Five District Partnership 1

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1 Five District Partnership 1 Grade 7 Math Year-Long Plan Overview Standards Shorthand Description Sept-Oct Nov-Dec Jan-Feb Mar-Apr May-June 7.RP.1 Compute unit rates 7.RP.2a Identify proportional relationships R 7.RP.2b Identify unit rates R Represent proportional relationships by R 7.RP.2c equations 7.RP.2d Coordinate points and unit rate R 7.RP.3 Solve multi-step ratio and percent problems 7.NS.1a Contextual opposite quantities Understand, show, and interpret sums of 7.NS.1b rational numbers 7.NS.1c Understand subtraction as additive inverse R Properties of addition and subtraction of rational 7.NS.1d numbers 7.NS.2a Multiply rational numbers R 7.NS.2b Divide rational numbers R Use properties for multiplication and division of 7.NS.2c rational numbers 7.NS.2d Rational numbers and decimal form Solve real world and mathematical problems R 7.NS.3 with rational numbers Add, subtract, factor, and expand linear 7.EE.1 expressions 7.EE.2 Understand conceptual equivalent expressions 7.EE.3 Solve multi-step problems with rational numbers 7.EE.4a Solve problems with 2-step linear equations R 7.EE.4b Solve problems with 2-step linear inequalities MA 7.EE.4c Arithmetic and geometric sequences 7.G.1 Scale drawings 7.G.2 Draw geometric shapes 7.G.3 Cross sections 7.G.4 Area and circumference of a circle 7.G.5 Solve multi-step angle problems Area, volume, and surface area of 2-D and 3-D 7.G.6 objects 7.SP.1 Population and sampling 7.SP.2 Generate samples and draw inferences 7.SP.3 Visual overlap of two data distributions Draw inferences from measures of center and 7.SP.4 variability 7.SP.5 Understanding probability and likelihood 7.SP.6 Approximate probability and predict frequency 7.SP.7a Uniform probability model 7.SP.7b Develop probability models from observations 7.SP.8a Understand probability and compound events 7.SP.8b Represent sample spaces for compound events Design and use a simulation to generate 7.SP.8c frequencies for compound events. R Last revised: June 23, 2014 The Five District Partnership Grade 7 Math

2 Five District Partnership 2 Grade 7 Math Overview: Ratios and Proportional Relationships Analyze proportional relationships and use them to solve realworld and mathematical problems. The Number System Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. Expressions and Equations Use properties of operations to generate equivalent expressions. Solve real-life and mathematical problems using numerical and algebraic expressions and equations. Geometry Draw, construct and describe geometrical figures and describe the relationships between them. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. Statistics and Probability Use random sampling to draw inferences about a population. Draw informal comparative inferences about two populations. STANDARDS FOR MATHEMATICAL PRACTICE 1. Make sense of problems and persevere in solving them. 3. Construct viable arguments and critique the reasoning of others. 5. Use appropriate tools strategically. 8. Look for an express regularity in repeated reasoning. Investigate chance processes and develop, use, and evaluate probability models. Last revised: June 23, 2014 The Five District Partnership Grade 7 Math

3 Five District Partnership 3 Grade 7 Math Sept-Oct 28 Teaching Days A1: 10/15-10/17 Standards Covered: PARCC emphasis: Assessed on A1? 7.NS.1a: 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. 7.NS.1b: 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 p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. 7.NS.1c: 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. 7.NS.1d: 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. 7.NS.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. 7.NS.2b: 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 nonzero divisor) is a rational number. If p and q are integers, then (p/q) = ( p)/q = p/( q). Interpret quotients of rational numbers by describing real-world contexts. 7.NS.2c: 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. 7.NS.2d: 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. 7.NS.3: Solve real-world and mathematical problems involving the four operations with rational numbers. Unit Name Time Frame Notes Unit 1 12 Days Unit 2 12 Days Use last 4 days for Unit 3 Resources Established Goals/Standards Notes Adding and Subtracting Rational Numbers 7.NS.1, 7.NS.3 Multiplying and Dividing Rational Numbers 7.NS.2, 7.NS.3 EngageNY module 2 7.NS.1, 7.NS.2, 7.NS.3, 7.EE.2, 7.EE.4 Last revised: June 23, 2014 The Five District Partnership Grade 7 Math

