TOWNSHIP OF UNION PUBLIC SCHOOLS

Grade 7 MathematicsCurriculum Guide 2013-14

Approved July 2013

Board Members

Francis “Ray” Perkins, President

Richard Galante, Vice President

David Arminio

Susana Cooley

Guy Francis

Linda Gaglione

Thomas Layden

Versie McNeil

Vito Nufrio

TOWNSHIP OF UNION PUBLIC SCHOOLSAdministration

District Superintendent …………………………………………………………………...………………………..Dr. Patrick Martin

Assistant Superintendent………….……………………………….………………………….…………………… Dr. Noreen Lishak

Assistant Superintendent ………..………………………………………………..……………………….…….…….Mr. Greg Tatum

Director of Elementary Curriculum ……………………………….………………………………..……………Mrs. Tiffany Moutis

Director of Student Information/Technology ………………………………..………………………….…………. Ms. Ann M. Hart

DEPARTMENT SUPERVISORS

Language Arts/Social Studies K-6 ……..………………………………….…………………………………….. Mr. Robert Ghiretti

Mathematics K-6; Science K-5…………………………………………….………………………………………. Ms. Deborah Ford

Mathematics 7-12…………………………………………….……………………………………...……………. Mr. Jason Mauriello

Guidance K-12/SAC …..………………………………………………………………………………….…………..Ms. Nicole Ahern

Language Arts/Library Services 7-12 ….………………………………….…………………………………….…Ms. Mary Malyska

Science 6-12 ……………………………...………………………………….………………………………….Ms. Maureen Guilfoyle

Social Studies/Business 7-12………………………………………………………………………………..…….Mrs. Libby Galante

World Language/ESL/Career Education>>………………………………………………………………….….Ms. Yvonne Lorenzo

Art/Music …………………………………………………………………………………………………………..….Mr. Ronald Rago

Physical Education/Health ………………………………………………………………………………………...…. Ms. Linda Ionta

Curriculum Committee7th Grade Mathematics

Robyn L. Furman

Jillian Semon

Lauren Wojcik

Table of Contents

Title Page

Board Members

Administration

Department Supervisors

Curriculum Committee

Table of Content

District Mission/Philosophy Statement

District Goals

Course Description

Recommended Texts

Course Proficiencies

Curriculum Units

Appendix: New Jersey Common Core State Standards

Mission Statement

The Township of Union Board of Education believes that every child is entitled to an education designed to meet his or her individual needs in an environment that is conducive to learning. State standards, federal and state mandates, and local goals and objectives, along with community input, must be reviewed and evaluated on a regular basis to ensure that an atmosphere of learning is both encouraged and implemented. Furthermore, any disruption to or interference with a healthy and safe educational environment must be addressed, corrected, or when necessary, removed in order for the district to maintain the appropriate educational setting.

Philosophy Statement

The Township of Union Public School District, as a societal agency, reflects democratic ideals and concepts through its educational practices. It is the belief of the Board of Education that a primary function of the Township of Union Public School System is to formulate a learning climate conducive to the needs of all students in general, providing therein for individual differences. The school operates as a partner with the home and community.

Statement of District Goals

Develop reading, writing, speaking, listening, and mathematical skills. Develop a pride in work and a feeling of self-worth, self-reliance, and self

discipline. Acquire and use the skills and habits involved in critical and constructive

thinking. Develop a code of behavior based on moral and ethical principals. Work with others cooperatively. Acquire a knowledge and appreciation of the historical record of human

achievement and failures and current societal issues. Acquire a knowledge and understanding of the physical and biological

sciences. Participate effectively and efficiently in economic life and the development

of skills to enter a specific field of work. Appreciate and understand literature, art, music, and other cultural

activities. Develop an understanding of the historical and cultural heritage. Develop a concern for the proper use and/or preservation of natural

resources. Develop basic skills in sports and other forms of recreation.

