Unit 1 Ratios and Proportions Content Area: Course(s): Time Period: Length: Status:
Mathematics Generic Course 1st Marking Period 7 Weeks 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. http://www.authenticeducation.org/ae_bigideas/article.lasso?artid=60
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. (7.RP.1) how to recognize and represent proportional relationships between quantities (7.RP.2) how to solve real‐world and mathematical problems involving the four operations with rational numbers (7.NS.3)
Students will be skilled at...
Students will be skilled at... Solving multi‐step ratio and percent problems. (7.RP.3) • Solving problems involving simple interest and tax. (7.RP.3) • Solving problems involving markups and markdowns, gratuities and commissions, and fees. (7.RP.3) • Solving problems involving percent increase, percent decrease, and percent (margin of) error. (7.RP.3) • Converting between rational number forms (whole numbers, fractions and decimals) to solve problems as appropriate. (7.EE.3) • Solve multi‐step mathematical problems posed with positive and negative rationingl numbers in any form (whole numbers, fractions, and decimals), using tools strategically. (7.EE.3) • Solving multi‐step real‐life problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. (7.EE.3) • Using mental computation and estimation strategies to assess the reasonableness of the answer. (7.EE.3)
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. (7.RP.A.1) Explain what a point (x, y)on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and (1, r) where r is the unit rate. (7.RP.A.2d) Use proportional relationships to solve multistep ratio and percent problems (for example, simple interest, tax,
markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error)
Target #1.1 (Level of Difficulty -2) SWBAT find unit rates. MA.7.CCSS.Math.Content.7.RP.A.2 MA.7.CCSS.Math.Content.7.RP.A.2a
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4 MA.K‐12.CCSS.Math.Practice.MP5
Recognize and represent proportional relationships between quantities. 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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically.
Target #1.2 (Level of Difficulty - 2) SWBAT simplify complex fractions. MA.7.CCSS.Math.Content.7.RP.A.1
MA.7.CCSS.Math.Content.7.NS.A.3 MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4 MA.K‐12.CCSS.Math.Practice.MP6
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics. Attend to precision.
Target #1.3 (Level of Difficulty - 3) SWBAT convert rates using rates and dimensional analysis.
MA.7.CCSS.Math.Content.7.RP.A.2 MA.7.CCSS.Math.Content.7.RP.A.3 MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4 MA.K‐12.CCSS.Math.Practice.MP5
Recognize and represent proportional relationships between quantities. Use proportional relationships to solve multistep ratio and percent problems. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically.
Target #1.4 (Level of Difficulty - 1) SWBAT identify proportional and nonproportional relationships. MA.7.CCSS.Math.Content.7.RP.A.2 MA.7.CCSS.Math.Content.7.RP.A.2a MA.7.CCSS.Math.Content.7.RP.A.2b
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
Recognize and represent proportional relationships between quantities. 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. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Target #1.5 (Level of Difficulty - 2) SWBAT identify proportional relationships by graphing on the coordinate plane. MA.7.CCSS.Math.Content.7.RP.A.2 MA.7.CCSS.Math.Content.7.RP.A.2a
Recognize and represent proportional relationships between quantities. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP2 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Target #1.6 (Level of Difficulty - 3) SWBAT use proportions to solve problems. MA.7.CCSS.Math.Content.7.RP.A.2 MA.7.CCSS.Math.Content.7.RP.A.2b
MA.7.CCSS.Math.Content.7.RP.A.2c MA.7.CCSS.Math.Content.7.RP.A.3 MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP2 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
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. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Target #1.7 (Level of Difficulty - 2) SWBAT represent and identify constant rates of change. MA.7.CCSS.Math.Content.7.RP.A.2 MA.7.CCSS.Math.Content.7.RP.A.2b MA.7.CCSS.Math.Content.7.RP.A.2d
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Target #1.8 (Level of Difficulty - 2) SWBAT identify slope using tables and graphs. MA.7.CCSS.Math.Content.7.RP.A.2 MA.7.CCSS.Math.Content.7.RP.A.2b
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Target #1.9 (Level of Difficulty - 3) SWBAT use direct variation to solve problems. MA.7.CCSS.Math.Content.7.RP.A.2 MA.7.CCSS.Math.Content.7.RP.A.2a MA.7.CCSS.Math.Content.7.RP.A.2b
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP2 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
Recognize and represent proportional relationships between quantities. 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. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Target #2.1 (Level of Difficulty - 3) SWBAT use percent diagrams to solve problems.