4 Unit of Study 1 Grade 7 Topic: Fundamentals of Rational Numbers Approximate Time Frame: 12 days *pretest recommended to determine time needed, if any, on each objective ANET: A1 Standard: Objectives: Focus SMP's PARCC Content Emphasis by Cluster 7.NS.1a: Describe situations in which opposite quantities combine to make 0. -Know and describe the property of opposites as it applies on a number line model and real world problems. -Understand absolute value as the distance that a number represents without direction. 5 7.NS.1b: Understand p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. 7.NS.1c: Understand subtraction of rational numbers as adding the additive inverse, p q = p + ( q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in realworld contexts. -Add all rational numbers, including negative numbers -Use number lines and other models to demonstrate addition of all rational numbers -Interpret sums by describing and solving real world problems -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 -understand and apply the additive inverse to show that a number and its opposite add to 0 -Subtract all rational numbers, including negative numbers -Use number lines and other models to demonstrate subtraction of all rational numbers -Interpret differences by describing and solving real world problems -Understand subtraction of rational numbers as adding the additive inverse, p-q = p + (-q). -Show that the absolute value of the difference between two rational numbers on a number line is the distance between those numbers 2, 3, 5, 7 2, 5, 7 7.NS.1d: Apply properties of operations as strategies to add and subtract rational numbers. Vocabulary: -Understand and use properties of operations such as distributive, associative, and commutative to add and subtract rational numbers ex/ (2/3 + 4/7) + (4/3 + 2/7) can be rearranged to be (2/3 + 4/3) + (4/7 + 2/7) 5, 7 absolute value, additive inverse, integer, opposite, rational numbers Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 3. Construct viable arguments and critique the reasoning of others. Additional Resources: Unit Name: Established Goals/Standards 5. Use appropriate tool strategically. 8. Look for and express regularity in repeated reasoning. Five District Partnership UbD Units EngageNY Module 1 7.NS.1, 7.NS.2, 7.NS.3

5 Unit of Study 2 Grade 7 Topic: More on Rational Numbers and Their Application to Problem Solving Approximate Time Frame: 12 days *pretest reccomended to determine time needed, if any, on each objective ANET: A1 Standard: Objectives: Focus SMP's PARCC Content Emphasis by Cluster 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. -Extend patterns and strategies used for multiplying and dividing whole numbers to multiply and divide rational numbers 6 7.NS.2.a 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. -Compute products of all rational numbers (including negative numbers) and model using number lines and other models i.e. area model -Interpret products of all rational numbers by describing real world contexts 2, 4, 7 7.NS.2.b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with nonzero 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. -Compute quotients of all rational numbers (including negative numbers) and model using number lines and other models i.e. area model -Interpret quotients of all rational numbers by describing real world contexts -Understand that if p and q are integers then -(p/q) = (-p)/q = p/(-q) 2, 4, 7 7.NS.2.c Apply properties of operations as strategies to multiply and divide rational numbers 7.NS.2.d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0's or eventually repeats. -Apply the properties of operations i.e associative, commutative, property of opposites, property of zero, additive and multiplicative inverses, identities, etc. (Especially distributive property) to multiply and divide strategically -Change rational numbers to decimals using long division. -Understand that all rational numbers in decimal form will terminate or repeat 7 7.NS.3 Solve real world and mathematical problems involving the four operations with rational numbers. -Solve real world problems using all types/forms of numbers and all operations 1, 4 Vocabulary: multiplicative inverse, rational number, reciprocal, repeating decimal, terminating decimal Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 3. Construct viable arguments and critique the reasoning of others. Additional Resources: Unit Name: EngageNY Module 1 Established Goals/Standards 7.NS.1, 7.NS.2, 7.NS.3 5. Use appropriate tool strategically. 8. Look for and express regularity in repeated reasoning. Five District Partenership UbD Units