Course Description

The seventh grade math curriculum is currently aligned with the CCSS. All skills required for mastery are a part of the seventh grade proficiency list. All lessons are created to address differentiated learning styles to ensure each lesson’s objective is obtained by each student. The seventh grade curriculum focuses on the units of ratios and proportional relationships, the number system, equations and expressions, geometry, and statistics and probability.

Recommended Textbooks

Holt McDougal 2012 Common Core Burger Series

Course Proficiencies

See Common Core State Standards

Curriculum Units

Unit 1: Ratios and Proportional Relationships Unit 2: The Number System

Unit 3: Expressions and Equations Unit 4: Geometry

Unit 5: Statistics and Probability

Pacing Guide7th Grade

Content Number of Days

Unit 1: Ratios and Proportional Relationships 44 days

Unit 2: The Number System 30 days

Unit 3: Expressions and Equations 32 days

Unit 4: Geometry 32 days

Unit 5: Statistics and Probability 42 days

TOTAL 180 DAYS

Unit 1: Ratios and Proportional Relationships

Essential QuestionsInstructional Objectives/ Skills and Benchmarks

(CPIs)Activities

Real world applications (tiered to ability), stations, problems around the room, ecr, tic-tac-toe, and choice menus across all units

Assessments

Quizzes, Chapter Tests, District Proficiency Exams,Performance Assessments,Cross-curricular Projects, spiral reviews, Teacher Observation across all units.

How can we represent proportional relationships?

Given a relationship, how can we determine if it is proportional?

How can we represent unit rates associated with fractions?

How can we identify the constant of proportionality?

How can we write equations to represent proportional relationships?

How can we use two points

1. (7.RP.A.1) Compute unit rates associated with ratios of fractions, including ratiosof lengths, areas and other quantities measured in like or differentunits. For example, if a person walks 1/2 mile in each 1/4 hour, computethe unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2miles per hour.2. (7.RP.A.2) Recognize and represent proportional

School Store (Students shop in another classroom, finding discount, tax)

Shopping School Supplies (Students use coupons from circulars to shop for school supplies and then find total with tax)

Better Buy (Open-Ended)

Planning a Party Activity (Students adjust serving sizes and find total costs of ingredients)

Dot Patterns Exemplar

Successive Percents ECR (Students compare a sale of 30%, then 10% with a sale of 40%)

Discount/Mark-Up Journal (Students find the discounted price of 20% off,

on a graph to represent proportional relationships?

How can we use proportions to solve real world problems involving percent discount, tax, commission, mark-up, interest, and scale drawings?

relationships betweenquantities.a. (7.RP.A.2a) Decide whether two quantities are in a proportional relationship,e.g., by testing for equivalent ratios in a table or graphing on acoordinate plane and observing whether the graph is a straightline through the origin.b. (7.RP.A.2b) Identify the constant of proportionality (unit rate) in tables,graphs, equations, diagrams, and verbal descriptions ofproportional relationships.c. (7.RP.A.2c) Represent proportional relationships by equations. For example, iftotal cost t is proportional to the number n of items

(Students choose AND explain which items are a better buy comparing different sizes and costs based on pictures and prices around the room)

Biggest Loser (Students watch a clip from the show “Biggest Loser”, they record their starting and ending weights, and find their percent of change. Before they do calculations, they predict who will be voted off, discuss if the weight loss is a fair way to win the game, then introduce the percent of weight loss.)

Comparing Ratio and Rates around the room activities (Students will compete in different activities around the room such as hitting target, making a basketball shop, hula hooping, and jump

then the mark-up of 20% on discounted price, then compare and explain the answers)

Let’s Spend Some Money Webquest- letsspendsomemoney.weebly.com

Album Release PartyWebquest-albumrealeaseparty.weebly.com

“Create Your Dream Home” (Students create a scale drawing of their dream home using a scale, showing all actual and scale measurements)

purchased ata constant price p, the relationship between the total cost and thenumber of items can be expressed as t = pn.d. (7.RP.A.2d) Explain what a point (x, y) on the graph of a proportionalrelationship means in terms of the situation, with special attentionto the points (0, 0) and (1, r) where r is the unit rate.3. (7.RP.A.3) Use proportional relationships to solve multistep ratio and percentproblems. Examples: simple interest, tax, markups and markdowns,gratuities and commissions, fees, percent increase and decrease, percenterror.

roping. Based on different times they need to find each person’s unit rate to find the winner of each competition.)

