F -A 7_Pre-Algebra_COS (2).pdfinverses). Interpret sums of rational numbers by describing real-world contexts. 7.NS.A.1c. Understand subtraction of rational numbers as adding the additive

COURSE OF STUDY UNIT PLANNING GUIDE FOR:

PRE-ALGEBRA

GRADE LEVEL: 7 PREPARED BY: HILARY GIBBS KERI LEHMANN TRACY MCGRORY EILEEN STEFFEN

SHANNON WARNOCK SUPERVISOR OF MATHEMATICS AND SCIENCE

JULY 2018

CHARLES A. SELZER AND LOVELL J. HONISS SCHOOLS

DUMONT, NEW JERSEY

BORN DATE: AUGUST 24, 2017 ALIGNED TO THE NJSLS AND B.O.E. ADOPTED AUGUST 23, 2018

COURSE REQUIREMENTS AND EXPECTATIONS The following criteria are used to determine the grade for the course:

A. Tests - 40% of the grade Tests will be given periodically. These may include alternative assessments that will count as tests.

B. Quizzes - 25% of the grade

Quizzes (announced and unannounced) based on class lessons or homework assignments will be given frequently to assess understanding of individual concepts. These may include alternative assessments that will count as quizzes.

C. Homework - 15% of the grade

Homework will be evaluated for completeness, neatness, and/or accuracy.

D. Class Participation/Class Work - 20% of the grade Class Participation/Class Work will be evaluated a minimum of twice per marking period according to the departmental rubric (see page 3). The grade is based on the student's participation/work during class. Thus, consistent attendance is imperative.

Middle School Mathematics Participation Rubric 1(40)

Inadequate 2(55)

Limited 3(70)

Partial 4(85)

Adequate 5(100)

Superior

Preparedness

-Almost never has pencil, books, calculators, and/or notebooks -Almost never has assignments on time -Never makes up work in timely fashion

-Rarely has pencil, books, calculators, and/or notebooks -Rarely has assignments on time -Rarely makes up work in timely fashion

-Sometimes has pencil, books, calculators, and/or notebooks -Sometimes has assignments on time -Sometimes makes up work in timely fashion

-Generally has pencil, books, calculators, and/or notebooks -Generally has assignments on time -Generally makes up work in timely fashion

-Always has pencil, books, calculators, and/or notebooks -Always has assignments on time -Always makes up work in a timely fashion

Oral Participation

-Almost never asks & answers questions without prompting

-Rarely asks & answers questions without prompting

-Sometimes asks & answers questions without prompting

-Generally asks & answers questions without prompting

-Always asks & answers questions without prompting (daily)

Written Participation

-Almost never takes notes -Almost never makes corrections on homework/ class work and/or applies teacher recommendations to writing

-Rarely takes notes -Rarely makes corrections on homework/ class work and/or applies teacher recommendations to writing

-Sometimes takes notes -Sometimes makes corrections on homework/ class work and/or applies teacher recommendations to writing

-Generally takes notes -Generally makes corrections on homework/ class work and applies teacher recommendations to writing

-Always takes notes -Always makes corrections on homework/ class work and applies teacher recommendations to writing

Cooperative Learning

-Almost never provides meaningful input -Almost never focused on the assignment -Almost never assumes a leadership role

-Rarely provides meaningful input -Rarely focused on the assignment -Rarely assumes a leadership role

-Sometimes provides meaningful input -Sometimes focused on the assignment -Sometimes assumes a leadership role

-Generally provides meaningful input -Generally focused on the assignment -Generally assumes a leadership role

-Always provides meaningful input -Always focused on the assignment -Usually assumes a leadership role

General Behavior

-Almost never shows respect for peers and teacher -Almost never remains focused on assignments -Almost never abides by all class & school rules

-Rarely shows respect for peers and teacher -Rarely remains focused on assignments -Rarely abides by all class & school rules

-Sometimes shows respect for peers and teacher -Sometimes remains focused on assignments -Sometimes abides by all class & school rules

-Generally shows respect for peers and teacher -Generally remains focused on assignments -Generally abides by all class & school rules

-Always shows respect for peers and teacher -Always remains focused on assignments -Always abides by all class & school rules

*Score of Zero Results from Limited or No Response to Class Participation/Class Work

Unit 1: The Number System

Number of Days ● 23

NJSLS-M ● 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.

● 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

● 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). 2c. 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.

Standards for Mathematical Practices

● MP.1 Make sense of problems and persevere in solving them. ● MP.2 Reason abstractly and quantitatively. ● MP.3 Construct viable arguments & critique the reasoning of others. ● MP.4 Model with mathematics. ● MP.5 Use appropriate tools strategically. ● MP.6 Attend to precision. ● MP.7 Look for and make use of structure. ● MP.8 Look for and express regularity in repeated reasoning.

Science and Engineering Practices (SEP)

● SEP.1 Asking Questions and Defining Problems ● SEP.2 Developing and Using Models ● SEP.5 Using Mathematics and Computational Thinking ● SEP.7 Engaging in Argument from Evidence ● SEP.8 Obtaining, Evaluating, and Communicating Information

NJSLS for ELA Companion Standards for Science: RST

● RST.6-8.2. Determine the central ideas or conclusions of a text; provide an accurate summary of the text distinct from prior knowledge or opinions.

● RST.6-8.3. Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.

● RST.6-8.4. Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 6-8 texts and topics.

● RST.6-8.7. Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually (e.g., in a flowchart, diagram, model, graph, or table).

● RST.6-8.9. Compare and contrast the information gained from experiments, simulations, video, or multimedia sources with that gained from reading a text on the same topic.

NJSLS for ELA Companion Standards for Science: WHST

● WHST.6-8.1. Write arguments focused on discipline-specific content. C. Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), counterclaims,

reasons, and evidence. D. Establish and maintain a formal/academic style, approach, and form. E. Provide a concluding statement or section that follows from and supports the argument presented.

