Unit 1 Ratios and Proportions

Transcription

1 Unit 1 Ratios and Proportions Content Area: Mathematics Course(s): Generic Course Time Period: 1st Marking Period Length: 7 Weeks Status: Published Unit Overview Analyze proportional relationships and use them to solve real world and mathematical problems Proportional relationships can be used to solve real world problems Determine whether the relationship between two quantities is proportional Use proportions to solve multi step problems Proportional relationships can be used to solve percent problems Find the percent of increase and decrease and use percents to solve problems involving sales tax, tips, markups and discounts, and simple interest Benchmark Assessment 1 will be given after chapter 2 at the end of this unit Transfer Students will be able to independently use their learning to apply rates, ratios, percentages and proportional relationships to problem solving situations such as interest, tax, discount, etc apply rates, ratios, percentages and proportional relationships to solve multi step ratio and percent problems apply scale drawings to problem solving situations involving geometric figures identify slope as a proportional relationship use mathematical expressions, equations, inequalities and graphs to represent and solve real world and mathematical problems For more information, read the following article by Grant Wiggins

2 Meaning Understandings Students will understand that Fractions, decimals, and percents can be used interchangeably Ratios use division to represent relationships between two quantities The constant of proportionality is also considered to be the unit rate Essential Questions Students will keep considering Unit: How can you use mathematics to describe change and model real world situations? Chapter 1: How can you show that two objects are proportional? Chapter 2: How can percent help you understand situations involving money? Application of Knowledge and Skill Students will know Students will know how to compute unit rates associated with fractions, including ratios of lengths, areas, and other quantities measured in like or different units (7RP1) how to recognize and represent proportional relationships between quantities (7RP2) how to solve real world and mathematical problems involving the four operations with rational numbers (7NS3) Students will be skilled at

3 Students will be skilled at Solving multi step ratio and percent problems (7RP3) Solving problems involving simple interest and tax (7RP3) Solving problems involving markups and markdowns, gratuities and commissions, and fees (7RP3) Solving problems involving percent increase, percent decrease, and percent (margin of) error (7RP3) Converting between rational number forms (whole numbers, fractions and decimals) to solve problems as appropriate (7EE3) Solve multi step mathematical problems posed with positive and negative rationingl numbers in any form (whole numbers, fractions, and decimals), using tools strategically (7EE3) Solving multi step real life problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically (7EE3) Using mental computation and estimation strategies to assess the reasonableness of the answer (7EE3) Academic Vocabulary Chapter 1 Complex fraction, constant of proportionality, constant rate of change, constant of variation, coordinate plane, cross products, dimensional analysis, direct variation, equivalent ratios, nonproportional, proportion, proportional, ordered pair, origin, quadrants, rate, rate of change, slope, unit rate, unit ratio, x axis, x coordinate, y axis, y coordinate Chapter 2 Discount, gratuity, markdown, markup, percent equation, percent error, percent of change, percent of decrease, percent of increase, percent proportion, principal, sales tax, selling price, simple interest, tip Learning Goal Analyze proportional relationships and use them to solve real world and mathematical problems Compute unit rates associated with ratios of fractions measured in like or unlike units (7RPA1) 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 (7RPA2d) Use proportional relationships to solve multistep ratio and percent problems (for example, simple interest, tax,

4 markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error) Target #11 (Level of Difficulty -2) SWBAT find unit rates MA7CCSSMathContent7RPA2 MA7CCSSMathContent7RPA2a MAK 12CCSSMathPracticeMP5 Target #12 (Level of Difficulty - 2) SWBAT simplify complex fractions Recognize and represent proportional relationships between quantities Decide whether two quantities are in a proportional relationship, eg, 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 Use appropriate tools strategically MA7CCSSMathContent7RPA1 MA7CCSSMathContent7NSA3 MAK 12CCSSMathPracticeMP6 Target #13 (Level of Difficulty - 3) SWBAT convert rates using rates and dimensional analysis Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units Solve real world and mathematical problems involving the four operations with rational numbers Attend to precision MA7CCSSMathContent7RPA2 MA7CCSSMathContent7RPA3 MAK 12CCSSMathPracticeMP5 Recognize and represent proportional relationships between quantities Use proportional relationships to solve multistep ratio and percent problems Use appropriate tools strategically Target #14 (Level of Difficulty - 1) SWBAT identify proportional and nonproportional relationships MA7CCSSMathContent7RPA2 MA7CCSSMathContent7RPA2a MA7CCSSMathContent7RPA2b Recognize and represent proportional relationships between quantities Decide whether two quantities are in a proportional relationship, eg, 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 Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships Target #15 (Level of Difficulty - 2) SWBAT identify proportional relationships by graphing on the coordinate plane MA7CCSSMathContent7RPA2 MA7CCSSMathContent7RPA2a Recognize and represent proportional relationships between quantities Decide whether two quantities are in a proportional relationship, eg, by testing for equivalent ratios in a