Decimal to Fraction to Percent Pair Up (Students will be given cards with a decimal, fraction or percent and have to find their match)

Unit 2: The Number System

Essential QuestionsInstructional Objectives/ Skills

and Benchmarks (CPIs) Activities Assessments

How can we use a number line to determine the placement of rational numbers after given operations?

Why is the additive inverse property to subtraction problems true? How can students use a number line to show that the distance between two points is the absolute value of the difference between their two coordinates?

How can we represent real world problems as multiplication and division of rational

1. (7.NS.A.1) Apply and extend previous understandings of addition and subtractionto add and subtract rational numbers; represent addition andsubtraction on a horizontal or vertical number line diagram.a. (7.NS.A.1a) Describe situations in which opposite quantities combine tomake 0. For example, a hydrogen atom has 0 charge because its twoconstituents are oppositely charged.b. (7.NS.A.1b) Understand p + q as the number located a distance |q| from p,

Gas Prices, Gas Prices, Ugh!!! (Students compare two scenarios, relating to changing gas prices. When should we have gotten gas?)

Bulls Eye Operations(Target on the floor with various numbers, throw two coins at integers, perform stated operation)

Human Number Line (Students order themselves from least to greatest based on the

Integer Project (Students explain rules for operations with integers, give examples of each, and display on poster)

Integer Perfect 10

Ordering Rational Numbers ECR

Decimal to Fraction ECR – ( given points plotted on a number line, create a decimal and a fraction that could represent each point. Find a decimal and a fraction between the two.)

Brochure-

numbers?

Why can a repeating decimal be written as a fraction?

How can we show a decimal represents a rational number?

How can we apply rational numbers and operations to solve real world problems?

How can we compare and contrast numbers?

What makes a computational strategy both effective and efficient?

How do operations affect numbers?

How can we decide when to use an exact

in the positive or negative direction depending on whether q ispositive or negative. Show that a number and its opposite havea sum of 0 (are additive inverses). Interpret sums of rationalnumbers by describing real-world contexts.c. (7.NS.A.1c) Understand subtraction of rational numbers as adding theadditive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value oftheir difference, and apply this principle in real-world contexts.d. (7.NS.A.1d) Apply properties of operations as strategies to add and subtractrational numbers.2. (7.NS.A.2) Apply and extend previous understandings of

integer they are holding, including absolute values)

Graphic Organizer (students fill in graphic organizer giving explanations of properties with examples)

24 game

Totally Mental (Multiplying Fractions) (Students use playing cards, A thru 9. Place the value of the card chosen in any empty box on game board. Once each player’s board in filled, the player with the largest product wins)

Integer War- Red cards represent negative and black cards represent positives. Flip two cards and find their

Use the rules for fractions, decimals and percents to create a how to brochure.

Integer ECR-If x is a positive integer and y is a negative integer what will the sum of y and the opposite of x be?

Absolute Value ECR-Are there any values for integers x and y such that | x + y| < |x| + |y|?

Pizza, Pizza, Pizza!!!! (Students solve a multi-step pizza question relating to fractions, then show the final answer in percent form.)

answer and when to use an estimate?

multiplication anddivision and of fractions to multiply and divide rational numbers.

a. (7.NS.A.2a) Understand that multiplication is extended from fractions torational numbers by requiring that operations continue tosatisfy the properties of operations, particularly the distributiveproperty, leading to products such as (–1)(–1) = 1 and the rulesfor multiplying signed numbers. Interpret products of rationalnumbers by describing real-world contexts.b. (7.NS.A.2b) Understand that integers can be divided, provided that the divisoris not zero, and every quotient of integers (with non-zero divisor)is a rational number. If p

sum. The player with the greatest sum wins the cards.