● WHST.6-8.2. Write informative/explanatory texts, including the narration of historical events, scientific procedures/experiments, or technical processes. A. Introduce a topic and organize ideas, concepts, and information using text structures (e.g. definition,

classification, comparison/contrast, cause/effect, etc.) and text features (e.g. headings, graphics, and multimedia) when useful to aiding comprehension.

D. Use precise language and domain-specific vocabulary to inform about or explain the topic. E. Establish and maintain a formal/academic style, approach, and form. F. Provide a concluding statement or section that follows from and supports the information or explanation

presented

Career Ready Practices (CRPs)

● CRP1. Act as a responsible and contributing citizen and employee. ● CRP2. Apply appropriate academic and technical skills. ● CRP4. Communicate clearly and effectively and with reason. ● CRP6. Demonstrate creativity and innovation. ● CRP8. Utilize critical thinking to make sense of problems and persevere in solving them.

● CRP9. Model integrity, ethical leadership and effective management. ● CRP11. Use technology to enhance productivity. ● CRP12. Work productively in teams while using cultural global competence.

21st Century: Personal Financial Literacy (9.1)

● NA

21st Century: Career Awareness, Exploration, and Preparation (9.2)

● 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.

Educational Technology (8.1)

● 8.1.8.A.1 Demonstrate knowledge of a real world problem using digital tools. Select and use applications effectively and productively.

● 8.1.8.A.4 Graph and calculate data within a spreadsheet and present a summary of the results. ● 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.

Technology Education, Engineering, Design, and Computational Thinking - Programming (8.2)

● NA

Students will be able to...

● Understand numeric fluency including both the understanding of and the ability to appropriately use numbers. ● Understand computational fluency including understanding the meaning and appropriate use of numerical

operations. ● Understand how the magnitude of numbers affects the outcome of operations on them.

Essential Questions ● What makes a computational strategy both effective and efficient? ● How does adding and subtracting affect numbers?

Activities ● Practice Problems: simplifying algebraic expressions, using order of operations, performing basic operations with integers, absolute value, and rational numbers

● Activity Lab: forming conjectures on rules for integer operations ● Solving real world word problems: requiring students to make and evaluate an expression using integer operations

● Modeling: integer operations using manipulatives including counters and number lines, utilize vertical and horizontal number line models for integers and absolute value

● Utilizing graphic organizer: construct a venn diagram to display the relationships between the sets in the real number system

● Cooperative learning groups: think, pair, share for activities including- finding the absolute value and discussing their findings and basic number properties

● Learning stations: review the number system, explore integer operations, investigate rational numbers ● Using real world databases to find extreme integers ● Study guide prior to assessment on the Number System

Resources ● Pearson Course 2 Textbook ● Pearson Course 3 Textbook ● LearnZillion ● NJCTL ● Illustrative Mathematics ● EngageNY ● GeorgiaStandards.org ● Mathematics Assessment Resource Service ● Open Up Resources ● http://www.mathplayground.com/ASB_IntegerWarp.html

Vocabulary ● variable ● algebraic expression ● opposites ● integer ● absolute value ● additive inverse ● inverse operations ● distributive property ● commutative property ● associative property ● identify property ● rational number ● relatively prime ● terminating decimal ● repeating decimal ● reciprocal

https://learnzillion.com/p/

https://njctl.org/courses/math/

https://www.illustrativemathematics.org/content-standards

https://www.engageny.org/

https://www.georgiastandards.org/Georgia-Standards/Pages/Math-6-8.aspx

http://map.mathshell.org/index.php

http://openupresources.org/

http://www.mathplayground.com/ASB_IntegerWarp.html

● multiplicative inverse

Technology/GAFE ● https://parcc.pearson.com/practice-tests/ ● Google Classroom ● SmartBoard ● Scientific Calculators ● iPads ● Laptop computer ● Study Island ● Khanacademy ● Quizlet

Special Education/504

● Copy of Notes ○ Highlighting: Number system vocabulary ○ Providing vocabulary definitions in interactive notebook (INB) on Number System using the Frayer model

providing a definition, picture, example and non example ● Modeling via powerpoint/Smartboard NB on Basic Number Properties ● Guided Notes on

○ Basic Number Properties ○ Steps for adding/subtracting/multiplication/division fractions

● Manipulatives/Visual Aides ○ Foldables on basic number properties (distributive, commutative, associative and identity) ○ Graphic Organizer: The real Number System (natural number, whole, integer and rational numbers) & Least

Common Multiple (LCM) ○ Use of a number line to understand absolute value

● IXL for additional practice on Number System ● Study guide prior to assessment on Number system ● Modified test/quizzes on Number system ● Extended time on assignments and assessments ● Calculator ● Extra help on the Number System

ELL (SEI) ● Bilingual math dictionary, frayer model, gallery walk of vocabulary words ● Native/Non-Native speaker groupings ● Providing modified/guided notes with prompts and native language definitions ● Bilingual practice problems of simplifying algebraic expressions, using order of operations, performing basic

operations with integers, absolute value and rational numbers

https://parcc.pearson.com/practice-tests/

● Modeling , chunking and scaffolding of simplifying algebraic expressions, using order of operations, performing basic operations with integers, absolute value and rational numbers

● Modified test/quizzes on the Number System ● Extended time on assignments and assessments ● Extra help on the Number System

At Risk of School Failure

● Copy of Notes ○ Highlighting: Number System vocabulary ○ Providing vocabulary definitions in interactive notebook (INB) on Number System using the Frayer model

providing a definition, picture, example and non example ● Modeling via powerpoint/Smartboard NB on Basic Number Properties ● Guided Notes on

○ Basic Number Properties ○ Steps for adding/subtracting/multiplication/dividing fractions