5 MAK 12CCSSMathPracticeMP2 Target #16 (Level of Difficulty - 3) SWBAT use proportions to solve problems table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin Reason abstractly and quantitatively MA7CCSSMathContent7RPA2 MA7CCSSMathContent7RPA2b MA7CCSSMathContent7RPA2c MA7CCSSMathContent7RPA3 MAK 12CCSSMathPracticeMP2 Target #17 (Level of Difficulty - 2) SWBAT represent and identify constant rates of change Recognize and represent proportional relationships between quantities Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships Represent proportional relationships by equations Use proportional relationships to solve multistep ratio and percent problems Reason abstractly and quantitatively MA7CCSSMathContent7RPA2 MA7CCSSMathContent7RPA2b MA7CCSSMathContent7RPA2d Target #18 (Level of Difficulty - 2) SWBAT identify slope using tables and graphs Recognize and represent proportional relationships between quantities Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships 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 MA7CCSSMathContent7RPA2 MA7CCSSMathContent7RPA2b Target #19 (Level of Difficulty - 3) SWBAT use direct variation to solve problems Recognize and represent proportional relationships between quantities Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships MA7CCSSMathContent7RPA2 MA7CCSSMathContent7RPA2a MA7CCSSMathContent7RPA2b MAK 12CCSSMathPracticeMP2 Target #21 (Level of Difficulty - 3) SWBAT use percent diagrams to solve problems Recognize and represent proportional relationships between quantities Decide whether two quantities are in a proportional relationship, eg, 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 Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships Reason abstractly and quantitatively

6 MA7CCSSMathContent7RPA3 MA7CCSSMathContent7EEB3 Target #22 (Level of Difficulty - 2) SWBAT Estimate the percent of a number Use proportional relationships to solve multistep ratio and percent problems 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 MA7CCSSMathContent7RPA3 MA7CCSSMathContent7EEB3 MAK 12CCSSMathPracticeMP5 Use proportional relationships to solve multistep ratio and percent problems 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 Use appropriate tools strategically Target #23 (Level of Difficulty - 3) SWBAT solve problems involving percents by using the percent proportion MA7CCSSMathContent7RPA3 Use proportional relationships to solve multistep ratio and percent problems Target #24 (Level of Difficulty - 3) SWBAT Solve problems involving percents by using the percent equation MA7CCSSMathContent7RPA2 MA7CCSSMathContent7RPA2c MA7CCSSMathContent7RPA3 MA7CCSSMathContent7EEB3 MAK 12CCSSMathPracticeMP2 Recognize and represent proportional relationships between quantities Represent proportional relationships by equations Use proportional relationships to solve multistep ratio and percent problems 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 Reason abstractly and quantitatively Target #25 (Level of Difficulty - 3) SWBAT solve problems involving percent increase and percent decrease MA7CCSSMathContent7RPA3 MA7CCSSMathContent7EEB3 MAK 12CCSSMathPracticeMP5 MAK 12CCSSMathPracticeMP6 Target #26 (Level of Diffculty - 4) Use proportional relationships to solve multistep ratio and percent problems 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 Use appropriate tools strategically Attend to precision