Fraction Distraction (Students use estimation to arrive at two different scenarios, comparing to the situation presented.)

Fraction Game board-Given a game board with various fractions, flip a coin twice two land on two different fractions and roll a die to determine if you need to add, subtract, multiply and divide them.

and q are integers, then –(p/q) = (–p)/q =p/(–q). Interpret quotients of rational numbers by describing real world contexts.c. (7.NS.A.2c) Apply properties of operations as strategies to multiply anddivide rational numbers.d. (7.NS.A.2d) Convert a rational number to a decimal using long division; knowthat the decimal form of a rational number terminates in 0s or eventually repeats.3. (7.NS.A.3) Solve real-world and mathematical problems involving the fouroperations with rational numbers.

Unit 3: Expressions and Equations

Essential QuestionsInstructional Objectives/ Skills and Benchmarks

(CPIs)Activities Assessments

How can we use equations and expression to represent real world problems?

How can we use variables in equations and expressions to represent real world quantities?

How can we use equivalent expressions to make a solution simpler?

How can we use rational numbers in equations and expressions and how

Use properties of operations to generate equivalent expressions.1. (7.EE.A.1) Apply properties of operations as strategies to add, subtract, factor,and expand linear expressions with rational coefficients.2. (7.EE.A.2) Understand that rewriting an expression in different forms in aproblem context can shed light on the problem and how the quantitiesin it are related. For example, a + 0.05a =

Human PEMDAS line(students stand in line in front of class to show the order of operations)

Order of Operations Bingo(bingo board with answers, teacher calls out expression, students solve to see if they have answer)

Bowling Game(students race to use order of operations to get every solution from 1-10 using the 4 numbers they roll with a number cube)

Write your own word problems(Based on an expression,

“Expression/Equation Match”(match sentence with its written expression and put in a table)

“??Inequality??”(Students match the written inequality statement with its equation, then solve and graph. Students display their answers on a poster)

ECR’s” (Solve extended constructed

can we use estimation to check the reasonableness of our answer?

How can we use sentences to verbally communicate our understanding of solutions to equations, expressions, and inequalities?

What makes an algebraic algorithm both effective and efficient?

1.05a means that “increase by5%” is the same as “multiply by 1.05.”Solve real-life and mathematical problems using numerical andalgebraic expressions and equations.3. (7.EE.B.3) Solve multi-step real-life and mathematical problems posed withpositive and negative rational numbers in any form (whole numbers,fractions, and decimals), using tools strategically. Apply properties ofoperations to calculate with numbers in any form; convert betweenforms as appropriate; and assess the reasonableness of answers usingmental computation and estimation strategies. For example: If a woman

equation, and/or inequality write a corresponding word problem that would require you to write that expression, equation, or inequality as your solution. Solve and interpret what the solution means.)

Hands on equation(Use the hands on equation system to show the students how solving an equation is like balancing a scale. Continue to use this to show how the distributive property, clt, and variables on both sides are all extensions to two step equations.)

responses which require students to write expressions, equations, and inequalities to solve)

making $25 an hour gets a 10% raise, she will make an additional 1/10 ofher salary an hour, or $2.50, for a new salary of $27.50. If you want to placea towel bar 9 3/4 inches long in the center of a door that is 27 1/2 incheswide, you will need to place the bar about 9 inches from each edge; thisestimate can be used as a check on the exact computation.4. (7.EE.B.4) Use variables to represent quantities in a real-world or mathematicalproblem, and construct simple equations and inequalities to solveproblems by reasoning about the quantities.a. (7.EE.B.4a) Solve word problems leading to equations of the form px

+ q = rand p(x + q) = r, where p, q, and r are specific rational numbers.Solve equations of these forms fluently. Compare an algebraicsolution to an arithmetic solution, identifying the sequence of theoperations used in each approach. For example, the perimeter of arectangle is 54 cm. Its length is 6 cm. What is its width?b. (7.EE.B.4b) Solve word problems leading to inequalities of the form px + q > ror px + q < r, where p, q, and r are specific rational numbers. Graphthe solution set of the inequality and interpret it in the context ofthe 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.