● Manipulatives/Visual Aides ○ Foldables on basic number properties (distributive, commutative, associative and identity) ○ Graphic Organizer: The real Number System (natural number, whole, integer and rational numbers) & Least

Common Multiple (LCM) ○ Use of a number line to understand absolute value

● Study guide prior to assessment on Number system ● Modified test/quizzes on number system ● Extended time on assignments and assessments ● Extra help on the number system

Gifted & Talented ● Individualized Pacing ● Supplemental Challenge Problems on number system

Formative, Summative, Benchmark, and Alternative Assessments

● Benchmark: (Summer Assignment Test) ● Benchmark: Constructed Response Tasks (CRT): Reasoning performance task on rational numbers and modeling

performance task on rational numbers ● Formative: Quizzes- Integer Operations, Rational Number Operations, Simplifying Algebraic Expressions, 1-3

Adding and Subtracting Integers ● Summative: Unit Test- The Number System ● Alternative: Study Island

Unit 2: Expressions & Equations


NJSLS-M ● 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.3. Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. 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.EE.B.4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities .

● 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?

● 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 persale. 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.



Science and Engineering Practices

● SEP.1 Asking Questions and Defining Problems ● SEP.2 Developing and Using Models

(SEP) ● SEP.5 Using Mathematics and Computational Thinking ● SEP.6 Constructing explanations (for science) and designing solutions (for engineering) ● SEP.7 Engaging in Argument from Evidence ● SEP.8 Obtaining, Evaluating, and Communicating Information













presented.


● CRP1. Act as a responsible and contributing citizen and employee. ● CRP2. Apply appropriate academic and technical skills. ● CRP4. Communicate clearly and effectively and with reason. ● CRP6. Demonstrate creativity and innovation. ● CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. ● CRP9. Model integrity, ethical leadership and effective management.

● CRP11. Use technology to enhance productivity. ● CRP12. Work productively in teams while using cultural global competence


● NA





● 8.1.8.A.4 Graph and calculate data within a spreadsheet and present a summary of the results.


● 8.2.8.C.1 Explain how different teams/groups can contribute to the overall design of a product.


● Explain how the terms of an algebraic expression are separated by plus and minus signs. ● Understand combining only like terms by addition or subtraction. ● Understand that there is an understood coefficient of 1 in front of a variable that does not have any numeric

coefficient. ● Understand that addition and subtraction are inverse operations that undo each other. Multiplication and division

are also inverse operations. ● Understand when you solve an equation, any operation that you do to one side you must also do to the other. ● Distinguish that when an equation has variables on both sides, you must bring all the variable terms to one side of

the equation to solve it. ● Interpret that on a graph, an open dot means that the point is not a solution; a closed dot means that the point is a

solution. ● Understand that when you solve an inequality by multiplying and dividing, if you multiply or divide by a negative

number, the inequality sign is reversed.

Essential Questions ● How can you use the properties of operations to rewrite algebraic expressions?

Activities ● Practice Problems: simplifying algebraic expressions, solving equations (one-step, two-step, multi-step), and inequalities

● Activity Lab: Solving Equations Puzzle, Doodle Notes Pages for Solving Equations/Distributive Property/Combining Like Terms

● Solving real world word problems: using equations and inequalities ● Modeling: visual examples of like/unlike terms, use Algebra Tiles to model solving equations using addition,

subtraction, multiplication & division ● Utilizing graphic organizer:

○ constructing a venn diagram to compare expressions and equations ○ foldable notes for combining like terms, and steps for solving equations ○ Utilize a number line when giving notes on inequalities

● Cooperative learning groups: think, pair, share simplifying algebraic expressions, cooperative pairs Simplifying Expressions game, Solving Equations Puzzles/game, “SNAKE” solving equations in groups of 3-4 to complete a puzzle

● Learning stations: review of Expressions & Equations for test preparation

Resources ● Pearson Course 2 Textbook ● Pearson Course 3 Textbook ● LearnZillion ● NJCTL ● Illustrative Mathematics ● EngageNY ● GeorgiaStandards.org ● Mathematics Assessment Resource Service ● Open Up Resources

Vocabulary ● term ● like terms ● factor ● equation ● solution ● isolate ● addition property of equality ● subtraction property of equality ● multiplication property of equality ● division property of equality










● Copy of Notes ○ Highlighting: Expression, Equation & Inequalities vocabulary ○ Providing vocabulary definitions in INB on Expressions, Equations, & Inequalities using the Frayer model

providing a definition, picture, example and non example ● Modeling via powerpoint/Smartboard NB on solving Expressions, Equations & Inequalities ● Guided Notes on Expressions, Equations, Inequalities ● Manipulatives/Visual Aides

○ Venn diagram comparing equations and expressions ○ Foldable on inequalities including vocabulary definition, numberline and example ○ Utilize a number line when giving notes on inequalities

● IXL for additional practice on expressions, equations and inequalities ● Study guide prior to Expressions and Equations assessment ● Modified test/quizzes on expressions and equations ● Extended time on assignments and assessments ● Calculator ● Extra help on Equations and Expressions

ELL (SEI) ● Bilingual math dictionary, frayer model, gallery walk of vocabulary words ● Native/Non-Native speaker groupings ● Providing modified/guided notes with prompts and native language definitions ● Bilingual practice problems of simplifying algebraic expressions, solving equations (one-step, two-step,

multi-step), and inequalities ● Modeling, chunking and scaffolding of simplifying algebraic expressions, solving equations (one-step, two-step,

multi-step), and inequalities ● Modified test/quizzes on expressions and equations ● Extended time on assignments and assessments ● Extra help on simplifying algebraic expressions, solving equations (one-step, two-step, multi-step), and inequalities



