Scope and Sequence: Math 7 - Florham Park School District

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7th Grade On-level Mathematics

Adopted August 27, 2018; Revised March 2020

Scope and Sequence: Math 7

Unit Key Concepts Standards Number of Instructional Days

September/ October Integers

● The distance of a number from zero is always positive. ● Addition of integers is a combining process. When the signs are the

same, the resulting sum will have the same sign as the addends; when the signs are different, zero pairs result and are removed.

● Integer subtraction expressions can be rewritten as addition expressions.

● Repeated addition is a model for integer multiplication. ● When integer factors have the same sign, the product is positive. ● When integer factors have different signs, the product is negative. ● Exponents signal repeated multiplication. ● When integer dividends and divisors have the same sign, the

quotient is positive. ● When integer dividends and divisors have different signs, the

quotient is negative.

7.NS.1 7.NS.1a, 7.NS.1b 7.NS.1c 7.NS.1d 7.NS.2 7.NS.2a 7.NS.2b 7.NS.2c 7.NS.3 ,

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October Rational Numbers

● The farther to the right the number is on the number line, the greater the value of that number.

● Fractions can be represented as decimal numbers which may be repeating or terminating decimals; decimal numbers can be represented as fractions.

● Number lines can be used to represent the sum of two rational numbers.

● Number lines can be used to represent the difference of two rational numbers.

● Subtraction is used to find the distance between two numbers on a number line.

● Addition and subtraction of rational numbers is similar to addition and subtraction of integers.

● Multiplying by -1 is the same thing as taking the opposite of a number.

7.NS.1a, 7.NS.1b 7.NS.1c 7.NS.1d 7.NS.2a 7.NS.2b 7.NS.2c 7.NS.2d 7.NS.3

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October / November

Expressions & Equations

● Algebraic expressions are composed of several terms. ● Terms that are alike can be combined. ● Simplifying an expression creates an expression that is equivalent to

the original one.

7.EE.1 7.EE.2 7.EE.4a

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● The coefficient of -x is -1. ● The coefficient of x is 1. ● The exponent in terms such as 5z and z is 1. ● Algebraic expressions can be added and subtracted. ● Algebraic expressions in which the exponent of the variable is 1 are

called linear expressions. ● The Commutative Property can be used when simplifying

expressions. ● The Distributive Property is useful when simplifying expressions. ● An algebraic term has factors just like numbers have factors. ● Subtracting a negative number is equivalent to adding a positive

number. ● The equals sign means both sides of an equation have the same

value. ● A graph presents information about a problem. ● Algebraic solutions to problems involve identifying what is

unknown, representing the unknown with a variable, and using inverse operations to find the value of the unknown quantity.

● Problem situations can be represented with equations. ● Dividing by a fraction is equivalent to multiplying by its reciprocal. ● Combining like terms is often the first step in solving 2-step

algebraic equations. ● Isolate the variable on one side of the equal sign by creating

equivalent equations using inverse operations. ● Solving an algebraic equation means finding the value for x needed

to make a true statement.

November/ December Inequalities

● There is an infinite number of solutions to inequality statements. ● There is a boundary point for the set of solutions. ● Solutions to inequalities are not limited to integers. ● Closed circles on inequality graphs indicate that the boundary

point is a solution to the inequality; open circles indicate that the boundary point is not included in the set of possible solutions.

● A graph of an inequality allows the solution set to be seen. It also shows what values are not part of the solution set.

● Words in a problem situation can be translated to inequalities that represent the situation.

● Inequalities involving addition and subtraction can be solved in the same way as algebraic equations.

7.EE.4b 12

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● Inequalities involving multiplication and division are not solved in the same way as algebraic equations.

● Solving multiplication or division inequalities using negative numbers results in a change of direction of the inequality symbol.

January Ratios & Proportions

● Rates can have fractions in the numerator, denominator, or both. ● A ratio table is an organizing structure and the units guide the

computations. ● Any equivalent ratio can be used to find the unit rate. ● A proportion is an equation stating that two ratios are equivalent. ● The graph of every proportional relationship is a line through the

origin. ● When two measures are being compared, the order in which they

are written does matter. ● A ratio table is a tool to show relationships between different

quantities.. ● A graph is a tool to show the relationship between two quantities. ● In the graph of a proportional relationship, the unit rate y can be

found from the point (1, y). ● A rate is a ratio. ● When two quantities vary directly, the ratio of one quantity to

another is a constant. ● The ordered pair (0,0) is always a solution of an equation that

describes two quantities that vary directly. ● The constant ratio is the slope of the line that is the graph of two

quantities that vary directly. ● When two quantities vary directly, it is said that they are directly

proportional.

7.RP.1 7.RP.2a 7.RP.2b 7.RP.2c 7.RP.2d 7.RP.3

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February Percents

● A percent can be written as a fraction and as a decimal. ● Percents do not need to involve whole numbers. ● The decimal point moves 2 places when converting between

decimals and percents. ● The farther to the right a number is on the number line, the greater

the number. ● The concept of a proportion can be used to solve different types of

percent problems. ● Move the decimal point one place to the left in a number to find

10% of that number. ● A ratio table can be used to answer a percent equation.

7.EE.3 7.RP.3

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● A percent bar model helps to estimate and consider the reasonableness of the answer.

● The percent proportion can be used to find a percent, to find a part, and to find the whole.

● There is a difference between amount of change and percent of change.

● When a quantity has doubled, it has increased 100%. ● The percent error compares the amount of error to the actual

amount. ● Finding an original price is the same as finding the whole. ● A discounted price can be found by multiplying the original price

by 1 minus the decimal form of the discount percent.

March Constructions and Scale Drawings

● It is important to provide supporting evidence for conjectures. ● Angles are named by the vertex alone or by three points with the

vertex listed in the middle. ● Adjacent angles share a side. ● Vertical angles have equal measure. ● Two angles are complementary if their angle measures total 90º. ● Two angles are supplementary if their angle measures total 180º. ● Triangle angle measures total 180º ● Triangles can be classified by the measure of their angles. ● Triangles can be classified by the length of their sides. ● An equation can be solved to find the third angle when the

measures of the other two angles are known. ● Isosceles triangles have at least two sides of equal length. ● Scalene triangles have no sides of equal length. ● Quadrilaterals can have more than one name. ● There are relationships among the various types of quadrilaterals. ● The interior angle measures of a quadrilateral total 360º ● In a parallelogram, opposite angles are congruent and adjacent

angles are supplementary. ● An equation can be written and solved in order to find a missing

angle measure of a quadrilateral. ● Ratio tables can be used to find scale factors.

7.G.1 7.G.2 7.G.5

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March/ April Circles and Area

● Pi is a calculable number. ● The formula for circumference can be used to solve real-life

problems. ● The radius of a circle is equal to one-half of the diameter.

7.G.4 7.G.6

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● The circumference of a circle can be found when given the radius or the diameter.

● The formula for circumference can be used to find the perimeter of a semi-circle.

● A variety of problem-solving skills can be used to find the perimeter of a composite figure

● Formulas can be used to find the perimeter of a composite figure. ● Pi can be rounded to 3 when estimating. ● Divide composite figures into familiar geometric shapes and use

known area formulas to find the total area.

April/May (mid) Surface Area & Volume

● The net of a prism can be used to find the surface area of the prism. ● The net of a rectangular prism can be used to derive a formula to

calculate the surface area of the rectangular prism. ● A rectangular prism has 3 pairs of congruent faces. ● The net of a pyramid can be used to find the surface area of that

pyramid. ● The net of a cylinder can be used to find the surface area of that

cylinder. ● Volume is found by finding the area of the base (B) and then

multiplying by the number of layers (h). ● The formula for the volume of a prism can be used to solve

problems. ● The volume of a pyramid is ⅓ the volume of a prism with the same

height and base.

7.G.3 7.G.4 7.G.6

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mid-May/ mid-June Probability & Statistics

● The probability of an event can be calculated. ● Probabilities can be represented as fractions, decimals, or percents. ● Relative frequencies can be used to find the probability of an event. ● When relative frequencies increase, the experimental probability

gets closer and closer to the theoretical probability. ● Tree diagrams can be used to visualize the possible outcomes of

events. ● When an experiment is performed randomly, all of the possible

outcomes are equally likely. ● The probability of an event is the ratio of the number of favorable

outcomes to the number of possible outcomes. ● The probability of an event is written a P(event).

7.SP.1 7.SP.2 7.SP3 7.SP.4 7.SP.5 7.SP.6 7.SP.7a 7.SP.7b 7.SP.8a 7.SP.8b 7.SP.8c

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● The relative frequency of an event is the fraction or percent of the time that the event occurs.

● Probability that is based on repeated trials of an experiment is called experimental probability.

● When all possible outcomes are equally likely, the theoretical probability of an event is the ratio of the number of favorable outcomes to the number of possible outcomes.

● The Fundamental Counting Principle multiplies the number of possible outcomes of the first event by the number of possible outcomes of the second event to find the total number of possible outcomes.

● The probability of a compound event is the ratio of the number of favorable outcomes to the number of possible outcomes.

● Events are independent events if the occurrence of one event does not affect the likelihood that the other event(s) will occur.

● An unbiased sample is representative of a population, selected at random, and is large enough to provide accurate data.

● A biased sample is not representative of a population. One or more parts of the population are favored over others.

Mathematics Curriculum Grade: 7 Unit: Integers New Jersey Student Learning Standards 7.NS.A.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. 7.NS.A.1a Describe situations in which opposite quantities combine to make 0. For example, in the first round of a game, Maria scored 20 points. In the second round of the same game, she lost 20 points. What is her score at the end of the second round? 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 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. 7.NS.A.1c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. 7.NS.A.1d Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.A.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. 7.NS.A.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. 7.NS.A.2b 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. 7.NS.A.2c Apply properties of operations as strategies to multiply and divide rational numbers. 7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers.

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Enduring Understandings/Goals Essential Questions ● The distance of a number from zero is always positive. ● Addition of integers is a combining process. When the signs

are the same, the resulting sum will have the same sign as the addends; when the signs are different, zero pairs result and are removed.

● Integer subtraction expressions can be rewritten as addition expressions.

● Repeated addition is a model for integer multiplication. ● When integer factors have the same sign, the product is

positive. ● When integer factors have different signs, the product is

negative. ● Exponents signal repeated multiplication. ● When integer dividends and divisors have the same sign, the

quotient is positive. ● When integer dividends and divisors have different signs, the

quotient is negative.

● How can you use integers to represent the velocity and the speed of an object? ● Is the sum of two integers positive, negative, or zero? How can you tell? ● How are adding integers and subtracting integers related? ● Is the product of two integers positive, negative, or zero? How can you tell? ● Is the quotient of two integers positive, negative, or zero? How can you tell?

Lesson Number Teaching Points Chapter Opener for Chapter 1: Integers

● Introduction ● Review commutative and associative properties ● Review properties of zero and One

Activity 1.1: Integers and Absolute Value MP6

Use the relationship between speed and velocity to find speed (the absolute value of velocity) when the velocity is known. ● Warm Up ● Falling Parachute activity to illustrate negative velocity ● Rising Balloons activity to illustrate positive velocity

Lesson 1.1: Integers and Absolute Value MP3, MP6

Think about the distance a number is from 0. This distance is always positive, just like the speed of an object. ● Warm Up ● Key Idea: absolute value is the distance between the number and zero on a number line. ● Find absolute values of positive and negative numbers. ● Use a number line to compare and order integers. ● Real-life application

Activity 1.2: Adding Integers

Use integer counters and a number line to add integers of the same sign and of different signs ● Warm Up ● Complete an activity that illustrates adding two negative integers.

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MP8, MP3 ● Complete an activity that illustrates adding integers with different signs with a negative sum. ● Complete an activity that illustrates adding integers with different signs with a positive sum. ● Use a number line to add two opposite integers.

Lesson 1.2: Adding Integers MP3, MP4, MP8

Add integers without the use of a visual or concrete model. ● Warm Up ● Key Idea: use absolute value to add integers with the same sign ● Use a number line to add integers with the same sign. ● Key Idea: to add integers with different signs subtract the lesser absolute value from the greater absolute value; use the sign of the number

with the greater absolute value. ● Use absolute value to add integers with different signs.

Activity 1.3: Subtracting Integers MP2, MP8

Use integer counters and a number line to subtract integers ● Warm Up ● Use counters to subtract two integers. ● Use counters to add integers with different signs that result in a positive sum. ● Use a number line to subtract a positive integer from a negative integer; move to the left on the number line to subtract a positive number

and move to the right to subtract a negative number. ●

Lesson 1.3: Subtracting Integers MP3, MP4

Use the idea that a subtraction problem can be rewritten as an addition problem ● Warm Up ● Key Idea: subtract an integer by adding the opposite ● Subtract integers by adding its opposite ● Real-life application

Sections 1.1–1.3 Study Help and Quiz

● Review ● Complete graphic organizer ● Administer quiz

Activity 1.4: Multiplying Integers MP4, MP7, MP8

Use repeated addition on a number line to develop a sense of integer multiplication ● Warm Up ● Use a number line and repeated addition to find the product of two integers with the same sign. ● Use a number line and repeated addition to find the product of two integers with different signs. ● Use a table to find the product of two integers with different signs by recognizing a pattern in the table. ● Use a table to find the product of two integers with the same signs by recognizing a pattern in the table.

Lesson 1.4: Multiplying Integers

Find products of integers with the same sign and products of integers with different signs ● Warm Up

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MP3, MP6, MP7

● Key Idea: the product of two integers with the same sign is positive; the product of two integers with different signs is negative. ● Rewrite exponents as repeated multiplication ● Real-life application

Activity 1.5: Dividing Integers MP7, MP8

Use fact families and what they know about multiplication of integers to develop a sense of integer division. ● Warm Up ● Use integer counters to divide integers with different signs. ● Write a product of two positive integers as a quotient in two different ways. ● Write a product of two negative integers as a quotient in two different ways. ● Write a product as a quotient of integers of different signs in two different ways.