7 SWBAT solve problems involving financial literacy, such as sales tax, tips, and markup MA7CCSSMathContent7RPA3 MA7CCSSMathContent7EEA2 MA7CCSSMathContent7EEB3 Target #27 (Level of Difficulty - 2) SWBAT solve problems involving discount Use proportional relationships to solve multistep ratio and percent problems 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 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 MA7CCSSMathContent7RPA3 MA7CCSSMathContent7EEB3 MAK 12CCSSMathPracticeMP5 Target#28 (Level of Difficulty - 2) SWBAT solve problems involving simple interest Use proportional relationships to solve multistep ratio and percent problems 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 Use appropriate tools strategically MA7CCSSMathContent7RPA3 MA7CCSSMathContent7EEB3 Summative Assessment Use proportional relationships to solve multistep ratio and percent problems 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 Journal Portfolio Project Quiz Test 21st Century Life and Careers See 21st Century Career Activity in each chapter WORK5 8918A2 WORK5 8918B1 WORK5 8918C1 Implement problem solving strategies to solve a problem in school or the community Use multiple points of view to create alternative solutions Determine an individual's responsibility for personal actions and contributions to group activities Formative Assessment and Performance Opportunities Use the Lists tab Clicker

8 Exit Ticket MAP Testing Status Check (Thumbs Up/Down) Student Persentation Student Teacjer Conference Differentiation / Enrichment Use the Lists tab Unit Resources Use Lists and attach Documents

9 Unit 2 The Number System Content Area: Mathematics Course(s): Generic Course Time Period: 2nd Marking Period Length: 6 Weeks Status: Published Unit Overview Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers Use negative integers in everday contexts that involve values below zero Add, subtract, multiply, and divide integers Solve multi step real life problems by performing operations on rational numbers Transfer Students will be able to independently use their learning to solve real world problems involving representing and using rational numbers in solve real life situation problems representing rational numbers with visuals (including distance models), language, and real life contexts using a number line model to represent the unique placement of any number in relation to other numbers apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers For more information, read the following article by Grant Wiggins Meaning Understandings Students will understand that One representation may sometimes be more helpful than another; and, used together, multiple

10 representations give a fuller understanding of a problem A quantity can be represented numerically in various ways Numeric fluency includes both the understanding of and the ability to appropriately use numbers Computational fluency includes understanding not only the meaning, but also the appropriate use of numerical operations In many cases, there are multiple algorithms for finding a mathematical solution, and those algorithms are frequently associated with different cultures Essential Questions Students will keep considering Unit 2: How can mathematical ideas be represented? Chapter 3: What happens when you add, subtract, multiply, and divide integers? Chapter 4: What happens when you add, subtract, multiply, and divide fractions? Application of Knowledge and Skill Students will know Students will know Negative integers can be used in everyday contact that involve values below zero Every quotient (with non zero divisor) is a rational number Students will be skilled at Students will be skilled at Add and subtract rational numbers (7NS1) Represent addition and subtraction on a horizontal or vertical number line diagram (7NS1) Use words, visuals and symbols to describe situations in which opposite quantities

11 combine to make 0 (7NS1) Represent addition of quantities with symbols, visuals and words by showing positive or negative direction from one quantity to the other (7NS1) Show that a number and its opposite have a sum of 0 using visuals, symbols, words and real world contexts (7NS1) Use the term additive inverse to describe 2 numbers whose sum is zero (7NS1) Use commutative, distributive, associative, identity, and inverse properties to add and subtract rational numbers (7NS1) Use the term absolute value to describe the distance from zero on number line diagram and with symbols (7NS1) Multiply and divide rational numbers (7NS2) Use the distributive property to multiply positive and negative rational numbers using symbols, visuals, words and real life contexts (7NS2) Interpret products of rational numbers by describing real world contexts (7NS2) Identify situations when integers can and cannot be divided (7NS2) Use words and real world contexts to explain why the quotient of two integers is a rational number (7NS2) Identify and apply properties used when multiplying and dividing rational numbers (7NS2) Convert a rational number to a decimal using long division (7NS2) Identify terminating or repeating decimal representations of rational numbers (7NS2) Solve real world and mathematical problems involving the four operations with rational numbers (7NS3) Academic Vocabulary Chapter 3 Absolute value, additive inverse, graph, integer, negative integer, opposites, positive integer, zero pair Chapter 4 Bar notation, common demoninator, least common denominator, like fractions, rational number, repeating decimal, terminating decimal, unlike fractions Learning Goal Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers

12 Objective #31 -- ( Level of Difficulty - 1) SWBAT: Read and write integers, and find the absolute value of an integer MA7CCSSMathContent7NSA1b MA7CCSSMathContent7NSA1c MAK 12CCSSMathPracticeMP5 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 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 Use appropriate tools strategically Objective #32 -- (Level of Difficulty - 2) SWBAT: Add integers MA7CCSSMathContent7NSA1 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 MA7CCSSMathContent7NSA1a Describe situations in which opposite quantities combine to make 0 MA7CCSSMathContent7NSA1b 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 MA7CCSSMathContent7NSA1d Apply properties of operations as strategies to add and subtract rational numbers MA7CCSSMathContent7NSA3 Solve real world and mathematical problems involving the four operations with rational numbers MA7CCSSMathContent7EEB3 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 MAK 12CCSSMathPracticeMP7 Look for and make use of structure Objective #33 -- (Level of Difficulty - 2) SWBAT: subtract integers MA7CCSSMathContent7NSA1 MA7CCSSMathContent7NSA1c MA7CCSSMathContent7NSA1d MA7CCSSMathContent7NSA3 MAK 12CCSSMathPracticeMP2 MAK 12CCSSMathPracticeMP5 MAK 12CCSSMathPracticeMP6 MAK 12CCSSMathPracticeMP7 Objective #34 -- (Level of Difficulty - 2) SWBAT: Multiply integers 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 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 Apply properties of operations as strategies to add and subtract rational numbers Solve real world and mathematical problems involving the four operations with rational numbers Reason abstractly and quantitatively Use appropriate tools strategically Attend to precision Look for and make use of structure

13 MA7CCSSMathContent7NSA2 MA7CCSSMathContent7NSA2a MA7CCSSMathContent7NSA2c MA7CCSSMathContent7NSA3 MA7CCSSMathContent7EEB3 MAK 12CCSSMathPracticeMP8 Objective #35 -- (Level of Difficulty - 2) SWABT: Divide integers Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers 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 Apply properties of operations as strategies to multiply and divide rational numbers Solve real world and mathematical problems involving the four operations with rational numbers 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 Look for and express regularity in repeated reasoning MA7CCSSMathContent7NSA2 MA7CCSSMathContent7NSA2a MA7CCSSMathContent7NSA2c MA7CCSSMathContent7NSA3 MA7CCSSMathContent7EEB3 MAK 12CCSSMathPracticeMP8 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers 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 Apply properties of operations as strategies to multiply and divide rational numbers Solve real world and mathematical problems involving the four operations with rational numbers 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 Look for and express regularity in repeated reasoning Objective #41 -- (Level of Difficulty - 2) SWBAT: Write fractions as terminating or repeating decimals and write decimals as fractions MA7CCSSMathContent7NSA2 MA7CCSSMathContent7NSA2d MA7CCSSMathContent7EEB3 MAK 12CCSSMathPracticeMP6 MAK 12CCSSMathPracticeMP7 Objective #42 - (Level of Difficulty - 2) SWBAT: Compare and order rational numbers Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers 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 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 Attend to precision Look for and make use of structure MA7CCSSMathContent7NSA2 MA7CCSSMathContent7NSA2b MA7CCSSMathContent7EEB3 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers 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 Solve multi step real life and mathematical problems posed with positive and negative rational numbers in any

14 Objective #43 - (Level of Difficulty - 2) MA7CCSSMathContent7NSA1 MA7CCSSMathContent7NSA1c MA7CCSSMathContent7NSA1d MA7CCSSMathContent7NSA3 MA7CCSSMathContent7EEB3 MAK 12CCSSMathPracticeMP7 Objective #44 - (Level of Difficulty - 2) SWBAT: Add and subtract fractions with unlike denominators 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 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 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 Apply properties of operations as strategies to add and subtract rational numbers Solve real world and mathematical problems involving the four operations with rational numbers 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 Look for and make use of structure MA7CCSSMathContent7NSA1 MA7CCSSMathContent7NSA1d MA7CCSSMathContent7NSA3 MA7CCSSMathContent7EEB3 Objective #45 - (Level of Difficulty - 2) SWBAT: Add and subtract mixed numbers 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 Apply properties of operations as strategies to add and subtract rational numbers Solve real world and mathematical problems involving the four operations with rational numbers 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 MA7CCSSMathContent7NSA MA7CCSSMathContent7NSA1d MA7CCSSMathContent7NSA3 MA7CCSSMathContent7EEB3 Objective #46 - (Level of Difficulty - 2) SWBAT: Multiply fractions and mixed numbers Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers Apply properties of operations as strategies to add and subtract rational numbers Solve real world and mathematical problems involving the four operations with rational numbers 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 MA7CCSSMathContent7NSA2 MA7CCSSMathContent7NSA2a Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers 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