● Copy of Notes ○ Highlighting: Expression, Equation & Inequalities vocabulary ○ Providing vocabulary definitions on Expressions, Equations, & Inequalities using the Frayer model

providing a definition, picture, example and non example ● Modeling via powerpoint/Smartboard NB on solving Expressions, Equations & Inequalities ● Guided Notes on Expressions, Equations, Inequalities ● Manipulatives/Visual Aides

○ Venn diagram comparing equations and expressions ○ Foldable on inequalities including vocabulary definition, number line and example ○ Utilize a number line when giving notes on inequalities

● Study guide prior to Expressions and Equations assessment ● Modified test/quizzes on expressions and equations ● Extended time on assignments and assessments ● Extra help on Equations, Expressions and Inequalities

Gifted & Talented ● Individualized Pacing ● Supplemental Challenge Problems on expressions, equations and inequalities


● Benchmark: Modeling Performance Task on Expressions & Equations ● Benchmark: Reasoning Performance Task on Expressions & Equations ● Formative: Quizzes- Simplifying/Evaluating Algebraic Expressions, Solving 1-Step Equations, Solving 2-Step

Equations, Solving Multi-Step Equations, Writing & Solving Equations from Word Problems ● Summative: Unit Test- Expressions & Equations ● Alternative: Study Island

Unit 3: Ratios & Proportional Relationships


NJSLS-M ● 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 4 1 2 1 mph, equivalently 2 mph.

● 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.RP.A.2. Recognize and represent proportional relationships between quantities. ● 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.




● SEP.1 Asking Questions and Defining Problems ● SEP.2 Developing and Using Models ● SEP.5 Using Mathematics and Computational Thinking ● SEP.6 Constructing explanations (for science) and designing solutions (for engineering) ● SEP.7 Engaging in Argument from Evidence ● SEP.8 Obtaining, Evaluating, and Communicating Information

NJSLS for ELA Companion Standards


for Science: RST ● RST.6-8.3. Follow precisely a multistep procedure when carrying out experiments, taking measurements, or performing technical tasks.










presented.


● CRP1. Act as a responsible and contributing citizen and employee. ● CRP2. Apply appropriate academic and technical skills. ● CRP4. Communicate clearly and effectively and with reason. ● CRP6. Demonstrate creativity and innovation. ● CRP8. Utilize critical thinking to make sense of problems and persevere in solving them. ● CRP9. Model integrity, ethical leadership and effective management. ● CRP11. Use technology to enhance productivity. ● CRP12. Work productively in teams while using cultural global competence


● N/A





● 8.1.8.A.4 Graph and calculate data within a spreadsheet and present a summary of the results.


● N/A


● Recognize lengths in similar figures form a proportion ● Extend understanding of ratios and proportions ● Use ratio and proportion to solve problems involving scale drawings of geometric figures. ● Graph proportional relationships ● Understand that the unit rate is related to the steepness of the line (slope) ● Distinguish proportional relationships from other relationships

Essential Questions ● What is the relationship between a ratio and a proportion? ● How can you recognize a proportional relationship?

Activities ● Practice Problems: finding rates/ratios/unit rates, solving proportions, comparing proportions, equivalent quantities, finding constant of proportionality, finding slope of proportional relationship graphs

● Activity Lab: Doodle Notes pages for Rates/Unit Rates/Proportions, solving proportions using cross products/equivalent fractions/equations

● Solving real world word problems: unit rate to find better buy, comparing prices/sales, real-life use of proportions for scale factor/models/map distances

● Modeling:number lines/strip diagrams to demonstrate proportional relationships, Similar Figures & proportional sides, Scale Models & Maps, graphing proportional relationships

● Utilizing graphic organizer: venn diagrams compare/contrast rates & ratios, foldable notes for steps to solve proportions, table of values for proportional relationships

● Cooperative learning groups: small groups of 3-4 research Exchange Rates & convert between currencies, think-pair-share solving similar figures

● Learning stations:review of Ratios & Proportional Relationships for test preparation


Vocabulary ● rate ● unit rate ● conversion factor ● similar figures ● congruent angles ● scale model ● scale ● indirect measurement ● proportion ● cross-products



● Copy of Notes ○ Highlighting: Ratios and Proportional relationship vocabulary ○ Providing vocabulary definitions in INB on Ratios and Proportional relationship using the Frayer model

providing a definition, picture, example and non example









● Modeling via powerpoint/Smartboard NB on Ratios and Proportional relationship ● Guided Notes on Ratios and Proportional relationship

○ Steps for find proportional relationships using cross products ○ Step by step finding whole, part and percent

● Manipulatives/Visual Aides ○ Flow chart of solving similar figures with proportions and scale drawings

● IXL for additional practice on ratios and proportional relationships ● Study guide prior to ratios and proportional relationship assessment ● Modified test/quizzes on ratios and proportional relationships ● Extended time on assignments and assessments ● Use of a calculator ● Extra help on Ratios and Proportional relationship

ELL (SEI) ● Bilingual math dictionary, frayer model, gallery walk of vocabulary words ● Native/Non-Native speaker groupings ● Providing modified/guided notes with prompts and native language definitions ● Bilingual practice problems of finding rates/ratios/unit rates, solving proportions, comparing proportions,

equivalent quantities, finding constant of proportionality, finding slope of proportional relationship graphs ● Modeling , chunking and scaffolding of finding rates/ratios/unit rates, solving proportions, comparing proportions,

equivalent quantities, finding constant of proportionality, finding slope of proportional relationship graphs ● Modified test/quizzes on finding rates/ratios/unit rates, solving proportions, comparing proportions, equivalent

quantities, finding constant of proportionality, finding slope of proportional relationship graphs ● Extended time on assignments and assessments ● Extra help on finding rates/ratios/unit rates, solving proportions, comparing proportions, equivalent quantities,

finding constant of proportionality, finding slope of proportional relationship graphs