Lesson 1.5: Dividing Integers MP6, MP7

Use the idea that when the signs of the dividend and divisor are the same, the quotient is positive; when the signs of the dividend and divisor are different, the quotient is negative. ● Warm Up ● Key Ideas: the quotient of two integers with the same sign is positive; the quotient of two integers with different signs is negative. ● Evaluate an expression given the values of the variables. ● Real-life application

Sections 1.4–1.5 Quiz and Chapter Review

● Introduction ● Chapter review

Differentiating the Lesson, Chapter 1 ● Section 1.2

○ Lesson 1: Adding Integers This lesson is for students who identify with the number line model from their textbooks, yet benefit from physically moving a counter along the number line. Students will complete various addition sentences using their number lines and counters to help them internalize the concepts of integer addition. Students learn how to use the Associative Property of Addition to partition a number so that it can be grouped with its opposite to form a sum of zero.

● Section 1.3 ○ Lesson 2: Missing Addend Model for Subtracting Integers This lesson is designed for students who have mastered addition of integers. Students apply

their strengths and knowledge of addition of integers to subtraction of integers. Capitalizing on the missing addend model for whole number subtraction, students use the same model for integer subtraction. This method works well for students who might become confused when too many different “rules” are introduced for the various operations on integers. It also emphasizes addition and subtraction as inverse operations.

● Section 1.5 ○ Lesson 3: Missing Factor Model for Dividing Integers This lesson is designed for students who can multiply integers and would benefit from an emphasis

on the connection between multiplication and division operations. By writing each division as a multiplication sentence with a missing factor, they can readily apply the rules of integer multiplication without having to memorize a new set of rules for division.

○ Lesson 4: Substituting Negative Values into Algebraic Expressions This lesson will benefit students who need a physical model for substituting values for variables in an algebraic expression similar to those in Example 3 of the textbook. It specifically focuses on substituting a negative value for a variable that

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follows a minus sign or a negative sign. Students use small sticky notes to physically cover variables in an expression with the substituting numerical values. Students are taught to only cover the variable, therefore keeping existing minus and negative signs within the expression intact. Because students demonstrate their understanding by placing a value on top of a variable, this lesson also works well with students needing accommodations which focus on limited writing.

Skills (Students will be able to…) ● Find absolute values of numbers ● Add integers ● Show that the sum of a number and its opposite is zero ● Subtract integers ● Multiply integers ● Divide integers

Evidence of Learning (Assessments) Accommodations and Modifications

Formative Assessments:

● Closure Activity ● Homework ● Mid-Chapter Quiz ● End-of-Chapter Quiz

Summative Assessments:

● Chapter Test ● End-of-Course Test

Benchmark Assessments:

● Initial LinkIt Benchmark: September ● Mid-year LinkIt Benchmark: December ● End of year LinkIt Benchmark: Last week in April ● Beginning of the Year, Mid-Year and End-of-Year Math Assessments

Alternative Assessments:

● G & T Assessments:Sages-2 Screening Assessment for Gifted Elementary: Mathematics/Science Language Arts/Social Studies

● Reasoning

Special Education

● Differentiation for All Students (Special Needs, ESL, Gifted Learners, & Mainstream Learners) ● Subgroup Accommodations and Modifications ● Curricular Modifications and Guidance for Students Educated in Special Class Settings

Differentiation: ● Preview content and concepts ● Behavior management plan ● Highlight text ● Small group setting

High-Prep Differentiation: ● Alternative formative and summative assessments ● Guided Reading ● Personal agendas ● Project-based learning ● Problem-based learning ● Stations/centers ● Tiered activities/assignments ● Varying organizers for instructions

Low-Prep Differentiation: ● Clubbing activities ● Exploration by interest ● Flexible groupings

English Language Learners

https://docs.google.com/document/d/1wJLHdjzj9_VQevaM2dMkSRDpIWpb-6q7N5rfa349-sY/edit?usp=sharing

https://drive.google.com/file/d/0B-_iTnCmF_gGRzFuemszSGJwQnl4MDdRbnB2MDRTaEtQazdN/view?usp=sharing

https://docs.google.com/document/d/1CojyW8KphR7mZgS-wgTxmO1y6z0uhZJwEpV5tJ_Aqk8/edit?usp=sharing

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● Dyslexia Screener ● PRIM checklist ● Computational Skills Grade Placement Test

● Differentiation for All Students (Special Needs, ESL, Gifted Learners, & Mainstream Learners) ● Unit 1: Curriculum for ELL ● Subgroup Accommodations and Modifications ● Multi-language glossary ● Pupil edition in Spanish ● Vocabulary flash cards

Students at Risk for Failure

● Differentiation for All Students (Special Needs, ESL, Gifted Learners, & Mainstream Learners) ● Subgroup Accommodations and Modifications

Gifted and Talented

● Differentiation for All Students (Special Needs, ESL, Gifted Learners, & Mainstream Learners) ● Subgroup Accommodations and Modifications ● Math in Focus or Big Ideas G & T Activities

Students with 504 Plans


Core Instructional and Supplemental Materials Professional Resources:

Core Instructional, Supplemental, Instructional, and Intervention Resources

Core Professional Resources:

● Big Ideas Chapter 1 ● 7.NS.1 Performance Task ● 7.NS.2 Performance Task ● 7.NS.3 Performance Task ● STEM video and Performance Task

Supplemental Professional Resources:

● Big Ideas Curriculum ● Denis Sheeran Training Resources ● http://www.corestandards.org/Math/Practice/

Core Instructional Resources:

● Big Ideas Chapter 1 ● 7.NS.1 Performance Task ● 7.NS.2 Performance Task ● 7.NS.3 Performance Task ● STEM video and Performance Task ● Internet Connected Computers/iPads

Supplemental Resources:

● Big Ideas Chapter 1 ● 7.NS.1 Performance Task


http://www.state.nj.us/education/modelcurriculum/ela/ellscaffolding/ku1.pdf








https://docs.google.com/presentation/d/1N-zzzn1IbL6QCbS6HkNh1WN0zda7ggwlN4AS7CxmFxw/edit#slide=id.g132b428022_0_300

http://www.corestandards.org/Math/Practice/

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● http://www.madisonpublicschools.org/page/231

● 7.NS.2 Performance Task ● 7.NS.3 Performance Task ● STEM video and Performance Task ● Math Centers ● 3 Act Lessons ● Robert Kaplinsky Lessons ● Open Middle - 7th Grade ● Which One Doesn’t Belong? ● Solve Me Puzzles ● Estimation 180 ● Same or Different ● Visual Patterns ● Esti-Mysteries ● 51 Esti-Mysteries ● Splat Math

Intervention Resources:

● Big Ideas Chapter 1 ● 7.NS.1 Performance Task ● 7.NS.2 Performance Task ● 7.NS.3 Performance Task ● STEM video and Performance Task ● iReady ● Linkit! ● IXL ● Big Ideas ● Classroom Manipulatives ● Online Manipulatives ● Content from previous grade levels ● Touch Math

Interdisciplinary Connections Integration of Technology through NJSLS

● Correlates to the Ancient Rome unit in Social Studies ● Correlates to the Interactions of Matter unit in Science.

8.1 Educational Technology 8.1.8.A.3 Use and/or develop a simulation that provides an environment to solve a real world problem or theory. 8.1.8.D.4 Assess the credibility and accuracy of digital content. 8.2 Technology Education, Engineering, Design, and Computational Thinking - Programming

● Listen to books on CDs, tapes, videos or podcasts if available. ● Listen to books on websites (pbskids.org/lions/index.html, storylineonline.net, storyit.com,

Elementary Connections Page) ● Use document camera or overhead projector for shared reading of texts. ● Use virtual manipulatives ● Use IXL.com

http://www.madisonpublicschools.org/page/231

https://drive.google.com/drive/folders/1OubdpzZC3Bo_NdLnOqgXxpcrc2Tln79p?usp=sharing

https://gfletchy.com/3-act-lessons/

https://robertkaplinsky.com/lessons/

https://www.openmiddle.com/category/grade-7/

http://wodb.ca/index.html

http://solveme.edc.org/

http://www.estimation180.com/

https://samedifferentimages.wordpress.com/

http://www.visualpatterns.org/

https://stevewyborney.com/2018/11/esti-mysteries-estimation-meets-math-mysteries/

https://stevewyborney.com/2019/09/51-esti-mysteries/

https://stevewyborney.com/2018/09/splat-for-google-slides-40-lessons/

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8.2.8.B.6 Compare and contrast the different types of intellectual property including copyrights, patents and trademarks. 8.2.8.D.2 Identify the design constraints and trade-offs involved in designing a prototype (e.g., how the prototype might fail and how it might be improved) by completing a design problem and reporting results in multimedia presentation, design portfolio or engineering notebook.

Integration of 21st Century Themes Media Literacy Integration

Learning and Innovation Skills: Critical Thinking & Problem Solving

● Reason Effectively ● Use Systems Thinking ● Making Judgements and Decisions ● Solve Problems

Communication and Collaboration ● Communicate Clearly

Life and Career Skills Initiative and Self Direction

● Manage Goals and Time ● Work Independently ● Be Self-directed Learners

● Have students practice skills using IXL ● Students create problems on the tablets and share them with classmates ● Kahn Academy ● Brain Pop

Career Education Global Perspectives

9.1 Personal Finance Literacy 9.1.8.A.1 Explain the meaning and purpose of taxes and tax deductions and why fees for various benefits (e.g., medical benefits) are taken out of pay. 9.1.8.B.4 Relate the concept of deferred gratification to [investment,] meeting financial goals, and building wealth. 9.1.8.D.4 Distinguish between income and investment growth. 9.2 Career Awareness, Exploration, and Preparation 9.2.8.B.4 Evaluate how traditional and nontraditional careers have evolved regionally, nationally, and globally.

● National Hispanic-Latino Month ● National Disability Employment Awareness Month ● International Dot Day (September 16) ● Week of Respect ● Red Ribbon Week ● National Italian American Heritage Month

Mathematics Curriculum Grade: 7 Unit: Rational Numbers New Jersey Student Learning Standards 7.NS.A.1a Describe situations in which opposite quantities combine to make 0. For example, in the first round of a game, Maria scored 20 points. In the second round of the same game, she lost 20 points. What is her score at the end of the second round? 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 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.

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7.NS.A.1c Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts\ 7.NS.A.1d Apply properties of operations as strategies to add and subtract rational numbers. 7.NS.A.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. 7.NS.A.2b 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. 7.NS.A.2c Apply properties of operations as strategies to multiply and divide rational numbers. 7.NS.A.2d 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.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers. Enduring Understandings/Goals Essential Questions

● The farther to the right the number is on the number line, the greater the value of that number.

● Fractions can be represented as decimal numbers which may be repeating or terminating decimals; decimal numbers can be represented as fractions.

● Number lines can be used to represent the sum of two rational numbers.

● Number lines can be used to represent the difference of two rational numbers.

● Subtraction is used to find the distance between two numbers on a number line.

● Addition and subtraction of rational numbers is similar to addition and subtraction of integers.

● Multiplying by -1 is the same thing as taking the opposite of a number.

● How can you use a number line to order rational numbers? ● How can you use what you know about adding integers to add rational numbers? ● How can you use what you know about subtracting integers to subtract rational numbers? ● Why is the product of two negative rational numbers positive?

Lesson Number Teaching Points Chapter Opener for Chapter 2: Rational Numbers

● Introduction ● Writing decimals and fractions ● Adding and subtracting fractions ● Multiplying and dividing fractions

Activity 2.1: Rational Numbers MP1, MP3, MP4

Order rational numbers ● Warm Up ● Use a number line to order rational numbers from least to greatest ● Compare and order rational numbers as part of a card game

Lesson 2.1: Rational Numbers

Order rational numbers including repeating decimals ● Warm Up ● Key Idea: a rational number is a number that can be written as a/b where a and b are integers and b ≠ 0

Table of Contents



MP1 ● Write rational numbers as decimals ● Write a decimal as a fraction ● Order rational numbers

Activity 2.2: Adding Rational Numbers MP2

Explore how to add rational numbers ● Warm Up ● Use a number line to add rational numbers with different signs. ● Add rational numbers with the same sign using a number line. ● Write an addition expression from a graph.

Lesson 2.2: Adding Rational Numbers MP2, MP6

Add rational numbers using a formal process. ● Warm Up ● Key Idea: to add rational numbers, use the same rules for signs as you used for integers. ● Add rational numbers: fractions ● Add rational numbers: decimals ● Evaluate expressions using rational numbers ● Real-life application

Sections 2.1-2.2 Study Help and Quiz

● Review ● Complete a graphic organizer ● Administer the quiz

Activity 2.3: Subtracting Rational Numbers MP2, MP4

Explore how to subtract rational numbers ● Warm Up ● Use a number line to subtract rational numbers with different signs. ● Use subtraction to find distances on a number line. ● Financial literacy: Balance a Checkbook

Lesson 2.3: Subtracting Rational Numbers MP4

Subtract rational numbers using a formal process. ● Warm Up ● Key Idea: to subtract rational numbers, use the same rules for signs as used for integers ● Subtract rational numbers: fractions ● Subtract rational numbers: decimals ● Finding distances between numbers on a number line by using the difference of the numbers. ● Real-life application

Table of Contents



Activity 2.4: Multiplying and Dividing Rational Numbers MP2, MP3, MP6

Use an analytic approach to show that the product of two negative numbers is positive. ● Warm Up ● Uss the Additive Inverse Property to show that (-1)(-1) = 1 ● Explore the result of multiplying numbers by -1 ● Understand that the product of two negative rational numbers is a positive number. ● Write a story that uses an operation with rational numbers

Lesson 2.4: Multiplying and Dividing Rational Numbers MP7

Learn the rules for multiplying and dividing rational numbers. ● Warm Up ● Key Idea: to multiply or divide rational numbers, use the same rules for signs as you used for integers. ● Divide mixed numbers ● Multiply decimals and signed numbers ● Multiply more than two rational numbers using properties of multiplication to make the product easier to find. ● Real-life application


● Introduction: quickly review chapter concepts ● Chapter review


○ Lesson 1: Rational Numbers These lessons are designed for students who would benefit from using a visual model to write a fraction as a decimal. ○ Lesson 1A: Writing Rational Numbers as Decimals In this lesson, students use paper folding to model how equivalent fractions can be used to write the

fraction as a decimal. ○ Lesson 1B: Writing Rational Numbers as Decimals In this lesson, students use a number line to recognize how division can be used to write a fraction as a

decimal. ● Section 2.4

○ In Section 2.4, students must be able to move flexibly between rational numbers in fraction form and decimal form. The computations may be overwhelming for some students who are trying to keep all the “rules” straight. These lessons are for students who have difficulty remembering the algorithms for decimal multiplication and decimal division or for those who want to understand why the algorithms work.

