TOWNSHIP OF UNION PUBLIC SCHOOLS

Grade 7 Accelerated Mathematics Curriculum Guide 2013-14

-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

Scott Cornacchia

Maria Grillias

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 Core Curriculum Content 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. Selected topics in Pre-Algebra will also be incorporated to help prepare students for Algebra I.

Recommended Textbooks

Holt McDougal: Mathematics Grade 7

Course Proficiencies

Students will be able to… solve problems using order of operations with exponents. understand percents (larger than 100% and less than 1%). solve problems with percents. explore ratio, proportion, and equivalency (fractions, decimals, percents). read, write, compose, and order integers. perform operations with integers and rational numbers. use proportions to create expressions and equations. use ratios and proportionality to solve percent and scale problems including tax, tip, discount and simple interest. calculate circumference, area, and perimeter of plane figures. measure with protractors. identify congruent figures and name their corresponding parts. Identify cross sections of three dimensional shapes. calculate the surface area and volume or prisms, pyramids, cones and cylinders. Identify vertical, adjacent, supplementary and complementary angles and be able to write equations to solve for these angles. describe and use angles based on their measures and relationships to other angles. solve and graph two-step equations and inequalities on a number line. translate a word phrase or sentence into expressions, equations, and inequalities. solve real world problems using numerical and algebraic expressions and equations. analyze data using mean, median, mode and range. determine probability of events (i.e. flipping a coin, spinners, dice). analyze data using line plots, frequency tables, stem-and-leaf plots, and box-and-whisker plots. determine function rules given function table graph function on a coordinate plane given function table find the slope of a linear equation Graphs of lineal inequalities simplify expressions using negative exponents identify and use the properties of exponents to simplify evaluate square and cube roots/perfect squares and cubes estimate square roots simplify radical expressions use the Pythagorean Theorem to find the unknown side in a triangle use the distance and midpoint formulas

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 Unit 6: Functions

Pacing Guide – Accelerated Math 7th Grade

Content Number of Days

Unit 1: Ratios and Proportional Relationships 34 days

Unit 2: The Number System 27 days

Unit 3: Expressions and Equations 38 days

Unit 4: Geometry 36 days

Unit 5: Statistics and Probability 25 days

Unit 6 Functions 12 days

NJ ASK Prep & Testing 8 days

TOTAL 180 DAYSUnit 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?

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 relationships betweenquantities.

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-

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, then the mark-up of 20% on discounted price, then

How can we use two points 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?

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 purchased ata constant price p, the

Ended)(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,

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)

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.

hula hooping, and jump 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 numbers?

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,in the positive or negative direction depending on whether q ispositive or negative. Show that a number and its

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 they are holding, including absolute values)

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

Integer ECR-

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 answer and when to use an estimate?

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

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

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.)

Approximating Square Roots MCWhich of the following is the

best approximation of √60a. 6b. 7.1c. 7.6d. 8

How do we use perfect squares and square roots to approximate the square root of a rational number?

How do we simplify radical expressions like below?

√125 y z2¿=5 z √5 y ¿

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 and q are integers, then –(p/q) = (–p)/q =p/(–q). Interpret quotients of rational numbers by describing real world

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.

Name that Square Root – Students will use a decimal number line in clear communicator to locate the approximation of the square root of a given number.

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.4. (8.NS.2) Use rational numbers to approximate and locate rational numbers on a number line and estimate the value of expressions involving 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

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

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

“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”

equations and expressions and how 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?

How can we write and evaluate expressions containing positive and negative exponents?

How can we simplify alegrabic expressions using properties of

example, a + 0.05a = 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.

(Based on an expression, 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.)

Penny ProblemMotivate students to understand the significance of exponents by posing the “penny problem.” Also have students play the “matching game” where students will be required to match an exponential expression with its proper solution.

(Solve extended constructed responses which require students to write expressions, equations, and inequalities to solve)

Integer Exponents SCRA blue whale may eat between 6 and 7 tons of krill each day. Krill are approximately 2

−5×3−1×5−1

of the length of the blue whale. Simplify this product.

Integer Exponents ECREvaluate 83 ,82 ,81 ,80 ,8−1 , and 8−2

. Then describe the pattern of the values. Use the pattern of the values to predict 8

−3.

Exponent Properties SCRA student claims that 103⋅10−5

is greater than 1. Explain whether the student is wrong or correct.

Error Analysis: Square Roots

exponents?

How do we find the square root of a number? Perfect square?