6 Five District Partnership 4 Grade 7 Math Nov-Dec 30 Teaching Days A2: 12/9-12/12 Standards Covered: PARCC emphasis: Assessed on A2? 7.RP.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. 7.RP.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 table, or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 7.RP.2b: 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. 7.RP.2c: Recognize and represent proportional relationships between quantities. Represent proportional relationships by equations. 7.RP.2d: Recognize and represent proportional relationships between quantities. 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.3: Use proportional relationships to solve multi-step ratio and percent problems. MA.7.EE.4c: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and yes inequalities to solve problems by reasoning about the quantities. Extend analysis of patterns to include analyzing, extending, and determining an expression for simple arithmetic and geometric sequences (e.g., compounding, increasing area), using tables, graphs, words, and expressions. 7.G.1: Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale Additional No drawing and reproducing a scale drawing at a different scale. 7.G.2: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. Additional Unit Name Time Frame Notes Unit 3 22 Days Unit 4 8 Days ANet Review Standards 7.NS.1.d, 7.NS.2.c **MA.7.EE.4.c is assessed on A2 so try to get to that standard along with the review Resources Established Goals/Standards Notes Proportions and Proportional Reasoning 7.RP.1, 7.RP.2, 7.RP.3 EngageNY Module 1 7.RP.1, 7.RP.2, 7.RP.3, 7.EE.4.a, 7.G.1 EngageNY Module 4 7.RP.1, 7.RP.2, 7.RP.3, 7.EE.3, 7.G.1 This unit focuses on percents EngageNY Module 6 7.G.2, 7.G.3, 7.G.5, 7.G.6 Last revised: June 23, 2014 The Five District Partnership Grade 7 Math

7 Unit of Study 3 Grade 7 Topic: Analyze proportional relationships and use them to solve real-world problems Approximate Time Frame: 22 days *pretest reccomended to determine time needed, if any, on each objective ANET: A2 Standard: Objectives: Focus SMP's PARCC Content Emphasis by Cluster 7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction ½/¼ miles per hour, equivalently 2 miles per hour. -Compute unit rates, including ratios that involve fractions -Compute unit rates including quantities in like and different units. 2, 4, 6 7.RP.2 Recognize and represent proportional relationships between quantities. -Recognize situations which result in proportional relationships between quantities 2, 4, 6 -Set up proportional relationships based on word problems, graphs, tables, and diagrams 7.RP.2.a. Decide whether two quantities are in a proportional relationship, e.g., -Find equivalent ratios on tables and use them to identify proportions by testing for equivalent ratios in a table, or graphing on a coordinate plane and -Decide whether two quantities are in a proportional relationship by graphing on a coordinate plane and observing whether the observing whether the graph is a straight line through the origin. graph is a straight line through the origin. 2, 5 b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. -Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions 2, 5, 8 c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. d. 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.3 Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Vocabulary: ratio, rate, unit rate, constant of proportionality, k value, dependent variable, independent variable, equivalent ratios, proportions, cross products Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 3. Construct viable arguments and critique the reasoning of others. Additional Resources: Unit Name: -write equations to represent proportional relationships, for example if the total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t=pn -know that points that fall on a line represent solutions to the situation -if given a point, decide if it is proportional to a given relationship -Explain what a point (x,y) on the graph of a proportional relationship means in terms of the situation -Explain what the points (0,0) and (1,r), where r is the unit rate, mean in terms of the situation. Use this in problem solving applications -solve proportions -Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. Established Goals/Standards 5. Use appropriate tool strategically. 8. Look for and express regularity in repeated reasoning. Five District Partenership UbD Units 2, 8 2, 4 1, 2, 5, 6 EngageNY Module 1 EngageNY Module 4 7.RP.1, 7.RP.2, 7.RP.3, 7.EE.4.a, 7.G.1 7.RP.1, 7.RP.2, 7.RP.3, 7.EE.3, 7.G.1