○ Lesson 2A: Multiplying Decimals In this lesson, students work with fraction equivalents of terminating decimals to multiply two decimals. As the lesson proceeds, the fraction equivalents are used to develop an understanding of the standard decimal algorithm for multiplying.

○ Lesson 2B: Dividing Decimals In this lesson, students learn that each decimal division problem can be written as a single fraction with a decimal numerator and denominator. Then using equivalent fractions they clear out the decimal in the divisor to create a fraction that has a whole number divisor. The lesson focuses on determining the power of ten factor that makes the divisor a whole number and creating the equivalent division expression that can then be used to find the quotient. Students need to already have strong command of decimal multiplication by 10, 100, and 1000 to employ the equivalent fraction model presented in this lesson.

Skills (Students will be able to…) ● Order rational numbers

Table of Contents



● Write rational numbers as decimals ● Write decimals as fractions ● Add rational numbers using a number line ● Write an addition expression shown on a number line ● Add rational numbers using the least common denominator ● Add signed decimal numbers ● Evaluate algebraic expressions when the value of the variable is provided ● Subtract rational numbers using a number line ● Find distances on a number line ● Subtract signed rational numbers: fractions ● Subtract signed rational numbers: decimals ● Multiply by negative 1 ● Divide signed rational numbers ● Multiply signed rational numbers








Special Education




Low-Prep Differentiation:




Table of Contents




● G & T Assessments:Sages-2 Screening Assessment for Gifted Elementary:

Mathematics/Science Language Arts/Social Studies ● Reasoning ● Dyslexia Screener ● PRIM checklist ● Computational Skills Grade Placement Test

● Clubbing activities ● Exploration by interest ● Flexible groupings





Gifted and Talented







● Big Ideas Chapter 2 ● 7.NS.1 Performance Task ● 7.NS.2 Performance Task ● 7.NS.3 Performance Task ● STEM video and performance task


● Big Ideas Chapter 2 ● 7.NS.1 Performance Task ● 7.NS.2 Performance Task ● 7.NS.3 Performance Task ● STEM video and performance task










Table of Contents




● Big Ideas Curriculum ● Denis Sheeran Training Resources ● http://www.corestandards.org/Math/Practice/ ● http://www.madisonpublicschools.org/page/231

● Internet Connected Computers/iPads


● Big Ideas Chapter 2 ● 7.NS.1 Performance Task ● 7.NS.2 Performance Task ● 7.NS.3 Performance Task ● STEM video and performance task ● Math Centers ● 3 Act Lessons ● Robert Kaplinsky Lessons ● Open Middle - 7th Grade ● Which One Doesn’t Belong? ● Solve Me Puzzles ● Estimation 180 ● Same or Different ● Visual Patterns ● Esti-Mysteries ● 51 Esti-Mysteries ● Splat Math


● Big Ideas Chapter 2 ● 7.NS.1 Performance Task ● 7.NS.2 Performance Task ● 7.NS.3 Performance Task ● STEM video and performance task ● iReady ● Linkit! ● IXL ● Big Ideas ● Classroom Manipulatives ● Online Manipulatives ● Content from previous grade levels ● Touch Math


● Correlates to the Ancient Americas and Middle Ages units in Social Studies ● Correlates to the Chemical Reactions and Structure & Properties of Matter units in

Science.


Elementary Connections Page) ● Use document camera or overhead projector for shared reading of texts.
















Table of Contents



8.1 Educational Technology 8.1.8.A.3 Use and/or develop a simulation that provides an environment to solve a real world problem or theory. 8.1.8.A.5 Create a database query, sort and create a report and describe the process, and explain the report results. 8.1.8.D.4 Assess the credibility and accuracy of digital content. 8.2 Technology Education, Engineering, Design, and Computational Thinking - Programming 8.2.8.B.4 Research examples of how humans can devise technologies to reduce the negative consequences of other technologies and present your findings. 8.2.8.C.5 Explain the interdependence of a subsystem that operates as part of a system. 8.2.8.D.4 Research a publish the steps for using and maintaining a product or system and incorporate diagrams or images throughout to enhance use comprehension.

● Use virtual manipulatives ● Use IXL.com









9.1 Personal Finance Literacy 9.1.8.A.5 Relate how the demand for certain skills determines an individual’s earning power. 9.1.8.C.2 Compare and contrast the financial products and services offered by different types of financial institution. 9.1.8.C.10 Determine when there is a need to seek credit counseling and appropriate times to utilize it. 9.1.8.E.6 Compare the value of goods or services from different sellers when purchasing large quantities and small quantities. 9.2 Career Awareness, Exploration, and Preparation 9.2.8.B.3 Evaluate communication, collaboration, and leadership skills that can be developed through school, home, work, and extracurricular activities for use in a career.

● Red Ribbon Week ● National Italian American Heritage Month

Table of Contents



Mathematics Curriculum Grade: 7 Unit: Expressions & Equations New Jersey Student Learning Standards 7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.” 7.EE.B.4a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width? Enduring Understandings/Goals Essential Questions

● Algebraic expressions are composed of several terms. ● Terms that are alike can be combined. ● Simplifying an expression creates an expression that is

equivalent to the original one. ● The coefficient of -x is -1. ● The coefficient of x is 1. ● The exponent in terms such as 5z and z is 1. ● Algebraic expressions can be added and subtracted. ● Algebraic expressions in which the exponent of the variable

is 1 are called linear expressions. ● The Commutative Property can be used when simplifying

expressions. ● The Distributive Property is useful when simplifying

expressions. ● An algebraic term has factors just like numbers have factors. ● Subtracting a negative number is equivalent to adding a

positive number. ● The equals sign means both sides of an equation have the

same value. ● A graph presents information about a problem. ● Algebraic solutions to problems involve identifying what is

unknown, representing the unknown with a variable, and using inverse operations to find the value of the unknown quantity.

● Problem situations can be represented with equations. ● Dividing by a fraction is equivalent to multiplying by its

reciprocal. ● Combining like terms is often the first step in solving 2-step

algebraic equations.

● How can you simplify an algebraic expression? ● How can you use algebra tiles to add or subtract algebraic expressions? ● How can you use algebra tiles to solve addition or subtraction equations? ● How can you use multiplication or division to solve equations? ● How can you use algebra tiles to solve a two-step equation?

Table of Contents



● Isolate the variable on one side of the equal sign by creating equivalent equations using inverse operations.

● Solving an algebraic equation means finding the value for x needed to make a true statement.

Lesson Number Teaching Points Chapter Opener for Chapter 3: Expressions and Equations

● Introduction ● Evaluate expressions ● Write algebraic expressions

Activity 3.1: Algebraic Expressions MP3, MP6, MP7

Explore how to simplify algebraic expression by evaluating two expression for more than one value of the variable. ● Warm Up ● Use the order of operations to evaluate algebraic expressions when x = 0, and when x = 1 ● Write a math lesson on simplifying an algebraic expression

Lesson 3.1: Algebraic Expressions MP6

Simplify expressions by combining like terms ● Warm Up ● Identify terms and like terms ● Simplify an algebraic expression with fractional coefficients ● Simplify an algebraic expression where the Distributive Property is needed. ● Real-life application

Activity 3.2: Adding and Subtracting Linear Expressions MP2

Use algebra tiles to develop an understanding of how to add and subtract algebraic expressions ● Warm Up ● Write algebraic expressions shown by algebra tiles ● Add algebraic expressions modeled by algebra tiles ● Subtract algebraic expressions modeled by algebra tiles ● Write the sum or difference of two algebraic expressions modeled by algebra tiles, then use the algebra tiles to simplify the expression.

Lesson 3.2: Adding and Subtracting Linear Expressions MP2, MP6, MP7

Use a horizontal or vertical format to add and subtract linear expressions ● Warm Up ● Add linear expressions ● Add linear expressions where the Distributive Property is needed. ● Subtract linear expressions ● Real-life application

Extension 3.2: Factoring Expressions

Factor linear expressions ● Warm Up

Table of Contents



MP7

● Factor out the GCF ● Factor out a fraction ● Factor out a negative number



Activity 3.3: Solving Equations Using Addition or Subtraction MP2, MP4

Use algebra tiles to model solving equations ● Warm Up ● Use algebra tiles to model and solve an algebraic equation ● Write and solve equations shown by algebra tiles ● Match an algebraic equation to a real-life application

Lesson 3.3: Solving Equations Using Addition or Subtraction MP4

Solve equations using the Addition and Subtraction Properties of Equality ● Warm Up ● Key Idea: adding the same number to each side of an equation produces an equivalent equation (Addition Property of Equality); subtracting

the same number from each side of an equation produces an equivalent equation (Subtraction Property of Equality) ● Solve one-step algebraic equations ● Write an algebraic equation when given a real-life application ● Real-life application

Activity 3.4: Solving Equations Using Multiplication or Division MP1, MP4

Use algebra tiles to model solving equations involving multiplication and division ● Warm Up ● Use algebra tiles to model and solve an algebraic equation using division ● Write and solve an equation shown by algebra tiles ● Choose and solve an equation that represents a real-life application

Lesson 3.4: Solving Equations Using Multiplication or Division MP4, MP7

Solve equations using the Multiplication and Division Properties of Equality ● Warm Up ● Key Idea: multiplying each side of an equation by the same number produces an equivalent equation; dividing each side of an equation by

the same number produces an equivalent equation. ● Solve an algebraic equation using multiplication and division ● Solve an algebraic equation using the reciprocal ● Real-life application

Activity 3.5: Solving Two-Step Equations

Use algebra tiles to model solving two-step equations ● Warm Up

Table of Contents



MP2, MP4, MP6, MP8

● Use algebra tiles to solve a two-step equaion ● Solve a two-step equation without using algebra tiles ● Write an equation shown by algebra tiles, then use the algebra tiles to model and solve the equation ● Write and solve an equation that requires working backwards

Lesson 3.5: Solving Two-Step Equations MP2

Solve equations by undoing operations in the reverse order of how the expression would have been evaluated. ● Warm Up ● Solve two-step equations ● Combine like terms before solving an algebraic equation ● Real-life application


● Quickly review chapter concepts ● Chapter review game


○ Lesson 1: Matching Phrases to Algebraic Expressions In this lesson, students use puzzles to determine which phrases translate into given algebraic expressions. The puzzles are self-correcting, so they allow first exposure students to use the puzzles to learn key words for the different mathematical operations. Students with prior knowledge of key words can use the puzzles to test their understanding and correct any misunderstandings. The lesson plan provides guidance for individual, small group, or whole group use. The completed puzzles can be used as a springboard for a discussion of “terms,” “like terms,” and “simplest form.” Additionally the association between word expressions and algebraic expressions helps prepare students for Sections 3.3 and 3.4 homework problems where they are asked to translate word sentences into equations prior to solving.

● Section 3.3 ○ Lesson 2: Solving Equations Using Addition and Subtraction This lesson is designed for students who would benefit from using concrete models to

solve equations. Using the concept of a “balance scale,” students will construct an equation and solve. The lesson will guide students to making a connection between the model and the abstract concept.

● Section 3.4 ○ Lesson 3: Solving Equations Using a Reciprocal This lesson is designed to support students who would benefit from an in-depth explanation as to why a

reciprocal can be used to solve an algebraic equation. ● Section 3.5

○ Lesson 4: Solving Two-Step Equations This lesson is for students who may be having difficulty solving equations when more than one operation occurs in a variable expression. Using a covering method, students visually eliminate some of the confusion, so they can focus on the first step that needs to be taken in order to work towards a solution.

○ Lesson 5: Alternative Methods for Solving Two-Step Equations This lesson is for advanced students who are ready for a challenge. It is assumed that these students can easily solve two-step equations using conventional methods presented in their textbooks. In this lesson, students explore ways to solve an equation without following the reverse order of operations. The teacher serves as a resource, posing new questions and problems to try, and offering explanations for why a method might work. Students should have a strong understanding of the Distributive Property and be able to solve problems with fraction operations.

Table of Contents



Skills (Students will be able to…) ● Simplify algebraic expressions ● Use algebra tiles to add and subtract expressions ● Add and subtract linear expressions ● Factor linear expressions ● Use algebra tiles to model solving equations ● Solve equations using addition or subtraction ● Solve equations using the Multiplication and Division Properties of Equality ● Use algebra tiles to model solving two-step equations ● Solve equations by undoing operations in the reverse order of how the expression would have been evaluated










● Reasoning

Special Education









Table of Contents



● Dyslexia Screener ● PRIM checklist ● Computational Skills Grade Placement Test




Gifted and Talented







● Big Ideas Chapter 3 ● 7.EE.1 Performance Task. ● 7.EE.2 Performance Task. ● 7.EE.4 Performance Task ● STEM video and performance task


● Big Ideas Curriculum ● Denis Sheeran Training Resources ● http://www.corestandards.org/Math/Practice/


● Big Ideas Chapter 3 ● 7.EE.1 Performance Task. ● 7.EE.2 Performance Task. ● 7.EE.4 Performance Task ● STEM video and performance task ● Internet Connected Computers/iPads


● Big Ideas Chapter 3 ● 7.EE.1 Performance Task.