● Copy of Notes ○ Highlighting: Ratios and Proportional relationship vocabulary ○ Providing vocabulary definitions using the Frayer model providing a definition, picture, example and non

example ● Modeling via powerpoint/Smartboard NB on Ratios and Proportional relationship ● Guided Notes on Ratios and Proportional relationship

○ Steps for find proportional relationships using cross products ○ Step by step finding whole, part and percent

● Manipulatives/Visual Aides ○ Flow chart of solving similar figures with proportions and scale drawings

● Study guide prior to ratios and proportional relationship assessment

● Modified test/quizzes on ratios and proportional relationships ● Extended time on assignments and assessments ● Extra help on Ratios and Proportional relationship

Gifted & Talented ● Individualized Pacing ● Supplemental Challenge Problems on ratio and proportional relationships


● Benchmark: Constructed Response Tasks (CRT): Reasoning and performance task ● Formative: Quizzes-Simplifying Ratios/Rates, Finding Unit Rates, Comparing Unit Rates, Solving Proportions ● Summative: Unit Test- Ratios & Proportional Reasoning ● Alternative: Study island

Unit 4: Percents


NJSLS-M ● 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













reasons, and evidence. D. Establish and maintain a formal/academic style, approach, and form.

E. Provide a concluding statement or section that follows from and supports the argument presented. ● WHST.6-8.2. Write informative/explanatory texts, including the narration of historical events, scientific

procedures/experiments, or technical processes. A. Introduce a topic and organize ideas, concepts, and information using text structures (e.g. definition,



presented.




● 9.1.8.C.1 Compare and contrast credit cards and debit cards and the advantages and disadvantages of using each. ● 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.D.1 Determine how saving contributes to financial well-being. ● 9.1.8.E.1 Explain what it means to be a responsible consumer and the factors to consider when making consumer

decisions. ● 9.1.8.E.3 Compare and contrast product facts versus advertising claims. ● 9.1.8.E.5 Analyze interest rates and fees associated with financial services, credit cards, debit cards, and gift cards. ● 9.1.8.E.8 Recognize the techniques and effects of deceptive advertising.





● 8.1.8.A.4 Graph and calculate data within a spreadsheet and present a summary of the results. ● 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to



● NA


● Understand that percents are a ratio out of 100. ● Understand thats percents are used to solve a variety of real-life problems

Essential Questions ● How can a proportion be used to solve percent problems? ● How are percents used in real-world situations?

Activities ● Practice Problems: finding percent of a number/discounts/selling price/markups/percent of change/simple interest, percent proportion/equation

● Activity Lab: doodle notes for percents, converting between fraction-decimal-percent ● Solving real world word problems: finding sale price/selling price/markups/discounts/tax, comparing sales, finding

simple interest rates and comparing interest rates on a variety of loans/debit & credit cards/bank accounts, Declaration of Independence data facts used in real-world percent word problems

● Modeling: Using double number lines to create percent proportions, percent diagrams/models ● Utilizing graphic organizer: foldable notes for consumer percents/steps for finding interest/solving

proportions/percent of change, fill in study notes ● Cooperative learning groups: tiered partners estimating with percents, small groups of 3-4 discuss Learn Zillion

video that demonstrates how percentages can be written as ratios, think-pair-share percent of change problems ● Learning stations: test review & preparation for percent

Resources ● Pearson Course 2 Textbook ● Pearson Course 3 Textbook ● LearnZillion ● NJCTL ● Illustrative Mathematics ● EngageNY ● GeorgiaStandards.org ● Mathematics Assessment Resource Service







● Open Up Resources

Vocabulary ● percent ● percent of change ● markup ● selling price ● interest ● interest rate ● principal ● simple interest ● balance



● Copy of Notes ○ Highlighting: Percent vocabulary ○ Providing vocabulary definitions in interactive notebook (INB) on percents using the Frayer model

providing a definition, picture, example and non example ● Modeling via powerpoint/Smartboard NB on Percents ● Guided Notes on

○ Finding selling price, markup and discount step by step ○ Percent of change (increase/decrease) step by step

● Manipulatives/Visual Aides ○ Graphic Organizer: Percent Doodle on whole, part, percent

● IXL for additional practice on percent ● Study guide prior to percent assessment ● Modified test/quizzes on percents ● Extended time on assignments and assessments ● Calculator



● Extra help on Percents

ELL (SEI) ● Bilingual math dictionary, frayer model, gallery walk of vocabulary words ● Native/Non-Native speaker groupings ● Providing modified/guided notes with prompts and native language definitions ● Bilingual practice problems of finding percent of a number/discounts/selling price/markups/percent of

change/simple interest, percent proportion/equation ● Modeling, chunking and scaffolding of finding percent of a number/discounts/selling price/markups/percent of

change/simple interest, percent proportion/equation ● Modified test/quizzes on finding percent of a number/discounts/selling price/markups/percent of change/simple

interest, percent proportion/equation ● Extended time on assignments and assessments ● Extra help on finding percent of a number/discounts/selling price/markups/percent of change/simple interest,

percent proportion/equation


● Copy of Notes ○ Highlighting: Percent vocabulary ○ Providing vocabulary definitions on percents using the Frayer model providing a definition, picture,

example and non example ● Modeling via powerpoint/Smartboard NB on Percents ● Guided Notes on

○ Finding selling price, markup and discount step by step ○ Percent of change (increase/decrease) step by step

● Manipulatives/Visual Aides ○ Graphic Organizer: Percent Doodle on whole, part, percent

● Study guide prior to percent assessment ● Modified test/quizzes on percents ● Extended time on assignments and assessments ● Extra help on Percents

Gifted & Talented ● Individualized Pacing ● Supplemental Challenge Problems on percents

Formative, Summative, Benchmark, and Alternative

● Benchmark: Constructed Response Tasks (CRT): Reasoning and performance task ● Alternative: Study Island ● Summative: Unit Test- Percents ● Formative: Quizzes- Percent Equation/Proportion, Percent of Change, Simple Interest

Assessments

Unit 5: Geometry


NJSLS-M ● 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.