8 Unit of Study 4 Grade 7 Topic: Working with Scale Drawings Approximate Time Frame: 8 days *pretest reccomended to determine time needed, if any, on each objective ANET: A2 Standard: Objectives: Focus SMP's PARCC Content Emphasis by Cluster 7.G.1 solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale 7.G.2: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. -Find the scale factor of a drawing, model, or other similar figures -Make scale models and scale drawings -Use ratios and proportions to find unknown measures in similar figures -Use ratios and proportions to compute actual lengths and areas in scale drawings -Reproduce a scale drawing using a different scale -Compare areas and lengths of scale models to that of the real object and to other drawings which used a different scale -Draw (freehand, with a ruler and protractor, and with technology) geometric shapes given conditions -Construct triangles from 3 measures of angles or sides -Understand and notice when the conditions determine a unique triangle, more than on trianle, or no triangle 2, 5 Additional 3, 5, 6 Additional 7.RP.2.c Represent proportional relationships by equations 2, 8 -Set up and solve proportional relationships based on scale drawings or word problems including scale models Vocabulary: similar, corresponding sides, corresponding angles, indirect measurement, scale drawing, scale factor, scale model, scale Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 3. Construct viable arguments and critique the reasoning of others. 5. Use appropriate tool strategically. 8. Look for and express regularity in repeated reasoning. Additional Resources: Unit Name: EngageNY Module 1 EngageNY Module 4 EngageNY Module 6 Five District Partenership UbD Units Established Goals/Standards 7.RP.1, 7.RP.2, 7.RP.3, 7.EE.4.a, 7.G.1 7.RP.1, 7.RP.2, 7.RP.3, 7.EE.3, 7.G.1 7.G.2, 7.G.3, 7.G.5, 7.G.6

9 Five District Partnership 5 Grade 7 Math Jan-Feb 32 Teaching Days A3: 2/10-2/13 Standards Covered: PARCC emphasis: Assessed on A3? 7.EE.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. 7.EE.2: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. 7.EE.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. 7.EE.4a: 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. 7.EE.4b: 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. MA.7.EE.4c: 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. Extend analysis of patterns to include analyzing, extending, and determining an expression for simple arithmetic and geometric sequences (e.g., compounding, increasing area), using tables, graphs, words, and expressions. 7.G.3: Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right Additional rectangular prisms and right rectangular pyramids. 7.G.4: Know the formulas for the area and circumference of a circle and solve problems; give an informal derivation of the relationship between the circumference and area of a circle. 7.G.5: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and use them to solve simple equations for an unknown angle in a figure. 7.G.6: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. MA.7.G.7: Surface area of spheres Unit Name Time Frame Notes Unit 5 Unit 6 Unit 7 20 Days 6 Days 6 Days Last revised: June 23, 2014 The Five District Partnership Grade 7 Math

10 Five District Partnership 6 ANet Review Standards 7.RP.2.b, 7.RP.2.c, 7.RP.2.d, 7.RP.3 Resources Established Goals/ Standards Notes EngageNY module 3 7.EE.1, 7.EE.2, 7.EE.3, 7.EE.4, 7.G.4, 7.G.5, 7.G.6 EngageNY module 6 7.G.2, 7.G.3, 7.G.5, 7.G.6 Last revised: June 23, 2014 The Five District Partnership Grade 7 Math