Table of Contents



● http://www.madisonpublicschools.org/page/231

● 7.EE.2 Performance Task. ● 7.EE.4 Performance Task ● STEM video and performance task ● Math Centers ● 3 Act Lessons ● Robert Kaplinsky Lessons ● Open Middle - 7th Grade ● Which One Doesn’t Belong? ● Solve Me Puzzles ● Estimation 180 ● Same or Different ● Visual Patterns ● Esti-Mysteries ● 51 Esti-Mysteries ● Splat Math


● Big Ideas Chapter 3 ● 7.EE.1 Performance Task. ● 7.EE.2 Performance Task. ● 7.EE.4 Performance Task ● STEM video and performance task ● iReady ● Linkit! ● IXL ● Big Ideas ● Classroom Manipulatives ● Online Manipulatives ● Content from previous grade levels ● Touch Math


● Correlates to the Ancient Arabia and Civilizations Asia units in Social Studies ● Correlates to the Structure & Function unit in Science.

8.1 Educational Technology 8.1.8.A.1 Demonstrate knowledge of a real world problem using digital tools. 8.1.8.C.1 Collaborate to develop and publish work that provides perspectives on a global problem for discussions with learners from other countries. 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem.
















Table of Contents



8.1.8.F.1 Explore a local issue, by using digital tools to collect and analyze data to identify a solution and make an informed decision. 8.2 Technology Education, Engineering, Design, and Computational Thinking - Programming 8.2.8.A.2 Examine a system, consider how each part relates to other parts, and discuss a part to redesign to improve the system. 8.2.8.B.2 Identify the desired and undesired consequences from the use of a product or system. 8.2.8.D.1 Design and create a product that addresses a real world problem using a design process under specific constraints.









9.1 Personal Finance Literacy 9.1.8.A.2 Relate how career choices, education choices, skills, entrepreneurship, and economic conditions affect income. 9.1.8.B.2 Construct a simple personal savings and spending plan based on various sources of income. 9.1.8.D.1 Determine how saving contributes to financial well-being. 9.2 Career Awareness, Exploration, and Preparation 9.2.8.B.1 Research careers within the 16 Career Clusters® and determine attributes of career success. 9.2.8.B.3 Evaluate communication, collaboration, and leadership skills that can be developed through school, home, work, and extracurricular activities for use in a career. 9.2.8.B.6 Demonstrate understanding of the necessary preparation and legal requirements to enter the workforce.

● Red Ribbon Week ● National Italian American Heritage Month ● National American Indian Heritage Month

Table of Contents



Mathematics Curriculum Grade: 7 Unit: Inequalities New Jersey Student Learning Standards 7.EE.B.4b 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. 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.

Enduring Understandings/Goals Essential Questions ● There is an infinite number of solutions to inequality

statements. ● There is a boundary point for the set of solutions. ● Solutions to inequalities are not limited to integers. ● Closed circles on inequality graphs indicate that the

boundary point is a solution to the inequality; open circles indicate that the boundary point is not included in the set of possible solutions.

● A graph of an inequality allows the solution set to be seen. It also shows what values are not part of the solution set

● Words in a problem situation can be translated to inequalities that represent the situation.

● Inequalities involving addition and subtraction can be solved in the same way as algebraic equations.

● Inequalities involving multiplication and division are not solved in the same way as algebraic equations.

● Solving multiplication or division inequalities using negative numbers results in a change of direction of the inequality symbol.

● How can you use a number line to represent solutions of an inequality? ● How can you use addition or subtraction to solve an inequality? ● How can you use multiplication or division to solve an inequality? ● How can you use an inequality to describe the dimension of a figure?

Lesson Number Teaching Points Chapter Opener for Chapter 4: Inequalities

● Introduction ● Graphing inequalities ● Comparing numbers

Activity 4.1: Writing and Graphing Inequalities MP1, MP6

Investigate writing and graphing inequalities ● Warm Up ● Understand inequality statements ● Understand inequality symbols ● Write and graph inequalities

Table of Contents



Lesson 4.1: Writing and Graphing Inequalities MP5

Translate inequalities from words to symbols and check to see whether a value is a solution of the inequality ● Warm Up ● Write a word sentence as an inequality ● Determine whether a value is a solution to an inequality ● Graph an inequality

Activity 4.2: Solving Inequalities Using Addition or Subtraction MP4, MP6

Investigate solving addition and subtraction inequalities ● Warm Up ● Match a given situation with an inequality, then graph the inequality ● Solve inequalities ● Write, solve, and graph an inequality that represents a real-life application

Lesson 4.2: Solving Inequalities Using Addition or Subtraction MP4

Use Properties of Inequality to solve addition and subtraction inequalities. ● Warm Up ● Key Idea: when the same number is added/subtracted to each side of an inequality, the inequality remains true ● Solve and graph an inequality using addition ● Solve and graph an inequality using subtraction ● Real-life application



Activity 4.3: Solving Inequalities Using Multiplication or Division MP1, MP3

Gain an intuitive understanding of solving inequalities involving multiplication or division ● Warm Up ● Copy and complete a table, decide which graph represents the solution of the inequality, then write the solution of the inequality ● Solve an inequality with a negative coefficient ● Use a table to solve inequalities involving multiplication and division.

Lesson 4.3: Solving Inequalities Using Multiplication or Division MP3

Use the Multiplication and Division Properties of Inequality to solve inequalities ● Warm Up ● Key idea: Multiplication and Division Properties of Inequality ● Solve and graph an inequality using multiplication ● Solve and graph an inequality using division ● Solve and graph an inequality with negative coefficients using multiplication ● Solve and graph an inequality with negative coefficients using division

Table of Contents



Activity 4.4: Solving Two-Step Inequalities MP3, MP6

Develop an intuitive understanding of solving two-step inequalities ● Warm Up ● Use the given condition to choose the inequality that can be used to find the possible values of the variable, justify the answer, and write four

values of the variable that satisfy the inequality

Lesson 4.4: Solving Two-Step Inequalities MP7

Solve and graph two-step inequalities. ● Warm Up ● Solve two-step inequalities ● Graph an inequality ● Real-life application


● Review chapter concepts ● Complete chapter review


○ Lesson 1: Inequality Statements and Graphs This lesson is designed for students who would benefit from a review of inequalities. Students will play a card game that allows them to find whole number solutions to a given inequality and mark those solutions on a number line. The teacher uses the game as a springboard for introducing how to represent all the solutions, not just integer solutions. This lesson covers reading, graphing, and interpreting inequality statements.

○ Lesson 2: Compound Inequalities This lesson is designed for advanced students who might benefit from a challenge. In this lesson, it is assumed students have prior knowledge of inequalities and skill in graphing simple inequalities, because students use the basic graphing of an inequality to graph compound inequalities. The lesson approaches the concept of compound inequalities through both the intersection and the union of two sets, first represented with Venn diagrams and then transferred to number lines. Students will find solutions where two sets share common elements, where one set is a subset of the other set, and where the two sets do not share any common elements. Statements will be written using inequality symbols and variables, as well as with the terms “and” and “or.”

● Sections 4.2 and 4.3 ○ Lesson 3: Solving One-Step Inequalities This lesson helps students realize that when solving inequalities you can add or subtract any rational number, and

multiply or divide by a positive value on each side of an inequality, yet the same is not true when multiplying or dividing by a negative factor on each side. In this lesson, students begin with a simple inequality, which they graph on a number line. Students then compare the inequality to a set of “one-step” inequalities to determine which of these have the same solution set as the original graphed inequality. Through observation and discussion, the focus becomes a question of which inequalities have the same solution and why. Teacher guidance leads students to realize that the inequalities that are merely transformations of adding or subtracting a value to each side of the original inequality produce the same solutions as the original. When this same principle is applied to multiplying, discussion ensues as to why it works sometimes (when the factor is positive) but not others (when the factor is negative). Through the activity, students see that the inequalities they graph are heading the reverse direction indicated by the inequality sign of the original inequality whenever a negative coefficient exists. These observations are then applied to actions that must be taken when solving one-step inequalities to ensure the solutions remains true.

Skills (Students will be able to…) ● Translate inequalities from words to symbols and check to see whether a value is a solution of the equality

Table of Contents



● Use Properties of Inequality to solve addition and subtraction inequalities ● Use Multiplication and Division Properties of Inequality to solve inequalities ● Solve and graph two-step inequalities










● Reasoning ● Dyslexia Screener ● PRIM checklist ● Computational Skills Grade Placement Test

Special Education














Table of Contents




Gifted and Talented







● Big Ideas Chapter 4 ● 7.EE.4 Performance Task ● STEM video and performance task




● Big Ideas Chapter 4 ● 7.EE.4 Performance Task ● STEM video and performance task ● Internet Connected Computers/iPads


● Big Ideas Chapter 4 ● 7.EE.4 Performance Task ● STEM video and performance task ● Math Centers ● 3 Act Lessons ● Robert Kaplinsky Lessons ● Open Middle - 7th Grade ● Which One Doesn’t Belong? ● Solve Me Puzzles ● Estimation 180 ● Same or Different ● Visual Patterns ● Esti-Mysteries ● 51 Esti-Mysteries





















Table of Contents



● Splat Math


● Big Ideas Chapter 4 ● 7.EE.4 Performance Task ● STEM video and performance task ● iReady ● Linkit! ● IXL ● Big Ideas ● Classroom Manipulatives ● Online Manipulatives ● Content from previous grade levels ● Touch Math


● Correlates to the Middle Ages unit in Social Studies ● Correlates to the Inheritance & Variation of Traits unit in Science.

8.1 Educational Technology 8.1.8.C.1 Collaborate to develop and publish work that provides perspectives on a global problem for discussions with learners from other countries. 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem. 8.2 Technology Education, Engineering, Design, and Computational Thinking - Programming 8.2.8.A.4 Redesign an existing product that impacts the environment to lessen its impact(s) on the environment. 8.2.8.C.7 Collaborate with peers and experts in the field to research and develop a product using the design process, data analysis and trends, and maintain a design log with annotated sketches to record the developmental cycle. 8.2.8.D.5 Explain the impact of resource selection and the production process in the development of a common or technological product or system





● Reason Effectively ● Use Systems Thinking ● Making Judgements and Decisions



Table of Contents



● Solve Problems Communication and Collaboration

● Communicate Clearly Life and Career Skills Initiative and Self Direction



9.1 Personal Finance Literacy 9.1.8.C.2 Compare and contrast the financial products and services offered by different types of financial institution. 9.1.8.E.6 Compare the value of goods or services from different sellers when purchasing large quantities and small quantities. 9.2 Career Awareness, Exploration, and Preparation 9.2.8.B.2 Develop a Personalized Student Learning Plan with the assistance of an adult mentor that includes information about career areas of interest, goals and an educational plan.

● National American Indian Heritage Month

Mathematics Curriculum Grade: 7 Unit: Ratios and Proportions New Jersey Student Learning Standards 7.RP.A.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 1/2 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.A.2a 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. 7.RP.A.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. 7.RP.A.2c 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 7.RP.A.2d Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. 7.RP.A.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.

Enduring Understandings/Goals Essential Questions ● Rates can have fractions in the numerator, denominator, or

both. ● A ratio table is an organizing structure and the units guide

the computations.

● How do rates help you describe real-life problems? ● How can proportions help you decide when things are “fair”? ● How can you write a proportion that solves a problem in real life? ● How can you use ratio tables and cross products to solve proportions?

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● Any equivalent ratio can be used to find the unit rate. ● A proportion is an equation stating that two ratios are

equivalent. ● The graph of every proportional relationship is a line

through the origin. ● When two measures are being compared, the order in which

they are written does matter. ● A ratio table is a tool to show relationships between

different quantities.. ● A graph is a tool to show the relationship between two

quantities. ● In the graph of a proportional relationship, the unit rate y

can be found from the point (1, y). ● A rate is a ratio. ● When two quantities vary directly, the ratio of one quantity

to another is a constant. ● The ordered pair (0,0) is always a solution of an equation

that describes two quantities that vary directly. ● The constant ratio is the slope of the line that is the graph of

two quantities that vary directly. ● When two quantities vary directly, it is said that they are

directly proportional.

● How can you compare two rates graphically? ● How can you use a graph to show the relationship between two quantities that vary directly?

How can you use an equation?