For example: If a womanmaking $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

Simplifying Whiteboard RacesStudents will compete in a race by simplifying algebraic expressions containing exponents and comparing answers. The student who simplifies correctly first wins the round.

Name that Square Root – Students will use a decimal number line in clear communicator from 1 to 10 to locate the exact value of the square root of a given number.

A student said that if square roots of a certain are 1.5 and -1.5, then that number must be their product (-.2.25). What error did the student make?

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.

5. (8.EE.1) Apply the

properties of integers to simplify and write equivalent numerical expressions.

6. (8.EE.2) Evaluate square roots and cubic roots of small perfect squares and cubes respectively and use square and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p where p is a positive rational number..

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

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

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)

represent 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

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 sections of right rectangular prisms

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 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

“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.

Pythagorean Theorem MCA flag pole is 40 ft tall. A roper is tied to the top of the flagpole and secured to the ground 9 ft from the base of the flagpole. What is the length of the rope to the nearest foot?

a. 19 ftb. 39 ftc. 41 ftd. 1519 ft

Hands On Lab 8:

phenomena?

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

How can measurements be used to solve problems?

How do you use the Pythagorean Theorem to find the measure of the unknown side of a right triangle?

How do we use the Distance formula to find the actual distance between two points in a coordinate plane?

and 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 figure.6. (7.G.B.6) Solve real-

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.)

Pythagoras Baseball-Students will use the Pythagorean Theorem to find the distance between home plate and 2nd base given that the distance between home plate and 1st base is 90 ft and the

Pythagorean TheoremSee Teacher Resource Guide

The Parachute jump:Students will work in pairs to create parachutes-the students will drop the parachutes and will find the distance between the two drops using the distance formula

How do we us the midpoint formula to find the midpoint between two points on a line?

world and mathematical problems involving area, volumeand surface area of two- and three-dimensional objects composed oftriangles, quadrilaterals, polygons, cubes, and right prisms.

7. (8.G.7) Utilize the Pythagorean Theorem to determine unknown side lengths of right triangles in two and three dimensions to solve real-world and mathematical problems

distance between 1st base and 2nd base is also 90ft and there is a right angle form at each base.

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

Use random sampling to draw inferences about a population.1. (7.SP.A.1) Understand that statistics can be used to

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

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

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? What inferences can be made?

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. 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

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.)

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

Raffle Problem

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?

What is the best way

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 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,

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?

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.

Unit 6: Functions

Essential QuestionsInstructional Objectives/ Skills and

Benchmarks (CPIs) Activities Assessments How can we determine

whether a relationship of numbers form a function?

How do we graph functions on a coordinate plane?

How do we find the slope of a linear equation using slope intercept form?

How do we read /find the equation of a line?

1. (8.F.1) Understand that a

function is a rule that assigns each input exactly one output. The graph a of a function is the set of ordered pairs consisting of an input and the corresponding output.

2. (8.F.2) Compare properties of two functions represented in a different way (algebraically, graphically, numerically in tables of in verbal descriptions)

Function Machine Students will use the visual representation of a the “function machine” to show what goes into the machine (input) changes after the machine in turned on to another number (output)

Function Match Up Students will be given one of 5 function tables and graph paper. They will be asked to graph the function on a coordinate plane. Teacher will then unveil 5 different function graphs around the room. Students are to travel around the room to find their matching graph for their table.

Functions? MCWhich relation does NOT represent a function?

a. (0,8) (3, 8) (1, 6)b.

x 4 6 8y 2 1 9

c. y = 3x + 17d. (0, 3) (2, 3) (2, 0)

Your Choice? FunctionsWrite a problem that involves the equation y = 2x+3

Hands on Lab 5: Graphs and Functions –See Teacher Resource Guide

How can we find the solution of systems of linear equations?

How we graph linear inequalities?

Graphing Functions ECRThe equation y = 2.5x-2000 represents the profit made by a manufacturer that sells a product for $2.50 each, where y is the profit and x is the number of units sold. Construct a table to find the number of units that must be sold for the manufacturer to break even. The break-even point is when the profit is equal to 0. Explain the data in the table.

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

ResponseThe response shows nearly complete understanding of the problem's essential

mathematical concepts. The student executes nearly all procedures and gives relevantresponses to most parts of the task. The response may have minor errors. The

explanation detailing how the problem was solved may not be clear, causing the readerto make some inferences.

1-PointResponse

The response shows limited understanding of the problem's essential mathematicalconcepts. 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.