● 7.G.A.2. Draw (with technology, with ruler and protractor as well as freehand) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle

● 7.G.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.

● 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.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.

















presented.




● NA






● 8.2.8.C.1 Explain how different teams/groups can contribute to the overall design of a product. ● 8.2.8.C.2 Explain the need for optimization in a design process.


● Explain that a pair of angles can be supplementary or complementary even though they are not adjacent, or even in the same figure.

● Understand that two lines that intersect to form equal adjacent angles are perpendicular. ● Understand that a transversal can intersect two lines that are, or are not, parallel to each other. If you know that

corresponding angles or alternate interior angles are congruent, then you can be sure that the lines intersected by the transversal are parallel.

● Analyze the order of angles and sides allowing them to determine whether two triangles are congruent. ● Interpret the area of a figure by the number of square units it encloses. ● Explain that the circumference of a circle is the distance around the circle, or its perimeter. ● Understand that the surface area of a solid is the area of its net. ● Find the height of a pyramid is different from the height of its lateral faces. ● Understand that the volume is an amount of three-dimensional space. ● Find the volume of a solid, the height is measured as perpendicular to the base. ● Slice a three-dimensional prism and understand that it will form plane figure.

Essential Questions ● How can angle relationships be used to solve equations for missing angle measures? ● How can tools and technology be used to draw shapes and angles to given specifications? ● How can measurements be used to solve problems? ● What figures will result from taking a cross-section of a three-dimensional figure?

Activities ● Practice Problems: identifying angles & lines, finding angle measurements, writing equations about angle relationships, finding circumference/area/surface area/volume, identifying cross sections

● Activity Lab: matching vocabulary to diagrams, complementary & supplementary angles lab ● Solving real world word problems: determining angle measurements on maps/diagrams, finding

area/circumference/surface area/volume of real-world figures ● Modeling:Frayer Model for new vocabulary words, geometric diagrams, interactive website for creating cross

sections

● Utilizing graphic organizer: gallery walk of examples of angles & lines, vocabulary chart, foldable study notes for angles/lines/2D & 3D figures/area/surface area/volume

● Cooperative learning groups: “Inside-Out” vocabulary game, think-pair-share defining new vocabulary/creating flashcards

● Learning stations: review game for types of measurement (2D & 3D figures), review/preparation for test on geometry


Vocabulary ● vertical angles ● adjacent angles ● supplementary angles ● complementary angles ● perpendicular ● transversal ● corresponding angles ● alternate interior angles ● alternate exterior angles ● compass ● similar ● congruent ● area ● surface area ● lateral area ● net ● volume ● circumference ● chord ● radius








● diameter ● slant height ● cross-section



● Copy of Notes ○ Highlighting: Geometry vocabulary ○ Providing vocabulary definitions in interactive notebook (INB) on geometry using the Frayer model

providing a definition, picture, example and non example ● Modeling via powerpoint/Smartboard NB on Geometry

○ use different colors to represent angels and assist in finding angle measurements ● Create flashcards for geometry vocabulary ● Guided Notes on

○ Procedures for solving area of polygons ○ Procedures for solving area and circumference of Circles ○ Procedures for Volume of Prims and Pyramids

● Manipulatives/Visual Aides ○ Foldables: supplementary, complementary, identifying angles and lines

● Modeling, chunking and scaffolding of identifying angles & lines, finding angle measurements, writing equations about angle relationships, finding circumference/area/surface area/volume, identifying cross sections

● IXL for additional practice on geometry ● Study guide prior to geometry assessment ● Modified test/quizzes on geometry ● Extra help on identifying angles & lines, finding angle measurements, writing equations about angle relationships,

finding circumference/area/surface area/volume, identifying cross sections

ELL (SEI) ● Bilingual math dictionary, frayer model, gallery walk of vocabulary words ● Native/Non-Native speaker groupings


● Providing modified/guided notes with prompts and native language definitions ● Bilingual practice problems of identifying angles & lines, finding angle measurements, writing equations about

angle relationships, finding circumference/area/surface area/volume, identifying cross sections ● Modeling, chunking and scaffolding of identifying angles & lines, finding angle measurements, writing equations

about angle relationships, finding circumference/area/surface area/volume, identifying cross sections ● Modified test/quizzes on identifying angles & lines, finding angle measurements, writing equations about angle

relationships, finding circumference/area/surface area/volume, identifying cross sections ● Extended time on assignments and assessments ● Extra help on identifying angles & lines, finding angle measurements, writing equations about angle relationships,



● Copy of Notes ○ Highlighting: Geometry vocabulary, formulas, steps and procedures ○ Providing vocabulary definitions using the Frayer model providing a definition, picture, example and non

example ● Modeling via powerpoint/Smartboard NB on identifying angles & lines, finding angle measurements, writing

equations about angle relationships, finding circumference/area/surface area/volume, identifying cross sections ● Guided Notes on identifying angles & lines, finding angle measurements, writing equations about angle

relationships, finding circumference/area/surface area/volume, identifying cross sections ● Steps for finding circumference/area/ surface area/ volume ● Manipulatives/Visual Aides using different colors to represent angels and assist in finding angle measurements ● Study guide prior to assessments on the following topics: identifying angles & lines, finding angle measurements,

writing equations about angle relationships, finding circumference/area/surface area/volume, identifying cross sections

● Modified test/quizzes on identifying angles & lines, finding angle measurements, writing equations about angle relationships, finding circumference/area/surface area/volume, identifying cross sections

● Extended time on assignments and assessments ● Extra help on identifying angles & lines, finding angle measurements, writing equations about angle relationships,