MA.7.CCSS.Math.Content.7.RP.A.3 MA.7.CCSS.Math.Content.7.EE.B.3
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Target #2.2 (Level of Difficulty - 2) SWBAT Estimate the percent of a number. MA.7.CCSS.Math.Content.7.RP.A.3 MA.7.CCSS.Math.Content.7.EE.B.3
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4 MA.K‐12.CCSS.Math.Practice.MP5
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically.
Target #2.3 (Level of Difficulty - 3) SWBAT solve problems involving percents by using the percent proportion.
MA.7.CCSS.Math.Content.7.RP.A.3 MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
Use proportional relationships to solve multistep ratio and percent problems. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Target #2.4 (Level of Difficulty - 3) SWBAT Solve problems involving percents by using the percent equation. MA.7.CCSS.Math.Content.7.RP.A.2 MA.7.CCSS.Math.Content.7.RP.A.2c MA.7.CCSS.Math.Content.7.RP.A.3 MA.7.CCSS.Math.Content.7.EE.B.3
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP2 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
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. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Target #2.5 (Level of Difficulty - 3) SWBAT solve problems involving percent increase and percent decrease. MA.7.CCSS.Math.Content.7.RP.A.3 MA.7.CCSS.Math.Content.7.EE.B.3
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4 MA.K‐12.CCSS.Math.Practice.MP5 MA.K‐12.CCSS.Math.Practice.MP6
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision.
Target #2.6 (Level of Diffculty - 4)
SWBAT solve problems involving financial literacy, such as sales tax, tips, and markup. MA.7.CCSS.Math.Content.7.RP.A.3 MA.7.CCSS.Math.Content.7.EE.A.2 MA.7.CCSS.Math.Content.7.EE.B.3
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Target #2.7 (Level of Difficulty - 2) SWBAT solve problems involving discount. MA.7.CCSS.Math.Content.7.RP.A.3 MA.7.CCSS.Math.Content.7.EE.B.3
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4 MA.K‐12.CCSS.Math.Practice.MP5
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically.
Target#2.8 (Level of Difficulty - 2) SWBAT solve problems involving simple interest. MA.7.CCSS.Math.Content.7.RP.A.3 MA.7.CCSS.Math.Content.7.EE.B.3
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Summative Assessment
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•Journal •Portfolio •Project •Quiz •Test
. . . .
21st Century Life and Careers See 21st Century Career Activity in each chapter.
WORK.5‐8.9.1.8.A.2 WORK.5‐8.9.1.8.B.1 WORK.5‐8.9.1.8.C.1
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
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•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.
. . . . .
Unit 2 The Number System Content Area: Course(s): Time Period: Length: Status:
Mathematics Generic Course 2nd Marking Period 6 Weeks 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. http://www.authenticeducation.org/ae_bigideas/article.lasso?artid=60
Meaning
Understandings Students will understand that... •
One representation may sometimes be more helpful than another; and, used together, multiple
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. (7.NS.1) • Represent addition and subtraction on a horizontal or vertical number line diagram. (7.NS.1) • Use words, visuals and symbols to describe situations in which opposite quantities
combine to make 0. (7.NS.1) • Represent addition of quantities with symbols, visuals and words by showing positive or negative direction from one quantity to the other. (7.NS.1) • Show that a number and its opposite have a sum of 0 using visuals, symbols, words and real‐world contexts. (7.NS.1) • Use the term “additive inverse” to describe 2 numbers whose sum is zero. (7.NS.1) • Use commutative, distributive, associative, identity, and inverse properties to add and subtract rational numbers. (7.NS.1) • Use the term “absolute value” to describe the distance from zero on number line diagram and with symbols. (7.NS.1) • Multiply and divide rational numbers. (7.NS.2) • Use the distributive property to multiply positive and negative rational numbers using symbols, visuals, words and real‐life contexts. (7.NS.2) • Interpret products of rational numbers by describing real‐world contexts. (7.NS.2) • Identify situations when integers can and cannot be divided. (7.NS.2) • Use words and real‐world contexts to explain why the quotient of two integers is a rational number. (7.NS.2) • Identify and apply properties used when multiplying and dividing rational numbers. (7.NS.2) • Convert a rational number to a decimal using long division. (7.NS.2) • Identify terminating or repeating decimal representations of rational numbers. (7.NS.2) • Solve real world and mathematical problems involving the four operations with rational numbers. (7.NS.3)
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.