15 MA7CCSSMathContent7NSA2c MA7CCSSMathContent7NSA3 MA7CCSSMathContent7EEB3 Apply properties of operations as strategies to multiply and divide rational numbers Solve real world and mathematical problems involving the four operations with rational numbers 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 Objective #47 - (Level of Difficulty - 2) SWBAT: Convert units of measure between the customary and metric systems MA7CCSSMathContent7RPA3 MA7CCSSMathContent7NSA2 MA7CCSSMathContent7NSA3 MAK 12CCSSMathPracticeMP5 MAK 12CCSSMathPracticeMP6 Objective #48 - (Level of Difficulty - 2) SWBAT: Divide fractions and mixed numbers Use proportional relationships to solve multistep ratio and percent problems Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers Solve real world and mathematical problems involving the four operations with rational numbers Use appropriate tools strategically Attend to precision MA7CCSSMathContent7NSA2 MA7CCSSMathContent7NSA2c MA7CCSSMathContent7NSA3 MA7CCSSMathContent7EEB3 MAK 12CCSSMathPracticeMP5 Summative Assessment Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers Apply properties of operations as strategies to multiply and divide rational numbers Solve real world and mathematical problems involving the four operations with rational numbers 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 Use appropriate tools strategically Journal Portfolio Project Quiz Test 21st Century Life and Careers See 21st Century Career activities in Chapters WORK5 8918A2 WORK5 8918B1 WORK5 8918C1 Implement problem solving strategies to solve a problem in school or the community Use multiple points of view to create alternative solutions Determine an individual's responsibility for personal actions and contributions to group activities Formative Assessment and Performance Opportunities Use the Lists tab Clicker Exit Ticket MAP Testing Status Check (Thumbs up/down)

16 Student Presentation Student Teacher Conference Differentiation / Enrichment Use the Lists tab Unit Resources Use Lists and attach Documents

17 Unit 3 Expressions and Equations Content Area: Mathematics Course(s): Generic Course Time Period: 2nd Marking Period Length: 7 Weeks Status: Published Unit Overview Use properties of operations to generate equivalent expressions Apply the properties of operations to simplify and evaluate algebraic expressions Use the properties of equality to solve equations algebraically Solve inqualities Benchmark Assessment 2 will be given after chapter 5 in this unit Transfer Students will be able to independently use their learning to solve real world problems involving Variables can be used to represent numbers in any type of mathematical problem Understand the difference between an expression and an equation Expressions you simplify and equations you solve for the variable s value Write and solve multi step equations including all rational numbers Some equations may have more than one solution and understand inequalities Properties of operations allow us to add, subtract, factor, and expand linear expressions For more information, read the following article by Grant Wiggins Meaning Understandings Students will understand that The symbolic language of algebra is used to communicate and generalize the patterns in mathematics

18 Algebraic representation can be used to generalize patterns and relationships Patterns and relationships can be represented graphically, numerically, symbolically, or verbally Mathematical models can be used to describe and quantify physical relationships Physical models can be used to clarify mathematical relationships One representation may sometimes be more helpful than another; and, used together, multiple representations give a fuller understanding of a problem Algebraic and numeric procedures are interconnected and build on one another to produce a coherent whole Reasoning and/or proof can be used to verify or refute conjectures or theorems in algebra Essential Questions Students will keep considering Unit 3: How can you communicate mathematical ideas effectively? Chapter 5: How can you use numbers and symbols to represent mathematical ideas? Chapter 6: What does it mean to say two quantities are equal? Application of Knowledge and Skill Students will know Students will know how to apply and extend previous understandings of arithmetic to algebraic expressions how to compute with all positive and negative rational numbers (7NS1 2) how to solve real world and mathematical problems with rational numbers (7NS3) how to apply properties of operations to add, subtract, factor and expand linear equations