11 Unit of Study 5 Grade 7 Topic: Application of numerical and algebraic expressions, equations, and inequalities. Approximate Time Frame: 20 days *pretest reccomended to determine time needed, if any, on each objective ANET: A3 Standard: Objectives: Focus SMP's PARCC Content Emphasis by Cluster 7.EE.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients -apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients 7 7.EE.2: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a a = 1.05a means that increase by 5% is the same as multiply by look for relationships uncovered when equations are rewritten -understand how simplifying and expanding expressions can show new relationships between quantities 7 7.EE.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using -Convert between different forms of numbers tools strategically. Apply properties of operations to calculate with numbers in any -Use estimation and mental computation to assess the reasonableness of answers form; convert between forms as appropriate; and assess the reasonableness of -perform the order of operations with numbers of all forms in the context of real world problems answers using mental computation and estimation strategies. -Solve multi-step problems where numbers are given in all forms, including percent problems 7.EE.4a: Use variables to represent quantities in a real-world or mathematical -Write and solve equations using variables to represent quantities from real world math problems problem, and construct simple equations and inequalities to solve problems by -Write multiple expressions representing a word problem or diagram reasoning about the quantities. Solve word problems leading to equations of the form -Explain how multiple expressions relate to the word problem and to each other px + q = r and p(x q) = r, where p, q, and r are specific rational numbers. Solve -Solve multi-step equations of the form px+q = r and p (x q)= r where p, q, and r are specific rations numbers FLUENTLY equations of these forms fluently. Compare an algebraic solution to an arithmetic -Use proper vocabulary to identify the steps used to solve equations solution, identifying the sequence of the operations used in each approach. -Compare algebraic to arithmetic approaches to problems such as the perimeter of a rectangle is 54 and the width is 6, what's the length? 7.EE.4b: Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. -Write and solve inequalities using variables to represent quantities from real world math problems -Graph solution sets to inequalities and connect the graph to the context of the problem 5 1, 2, 6, 7 1, 2, 5, 6, 7 MA.7.EE.4c: Extend analysis of patterns to include analyzing, extending, and determining an expression for simple arithmetic and geometric sequences (e.g., compounding, increasing area), using tables, graphs, words, and expressions. -analyze, extend, and write an expression for arithmetic and geometric sequences -I can analyze, extend, and write expressions based on patterns given in the form of tables, graphs, words, or expressions 2, 7, 8 N/A Vocabulary: addition property of equality, algebraic expression, algebraic inequality, associative property, coefficient, commutative property, compound inequality, constant, distributive property, division property of equality, equation, evaluate, factor, identity property, inequality, inverse operations, multiplication property of equality, solution, solution set, subtraction property of equality, term, variable Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 3. Construct viable arguments and critique the reasoning of others. Additional Resources: Unit Name: EngageNY Module 3 Established Goals/Standards 7.EE.1, 7.EE.2, 7.EE.3, 7.EE.4, 7.G.4, 7.G.5, 7.G.6 5. Use appropriate tool strategically. 8. Look for and express regularity in repeated reasoning. Five District Partenership UbD Units

12 Unit of Study 6 Grade 7 Topic: Draw, construct, and describe geometrical figures and describe the relationships between them. Approximate Time Frame: 6 days *pretest recommended to determine time needed, if any, on each objective ANET: A3 Standard: 7.G.3: Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. Objectives: -Describe the 2D figures that result from slicing 3D figures, as in plane sections of right rectangular prisms and right rectangular pyramids Focus SMP's PARCC Content Emphasis by Cluster 5 Additional 7.G.5: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and use them to solve simple equations for an unknown angle in a figure. -Know and understand angle relationships (vertical, supplementary, complementary, and adjacent) -Use relationships between angles in a multi-step problem to solve one and two step equations for an unknown angle in a figure 5, 6 Additional Vocabulary: 2-D, 3-D, acute angle, adjacent angles, angle, area, complementary angles, cube, diagonal, obtuse angle, plane, polygon, prism, protractor, right angle, straight angle, supplementary angles, vertex, vertical angles Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 5. Use appropriate tool strategically. 3. Construct viable arguments and critique the reasoning of others. 8. Look for and express regularity in repeated reasoning. Additional Resources: Unit Name: Established Goals/Standards Five District Partnership UbD Units EngageNY Module 3 EngageNY Module 6 7.EE.1, 7.EE.2, 7.EE.3, 7.EE.4, 7.G.4, 7.G.5, 7.G.6 7.G.2, 7.G.3, 7.G.5, 7.G.6

13 Unit of Study 7 Grade 7 Topic: Solve real-life and mathematical problems involving area, surface area, and volume Approximate Time Frame: 6 days *pretest recommended to determine time needed, if any, on each objective ANET: A3 Standard: 7.G.4: Know the formulas for the area and circumference of a circle and solve problems; give an informal derivation of the relationship between the circumference and area of a circle. Objectives: -KNOW the formula for the area and circumference of a circle -Use the formulas for area and circumference of circles to solve problems -Give an informal derivation for the relationship between the circumference and area of a circle Focus SMP's 2, 4, 5 PARCC Content Emphasis by Cluster 7.G.6: Solve real-world and mathematical problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. -Solve real world and mathematical problems involving area of 2D shapes -Solve real world and mathematical problems involving volume and surface area of 3D objects -Solve area, surface area, and volume problems involving shapes composed of other shapes 1, 5 MA.7.G.7: Solve real-world and mathematical problems involving the surface area of spheres Vocabulary: area, surface area, volume, circumference, 2D, 3D, polygon, prism, sphere Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 3. Construct viable arguments and critique the reasoning of others. Additional Resources: Unit Name: -Solve real world and mathematical problems involving the surface area of a sphere Established Goals/Standards 5. Use appropriate tool strategically. 8. Look for and express regularity in repeated reasoning. Five District Partnership UbD Units EngageNY Module 4 EngageNY Module 6 Surface Area and Volume 7.RP.1, 7.RP.2, 7.RP.3, 7.EE.3, 7.G.1 7.G.2, 7.G.3, 7.G.5, 7.G.6 7.G.4, 7.G.6