Objective #3.1 -- ( Level of Difficulty - 1) SWBAT: Read and write integers, and find the absolute value of an integer. MA.7.CCSS.Math.Content.7.NS.A.1b
MA.7.CCSS.Math.Content.7.NS.A.1c
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4 MA.K‐12.CCSS.Math.Practice.MP5
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically.
Objective #3.2 -- (Level of Difficulty - 2) SWBAT: Add integers. MA.7.CCSS.Math.Content.7.NS.A.1 MA.7.CCSS.Math.Content.7.NS.A.1a MA.7.CCSS.Math.Content.7.NS.A.1b
MA.7.CCSS.Math.Content.7.NS.A.1d MA.7.CCSS.Math.Content.7.NS.A.3 MA.7.CCSS.Math.Content.7.EE.B.3
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4 MA.K‐12.CCSS.Math.Practice.MP7
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. Describe situations in which opposite quantities combine to make 0. 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. 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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics. Look for and make use of structure.
Objective #3.3 -- (Level of Difficulty - 2) SWBAT: subtract integers. MA.7.CCSS.Math.Content.7.NS.A.1 MA.7.CCSS.Math.Content.7.NS.A.1c
MA.7.CCSS.Math.Content.7.NS.A.1d MA.7.CCSS.Math.Content.7.NS.A.3 MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP2 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4 MA.K‐12.CCSS.Math.Practice.MP5 MA.K‐12.CCSS.Math.Practice.MP6 MA.K‐12.CCSS.Math.Practice.MP7
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. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure.
Objective #3.4 -- (Level of Difficulty - 2) SWBAT: Multiply integers.
MA.7.CCSS.Math.Content.7.NS.A.2 MA.7.CCSS.Math.Content.7.NS.A.2a
MA.7.CCSS.Math.Content.7.NS.A.2c MA.7.CCSS.Math.Content.7.NS.A.3 MA.7.CCSS.Math.Content.7.EE.B.3
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4 MA.K‐12.CCSS.Math.Practice.MP8
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics. Look for and express regularity in repeated reasoning.
Objective #3.5 -- (Level of Difficulty - 2) SWABT: Divide integers. MA.7.CCSS.Math.Content.7.NS.A.2 MA.7.CCSS.Math.Content.7.NS.A.2a
MA.7.CCSS.Math.Content.7.NS.A.2c MA.7.CCSS.Math.Content.7.NS.A.3 MA.7.CCSS.Math.Content.7.EE.B.3
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4 MA.K‐12.CCSS.Math.Practice.MP8
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics. Look for and express regularity in repeated reasoning.
Objective #4.1 -- (Level of Difficulty - 2) SWBAT: Write fractions as terminating or repeating decimals and write decimals as fractions. MA.7.CCSS.Math.Content.7.NS.A.2 MA.7.CCSS.Math.Content.7.NS.A.2d MA.7.CCSS.Math.Content.7.EE.B.3
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4 MA.K‐12.CCSS.Math.Practice.MP6 MA.K‐12.CCSS.Math.Practice.MP7
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics. Attend to precision. Look for and make use of structure.
Objective #4.2 - (Level of Difficulty - 2) SWBAT: Compare and order rational numbers. MA.7.CCSS.Math.Content.7.NS.A.2 MA.7.CCSS.Math.Content.7.NS.A.2b
MA.7.CCSS.Math.Content.7.EE.B.3
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
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Objective #4.3 - (Level of Difficulty - 2) MA.7.CCSS.Math.Content.7.NS.A.1 MA.7.CCSS.Math.Content.7.NS.A.1c
MA.7.CCSS.Math.Content.7.NS.A.1d MA.7.CCSS.Math.Content.7.NS.A.3 MA.7.CCSS.Math.Content.7.EE.B.3
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4 MA.K‐12.CCSS.Math.Practice.MP7
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics. Look for and make use of structure.