19 Students will be skilled at Students will be skilled at Using Commutative, Associative, Distributive, Identity, and Inverse Properties to add and subtract linear expressions with rational coefficients (7EE1) Using Commutative, Associative, Distributive, Identity, and Inverse Properties to factor and expand linear expressions with rational coefficients (7EE1) Rewriting an expression in a different form (7EE2) Choose the form of an expression that works best to solve a problem (7EE2) Explaining your reasoning for the choice of expression used to solve a problemuse commutative, associative, distributive, identity, and inverse properties to calculate with numbers in any form (whole numbers, fractions and decimals) (7EE3) Convert between rational number forms (whole numbers, fractions and decimals) to solve problems as appropriate (7EE3) Solve multi step mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically (7EE3) Solve multi step real life problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically (7EE3) Use mental computation and estimation strategies to assess the reasonableness of the answer (7EE3) Translate words or real life situations into variable equations (7EE4) Translate words or real life situations into variable inequalities (7EE4) Solve one or two step equations with rational numbers fluently (7EE4) Solve word problems leading to one or two step equations with rational numbers (7EE4) Construct simple equations and inequalities with rational numbers to solve problems (7EE4) Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach (7EE4) Solve word problems leading to one or two step inequalities with rational numbers (7EE4) Graph the solution set of inequalities and interpret it in the context of the problem (7EE4) Know the formulas for the area and circumference of a circle (7G4) Use the formulas for area and circumference of a circle to solve problems (7G4) Informally, derive the area formula for a circle based on circumference (7G4)

20 Academic Vocabulary Chapter 5 Additive identity property, algebra, algebraic expression, arithmetic sequence, associative property, coefficient, commutative property, constant, counterexample, define a variable, distributive property, equivalent expressions, factor, factored form, like terms, linear expression, monomial, multiplicative identity property, multiplicative property of zero, property, sequence, simplest form, term, variable Chapter 6 Addition property of equality, addition property of inequality, coefficient, division property of equality, division property of inequality, equation, equivalent equation, inequality, multiplication property or equality, multiplication property or inequality, solution, subtraction property of equality, subtraction property of inequality, two step equation, two step inequality Learning Goal #1 Students will use properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients Rewrite expressions in different forms in a problem context to demonstrate how quantities are related Objective # (Level of Difficulty - 3) SWBAT evaluate simple algebraic expressions MA7CCSSMathContent7EEA1 MA7CCSSMathContent7EEA2 MAK 12CCSSMathPracticeMP2 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients 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 Reason abstractly and quantitatively Objective # (Level of Difficulty - 2) SWBAT describe the relationships and extend terms in arithmetic sequences MA7CCSSMathContent7EEA1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients MA7CCSSMathContent7EEA2 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 MAK 12CCSSMathPracticeMP2 Reason abstractly and quantitatively Objective # (Level of Difficulty - 2)

21 SWBAT identify and use mathematical properties to simplify algebraic expressions MA7CCSSMathContent7EEA1 MA7CCSSMathContent7EEA2 MAK 12CCSSMathPracticeMP5 MAK 12CCSSMathPracticeMP7 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients 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 Use appropriate tools strategically Look for and make use of structure Objective # (Level of Difficulty - 3) SWBAT apply the distributive property to rewrite algebraic expressions MA7CCSSMathContent7EEA1 MA7CCSSMathContent7EEA2 MAK 12CCSSMathPracticeMP5 MAK 12CCSSMathPracticeMP7 Objective # (Level of Difficulty - 2) SWBAT simplify algebraic expressions Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients 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 Use appropriate tools strategically Look for and make use of structure MA7CCSSMathContent7EEA1 MA7CCSSMathContent7EEA2 MAK 12CCSSMathPracticeMP2 MAK 12CCSSMathPracticeMP6 Objective # (Level of Difficulty - 2) SWBAT add linear expressions Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients 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 Reason abstractly and quantitatively Attend to precision MA7CCSSMathContent7EEA1 MA7CCSSMathContent7EEA2 MAK 12CCSSMathPracticeMP2 Objective # (Level of Difficulty - 2) SWBAT subtract linear expressions Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients 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 Reason abstractly and quantitatively MA7CCSSMathContent7EEA1 MA7CCSSMathContent7EEA2 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients 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

