportion or scale factor)

Merritt Bakery [8th Grade 2004] (Use circle diameter and

circumference relationship; write one variable in terms

of another variable and write a mathematical

explanation of why a given statement is incorrect)

Wallpaper [7th Grade 2011] (Understand how to

determine the number of strips of wallpaper and rolls of

wallpaper needed to cover a wall with given dimensions

for the wall and the wallpaper)

Roxie’s Photo [7th Grade 2013] (Work with ratios and

proportional relationships in the context of enlarging

and reducing a given picture)




Unit 6: Probability Unit 7: Statistics

Will it Happen? [7th Grade 2008] (Describe events as

likely/unlikely; find numerical probability of various

outcomes of rolling a number cube)

Flora, Freddy, and the Future [8th Grade 2008] (Use terms

“likely” and “unlikely” for events and use numbers 0 to 1 as

measures of likelihood)

Duck Game [7th Grade 2001] (Find probabilities of a game with

different constraints)

Dice Game [7th Grade 2002] (Find all possible outcomes in a

table and calculate probabilities)

Fair Game? [7th Grade 2003] (Use probability to judge the

fairness of a game)

Counters [7th Grade 2004] (Probability of selecting a

particular color from a bag and then determining the fairness

of attributing $ amounts to the color in a game at the fair)

Basketball [6th Grade 2002] (Interpret results of a survey;

use mode; use percents)

Basketball Players [6th Grade 2003] (Work with the

mean)

Money [6th Grade 2005] (Interpret and compare bar

graphs)

Supermarket [7th Grade 2000] (Use measures of central

tendency for comparison)

TV Hours [7th Grade 2002] (Analysis of data from a stem

and leaf plot]

Ducklings [7th Grade 2005] (Use a frequency table to

determine median and mean of data)

Suzi’s Company [7th Grade 2007] (Complete a given data

table and interpret the data to determine and interpret

the mean, median, mode)

Archery [7th Grade 2009] (Use given data, draw a box and

whiskers plot and make interpretations and comparisons

between the two data sets)

Population [7th Grade 2011] (Interpret two back-to-back

histograms on population data; calculate the percent of

increase in population between 1950 and 2000; calculate

the population in 2050 if this rate continues; describe

differences between the two back-to-back histograms)