8th Grade Standards Aligned With the 8 Grade PARCC … · 2017. 7. 19. · Curriculum Guide...

Curriculum Guide 2014-2015 8th Grade Poudre School District

8th Grade Standards Aligned With the 8th Grade PARCC Assessment Performance Based Assessment (PBA/MYA) and End Of Year (EOY)

Cluster Standard PBA/MYA EOY

Unit 1: Geometry 8.G.A Understand congruence and similarity using physical models, transparencies, or geometry software.

8.G.A.1 X X 8.G.A.2 X X 8.G.A.3 X X 8.G.A.4 X X 8.G.A.5 X

Unit 2: Solving Equations 8.EE.C Analyze and solve equations and pairs of simultaneous linear equations.

8.EE.C.7 X X

Unit 3: Linear Relationships 8.F.A Define, evaluate, and compare functions.

8.F.A.1 X X 8.F.A.2 X 8.F.A.3 X X

8.F.B Use functions to model relationships between quantities.

8.F.B.4 X 8.F.B.5 X

8.EE.B Understand the connections between proportional relationships, lines, and linear equations.

8.EE.B.5 X X

8.EE.B.6 X X 8.EE.C Analyze and solve linear equations and pairs of simultaneous linear equations.

8.EE.C.8 X X

Unit 4: (E3) Exponential Expressions and Equations 8.EE.A Work with radicals and integer exponents.

8.EE.A.1 X X 8.EE.A.2 X 8.EE.A.3 X X 8.EE.A.4 X X

8.NS.A Know that there are numbers that are not rational, and approximate them by rational numbers.

8.NS.A.1 X

8.NS.A.2 X 8.G.B Understand and apply the Pythagorean Theorem.

8.G.B.6 8.G.B.7 X 8.G.B.8 X

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8th Grade Standards Aligned With the 8th Grade PARCC Assessment Performance Based Assessment (PBA/MYA) and End Of Year (EOY)

Cluster Standard PBA/MYA EOY

Unit 5: Volume 8.G.C Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

8.G.C.9 X

Unit 6: Data Analysis 8.SP.A Investigate patterns of association in bivariate data.

8.SP.A.1 X 8.SP.A.2 X 8.SP.A.3 X 8.SP.A.4 X

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Course Overview

In 8th grade, students will build upon their knowledge and understanding of generating equivalent expressions, ratios and proportions, exponents, and volume of prisms gained in 6th and 7th grade. In this course, students will apply their knowledge of expressions both algebraically and geometrically. Students will explore congruence and similarity of figures in the coordinate plane and write algebraic expressions to describe the transformations. Students will use their knowledge of generating equivalent expressions to solve single-variable linear equations. They will analyze the solution set to include one solution, no solutions, and infinitely many solutions. Students will build upon their understanding of proportional relationships to create linear functions in a graph, table of values, equation, and story problem. They will then examine the similarities and differences between linear and non-linear models, exploring the commonalities and differences among rational and irrational numbers. Students will approximate the location of simple square and cube root values on a number line. Students will expand upon their understanding of volume of prisms to know and apply the formulas for volume of cylinders, cones, and spheres. Students will apply their knowledge of linear relationships to analyze and make conjectures about two-way data displays, tying together the components of this course. The 8th grade standards have been divided into six critical areas, or units, as follows.

Unit 1: Geometry

Students will explore congruence and similarity through geometric transformations (translations, rotations, and dilations). Students will apply their understanding of congruence and similarity to two-dimensional figures in the coordinate plane. Building upon their knowledge of parallel lines, gained in Unit 2, students will explore the angle relationships formed when two parallel lines are cut by a transversal. They will apply their understanding of angle relationships to informally develop conjectures about angle sum and the exterior angles of a triangle. Students will tie together the components of this unit by investigating the angle-angle criteria of similar triangles. Students will be able to… • Understand congruence and similarity using physical models, transparencies, or geometry

software. 8.G.A.1, 8.G.A.2, 8.G.A.3, 8.G.A.4, 8.G.A.5

Unit 2: Solving Equations

Students will be able to solve linear equations in one variable, expanding upon their understanding of combining like terms and the distributive property. They will be able to analyze equations to give an example for the number of possible solutions: one solution, no solutions, or infinitely many solutions. Students will be able to… • Analyze and solve linear equations and pairs of simultaneous linear equations.

8.EE.C.7

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Unit 3: Linear Relationships

Students will define a function, understanding the correlation between domain and range. Students will be able to analyze the connections between a graph, tables of values, equation and story problem of a linear function. Students will explore the slope of an equation using similar triangles, for any two points along a line. Students will build upon their knowledge of proportional relationships (7.RP.2) from 7th grade to interpret the unit rate as the slope of the graph. Students will compare and contrast linear and non-linear models along all four faces of a function. They will be able to interpret the slope and beginning value, constructing a linear model, given any one of the three remaining faces. Students will expand upon their work with linear equations to solve systems of simultaneous linear equations. Students will be able to… • Define, evaluate, and compare functions.

8.F.A.1, 8.F.A.2, 8.F.A.3 • Use functions to model relationships between quantities.

8.F.B.4, 8.F.B.5 • Understand the connections between proportional relationships, lines, and linear equations.

8.EE.B.5, 8.EE.B.6 • Analyze and solve linear equations and pairs of simultaneous linear equations.