Unit 4: Geometry

Essential QuestionsInstructional Objectives/ Skills and Benchmarks

(CPIs)Activities Assessments

How can we determine the space occupied by 2-D figures?

How can we represent

Geometry 7.GDraw, construct, and describe geometrical figures and describe

How Am I Special (Students create a “How Am I Special” poster, describing all different polygons, showing examples of each)

“Geometry For Dummies”(students create a book explaining properties and examples of angles, quadrilaterals, triangles)

the size and capacity of 3-D figures?

What 2-D figure results from slicing a 3-D figure?

How can we connect geometry to real world problems?

How can we use algebraic expressions and equations to represent and find relationships amongst different angles?

How can spatial relationships be described by careful use of geometric language?

How do geometric relationships help in solving problems and/or make sense of phenomena?

therelationships between them.1. (7.G.A.1) Solve problems involving scale drawings of geometric figures,including computing and reproducing a scale drawing at a different scale.2. (7.G.A.2) Draw (freehand, with ruler and protractor, and with technology)geometric shapes with given conditions. Focus on constructingtriangles from three measures of angles or sides, noticing when theconditions determine a unique triangle, more than one triangle, or notriangle.3. (7.G.A.3) Describe the two-dimensional figures that result from slicing threedimensionalfigures, as in plane

Classroom Coordinate Plane (Students physically plot points on floor coordinate plane to create a figure)

Measure Me (Students are given a variety of objects to measure in cm & in. to the nearest whole unit, then determine which is the best measurement for each object)

Create a Figure (Students

“Create Your Dream Home” (Students create a scale drawing of their dream home using a scale, showing all actual and scale measurements)

ECRHave students solve various ECR questions dealing with area and circumference of 2-D shapes and volume and surface area of 3-D shapes.

How can geometric/algebraic relationships best be represented and verified?

How can measurements be used to solve problems?

sections of right rectangular prismsand right rectangular pyramids.Solve real-life and mathematical problems involving angle measure,area, surface area, and volume.4. (7.G.B.4) Know the formulas for the area and circumference of a circle and usethem to solve problems; give an informal derivation of the relationshipbetween the circumference and area of a circle.5. (7.G.B.5) Use facts about supplementary, complementary, vertical, and adjacentangles in a multi-step problem to write and solve simple equations foran unknown angle in a

use manipulative shapes to create complex figures, then find the total area of their figure)

Solve for Surface Area and Volume of 3-D objects(students will find the surface area and volume of 3-D objects such as a can, cereal box, tissue box, party hat, etc)

Find missing angles(given two parallel lines that can be slide up and down a transversal, have students slide one parallel line onto another to see angle relationships. Given two intersecting lines, have students move the lines toward each other and away from each other to make conclusions about vertical angles.)

Cross Section(Have students cut through a 3-D shape to explore cross sections.)

figure.6. (7.G.B.6) Solve real-world and mathematical problems involving area, volumeand surface area of two- and three-dimensional objects composed oftriangles, quadrilaterals, polygons, cubes, and right prisms.

Unit 5: Statistics and Probability

Essential QuestionsInstructional Objectives/ Skills and Benchmarks

(CPIs)Activities Assessments

How can we distinguish between valid and invalid data samples?

How can we use random sampling to produce a representative sample?

How can we make inferences about a population?

How can we examine variations in estimates using multiple samples of varying sizes?

How can we examine the differences between experimental and theoretical probability?

How can we use experimental probability to make predictions?

What does the likeness of an event tell us?