Gifted & Talented ● Individualized Pacing ● Supplemental Challenge Problems on geometry


● Benchmark: Constructed Response Tasks (CRT): Reasoning and performance task ● Alternative: Study Island ● Summative: Unit Test- Geometry ● Formative: Quizzes- Angles/Lines, Finding Angle Measurements, Area & Circumference, Surface Area & Volume,

Assessments Cross Sections ● Formative: Create a vocabulary dictionary ● Alternative: Triangle inequality lab

Unit 6: Statistics


NJSLS-M ● 7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

● 7.SP.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 comparative 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












● WHST.6-8.1. Write arguments focused on discipline-specific content. ○ C. Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s),

counterclaims, reasons, and evidence. ○ D. Establish and maintain a formal/academic style, approach, and form. ○ E. Provide a concluding statement or section that follows from and supports the argument presented.

● WHST.6-8.2. Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes.

○ A. Introduce a topic and organize ideas, concepts, and information using text structures (e.g. definition, classification, comparison/contrast, cause/effect, etc.) and text features (e.g. headings, graphics, and multimedia) when useful to aiding comprehension.

○ D. Use precise language and domain-specific vocabulary to inform about or explain the topic. ○ E. Establish and maintain a formal/academic style, approach, and form. ○ F. Provide a concluding statement or section that follows from and supports the information or explanation

presented.



21st Century: Personal Financial

● NA

Literacy (9.1)





● 8.1.8.A.2 Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or 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.A.4 Graph and calculate data within a spreadsheet and present a summary of the results. ● 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to



● NA


● A population can be represented by sample that should be chosen randomly. ● Analyze/understand that outliers do not greatly affect the mode or the median, but they may make the mean a less

effective way to represent the central tendency of a particular set of data. ● Use the mode to represent a data set when the data are not numerical. Use the mean when there are no outliers and

the values are fairly close together. The number of times a data item occurs is the frequency of the item. ● Use both frequency tables and line plots show the distribution or shape of a set of data. ● Understand that a stem-and-leaf plot can quickly show the distribution of a data set and retains each data value. ● Understand that box-and-whisker plots are useful with very large data sets or for making comparison between data

sets. ● Use a scatter plot to help decide whether one set of data relates to another. ● Use trend lines to make predictions about data values that do not appear on a scatter plot.

Essential Questions ● What is a random sample and how is it used to make generalizations about a population? ● How can measures of central tendency be used to describe the shape and distribution of data?

Activities ● Practice Problems: sampling/surveys, measures of central tendency, displaying frequency/data/MAD, creating/interpreting data displays

● Activity Lab: doodle notes on measures of central tendency, interpreting MAD statistical plots ● Solving real world word problems: describing data sets, determining best measure of central tendency to represent

a data set, creating unbiased survey questions, determining validity of survey/data samples ● Modeling: frequency table, histograms, stem & leaf plots, box & whisker plots, line/dot plots, MAD table ● Utilizing graphic organizer: foldable notes on steps and procedures of data displays ● Cooperative learning groups: think-pair-share determining best measure of central tendency, partners to complete

practice problems on statistics, small groups of 3-4 creating/interpreting data displays ● Learning stations: test review & preparation for Statistics


Vocabulary ● population ● sample ● random sample ● biased questions ● inferences ● mean ● median ● mode ● range ● outlier ● frequency ● line plot (dot plot) ● stem-and-leaf plot ● box-and-whisker plot ● quartile ● scatter plot








● positive trend ● negative trend ● no trend ● trend line ● variability



● Copy of Notes ○ Highlighting: statistic vocabulary ○ Providing vocabulary definitions in interactive notebook (INB) on statistics using the Frayer model

providing a definition, picture, example and non example ● Modeling via powerpoint/Smartboard NB on Statistics

○ Line plot, scatter plot and box-and-whisker plot ○ Modeling, chunking and scaffolding of mean, median, mode, central tendency, displaying frequency/data/

MAD, creating/interpreting data displays ● Guided Notes on

○ Finding the mean, median, mode and range of data ○ Constructing a frequency table and creating a histogram ○ Positive and negative trends

● Manipulatives/Visual Aides ○ Foldables: mean, median, mode and range ○ Graphic organizer: trends

● IXL for additional practice on statistics ● Study guide prior to statistics assessment ● Modified test/quizzes on statistics ● Extended time on assignments and assessments ● Extra help on the statistics


ELL (SEI) ● Bilingual math dictionary, frayer model, gallery walk of vocabulary words ● Native/Non-Native speaker groupings ● Providing modified/guided notes with prompts and native language definitions ● Bilingual practice problems of sampling/surveys, measures of central tendency, displaying frequency/data/MAD,

creating/interpreting data displays ● Modeling, chunking and scaffolding of sampling/surveys, measures of central tendency, displaying

frequency/data/MAD, creating/interpreting data displays ● Modified test/quizzes on sampling/surveys, measures of central tendency, displaying frequency/data/MAD,

creating/interpreting data displays ● Extended time on assignments and assessments ● Extra help on sampling/surveys, measures of central tendency, displaying frequency/data/MAD,

creating/interpreting data displays


● Copy of Notes ○ Highlighting: vocabulary and data ○ Providing vocabulary definitions using the Frayer model providing a definition, picture, example and non

example ● Modeling via powerpoint/Smartboard NB on sampling/surveys, measures of central tendency, displaying

frequency/data/MAD, creating/interpreting data displays ● Guided Notes on sampling/surveys, measures of central tendency, displaying frequency/data/MAD,

creating/interpreting data displays ● Steps for creating and finding data in a data displays ● Manipulatives/Visual aides using different colors to display trends ● Study guide prior to assessments on the following topics: ● Modified test/quizzes on sampling/surveys, measures of central tendency, displaying frequency/data/MAD,

creating/interpreting data displays ● Extended time on assignments and assessments ● Extra help on sampling/surveys, measures of central tendency, displaying frequency/data/MAD,

creating/interpreting data displays

Gifted & Talented ● Individualized Pacing ● Supplemental Challenge Problems


● Benchmark: Constructed Response Tasks (CRT): Reasoning and performance task ● Alternative: Study Island ● Summative: Unit Test: Statistics ● Formative: Quizzes: Measures of Central Tendency, Surveys/Samples, Frequency Displays, MAD