Objective #4.4 - (Level of Difficulty - 2) SWBAT: Add and subtract fractions with unlike denominators. MA.7.CCSS.Math.Content.7.NS.A.1 MA.7.CCSS.Math.Content.7.NS.A.1d MA.7.CCSS.Math.Content.7.NS.A.3 MA.7.CCSS.Math.Content.7.EE.B.3
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Objective #4.5 - (Level of Difficulty - 2) SWBAT: Add and subtract mixed numbers. MA.7.CCSS.Math.Content.7.NS.A MA.7.CCSS.Math.Content.7.NS.A.1d MA.7.CCSS.Math.Content.7.NS.A.3 MA.7.CCSS.Math.Content.7.EE.B.3
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Objective #4.6 - (Level of Difficulty - 2) SWBAT: Multiply fractions and mixed numbers. MA.7.CCSS.Math.Content.7.NS.A.2 MA.7.CCSS.Math.Content.7.NS.A.2a
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.
MA.7.CCSS.Math.Content.7.NS.A.2c MA.7.CCSS.Math.Content.7.NS.A.3 MA.7.CCSS.Math.Content.7.EE.B.3
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Objective #4.7 - (Level of Difficulty - 2) SWBAT: Convert units of measure between the customary and metric systems. MA.7.CCSS.Math.Content.7.RP.A.3 MA.7.CCSS.Math.Content.7.NS.A.2
MA.7.CCSS.Math.Content.7.NS.A.3 MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4 MA.K‐12.CCSS.Math.Practice.MP5 MA.K‐12.CCSS.Math.Practice.MP6
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision.
Objective #4.8 - (Level of Difficulty - 2) SWBAT: Divide fractions and mixed numbers. MA.7.CCSS.Math.Content.7.NS.A.2 MA.7.CCSS.Math.Content.7.NS.A.2c MA.7.CCSS.Math.Content.7.NS.A.3 MA.7.CCSS.Math.Content.7.EE.B.3
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4 MA.K‐12.CCSS.Math.Practice.MP5
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically.
Summative Assessment
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•Journal •Portfolio •Project •Quiz •Test
. . . .
21st Century Life and Careers See 21st Century Career activities in Chapters.
WORK.5‐8.9.1.8.A.2 WORK.5‐8.9.1.8.B.1 WORK.5‐8.9.1.8.C.1
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...)
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•Student Presentation •Student‐Teacher Conference
Differentiation / Enrichment Use the Lists tab.
Unit Resources Use Lists and attach Documents.
. .
Unit 3 Expressions and Equations Content Area: Course(s): Time Period: Length: Status:
Mathematics Generic Course 2nd Marking Period 7 Weeks 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. http://www.authenticeducation.org/ae_bigideas/article.lasso?artid=60
Meaning
Understandings Students will understand that... •
The symbolic language of algebra is used to communicate and generalize the patterns in mathematics.
•
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 (7.NS.1‐2)
•
how to solve real‐world and mathematical problems with rational numbers (7.NS.3)
•
how to apply properties of operations to add, subtract, factor and expand linear equations.
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. (7.EE.1) • Using Commutative, Associative, Distributive, Identity, and Inverse Properties to factor and expand linear expressions with rational coefficients. (7.EE.1) • Rewriting an expression in a different form. (7.EE.2) • Choose the form of an expression that works best to solve a problem. (7.EE.2) • Explaining your reasoning for the choice of expression used to solve a problem.Use commutative, associative, distributive, identity, and inverse properties to calculate with numbers in any form (whole numbers, fractions and decimals). (7.EE.3) • Convert between rational number forms (whole numbers, fractions and decimals) to solve problems as appropriate. (7.EE.3) • Solve multi‐step mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. (7.EE.3) • Solve multi‐step real‐life problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. (7.EE.3) • Use mental computation and estimation strategies to assess the reasonableness of the answer. (7.EE.3) • Translate words or real‐life situations into variable equations. (7.EE.4) • Translate words or real‐life situations into variable inequalities. (7.EE.4) • Solve one‐ or two‐step equations with rational numbers fluently. (7.EE.4) • Solve word problems leading to one‐ or two‐step equations with rational numbers. (7.EE.4) • Construct simple equations and inequalities with rational numbers to solve problems. (7.EE.4) • Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. (7.EE.4) • Solve word problems leading to one‐ or two‐step inequalities with rational numbers. (7.EE.4) • Graph the solution set of inequalities and interpret it in the context of the problem. (7.EE.4) • Know the formulas for the area and circumference of a circle. (7.G.4) • Use the formulas for area and circumference of a circle to solve problems. (7.G.4) • Informally, derive the area formula for a circle based on circumference. (7.G.4)
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 # 5.1 -- (Level of Difficulty - 3) SWBAT evaluate simple algebraic expressions. MA.7.CCSS.Math.Content.7.EE.A.1 MA.7.CCSS.Math.Content.7.EE.A.2
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP2 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
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. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Objective # 5.2 -- (Level of Difficulty - 2) SWBAT describe the relationships and extend terms in arithmetic sequences. MA.7.CCSS.Math.Content.7.EE.A.1 MA.7.CCSS.Math.Content.7.EE.A.2
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP2 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
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. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Objective # 5.3 -- (Level of Difficulty - 2)
SWBAT identify and use mathematical properties to simplify algebraic expressions. MA.7.CCSS.Math.Content.7.EE.A.1 MA.7.CCSS.Math.Content.7.EE.A.2
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4 MA.K‐12.CCSS.Math.Practice.MP5 MA.K‐12.CCSS.Math.Practice.MP7
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure.