Lesson Number Teaching Points Chapter Opener for Chapter 5: Ratios and Proportions

● Introduction ● Simplifying fractions ● Identifying equivalent fractions ● Solving equations

Activity 5.1: Ratios and Rates MP7

Students explore rates ● Warm Up ● Find reasonable rates ● Simplify expressions that contain fractions ● Use ratio tables to find equivalent rates ● Unit (dimensional) analysis

Lesson 5.1: Ratios and Rates

Determine rates from words, tables, and graphs. ● Warm Up

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MP1, MP2, MP3, MP4, MP7

● Find ratios and rates ● Find a rate from a ratio table ● Find a rate from a graph ● Solve a ratio problem

Activity 5.2: Proportions MP3

Examine pairs of rates and decide if they are equivalent, or fair. ● Warm Up ● Determine proportions ● Check a proportion ● Determine fairness

Extension 5.2: Graphing Proportional Relationships MP6

Graph proportional relationships ● Warm Up ● Determine whether two quantities are proportional ● Interpret the graph of a proportional relationship

Lesson 5.2: Proportions MP3

Use multiplication and division, and the Cross Products Property to decide if two ratios are equal ● Warm Up ● Key Idea: definition of proportion ● Determine whether ratios form a proportion ● Determine whether two quantities are proportional ● Key Idea: Cross Products Property ● Identify proportional relationships

Activity 5.3: Writing Proportions MP2, MP8

Write and solve proportions related to baseball that use simple mental math ● Warm Up ● Write proportions ● Use proportions and information contained in a table to solve problems

Lesson 5.3: Writing Proportions MP2, MP4

Write and solve a proportion using mental math. ● Warm Up ● Write a proportion ● Solve proportions using mental math


● Review ● Complete graphic organizer ● Administer the quiz

Table of Contents



Activity 5.4: Solving Proportions MP2, MP3, MP4

Solve proportions using the Cross Products Property. ● Warm Up ● Solve a proportion in science ● Play the game of Criss Cross

Lesson 5.4: Solving Proportions MP1, MP6

Solve proportions using different strategies ● Warm Up ● Solve proportions using multiplication ● Solve proportions using the Cross Products Property ● Real-life application

Activity 5.5: Slope MP4, MP8

Explore constant rates of speed in a table and on a graph ● Warm Up ● Compare unit rates ● Compare two rates graphically

Lesson 5.5: Slope MP3, MP5

Define slope and determine the slope of a line from its graph ● Warm Up ● Key Idea; definition and formula of slope ● Find the slope of a graphed line ● Graph data, find and interpret the slope of a line through the points

Activity 5.6: Direct Variation MP4, MP6

Complete a table of values, plot ordered pairs, and write equations to develop an understanding of quantities that vary directly. ● Warm Up ● Complete a data table from a story ● Draw a graph of the data ● Draw graphs and write the equation that describes the relationship between the two quantities

Lesson 5.6: Direct Variation MP4

Use a formal definition of direct variation ● Warm Up ● Key Idea: definition of direct variation ● Identify direct variation by using a table of values ● Identify direct variation by using an equation ● Real-life application



Differentiating the Lesson, Chapter 5

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● Section 5.1 ○ Lesson 1: Ratios This lesson supports students who may benefit from a concrete/visual model to understand the concept of ratios. Students use color tiles

to model a ratio and make the connection between the concrete and abstract concepts related to equivalent fractions that are used in determining ratios. ○ Lesson 2: Unit Rates In this lesson, students are provided with a visual representation to understand the concept of a unit rate. Students will use a grid to

represent a rate, and then use it to find the equivalent unit rate. ○ Lesson 3: Ratio Extension This lesson is designed for students who have mastered the concept of ratios and would benefit from a challenge. Students are

given access to a variety of manipulative materials to use for support as they work independently, or in pairs, to develop a solution to a situation involving ratios.

● Section 5.2 and 5.3 ○ Lesson 4: Representing Proportional Relationships In this lesson, students create proportions through an activity in which students imagine they are

testers for a shoe company. Using role play, they are paid a given amount for every x number of steps they take in the test shoes. Students record the results of each scenario in a table and on a graph.

Skills (Students will be able to…) ● determine rates from words, tables, and graphs. ● graph proportional relationships ● use multiplication and division, and the Cross Products Property to decide if two ratios are equal. ● write and solve a proportion using mental math ● solve proportions using different strategies ● define slope and determine the slope of a line from its graph ● use a formal definition of direct variation






Special Education



High-Prep Differentiation: ● Alternative formative and summative assessments ● Guided Reading




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● Personal agendas ● Project-based learning ● Problem-based learning ● Stations/centers ● Tiered activities/assignments ● Varying organizers for instructions






Gifted and Talented

















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● Big Ideas Chapter 5 ● 7.RP.1 Performance Task ● 7.RP.2 Performance Task ● 7.RP.3 Performance Task ● STEM video and performance task



● Big Ideas Chapter 5 ● 7.RP.1 Performance Task ● 7.RP.2 Performance Task ● 7.RP.3 Performance Task ● STEM video and performance task ● Internet Connected Computers/iPads


● Big Ideas Chapter 5 ● 7.RP.1 Performance Task ● 7.RP.2 Performance Task ● 7.RP.3 Performance Task ● STEM video and performance task ● Math Centers ● 3 Act Lessons ● Robert Kaplinsky Lessons ● Open Middle - 7th Grade ● Which One Doesn’t Belong? ● Solve Me Puzzles ● Estimation 180 ● Same or Different ● Visual Patterns ● Esti-Mysteries ● 51 Esti-Mysteries ● Splat Math


● Big Ideas Chapter 5 ● 7.RP.1 Performance Task ● 7.RP.2 Performance Task ● 7.RP.3 Performance Task ● STEM video and performance task ● iReady ● Linkit! ● IXL ● Big Ideas ● Classroom Manipulatives ● Online Manipulatives ● Content from previous grade levels ● Touch Math

















Table of Contents



● Correlates to the Ancient Rome and Economy units in Social Studies ● Correlates to the Chemical Reactions and Structure & Properties of Matter units in

Science.

8.1 Educational Technology 8.1.8.A.1 Demonstrate knowledge of a real world problem using digital tools. 8.1.8.C.1 Collaborate to develop and publish work that provides perspectives on a global problem for discussions with learners from other countries. 8.2 Technology Education, Engineering, Design, and Computational Thinking - Programming 8.2.8.A.1 Research a product that was designed for a specific demand and identify how the product has changed to meet new demands (i.e. telephone for communication – smart phone for mobility needs). 8.2.8.B.1 Evaluate the history and impact of sustainability on the development of a designed product or system over time and present results to peers. 8.2.8.E.1 Identify ways computers are used that have had an impact across the range of human activity and within different careers where they are used.











9.1 Personal Finance Literacy 9.1.8.A.2 Relate how career choices, education choices, skills, entrepreneurship, and economic conditions affect income. 9.1.8.C.7 Determine potential consequences of using “easy access” credit (e.g., using a line of credit vs. obtaining a load for a specific purpose). 9.1.8.F.2 Examine the implications of legal and ethical behaviors when making financial decisions. 9.2 Career Awareness, Exploration, and Preparation

● Black History Month ● Kindness Month

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9.2.8.B.6 Demonstrate understanding of the necessary preparation and legal requirements to enter the workforce.

Mathematics Curriculum Grade: 7 Unit: Percents New Jersey Student Learning Standards 7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and d ecimals), 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. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. 7.RP.A.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. Enduring Understandings/Goals Essential Questions

● A percent can be written as a fraction and as a decimal. ● Percents do not need to involve whole numbers. ● The decimal point moves 2 places when converting between

decimals and percents. ● The farther to the right a number is on the number line, the

greater the number. ● The concept of a proportion can be used to solve different

types of percent problems. ● Move the decimal point one place to the left in a number to

find 10% of that number. ● A ratio table can be used to answer a percent equation. ● A percent bar model helps to estimate and consider the

reasonableness of the answer. ● The percent proportion can be used to find a percent, to

find a part, and to find the whole. ● There is a difference between amount of change and percent

of change. ● When a quantity has doubled, it has increased 100%. ● The percent error compares the amount of error to the actual

amount. ● Finding an original price is the same as finding the whole. ● A discounted price can be found by multiplying the original

price by 1 minus the decimal form of the discount percent.

● How does the decimal point move when you rewrite a percent as a decimal and when you rewrite a decimal as a percent?

● How can you order numbers that are written as fractions, decimals, and percents? ● How can you use models to estimate percent questions? ● How can you use an equivalent form of the percent proportion to solve a percent problem? ● What is a percent of decrease? ● What is a percent of increase? ● How can you find discounts and selling prices? ● How can you find the amount of simple interest earned on a savings account? ● How can you find the amount of interest owed on a loan?

Lesson Number Teaching Points

Table of Contents



Chapter Opener for Chapter 6: Percents

● Introduction ● Write percents and fractions ● Write fractions as percents

Activity 6.1: Percents and Decimals MP3, MP4, MP6

Use a visual model to represent percents, then write the percents as decimals. ● Warm Up ● Write percents as decimals ● Write percents that do not involve whole numbers as decimals ● Write decimals as percents

Lesson 6.1: Percents and Decimals MP3

Convert between percents and decimals ● Warm Up ● Key Idea: writing percents as decimals by moving the decimal point ● Write percents as decimals ● Key Idea: writing decimals as percents ● Write decimals as percents ● Write a fraction as a percent and a decimal ● Real-life application

Activity 6.2: Comparing and Ordering Fractions, Decimals, and Percents MP2

Compare and order common percents, decimals, and fractions ● Warm Up ● Use fractions, decimals, and percents in situations where most appropriate ● Order fractions, decimals, and percents ● Play the game of Math Card War

Lesson 6.2: Comparing and Ordering Fractions, Decimals, and Percents MP2, MP3, MP8

Compare and order less common percents, decimals, and fractions ● Warm Up ● Compare fractions, decimals, and percents ● Real-life applications

Activity 6.3: The Percent Proportion MP2, MP4, MP5

Use the percent bar model to explore three types of percent problems. ● Warm Up ● Estimate a part using a model ● Estimate a percent using a model ● Estimate the whole using a model ● Use ratio tables to answer a percent question

Table of Contents



Lesson 6.3: The Percent Proportion MP2, MP4

Use the percent proportion to solve three types of percent problems ● Warm Up ● Key Idea: the percent proportion ● Find a percent using the percent proportion ● Find a part using the percent proportion ● Find the whole using the percent proportion ● Real-life application

Activity 6.4: The Percent Equation MP3

Explore the connection between the percent proportion and the percent equation ● Warm Up ● Solve percent problems using different methods ● Find parts using different methods ● Derive the percent equation ● Identify different equations

Lesson 6.4: The Percent Equation MP2, MP3, MP4

Use the percent equation to solve three types of percent problems ● Warm Up ● Key Idea: the percent equation ● Find part of a number using the percent equation ● Find a percent using the percent equation ● Find the whole using the percent equation ● Real-life application

Sections 6.1-6.4 Study Help and Quiz


Activity 6.5: Percents of Increase and Decrease MP1, MP5, MP8

Explore two real-life problems with quantities that decreased or increased by a percent. ● Warm Up ● Find the percent decrease in a problem ● Find the percent increase in a problem

Lesson 6.5: Percents of Increase and Decrease MP4, MP5

Use a percent of change formula to solve problems ● Warm Up ● Key Idea: definition of percent of increase and percent of decrease ● Find a percent of increase ● Find a percent of decrease ● Key Idea: define percent error

Table of Contents



● Find a percent error

Activity 6.6: Discounts and Markups MP2, MP3, MP4

Explore discounts and selling prices using a percent bar model. ● Warm Up ● Comparing discounts ● Find the original price ● Find the selling price

Lesson 6.6: Discounts and Markups MP2, MP3

Use the percent equation to find discounts and markups of items ● Warm Up ● Key Idea: define discounts and markups ● Find a sale price ● Find an original price ● Find a selling price ●

Activity 6.7: Simple Interest MP2, MP4, MP5, MP6

Explore the simple interest formula, applying it to several consumer applications ● Warm Up ● Find simple interest ● Financial Literacy: write a report about credit cards ● Financial Literacy: find the interest paid on the national debt each year

Lesson 6.7: Simple Interest MP2

Use the simple interest formula and knowledge of equation solving to solve for different variables in the formula ● Warm Up ● Key Idea: define simple interest ● Find interest earned ● Find an annual interest rate ● Find an amount of time (to earn a particular amount of interest) ● Find an amount paid on a loan


● Review chapter concepts ● Chapter review


○ Lesson 1: Writing Whole Number Percents as Decimals and Decimals as Percents This lesson makes the connection between base ten block models and decimals. Students use the blocks as necessary, which continues to support kinesthetic learners and those who may not have a solid understanding of decimal place value. To preserve the use of only whole number percents, decimals do not extend beyond the hundredths place.

○ Lesson 2: Percents with Decimal Parts, as Fractions and Decimals

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○ Lesson 2A: Writing Percents with Decimal Parts as Fractions and Decimals This lesson is for students who have had some exposure to percents, or who learn quickly, but will still benefit from a kinesthetic learning style. It can also serve as a review and extension for students who have shown success with whole number percents in Lesson 1 and are ready to move on. In this lesson, the majority of percent work is done with base ten blocks. Students begin with a few whole number percents and percents greater than 100, but quickly move to percents with decimal or fractional parts.

○ Lesson 2B: Writing Decimals and Fractions as Percents with Decimal Parts This lesson uses the understanding of base ten blocks and place value to make conversions from decimals or fractions to percents. Students use the blocks to write equivalent fractions with denominators of 10, 100, or 1000 by building a flat with 10 rods, 100 units, or 1000 chips. They even imagine building a flat with 10,000 bits. Students reflect on the results of their work with blocks to generalize patterns they notice.

● Sections 6.4–6.7 ○ Lesson 3: Project: Percents in the Real World In this project, each student will take on the role of a waiter/waitress, news reporter, a retail store owner,

an advertising agent, or a toy manufacturer, based on their individual interests. Throughout lessons on the percent equation, percents of increase and decrease, discounts and markups, and simple interest, each student will work on the solution to an essential question related to a chosen role, while also determining how to apply one skill from each lesson to the context of that role. Students will then present their essential question solutions and four-skill demonstrations in a format of their choice: written report, video, oral presentation, poster, or other teacher-approved format.