14 Five District Partnership 7 Grade 7 Math March-April 30 Teaching Days A4: 4/13-4/17 Standards Covered: PARCC emphasis: Assessed on A4? 7.SP.1: Understand that statistics can be used to gain information about a population by examining a sample of the population; Supporting generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. 7.SP.2: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Supporting Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. 7.SP.3: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the Additional difference between the centers by expressing it as a multiple of a measure of variability. 7.SP.4: Use measures of center and measures of variability for numerical data from random samples to draw informal Additional comparative inferences about two populations. 7.SP.5: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event Supporting occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. 7.SP.6: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its Supporting long-run relative frequency, and predict the approximate relative frequency given the probability. 7.SP.7a: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed Supporting frequencies; if the agreement is not good, explain possible sources of the discrepancy. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. 7.SP.7b: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed Supporting frequencies; if the agreement is not good, explain possible sources of the discrepancy. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. 7.SP.8a: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Understand that, just Supporting as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. 7.SP.8b: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. Represent sample Supporting spaces for compound events using methods such as organized lists, tables, and tree diagrams. For an event described in everyday language (e.g., rolling double sixes ), identify the outcomes in the sample space which compose the event. 7.SP.8c: Design and use a simulation to generate frequencies for compound events. Supporting Unit Name Time Frame Notes Unit 8 10 Days Unit 9 20 Days ANet Review Standards 7.EE.1, 7.EE.3, 7.EE.4a, 7.EE.4b, 7.NS.3, 7.RP.3 Resources Established Goals/Standards Notes Statistics 7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4, SMP.1, SMP.2, SMP.3, SMP.4, SMP.5, SMP.6 Surface Area and Volume 7.G.4, 7.G.6, SMP.1, SMP.2, SMP.3, SMP.4, SMP.5, SMP.6 Last revised: June 23, 2014 The Five District Partnership Grade 7 Math

15 Five District Partnership 8 EngageNY Module 5 7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4, 7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8 Last revised: June 23, 2014 The Five District Partnership Grade 7 Math

16 Unit of Study 8 Grade 7 Topic: Using statistical methods to draw inferences about one or two populations Approximate Time Frame: 10 Days *pretest recommended to determine time needed, if any, on each objective ANET: A4 Standard: Objectives: Focus SMP's PARCC Content Emphasis by Cluster 7.SP.1: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. -Recognize sampling techniques such as convenience, random, systematic, and voluntary -Identify if a sample is random and if so understand that it is representative of the population -Understand that generalizations about a population from a sample are valid only if the sample is random and representative of that population -Identify an appropriate sample size 4 Supporting 7.SP.2: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. 7.SP.3: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. 7.SP.4: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. Vocabulary: Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 3. Construct viable arguments and critique the reasoning of others. Additional Resources: Unit Name: EngageNY Module 5 Statistics -Understand that having multiple samples for the same population allows for gauging the variation of estimates or predictions. -Generate multiple samples (or simulated samples) of the same size to determine the variation in estimates or predictions by comparing and contrasting the samples -Analyze and interpret data from a random sample to draw inferences about a population with an unknown characteristic of interest -Use proportional reasoning to make estimates and predictions about a population -Understand how to use the mean (or other measures of central tendency) to find the difference between the centers as a measure of variability -Compare the differences in the measure of central tendency in two numerical data distributions by measuring the difference between the centers and expressing it as a multiple of a measure of variability -Select and use appropriate graphical representations of data including histograms, box plots, and scatter plots -Understand data displays are used to visually compare data sets and draw informal comparisons -Compare two numerical data distributions on a graph by visually comparing data displays, and assessing the degree of visual overlap -Identify measure of variation including upper quartile, lower quartile, maximum, minimum, range, interquartile range, and mean absolute deviation -Find and apply statistics such as mean, median, mode, range, IQR, and MAD to gain information about a population from a sample of the population given a characteristic to consider -Understand that MAD is an element of a data set that is the absolute difference between that element and a given point. Typically the point from which the deviation is measured is a measure of central tendency, most often the median or sometimes the mean -Make conjectures about data by selecting and using appropriate measure of center and variability Established Goals/Standards 4 Supporting 4 Additional 4 Additional biased and unbiased, biased sample, convenience sample, distribution, generalizations, inferences, interquartile range, mean, Mean Absolute Deviation, (MAD), measures of center, measures of variability, median, mode, outlier, population, sample, sample size, random sample, range, valid, variability, variation 7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4 5. Use appropriate tool strategically. 8. Look for and express regularity in repeated reasoning. Five District Partnership UbD Units 7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4, 7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8