22 MAK 12CCSSMathPracticeMP2 Reason abstractly and quantitatively Objective # (Level of Difficulty - 2) SWBAT read and write integers, and find the absolute value of an integer MA7CCSSMathContent7EEA1 MA7CCSSMathContent7EEA2 MAK 12CCSSMathPracticeMP2 Objective # (Level of Difficulty - 3) SWBAT solve addition and subtraction equations Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients 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 Reason abstractly and quantitatively MA7CCSSMathContent7EEB4 MA7CCSSMathContent7EEB4a MAK 12CCSSMathPracticeMP2 MAK 12CCSSMathPracticeMP5 Objective # (Level of Difficulty - 3) SWBAT solve one stop multiplication and division equations 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 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 Reason abstractly and quantitatively Use appropriate tools strategically MA7CCSSMathContent7EEB4 MA7CCSSMathContent7EEB4a MAK 12CCSSMathPracticeMP2 MAK 12CCSSMathPracticeMP7 Objective # (Level of Difficulty - 3) SWBAT solve one step equations with rational coefficients 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 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 Reason abstractly and quantitatively Look for and make use of structure MA7CCSSMathContent7EEB4 MA7CCSSMathContent7EEB4a MAK 12CCSSMathPracticeMP2 Objective # (Level of Difficulty - 3) 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 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 Reason abstractly and quantitatively

23 SWBAT solve two step equations MA7CCSSMathContent7EEB4 MA7CCSSMathContent7EEB4a MAK 12CCSSMathPracticeMP2 Objective # (Level of Difficulty - 3) SWBAT solve two step equations of the form p(x + q) = r 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 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 Reason abstractly and quantitatively MA7CCSSMathContent7EEB4 MA7CCSSMathContent7EEB4a MAK 12CCSSMathPracticeMP2 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 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 Reason abstractly and quantitatively Objective # (Level of Difficulty - 3) SWBAT solve inequalities by using the Addition and Subtraction Properties of Inequality MA7CCSSMathContent7EEB4 MA7CCSSMathContent7EEB4b MAK 12CCSSMathPracticeMP2 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 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 Reason abstractly and quantitatively Objective # (Level of Difficulty - 3) SWBAT solve inequalities by using the Multiplication or Division Properties of Inequality MA7CCSSMathContent7EEB4 MA7CCSSMathContent7EEB4b MAK 12CCSSMathPracticeMP2 MAK 12CCSSMathPracticeMP7 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 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 Reason abstractly and quantitatively Look for and make use of structure Objective # (Level of Difficulty - 3) SWBAT model and solve two step inequalities and represent the solution on the number line MA7CCSSMathContent7EEB4 MA7CCSSMathContent7EEB4b 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 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

24 MAK 12CCSSMathPracticeMP2 MAK 12CCSSMathPracticeMP5 Summative Assessment Reason abstractly and quantitatively Use appropriate tools strategically Journal Portfolio PRoject Quiz Test 21st Century Life and Careers See 21st Century Career activities in Chapters WORK5 8918A2 WORK5 8918B1 WORK5 8918C1 Implement problem solving strategies to solve a problem in school or the community Use multiple points of view to create alternative solutions Determine an individual's responsibility for personal actions and contributions to group activities Formative Assessment and Performance Opportunities Use the Lists tab Clicker Exit Ticket MAP Testing Status Check (Thumbs up/down) Student Presentation Student Teacher Conference Differentiation / Enrichment Use the Lists tab Unit Resources

25 Unit 4 Geometry Content Area: Mathematics Course(s): Generic Course Time Period: 3rd Marking Period Length: 7 Weeks Status: Published Unit Overview Draw, construct, and describe geometric figures and describe the relationships between them Draw two and three dimensional figures Solve problems involving scale drawings of geometric figures Use formulas to find the area and circumference of a circle and to find the surface area and volume of prisms and pyramids Benchmark Assessment 3 will be given after chapter 7 in this unit Transfer Students will be able to independently use their learning to Real world and geometric structures are composed of shapes and spaces with specific properties Shapes are defined by their properties Shapes have a purpose for designing structures Three dimensional figures have relationships to specific two dimensional figures Planes that cut polyhedra create related two dimensional figures For more information, read the following article by Grant Wiggins Meaning Understandings Students will understand that Everyday objects have a variety of attributes, each of which can be measured in many ways