○ This project can be used with individual students who are seeking real-world applications of mathematics for the topic of percents. It also provides an alternative assessment of student understanding for the concepts of the percent equation, percents of increase and decrease, discounts and markups, and simple interest. This project can be assigned to individuals or to all the students in the class. With an all-class assignment, students might be placed in small groups according to the roles they choose to take on during this chapter. Placing students in groups by interests will allow students of varying ability levels to work with peers they may not regularly be grouped with academically

Skills (Students will be able to…) ● convert between percents and decimals ● compare and order less common percents, decimals, and fractions ● use the percent proportion to solve three types of percent problems ● use the percent equation to solve three types of percent problems ● use a percent of change formula to solve problems ● use the percent equation to find discounts and markups of items ● use the simple interest formula and knowledge of equation solving to solve for different variables in the formula



● Closure Activity

Special Education

● Differentiation for All Students (Special Needs, ESL, Gifted Learners, & Mainstream Learners)


Table of Contents



● Homework ● Mid-Chapter Quiz ● End-of-Chapter Quiz








● Subgroup Accommodations and Modifications

● Curricular Modifications and Guidance for Students Educated in Special Class Settings Differentiation:

● Preview content and concepts ● Behavior management plan ● Highlight text ● Small group setting







Gifted and Talented













Table of Contents







● Big Ideas Chapter 6 ● 7.EE.3 Performance Task ● 7.RP.3 Performance Task ● STEM video and performance task




● Big Ideas Chapter 6 ● 7.EE.3 Performance Task ● 7.RP.3 Performance Task ● STEM video and performance task ● Internet Connected Computers/iPads


● Big Ideas Chapter 6 ● 7.EE.3 Performance Task ● 7.RP.3 Performance Task ● STEM video and performance task ● Math Centers ● 3 Act Lessons ● Robert Kaplinsky Lessons ● Open Middle - 7th Grade ● Which One Doesn’t Belong? ● Solve Me Puzzles ● Estimation 180 ● Same or Different ● Visual Patterns ● Esti-Mysteries ● 51 Esti-Mysteries ● Splat Math


● Big Ideas Chapter 6 ● 7.EE.3 Performance Task ● 7.RP.3 Performance Task ● STEM video and performance task ● iReady ● Linkit!


















Table of Contents



● IXL ● Big Ideas ● Classroom Manipulatives ● Online Manipulatives ● Content from previous grade levels ● Touch Math


● Correlates to the Exploration & Colonization unit in Social Studies ● Correlates to the Chemical Reactions and Earth Systems units in Science.

8.1 Educational Technology 8.1.8.A.1 Demonstrate knowledge of a real world problem using digital tools. 8.1.8.C.1 Collaborate to develop and publish work that provides perspectives on a global problem for discussions with learners from other countries. 8.1.8.F.1 Explore a local issue, by using digital tools to collect and analyze data to identify a solution and make an informed decision. 8.2 Technology Education, Engineering, Design, and Computational Thinking - Programming 8.2.8.A.5 Describe how resources such as material, energy, information, time, tools, people, and capital contribute to a technological product or system. 8.2.8.C.3 Evaluate the function, value, and aesthetics of a technological product or system, from the perspective of the user and the producer.











Table of Contents



9.1 Personal Finance Literacy 9.1.8.A.7 Explain the purpose of the payroll deduction process, taxable income, and employee benefits. 9.1.8.B.7 Construct a budget to save for long-term, short-term, and charitable goals. 9.1.8.D.3 Differentiate among various investment opportunities. 9.1.8.F.1 Explain how the economic system of production and consumption may be a means to achieve significant societal goals. 9.2 Career Awareness, Exploration, and Preparation 9.2.8.B.5 Analyze labor market trends using state and federal labor market information and other resources available online.

● Black History Month ● Kindness Month

Mathematics Curriculum Grade: 7 Unit: Constructions and Scale Drawings New Jersey Student Learning Standards 7.G.A.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 7.G.A.2 Draw (with technology, with ruler and protractor, as well as freehand) geometric shapes with given conditions. Foc us 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.B.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. Enduring Understandings/Goals Essential Questions

● It is important to provide supporting evidence for conjectures.

● Angles are named by the vertex alone or by three points with the vertex listed in the middle.

● Adjacent angles share a side. ● Vertical angles have equal measure. ● Two angles are complementary if their angle measures total

90º. ● Two angles are supplementary if their angle measures total

180º. ● Triangle angle measures total 180º ● Triangles can be classified by the measure of their angles. ● Triangles can be classified by the length of their sides. ● An equation can be solved to find the third angle when the

measures of the other two angles are known. ● Isosceles triangles have at least two sides of equal length. ● Scalene triangles have no sides of equal length. ● Quadrilaterals can have more than one name.

● What can you conclude about the angles formed by two intersecting lines? ● How can you classify two angles as complementary or supplementary? ● How can you construct triangles? ● How can you classify quadrilaterals? ● How can you enlarge or reduce a drawing proportionally?

Table of Contents



● There are relationships among the various types of quadrilaterals.

● The interior angle measures of a quadrilateral total 360º ● In a parallelogram, opposite angles are congruent and

adjacent angles are supplementary. ● ● An equation can be written and solved in order to find a

missing angle measure of a quadrilateral. ● Ratio tables can be used to find scale factors.

Lesson Number Teaching Points Chapter Opener for Chapter 7: Constructions and Scale Drawings

● Introduction ● Measure angles ● Draw angles

Activity 7.1: Adjacent and Vertical Angles MP3, MP6

Explore drawing, naming, and measuring angles, and investigate relationships between angles. ● Warm Up ● Draw angles and relate the classification of angles to the hands of a clock ● Name angles and discover what it means for angles to be adjacent ● Measure angles created by a pair of intersecting lines and discover that vertical angles have the same measure.

Lesson 7.1: Adjacent and Vertical Angles MP3

Identify adjacent or vertical angles ● Warm Up ● Key Idea: definitions of adjacent and vertical angles ● Identify and name vertical and adjacent angles ● Use adjacent and vertical angles to find the value of x ● Construct vertical angles with a given measure

Activity 7.2: Complementary and Supplementary Angles MP3, MP5

Explore complementary and supplementary angles. ● Warm Up ● Read ordered pairs from the graphs to complete the tables of complementary and

supplementary angles in order to discover how to know when two angles are complementary or supplementary. ● Explore rules about angles ● Classify pairs of angles ● Identify angles in the context of a problem

Lesson 7.2: Complementary and Supplementary Angles

Classify several pairs of angles as complementary or supplementary. ● Warm Up ● Key Idea: summarize complementary and supplementary angles ● Classify pairs of angles

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MP3, MP5 ● Use complementary and supplementary angles to write and solve an equation for the value of x ● Construct a pair of adjacent supplementary angles with one angle having a given measure.

Activity 7.3: Triangles (Day 1) MP3, MP5

Investigate constructing triangles using side lengths and angle measures ● Warm Up ● Construct triangles using side lengths ● Use geometry software to draw a triangle with two given side lengths, then find the third side.

Activity 7.3: Triangles (Day 2) MP5

Investigate constructing triangles using side lengths and angle measures. ● Warm Up ● Construct triangles using angle measures ● Using technology to draw triangles (angle measure)

Extension 7.3: Angle Measures of Triangles MP1, MP3

Find the missing angle measure of a triangle and classify the triangle. ● Warm Up ● Key Idea: the sum of the angle measures of a triangle is 180º ● Find the missing angle measure when given the other two angle measures ● Write and solve an equation to find missing angles in a triangle

Lesson 7.3: Triangles MP3, MP6

Classify and further investigate constructing triangles ● Warm Up ● Key Idea: how to classify triangles by angles and sides ● Classify triangles by both angles and sides ● Use a straight edge and protractor to construct and classify triangles with given angle measures ● Use a protractor and ruler to construct a triangle with two given side lengths that meet at a given angle measure.

Sections 7.1 – 7.3 Study Help and Quiz

● Introduction ● Complete graphic organizer ● Administer quiz

Activity 7.4: Quadrilaterals (Day 1) MP3, MP5

Explore properties of quadrilaterals ● Warm Up ● Use descriptions to form quadrilaterals ● Name quadrilaterals ● Form quadrilaterals

Activity 7.4: Quadrilaterals (Day 2)

Explore properties of quadrilaterals ● Warm Up

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MP3, MP5

● Use geometry software to draw a quadrilateral that fits a given description

Lesson 7.4: Quadrilaterals MP4

Classify quadrilaterals by the attributes they possess ● Warm Up ● Classify quadrilaterals ● Key Idea: the equation used to represent the sum of the angle measures of a quadrilateral ● Write and solve an equation in order to find a missing angle measure of a quadrilateral ● Draw a quadrilateral with a given name and angle measures.

Activity 7.5: Scale Drawings MP3, MP6

Compare measurements and recreate drawings ● Warm Up ● Compare measurements to find a scale factor and solve a problem ● Recreate a drawing using a different scale

Lesson 7.5: Scale Drawings MP3, MP6

Use a scale drawing to find a missing measure ● Warm Up ● Key Ideas: scale drawings, scale models, scale ● Find an actual distance on a map using the map scale factor ● Find a dimension of a scale model when given the actual length and the scale ● Find a scale factor ● Find an actual perimeter and area

Sections 7.4 – 7.5 Quiz and Chapter Review


Differentiating the Lesson, Chapter 7 ● Sections 7.1 and 7.2

○ Lesson 1: Complementary, Supplementary, and Vertical Angles This lesson is designed for students who are visual or kinesthetic learners and need to see numerous representations before determining generalizations about the relationships between angles. Using uncooked spaghetti to represent lines and rays, students can easily see relationships and observe changes that occur when the ray represented by the spaghetti is moved. Students observe relationships between complementary angles, supplementary angles, and vertical angles.

● Section 7.2 ○ Lesson 2: Writing Equations to Find Angle Measures This lesson challenges students to write and solve their own equations involving complementary

and supplementary angles. Students will represent unknown angle measures using variable expressions, write an equation using angle relationships, and then solve their equations to find the unknown angle measures. Students should be proficient in combining like terms and solving two-step equations.

● Section 7.3 ○ Lesson 3: Classifying Triangles In this lesson, students will explore which angle classifications (acute, obtuse, or right) and which side length classifications

(scalene, isosceles, or equilateral) can be combined to form a triangle. Students will draw possible combinations and identify which combinations are impossible. Students must justify why certain combinations are impossible based on the sum of the angle measures in a triangle.

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● Section 7.4 ○ Lesson 4: Classifying Quadrilaterals This lesson provides a resource for students who are having difficulty classifying quadrilaterals. Using cutouts of

quadrilaterals, students physically slide a quadrilateral through a sieve (or flowchart). They answer questions at each step to determine which characteristics the quadrilateral has, therefore identifying to which categories of quadrilaterals the figure belongs. Upon reaching the end of a route, students identify the quadrilateral’s most specific name. Students use their experience with the sieve and their collected results to write true/false statements about quadrilaterals

● Section 7.5 ○ Lesson 5: Scale Models The purpose of this lesson is to create interest in the use of scale through a student’s area of interest. Students select a cartoon

drawing, toy, action figure, or other item that is not true size. Students then use measurements and concepts of scale to determine the approximate scale of their selected items.

Skills (Students will be able to…) ● Identify adjacent or vertical angles ● Classify angles as complementary or supplementary ● Find the missing angle measure of a triangle and classifying the triangle ● Classify and construct triangles ● Classify quadrilaterals ● Use scale drawings to find missing measurements







● Initial LinkIt Benchmark: September ● Mid-year LinkIt Benchmark: December ● End of year LinkIt Benchmark: Last week in April

Special Education



High-Prep Differentiation: ● Alternative formative and summative assessments ● Guided Reading ● Personal agendas ● Project-based learning ● Problem-based learning ● Stations/centers ● Tiered activities/assignments




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● Beginning of the Year, Mid-Year and End-of-Year Math Assessments




● Varying organizers for instructions Low-Prep Differentiation:

● Clubbing activities ● Exploration by interest ● Flexible groupings





Gifted and Talented







● Big Ideas Chapter 7 ● 7.G.1 Performance Task ● 7.G.2 Performance Task


● Big Ideas Chapter 7 ● 7.G.1 Performance Task ● 7.G.2 Performance Task










Table of Contents



● 7.G.5 Performance Task ● STEM video and performance task



● 7.G.5 Performance Task ● STEM video and performance task ● Internet Connected Computers/iPads


● Big Ideas Chapter 7 ● 7.G.1 Performance Task ● 7.G.2 Performance Task ● 7.G.5 Performance Task ● STEM video and performance task ● Math Centers ● 3 Act Lessons ● Robert Kaplinsky Lessons ● Open Middle - 7th Grade ● Which One Doesn’t Belong? ● Solve Me Puzzles ● Estimation 180 ● Same or Different ● Visual Patterns ● Esti-Mysteries ● 51 Esti-Mysteries ● Splat Math


● Big Ideas Chapter 7 ● 7.G.1 Performance Task ● 7.G.2 Performance Task ● 7.G.5 Performance Task ● STEM video and performance task ● iReady ● Linkit! ● IXL ● Big Ideas ● Classroom Manipulatives ● Online Manipulatives ● Content from previous grade levels ● Touch Math


● Correlates to the Exploration & Colonization unit in Social Studies ● Listen to books on CDs, tapes, videos or podcasts if available.
















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● Correlates to the Body Systems and Organization for Matter & Energy Flow in Organisms in Science.

8.1 Educational Technology 8.1.8.A.2 Create a document (e.g., newsletter, reports, personalized learning plan, business letters or flyers) using one of more digital applications to be critiqued by professionals for usability. 8.1.8.A.3 Use and/or develop a simulation that provides an environment to solve a real world problem or theory. 8.1.8.D.2 Demonstrate the application of appropriate citations to create digital content. 8.2 Technology Education, Engineering, Design, and Computational Thinking - Programming 8.2.8.A.5 Describe how resources such as material, energy, information, time, tools, people, and capital contribute to a technological product or system. 8.2.8.C.7 Collaborate with peers and experts in the field to research and develop a product using the design process, data analysis and trends, and maintain a design log with annotated sketches to record the developmental cycle. 8.2.8.D.1 Design and create a product that addresses a real world problem using a design process under specific constraints.