17 Unit of Study 9 Grade 7 Topic: Investigate chance processes and develop, use, and evaluate probability models. Approximate Time Frame: 20 days *pretest recommended to determine time needed, if any, on each objective ANET: A4 Standard: 7.SP.5: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. 7.SP.6: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. Objectives: - determine and understand that probability in a uniform probability model is the number of favorable outcomes as 1 (numerator) out of the number of all possible outcomes (denominator) -understand that probability is expressed as a number between 0 and 1 - draw conclusions to determine that a greater likelihood occurs as the number of favorable outcomes approaches the total number of outcomes. -explain the benchmark of ½, where events are equally likely to occur, and use it to determine if an event is more or less likely to occur. They will know that as probability moves closer to 1 it is increasingly likely to happen and as probability moves closer to 0 it is decreasingly likely to happen -use theoretical and experimental probability, equivalent fractions, and proportional reasoning to make approximate predictions - determine the relationship between experimental and theoretical probabilities by using the law of large numbers -predict the relative frequency (experimental probability) of an event based on the (theoretical) probability -recognize uniform (equally likely) probability. Focus SMP's PARCC Content Emphasis by Cluster 4 Supporting 4 Supporting 7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. a. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected. b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? - use models to determine the probability of events -develop a uniform probability model and use it to determine the probability of each outcome/event -develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process -compare probability from a model to that of the probability observed and explain any source of potential discrepancy 4 Supporting 7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. a. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. b. Represent sample spaces for compound events using methods such as organized lists, tables, and tree diagrams. For an event described in everyday language (e.g., rolling double sixes ), identify the outcomes in the sample space which compose the event. c. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood? Vocabulary: complement, compound event, equally likely, event, experiment, experimental probability, fair, outcome, probability, simple, sample space, theoretical probability, trial Standards for Mathematical Practice: 1. Make sense of problems and persevere in solving them. 3. Construct viable arguments and critique the reasoning of others. Additional Resources: Unit Name: EngageNY Module 5 -define and understand simulation -define and describe a compound event -understand how to write probability for compound events as a fraction -choose and create the appropriate method such as organized lists, tables and tree diagrams to represent sample spaces for compound events -find probabilities of compound events using organized lists, tables, tree diagrams, etc. and analyze the outcomes. -design and use a simulation to generate frequencies for compound events Established Goals/Standards 7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4, 7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8 5. Use appropriate tool strategically. 8. Look for and express regularity in repeated reasoning. Five District Partnership UbD Units 4, 5 Supporting

18 Five District Partnership 9 Grade 7 Math May-June Suggested standards for Review Standards Covered: 7.RP.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 table, or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. 7.RP.2b: 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. 7.RP.2c: Recognize and represent proportional relationships between quantities. Represent proportional relationships by equations. 7.RP.2d: Recognize and represent proportional relationships between quantities. 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.NS.1b: 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 p + q as the number located a distance q from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. 7.NS.1c: 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. 7.NS.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. 7.NS.2b: 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. 7.NS.3: Solve real-world and mathematical problems involving the four operations with rational numbers. 7.EE.4a: 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. Unit Name Established Goals/Standards Notes PARCC emphasis: Last revised: June 23, 2014 The Five District Partnership Grade 7 Math