Objective # 5.4 -- (Level of Difficulty - 3) SWBAT apply the distributive property to rewrite algebraic expressions. MA.7.CCSS.Math.Content.7.EE.A.1 MA.7.CCSS.Math.Content.7.EE.A.2
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4 MA.K‐12.CCSS.Math.Practice.MP5 MA.K‐12.CCSS.Math.Practice.MP7
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. Make sense of problems and persevere in solving them. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Look for and make use of structure.
Objective # 5.5 -- (Level of Difficulty - 2) SWBAT simplify algebraic expressions. MA.7.CCSS.Math.Content.7.EE.A.1 MA.7.CCSS.Math.Content.7.EE.A.2
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP2 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4 MA.K‐12.CCSS.Math.Practice.MP6
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. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Attend to precision.
Objective # 5.6 -- (Level of Difficulty - 2) SWBAT add linear expressions. MA.7.CCSS.Math.Content.7.EE.A.1 MA.7.CCSS.Math.Content.7.EE.A.2
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP2 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
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. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Objective # 5.7 -- (Level of Difficulty - 2) SWBAT subtract linear expressions. MA.7.CCSS.Math.Content.7.EE.A.1 MA.7.CCSS.Math.Content.7.EE.A.2
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.
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP2 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Objective # 5.8 -- (Level of Difficulty - 2) SWBAT read and write integers, and find the absolute value of an integer. MA.7.CCSS.Math.Content.7.EE.A.1 MA.7.CCSS.Math.Content.7.EE.A.2
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP2 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
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. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Objective # 6.1 -- (Level of Difficulty - 3) SWBAT solve addition and subtraction equations. MA.7.CCSS.Math.Content.7.EE.B.4 MA.7.CCSS.Math.Content.7.EE.B.4a
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP2 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4 MA.K‐12.CCSS.Math.Practice.MP5
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. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically.
Objective # 6.2 -- (Level of Difficulty - 3) SWBAT solve one‐stop multiplication and division equations. MA.7.CCSS.Math.Content.7.EE.B.4 MA.7.CCSS.Math.Content.7.EE.B.4a
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP2 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4 MA.K‐12.CCSS.Math.Practice.MP7
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. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Look for and make use of structure.
Objective # 6.3 -- (Level of Difficulty - 3) SWBAT solve one‐step equations with rational coefficients. MA.7.CCSS.Math.Content.7.EE.B.4 MA.7.CCSS.Math.Content.7.EE.B.4a
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP2 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
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. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Objective # 6.4 -- (Level of Difficulty - 3)
SWBAT solve two‐step equations. MA.7.CCSS.Math.Content.7.EE.B.4 MA.7.CCSS.Math.Content.7.EE.B.4a
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP2 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
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. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Objective # 6.5 -- (Level of Difficulty - 3) SWBAT solve two‐step equations of the form p(x + q) = r. MA.7.CCSS.Math.Content.7.EE.B.4 MA.7.CCSS.Math.Content.7.EE.B.4a
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP2 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
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. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics.
Objective # 6.6 -- (Level of Difficulty - 3) SWBAT solve inequalities by using the Addition and Subtraction Properties of Inequality. MA.7.CCSS.Math.Content.7.EE.B.4 MA.7.CCSS.Math.Content.7.EE.B.4b
MA.K‐12.CCSS.Math.Practice.MP1 MA.K‐12.CCSS.Math.Practice.MP2 MA.K‐12.CCSS.Math.Practice.MP3 MA.K‐12.CCSS.Math.Practice.MP4
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 or px + q r or px + q