Use random sampling to draw inferences about a population.1. (7.SP.A.1) Understand that statistics can be used to gain information about apopulation by examining a sample of the population; generalizationsabout a population from a sample are valid only if the sample isrepresentative of that population. Understand that random samplingtends to produce representative samples and support valid inferences.2. (7.SP.A.2) Use data from a random sample to draw inferences about a populationwith an unknown characteristic of interest.

Horse Race (Roll 2 dice, horses numbered 1-12 are racing, students choose the horse they want to win, see results; compare possible outcomes and fairness of race)

Lets Take a Spin (Students look at a spinner with pieces unevenly divided. They predict who they think will win a proposed game. Then students are asked to change the rules of the game – not the division of the spinner – to make the game fair.)

Pi Day Activity:(Have students make a frequency table from the first 100 digits of pi, make a bar graph and analyze the percent of each digit that appears.)

“Analyze This” Project(Using student surveys, create different representations of data, analyzing using mean, median, mode, range.)

Data Analysis Choice Menu (A selection of different activities involving data analysis that students choose from to show mastery of unit.)

Raffle Problem

What inferences can be made?

How can we use tree diagrams, organized lists, and the counting principle to find the total outcomes? How can we use these representations to find the probability of events?

How can the collection, organization, interpretation, and display of data be used to answer questions?

How can experimental and theoretical probabilities be used to make predictions or draw conclusions?

How can attributes be used to classify data/objects?

Generate multiple samples(or simulated samples) of the same size to gauge the variation inestimates or predictions. For example, estimate the mean word length ina book by randomly sampling words from the book; predict the winner ofa school election based on randomly sampled survey data. Gauge how faroff the estimate or prediction might be.Draw informal comparative inferences about two populations.3. (7.SP.B.3) Informally assess the degree of visual overlap of two numericaldata distributions with similar variabilities, measuring the differencebetween the centers by

What is the best way to solve this? What counting strategy works best here?

How can visual tools such as networks (vertex-edge graphs) be used to answer questions?

How can algorithmic thinking be used to solve problems?

expressing it as a multiple of a measure ofvariability. For example, the mean height of players on the basketballteam is 10 cm greater than the mean height of players on the soccer team,about twice the variability (mean absolute deviation) on either team; ona dot plot, the separation between the two distributions of heights isnoticeable.4. (7.SP.B.4) Use measures of center and measures of variability for numerical datafrom random samples to draw informal comparative inferences abouttwo populations. For example, decide whether the words in a chapterof a seventh-grade science book are

generally longer than the words in achapter of a fourth-grade science book.Investigate chance processes and develop, use, and evaluateprobability models.5. (7.SP.C.5) Understand that the probability of a chance event is a numberbetween 0 and 1 that expresses the likelihood of the event occurring.Larger numbers indicate greater likelihood. A probability near 0indicates an unlikely event, a probability around 1/2 indicates an eventthat is neither unlikely nor likely, and a probability near 1 indicates alikely event.

New Jersey Scoring Rubric

Table C.4: NJ ASK Generic Mathematics Rubric3-Point

ResponseThe response shows complete understanding of the problem's essential mathematicalconcepts. The student executes procedures completely and gives relevant responses to

all parts of the task. The response contains few minor errors, if any. The responsecontains a clear, effective explanation detailing how the problem was solved so that the

reader does not need to infer how and why decisions were made.2-Point

Response

The response shows nearly complete understanding of the problem's essentialmathematical concepts. The student executes nearly all procedures and gives relevant

responses to most parts of the task. The response may have minor errors. Theexplanation detailing how the problem was solved may not be clear, causing the reader

to make some inferences.1-Point

ResponseThe response shows limited understanding of the problem's essential mathematical

concepts. The response and procedures may be incomplete and/or may contain majorerrors. An incomplete explanation of how the problem was solved may contribute to

questions as to how and why decisions were made.0-Point

ResponseThe response shows insufficient understanding of the problem's essential mathematicalconcepts. The procedures, if any, contain major errors. There may be no explanation of

the solution or the reader may not be able to understand the explanation. The readermay not be able to understand how and why decisions were made.