Assessments ● Alternative: Data Collection and Analysis project

Unit 7: Probability


NJSLS-M ● 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 observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

● 7.SP.C.7. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

● 7.SP.C.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation












● WHST.6-8.1. Write arguments focused on discipline-specific content. C. Use words, phrases, and clauses to create cohesion and clarify the relationships among claim(s), counterclaims, reasons, and evidence. D. Establish and maintain a formal/academic style, approach, and form. E. Provide a concluding statement or section that follows from and supports the argument presented.

● WHST.6-8.2. Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes. A. Introduce a topic and organize ideas, concepts, and information using text structures (e.g. definition,



presented.




● NA





● 8.1.8.A.2 Create a document (e.g. newsletter, reports, personalized learning plan, business letters or flyers) using one or 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.A.4 Graph and calculate data within a spreadsheet and present a summary of the results. ● 8.1.8.E.1 Effectively use a variety of search tools and filters in professional public databases to find information to



● NA


● Understand that probability is expressed as a number from 0 (impossible) to 1 (certain) that tells how often an event will occur.

Essential Questions ● How is the probability of an event determined and described?

Activities ● Practice Problems: expressing probability, calculating theoretical & experimental probabilities, finding probability of compound events, displaying sample spaces, counting outcomes

● Activity Lab: simulating probability events, displaying sample spaces ● Solving real world word problems: using probability to determine the fairness of games ● Modeling: probability scale, tree diagram, organized list, and tables ● Utilizing graphic organizer: foldable notes to describe procedures of calculating probability ● Cooperative learning groups: think-pair-share for identifying types of compound events, small groups of 3-4

students to collaborate and design probability simulations ● Learning stations: test review & preparation for probability

Resources ● Pearson Course 2 Textbook ● Pearson Course 3 Textbook ● LearnZillion ● NJCTL ● Illustrative Mathematics ● EngageNY





● GeorgiaStandards.org ● Mathematics Assessment Resource Service ● Open Up Resources

Vocabulary ● probability ● event ● outcome ● complement of event ● theoretical probability



● Copy of Notes ○ Highlighting: probability vocabulary ○ Providing vocabulary definitions in interactive notebook (INB) on probability using the Frayer model

providing a definition, picture, example and non example ● Modeling via powerpoint/Smartboard NB on probability

○ probability scale, tree diagram, organized list, tables ● Guided Notes on

○ expressing probability, calculating theoretical & experimental probabilities, finding probability of compound events, displaying sample spaces, counting outcomes

○ Tree Diagram ● Manipulatives/Visual Aides

○ Use of dice to find probability ○ Foldable: calculate probability ○ Venn Diagram to compare theoretical and experimental probability

● IXL for additional practice on probability ● Study guide prior to probability assessment ● Use of calculator





● Extended time on assessments and assignments ● Extra help on the probability

ELL (SEI) ● Bilingual math dictionary, frayer model, gallery walk of vocabulary words ● Native/Non-Native speaker groupings ● Providing modified/guided notes with prompts and native language definitions ● Bilingual practice problems of expressing probability, calculating theoretical & experimental probabilities, finding

probability of compound events, displaying sample spaces, counting outcomes ● Modeling , chunking and scaffolding of expressing probability, calculating theoretical & experimental

probabilities, finding probability of compound events, displaying sample spaces, counting outcomes ● Modified test/quizzes on expressing probability, calculating theoretical & experimental probabilities, finding

probability of compound events, displaying sample spaces, counting outcomes ● Extended time on assignments and assessments ● Extra help on expressing probability, calculating theoretical & experimental probabilities, finding probability of

compound events, displaying sample spaces, counting outcomes


● Copy of Notes ○ Highlighting: probability vocabulary ○ Providing vocabulary definitions using the Frayer model providing a definition, picture, example and non

example ● Modeling via powerpoint/Smartboard NB on expressing probability, calculating theoretical & experimental

probabilities, finding probability of compound events, displaying sample spaces, counting outcomes ● Guided Notes on expressing probability, calculating theoretical & experimental probabilities, finding probability of

compound events, displaying sample spaces, counting outcomes ● Manipulatives/visual aides using different colors to display sample spaces and counting outcomes ● Study guide prior to assessments on the following topics: expressing probability, calculating theoretical &

experimental probabilities, finding probability of compound events, displaying sample spaces, counting outcomes ● Modified test/quizzes on expressing probability, calculating theoretical & experimental probabilities, finding

probability of compound events, displaying sample spaces, counting outcomes ● Extended time on assignments and assessments ● Extra help on expressing probability, calculating theoretical & experimental probabilities, finding probability of

compound events, displaying sample spaces, counting outcomes

Gifted & Talented ● Individualized Pacing ● Supplemental Challenge Problems

Formative, ● Benchmark: Constructed Response Tasks (CRT): Reasoning and performance task

Summative, Benchmark, and Alternative Assessments

● Alternative: Study Island ● Summative: Unit Test- Probability ● Formative: Quizzes- Experimental & Theoretical, Compound Events, Sample Spaces, Counting Outcomes

Documents

F -A 7_Pre-Algebra_COS (2).pdfinverses). Interpret sums of rational numbers by describing real-world contexts. 7.NS.A.1c. Understand subtraction of rational numbers as adding the additive