● Listen to books on websites (pbskids.org/lions/index.html, storylineonline.net, storyit.com, Elementary Connections Page)

● Use document camera or overhead projector for shared reading of texts. ● Use virtual manipulatives ● Use IXL.com









9.1 Personal Finance Literacy 9.1.8.A.4 Relate earning power to quality of life across cultures. 9.1.8.C.5 Calculate the cost of borrowing various amounts of money using different types of credit (e.g., credit cards, installment loans, mortgages). 9.1.8.E.6 Compare the value of goods or services from different sellers when purchasing large quantities and small quantities.

● National Women’s History Month ● National Irish-American Heritage Month

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9.2 Career Awareness, Exploration, and Preparation 9.2.8.B.4 Evaluate how traditional and nontraditional careers have evolved regionally, nationally, and globally.

Mathematics Curriculum Grade: 7 Unit: Circles and Area New Jersey Student Learning Standards 7.G.B.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.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Enduring Understandings/Goals Essential Questions

● Pi is a calculable number. ● The formula for circumference can be used to solve real-life

problems. ● The radius of a circle is equal to one-half of the diameter. ● The circumference of a circle can be found when given the

radius or the diameter. ● The formula for circumference can be used to find the

perimeter of a semi-circle. ● A variety of problem-solving skills can be used to find the

perimeter of a composite figure ● Formulas can be used to find the perimeter of a composite

figure. ● Pi can be rounded to 3 when estimating. ● Divide composite figures into familiar geometric shapes and

use known area formulas to find the total area.

● How can you find the circumference of a circle? ● How can you find the perimeter of a composite figure? ● How can you find the area of a circle? ● How can you find the area of a composite figure?

Lesson Number Teaching Points

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Chapter Opener for Chapter 8: Circles and Area

● Introduction ● Classify figures ● Square numbers and use order of operations

Activity 8.1: Circles and Circumference MP3, MP5, MP6, MP8

Investigate a technique for calculating the value of pi. ● Warm Up ● Approximating pi using a square and a circle ● Approximating pi using different polygons

Lesson 8.1: Circles and Circumference MP1

Use the formula for circumference to solve real-life problems. ● Warm Up ● Key Idea: definitions of radius and diameter ● Find a radius and a diameter ● Key Idea: circumference of a circle ● Find the circumference of a circle given either the radius or diameter ● Estimate the diameter given the circumference ● Find the perimeter of a semicircular region

Activity 8.2: Perimeters of Composite Figures MP3, MP4, MP6

Use a variety of problem-solving skills to find the perimeter of several composite figures. ● Warm Up ● Use a pattern to find the perimeter of a figure ● Combine figures and determine the perimeter ● Combine figures to determine the perimeter to solve a problem

Lesson 8.2: Perimeters of Composite Figures MP3, MP6

Use formulas to find the perimeter of composite figures ● Warm Up ● Estimate a perimeter using grid paper ● Find a perimeter of a composite figure ● Find the perimeter of a composite figure to solve a problem


● Review ● Complete the graphic organizer ● Administer the quiz

Activity 8.3: Areas of Circles MP1, MP4, MP8

Develop an intuitive understanding of how to find the area of a circle ● Warm Up ● Estimate the area of a circle using grid paper ● Approximating the area of a circle using a model

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Lesson 8.3: Areas of Circles MP4

Use the formula for area to solve real-life problems ● Warm Up ● Key Idea: area of a circle ● Use the area formula to find the area of a circle ● Use the area formula to solve a problem ● Find the area of a semicircle to solve a problem

Activity 8.4: Areas of Composite Figures MP1

Develop an intuitive understanding of how to find the area of composite figures ● Warm Up ● Estimate the area of a figure using different methods ● Look at patterns that fill a square with circles

Lesson 8.4: Areas of Composite Figures MP3

Divide composite figures into familiar geometric shapes and use known area formulas to find the total area ● Warm Up ● Find area using grid paper ● Find the area of a composite figure using multiple area formulas


● Introduction ● Chapter review ●


○ Lesson 1: Circles and Circumference This lesson offers students a concrete method of determining an approximation for pi. Using circular lids and string, students compare the circumference to the diameter of circles. This is followed by a quick and simple activity in which students use a piece of string to develop the concept of radius and create a visual aid to support them in the use of the formula for the circumference of a circle.

● Section 8.4 ○ Lesson 2: Finding Areas of Composite Figures using Enclosure This lesson provides students with a visual/manipulative alternative method of

determining areas of composite figures. Using grid paper, students will develop a strategy using the enclosure method to determine the areas of composite figures. This strategy will then be applied to figures that are not drawn on a grid.

○ Lesson 3: Areas of Composite Figures – Pick’s Theorem (Challenge) This lesson is designed for students who would benefit from a challenge. By analyzing polygons created on a geoboard, students discover a formula for finding the area of any polygon on a geoboard. This is known as Pick's Theorem which was developed by Georg Alexander Pick in 1899.

Skills (Students will be able to…) ● Estimate and calculate the circumference of circles using estimates for pi ● Find the perimeters of composite figures ● Find the area of a circle and a semicircle ● Find the areas of composite figures

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● G & T Assessments:Sages-2 Screening Assessment for Gifted Elementary:

Mathematics/Science Language Arts/Social Studies ● Reasoning ● Dyslexia Screener ● PRIM checklist ● Computational Skills Grade Placement Test

Special Education

















Table of Contents



Gifted and Talented







● Big Ideas Chapter 8 ● 7.G.4 Performance Task ● 7.G.6 Performance Task ● STEM video and performance task




● Big Ideas Chapter 8 ● 7.G.4 Performance Task ● 7.G.6 Performance Task ● STEM video and performance task ● Internet Connected Computers/iPads


● Big Ideas Chapter 8 ● 7.G.4 Performance Task ● 7.G.6 Performance Task ● STEM video and performance task ● Math Centers ● 3 Act Lessons ● Robert Kaplinsky Lessons ● Open Middle - 7th Grade ● Which One Doesn’t Belong? ● Solve Me Puzzles ● Estimation 180 ● Same or Different ● Visual Patterns ● Esti-Mysteries ● 51 Esti-Mysteries ● Splat Math




















Table of Contents




● Big Ideas Chapter 8 ● 7.G.4 Performance Task ● 7.G.6 Performance Task ● STEM video and performance task ● iReady ● Linkit! ● IXL ● Big Ideas ● Classroom Manipulatives ● Online Manipulatives ● Content from previous grade levels ● Touch Math


● Correlates to the Ancient Rome and Ancient Arabia units in Social Studies ● Correlates to the Earth Systems unit in Science.

8.1 Educational Technology 8.1.8.A.3 Use and/or develop a simulation that provides an environment to solve a real world problem or theory. 8.1.8.C.1 Collaborate to develop and publish work that provides perspectives on a global problem for discussions with learners from other countries. 8.2 Technology Education, Engineering, Design, and Computational Thinking - Programming 8.2.8.A.2 Examine a system, consider how each part relates to other parts, and discuss a part to redesign to improve the system. 8.2.8.C.3 Evaluate the function, value, and aesthetics of a technological product or system, from the perspective of the user and the producer. 8.2.8.D.5 Explain the impact of resource selection and the production process in the development of a common or technological product or system






Communication and Collaboration


Table of Contents



● Communicate Clearly Life and Career Skills Initiative and Self Direction



9.1 Personal Finance Literacy 9.1.8.A.2 Relate how career choices, education choices, skills, entrepreneurship, and economic conditions affect income. 9.1.8.B.8 Develop a system for keeping and using financial records. 9.1.8.E.4 Prioritize personal wants and needs when making purchases. 9.2 Career Awareness, Exploration, and Preparation 9.2.8.B.3 Evaluate communication, collaboration, and leadership skills that can be developed through school, home, work, and extracurricular activities for use in a career.

● National Women’s History Month ● National Irish-American Heritage Month

Mathematics Curriculum Grade: 7 Unit: Surface Area and Volume New Jersey Student Learning Standards 7.G.A.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. 7.G.B.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.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Enduring Understandings/Goals Essential Questions

● The net of a prism can be used to find the surface area of the prism.

● The net of a rectangular prism can be used to derive a formula to calculate the surface area of the rectangular prism.

● A rectangular prism has 3 pairs of congruent faces. ● The net of a pyramid can be used to find the surface area of

that pyramid.

● How can you find the surface area of a prism? ● How can you find the surface area of a pyramid? ● How can you find the surface area of a cylinder? ● How can you find the volume of a prism? ● How can you find the volume of a pyramid?

Table of Contents



● The net of a cylinder can be used to find the surface area of that cylinder.

● Volume is found by finding the area of the base (B) and then multiplying by the number of layers (h).

● The formula for the volume of a prism can be used to solve problems.

● The volume of a pyramid is ⅓ the volume of a prism with the same height and base

Lesson Number Teaching Points Chapter Opener for Chapter 9: Surface Area and Volume

● Introduction ● Find areas of squares and rectangle ● Find areas of triangles ●

Activity 9.1: Surface Areas of Prisms MP4, MP3

Explore surface area using the nets of two prisms. ● Warm Up ● Review finding surface area of a prism using nets ● Find the surface area of a triangular prism ● Form rectangular prisms

Lesson 9.1: Surface Areas of Prisms MP4

Work with a formula for the surface area of a prism. ● Warm Up ● Key Idea: how to find the surface area of a rectangular prism ● Find the surface area of a rectangular prism ● Learn the formula for the surface area of a prism ● Find the surface area of a triangular prism ● Find the surface area of a cube ● Real-life application ●

Activity 9.2: Surface Areas of Pyramids (Day 1) MP4, MP8

Discover how to find the surface area of a pyramid by examining the net that makes up a pyramid ● Warm Up ● Draw a net to scale for a square pyramid

Activity 9.2: Surface Areas of Pyramids (Day 2) MP4

Explore how to find the surface area of a pyramid by examining the net that makes up a pyramid. ● Warm Up ● Estimate the surface area of an octagonal pyramid ● Compare surface areas of different pyramids ●

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Lesson 9.2: Surface Areas of Pyramids MP2, MP4

Work with a formula for the surface area of a pyramid. ● Warm Up ● Key Idea: formula for finding the surface area of a pyramid ● Find the surface area of a square pyramid ● Find the surface area of a triangular pyramid ● Real-life application

Lesson 9.3: Surface Areas of Cylinders MP1

Work with a formula for the surface area of a cylinder. ● Warm Up ● Key Idea: surface area of a cylinder formula ● Find the surface area of a cylinder ● Find the lateral surface area of the cylinder ● Real-life application

Lesson 9.4: Volumes of Prisms MP1

Use the formula for the volume of a prism to solve problems ● Warm Up ● Key Idea: formula for the volume of a prism in words and algebraically ● Find the volume of a prism ● Real-life application

Activity 9.5: Volumes of Pyramids MP2, MP4, MP5, MP6, MP7

Develop an understanding of how to find the volume of a pyramid by comparing it to the volume of a prism with the same base area and height. ● Warm Up ● Find a formula experimentally ● Compare the volumes of two pyramids ● Find and use a pattern to find the volume of a pyramid ● Breaking a prism into pyramids

Extension 9.5: Cross Sections of Three-Dimensional Figures MP1, MP4

Describe cross sections of three-dimensional figures ● Warm Up ● Describe the intersection of a plane and a solid ● Investigate the cross sections for a cylinder and a cone

Lesson 9.5: Volumes of Pyramids MP2

Work with a formula for the volume of a pyramid. ● Warm Up ● Key Idea: Volume of a Pyramid formula ● Use the formula to find the volume of a pyramid ● Real-life application

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Differentiating the Lesson, Chapter 9 ● Sections 9.1 and 9.4

○ Lesson 1: Using Number Cubes to Find Surface Area and Volume This lesson supports students who are still developing spatial skills and therefore benefit from building a structure in lieu of trying to visualize the three-dimensional structure from a sketch in a book. Students will use number cubes to build different structures. This activity builds the concept of volume through the counting of number cubes used to build each structure. The dots on the number cubes will be used to assist students in finding the sum of all the faces for the surface area.

● Section 9.1 ○ Lesson 2: Surface Areas of Rectangular Prisms and Composite Solids This lesson allows for practice with surface areas of rectangular prisms, but in a

new context. Students use two identical prisms to investigate the surface area of composite solids. First, students find the total surface area of the two prisms when they are separate. Next, students match congruent faces and explore how this alters the total surface area they calculated earlier. Lastly, students connect the two prisms together using non-congruent faces and find the surface area

● Section 9.4 ○ Lesson 3: Volumes of Prisms This lesson is designed for students who would benefit from interaction with models to grasp the concepts of calculating the

volume of prisms. Students will use pattern blocks to visually understand the concept of stacking to find volume. This concept will be connected to the volume formula for prisms by having students add the stacking lines to create a visual representation of the formula.

Skills (Students will be able to…) ● Find the surface area of a prism using a formula ● Find the surface area of a pyramid using a formula ● Find the surface area of a cylinder using a formula ● Find the volume of prisms ● Describe cross sections of three-dimensional figures ● Find the volumes of pyramids





● Chapter Test

Special Education



High-Prep Differentiation:




Table of Contents



● End-of-Course Test






● Alternative formative and summative assessments ● Guided Reading ● Personal agendas ● Project-based learning ● Problem-based learning ● Stations/centers ● Tiered activities/assignments ● Varying organizers for instructions






Gifted and Talented















Table of Contents




● Big Ideas Chapter 9 ● 7.G.3 Performance Task ● 7.G.4 Performance Task ● 7.G.6 Performance Task ● STEM video and performance task




● Big Ideas Chapter 9 ● 7.G.3 Performance Task ● 7.G.4 Performance Task ● 7.G.6 Performance Task ● STEM video and performance task ● Internet Connected Computers/iPads


● Big Ideas Chapter 9 ● 7.G.3 Performance Task ● 7.G.4 Performance Task ● 7.G.6 Performance Task ● STEM video and performance task ● Math Centers ● 3 Act Lessons ● Robert Kaplinsky Lessons ● Open Middle - 7th Grade ● Which One Doesn’t Belong? ● Solve Me Puzzles ● Estimation 180 ● Same or Different ● Visual Patterns ● Esti-Mysteries ● 51 Esti-Mysteries ● Splat Math


● Big Ideas Chapter 9 ● 7.G.3 Performance Task ● 7.G.4 Performance Task ● 7.G.6 Performance Task ● STEM video and performance task ● iReady ● Linkit! ● IXL ● Big Ideas ● Classroom Manipulatives ● Online Manipulatives ● Content from previous grade levels ● Touch Math
















Table of Contents




● Correlates to the Exploration & Colonization and Civilizations Asia unit in Social Studies ● Correlates to the Earth Systems unit in Science.

8.1 Educational Technology 8.1.8.A.3 Use and/or develop a simulation that provides an environment to solve a real world problem or theory. 8.1.8.D.3 Demonstrate an understanding of fair use and Creative Commons to intellectual property. 8.2 Technology Education, Engineering, Design, and Computational Thinking - Programming 8.2.8.B.2 Identify the desired and undesired consequences from the use of a product or system. 8.2.8.C.4 Identify the steps in the design process that would be used to solve a designated problem. 8.2.8.E.3 Develop an algorithm to solve an assigned problem using a specific set of commands and use peer review to critique the solution.











9.1 Personal Finance Literacy 9.1.8.A.5 Relate how the demand for certain skills determines an individual’s earning power. 9.1.8.B.3 Justify the concept of “paying yourself first” as a financial savings strategy. 9.1.8.E.3 Compare and contrast product facts versus advertising claims. 9.2 Career Awareness, Exploration, and Preparation 9.2.8.B.6 Demonstrate understanding of the necessary preparation and legal requirements to enter the workforce.

● Asian Pacific American Heritage Month ● Older Americans’ Month ● Jewish American Heritage Month

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Mathematics Curriculum Grade: 7 Unit: Probability and Statistics New Jersey Student Learning Standards 7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the popula tion; 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.A.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. 7.SP.B.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. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. 7.SP.B.4 Use measures of center and measures of variability for numerical data from random samples to draw informal compara tive inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book. 7.SP.C.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.C.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and obser ving 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.C.7a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determi ne 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. 7.SP.C.7b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? 7.SP.C.8a 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. 7.SP.C.8b 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. 7.SP.C.8c 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? Enduring Understandings/Goals Essential Questions

● The probability of an event can be calculated. ● Probabilities can be represented as fractions, decimals, or

percents. ● Relative frequencies can be used to find the probability of

an event. ● When relative frequencies increase, the experimental

probability gets closer and closer to the theoretical probability.

● Tree diagrams can be used to visualize the possible outcomes of events.

● When an experiment is performed randomly, all of the possible outcomes are equally likely.

● The probability of an event is the ratio of the number of favorable outcomes to the number of possible outcomes.

● In an experiment, how can you determine the number of possible results? ● How can you describe the likelihood of an event? ● How can you use relative frequencies to find probabilities? ● How can you find the number of possible outcomes of one or more events? ● What is the difference between dependent and independent events? ● How can you determine whether a sample accurately represents a population? ● How can you compare data sets that represent two populations?

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● The probability of an event is written a P(event). ● The relative frequency of an event is the fraction or percent

of the time that the event occurs. ● Probability that is based on repeated trials of an experiment

is called experimental probability. ● When all possible outcomes are equally likely, the theoretical

probability of an event is the ratio of the number of favorable outcomes to the number of possible outcomes.

● The Fundamental Counting Principle multiplies the number of possible outcomes of the first event by the number of possible outcomes of the second event to find the total number of possible outcomes.

● The probability of a compound event is the ratio of the number of favorable outcomes to the number of possible outcomes.

● Events are independent events if the occurrence of one event does not affect the likelihood that the other event(s) will occur.

● An unbiased sample is representative of a population, selected at random, and is large enough to provide accurate data.

● A biased sample is not representative of a population. One or more parts of the population are favored over others.

Lesson Number Teaching Points Chapter Opener for Chapter 10: Probability and Statistics

● Introduction ● Writing ratios

Activity 10.1: Outcomes and Events MP1, MP3, MP4

Count the number of possible outcomes of an experiment ● Warm Up ● Conduct experiments and determine possible outcomes ● Compare different results ● Conduct an experiment playing the game Rock Paper Scissors

Lesson 10.1: Outcomes and Events MP1

Describe the outcomes of an experiment ● Warm Up ● Key Ideas: Outcomes and Events ● Identify outcomes ● Counting outcomes

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Activity 10.2: Probability MP3, MP6

Develop an intuitive understanding of how to predict the likelihood of the results of a spinner. ● Warm Up ● Black-and-White spinner game ● Think about the likelihood of an event happening based on the central angle measure of the spinners. ● Is This Game Fair?

Lesson 10.2: Probability MP6

Compute the probability of an event. ● Warm Up ● Key Idea: definition of probability ● Describe the likelihood of an event ● Key Idea: finding the probability of an event using a ratio ● Find the probability of an event

Activity 10.3: Experimental and Theoretical Probability MP3, MP4, MP5, MP6

Use relative frequencies to find the probabilities. ● Warm Up ● Find relative frequencies ● Use relative frequencies ● Conduct an experiment

Lesson 10.3: Experimental and Theoretical Probability MP2

Compute the experimental probability of an event and the theoretical probability of an even ● Warm Up ● Key Idea: definition of experimental probability ● Find the experimental probability ● Making a prediction ● Theoretical probability ● Find a theoretical probability ● Use theoretical probability ● Compare experimental and theoretical probability

Activity 10.4: Compound Events MP4, MP6, MP7

Explore how the number of choices on locks and in passwords affects the total number of combinations possible. ● Warm Up ● Compare combination locks ● Compare password security

Lesson 10.4: Compound Events

Find the number of outcomes of compound events. ● Warm Up ● Find a sample space

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MP4 ● Key Idea: Fundamental Counting Principle ● Find the total number of possible outcomes ● Find the probability of a compound event

Activity 10.5: Independent and Dependent Events MP3, MP4, MP6

Develop an understanding of the difference between independent events and dependent events. ● Warm Up ● Draw marbles from a bag with replacement ● Draw marbles from a bag without replacement ● Conduct an experiment and determine independent and dependent events

Extension 10.5: Simulations MP5

Perform simulations to find probabilities of compound events ● Warm Up ● Simulating outcomes that are equally likely ● Simulating outcomes that are not equally likely ● Using a spreadsheet to simulate outcomes

Lesson 10.5: Independent and Dependent Events MP3a, MP4

Use a formal definition to compute theoretical probabilities of independent and dependent events ● Warm Up ● Key Idea: probability of independent events ● Find the probability of independent events ● Key Idea: probability of dependent events ● Find the probability of dependent events ● Find the probability of a compound event



Activity 10.6: Samples and Populations MP2, MP3

Identify samples and populations. ● Warm Up ● Identify populations and samples ● Identify random samples ● Identify representative samples

Extension 10.6: Generating Multiple Samples

Generate multiple samples of data and draw inferences about a population. ● Warm Up ● Use multiple random samples ● Use a simulation to make an inference about a population

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MP3, MP5 Lesson 10.6: Samples and Populations MP3

Identify biased and unbiased samples and determine whether a sample can be used to draw conclusions and make predictions about a population ● Warm Up ● Identify an unbiased sample ● Determine whether conclusions are valid ● Make predictions based on information given from a sample

Activity 10.7: Comparing Populations MP2, MP5

Explore overlap between data sets ● Warm Up ● Compare two data distributions using measures of center and variation ● Compare two data distributions to determine if the data overlap

Lesson 10.7: Comparing Populations MP1, MP3a, MP5, MP6

Compare two populations using measures of center, measures of variation, and overlap. ● Warm Up ● Compare populations using measures of center and variation ● Use random samples to compare populations




○ Lesson 1: Probability This lesson provides further exposure to likely and unlikely events as well as determining the probability of an event through favorable outcomes. Students play a game of concentration, matching the vocabulary impossible, unlikely, likely, and certain to spinners with different shaded sections. The spinner cards are then used again as students match them to probabilities in percent, decimal, or fraction form.

● Section 10.3 ○ Lesson 2: Theoretical Probability This lesson is designed to provide a concrete way of understanding theoretical probability. Students will use color tiles to

model what should happen in a given event and write the ratio using probability notation. ○ Lesson 3: Experimental Probability This lesson is designed to provide a concrete way of understanding experimental probability. Students will use color

tiles to model what does happen in a given event by conducting experiments and writing ratios using probability notation. ○ Lesson 4: Relating Theoretical and Experimental Probabilities Students will first determine the theoretical probability of an event and then conduct an

experiment to explore how the theoretical and experimental probabilities compare. Students will explore the concept of how repeating an experiment numerous times will bring the experimental probability closer to its theoretical probability.

● Section 10.4 and 10.5 ○ Lesson 5: Independent and Dependent Events In this lesson, students use a rectangular array model in lieu of a tree diagram to develop the concept of

independent and dependent events. A rectangle is divided into rows and columns that reflect the possible outcomes of each event. Using chips, students mark the favorable outcomes and find the probability of one event followed by another, both with and without replacement. From this model, the students see how multiplication of individual probabilities can be used to find the probability of consecutive events

Skills (Students will be able to…)

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● Identify the favorable outcomes of an event ● Find the probability of an event ● Find the experimental probability of an event and the theoretical probability of an event ● Use sample spaces and the total number of possible outcomes to find probabilities of compound events ● Perform simulations to find probabilities of compound events ● Identify and find probabilities of independent events and dependent events ● Generate multiple samples of data and drawing inferences about a population ● Identify biased and unbiased samples and determine whether a sample can be used to draw conclusions and make predictions about a population ● Compare populations










● Reasoning ● Dyslexia Screener

Special Educat ion






● Differentiation for All Students (Special Needs, ESL, Gifted Learners, & Mainstream Learners) ● Unit 1: Curriculum for ELL






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● PRIM checklist ● Computational Skills Grade Placement Test

● Subgroup Accommodations and Modifications ● Multi-language glossary ● Pupil edition in Spanish ● Vocabulary flash cards



Gifted and Talented







● Big Ideas Chapter 10 ● 7.SP.1 Performance Task ● 7.SP.2 Performance Task ● 7.SP3 Performance Task. ● 7.SP.4 Performance Task ● 7.SP.5 Performance Task ● 7.SP.6 Performance Task ● 7.SP.7 Performance Task ● 7.SP.8 Performance Task ● STEM video and performance task



● Big Ideas Chapter 10 ● 7.SP.1 Performance Task ● 7.SP.2 Performance Task ● 7.SP3 Performance Task. ● 7.SP.4 Performance Task ● 7.SP.5 Performance Task ● 7.SP.6 Performance Task ● 7.SP.7 Performance Task ● 7.SP.8 Performance Task ● STEM video and performance task ● Internet Connected Computers/iPads









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● Big Ideas Chapter 10 ● 7.SP.1 Performance Task ● 7.SP.2 Performance Task ● 7.SP3 Performance Task. ● 7.SP.4 Performance Task ● 7.SP.5 Performance Task ● 7.SP.6 Performance Task ● 7.SP.7 Performance Task ● 7.SP.8 Performance Task ● STEM video and performance task ● Math Centers ● 3 Act Lessons ● Robert Kaplinsky Lessons ● Open Middle - 7th Grade ● Which One Doesn’t Belong? ● Solve Me Puzzles ● Estimation 180 ● Same or Different ● Visual Patterns ● Esti-Mysteries ● 51 Esti-Mysteries ● Splat Math


● Big Ideas Chapter 10 ● 7.SP.1 Performance Task ● 7.SP.2 Performance Task ● 7.SP3 Performance Task. ● 7.SP.4 Performance Task ● 7.SP.5 Performance Task ● 7.SP.6 Performance Task ● 7.SP.7 Performance Task ● 7.SP.8 Performance Task ● STEM video and performance task ● iReady ● Linkit! ● IXL ● Big Ideas ● Classroom Manipulatives ● Online Manipulatives ● Content from previous grade levels ● Touch Math
















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● Correlates to the Economy unit in Social Studies ● Correlates to the Structure & Function and Inheritance & Variation of Traits units in

Science.

8.1 Educational Technology 8.1.8.A.2 Create a document (e.g., newsletter, reports, personalized learning plan, business letters or flyers) using one of more digital applications to be critiqued by professionals for usability. 8.1.8.B.1 Synthesize and publish information about a local or global issue or event (ex. Telecollaborative project, blog, school web) 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to solve a real world problem. 8.2 Technology Education, Engineering, Design, and Computational Thinking - Programming 8.2.8.B.5 Identify new technologies results from demands, values, and interest of individuals, businesses, industries and societies. 8.2.8.D.1 Design and create a product that addresses a real world problem using a design process under specific constraints.











9.1 Personal Finance Literacy 9.1.8.A.3 Differentiate among ways that workers can improve earning power through the acquisition of new knowledge and skills. 9.1.8.C.8 Explain the purpose of a credit score and credit record, and summarize borrowers’ credit report rights.

● Asian Pacific American Heritage Month ● Older Americans’ Month ● Jewish American Heritage Month

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9.1.8.D.5 Explain the economic principle of supply and demand. 9.2 Career Awareness, Exploration, and Preparation 9.2.8.B.1 Research careers within the 16 Career Clusters® and determine attributes of career success.

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Scope and Sequence: Math 7 - Florham Park School District

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