8.EE.C.8

Unit 4: (E3) Exponential Expressions and Equations

In this unit students will expand upon their understanding of rational numbers, with integer exponents, developed in 7th grade, to analyze properties of exponents. Students will explore beyond the rational numbers to investigate irrational numbers, including square and cube roots. Students will build upon their knowledge of exponents to generate equivalent exponential expressions. They will apply their understanding of exponents to estimate small and large numbers using scientific notation. Students will analyze their answer using appropriate units of measure. Students will conceptually understand the similarities and differences between rational and irrational numbers. They will be able to create a rational approximation for irrational numbers, including square and cube roots, and locate them on a number line. Building upon their understanding of square roots, students will solve simple square and cube root equations. They will then apply their understanding of irrational numbers and solving square root equations to the Pythagorean Theorem. Students will be able to prove the Pythagorean Theorem and its converse, applying it to two- and three-dimensions. Students will be able to… • Work with radicals and integer exponents.

8.EE.A.1, 8.EE.A.2, 8.EE.A.3, 8.EE.A.4 • Know that there are numbers that are not rational, and approximate them by rational numbers.

8.NS.A.1, 8.NS.A.2 • Understand and apply the Pythagorean Theorem.

8.G.B.6, 8.G.B.7, 8.G.B.8

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Unit 5: Volume

Students will apply their understanding of volume to cylinders, cones, and spheres. Students will know and apply the formulas for volume to real-world and mathematical problems. Students will be able to… • Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

8.G.C.9

Unit 6: Data Analysis

Students will build upon their previous understanding of samples and populations, creating data displays and making conjectures about the data. Students will investigate patterns such as clustering, outliers, positive or negative association, linear and non-linear association for bivariate data. Students will fit linear models to scatter plots and make conjectures about the data using the equations. Students will use two-way tables to analyze frequencies and describe a possible association between the variables. Students will be able to… • Investigate patterns of association in bivariate data.

8.SP.A.1, 8.SP.A.2, 8.SP.A.3, 8.SP.A.4

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Unit 1: Geometry

Students will explore congruence and similarity through geometric transformations (translations, rotations, and dilations). Students will apply their understanding of congruence and similarity to two-dimensional figures in the coordinate plane. Building upon their knowledge of parallel lines, gained in Unit 2, students will explore the angle relationships formed when two parallel lines are cut by a transversal. They will apply their understanding of angle relationships to informally develop conjectures about angle sum and the exterior angles of a triangle. Students will tie together the components of this unit by investigating the angle-angle criteria of similar triangles.

Sub-Unit A: Geometric

Transformations

8.G.A.1

8.G.A.2

8.G.A.3

8.G.A.4

Sub-Unit B:

Angle Relationships

8.G.A.5

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Unit 1: Geometry Sub-Unit A: Geometric Transformations Start of Quarter 1 – September 12, 2014

Common Core State Standards Explanations/Examples Resources 8.G.A: Understand congruence and similarity using physical models, transparencies, or geometry software.

8.G.A.1 Verify experimentally the properties of rotations, reflections, and translations: a. Lines are taken to lines, and line segments to

line segments of the same length. b. Angles are taken to angles of the same

measure. c. Parallel lines are taken to parallel lines.

8.G.A.1 Students need multiple opportunities to explore the transformation of figures so that they can appreciate that points stay the same distance apart and lines stay at the same angle after they have been rotated, reflected, and/or translated. Students are not expected to work formally with properties of dilations until high school.

Lessons 8.G.A CMP • Common Core Additional

Investigations (8) o Investigation 3 (C, P)

• Kaleidoscopes, Hubcaps, and Mirrors (2nd ed) o Investigation 1 (C) o Investigation 2 (P) o Investigation 3 (A)

8.G.A.3 MARS Shell Center • Identifying Similar Triangles (C)

8.G.A.4 CMP • Stretching and Shrinking (1st ed)

o Investigation 2.1-2.2 (C, A) o Investigation 5.1-5.3 (A)

Tasks 8.G.A.1/8.G.A.2 MARS Shell Center • Aaron’s Designs (P)

8.G.A.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

8.G.A.2 • Is Figure A congruent to Figure A’? Explain how you

know.

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http://map.mathshell.org/materials/lessons.php?taskid=492&subpage=concept

http://map.mathshell.org/materials/tasks.php?taskid=361%23task361



Common Core State Standards Explanations/Examples Resources 8.G.A.2 (continued) 8.G.A.2 (continued)

• Describe the sequence of transformations that results in the transformation of Figure A to Figure A’.

Tasks (continued) 8.G.A.1 Inside Mathematics • Cut It Out (C) • Cutting a Cube (C)

8.G.A.2/8.G.A.3 Illustrative Mathematics • Triangle Congruence with Coordinates

(C)

8.G.A.2 Illustrative Mathematics • Congruent Rectangles (C) • Congruent Triangles (C)

8.G.A.3 Illustrative Mathematics • Reflecting Reflections (A)

Inside Mathematics • The Shape of Things (C, A)

Activities Practice 8.G.A.1 Math’s Mate Skill Builder Blue/Green • 25.4 Recognizing Basic

Transformations of Two- Dimensional Shapes (P)

8.G.A.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

8.G.A.3 A dilation is a transformation that moves each point along a ray emanating from a fixed center, and multiplies distances from the center by a common scale factor. In dilated figures, the dilated figure is similar to its pre-image. Translation: A translation is a transformation of an object that moves the object so that every point of the object moves in the same direction as well as the same distance. In a translation, the translated object is congruent to its pre-image. has been translated 7 units to the right and 3 units up. To get from A (1,5) to A’ (8,8), move A 7 units to the right (from x = 1 to x = 8) and 3 units up (from y = 5 to y = 8). Points B and C also move in the same direction (7 units to the right and 3 units up).

ABC∆

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http://insidemathematics.org/problems-of-the-month/pom-cutitout.pdf

http://insidemathematics.org/problems-of-the-month/pom-cuttingacube.pdf

http://www.illustrativemathematics.org/illustrations/1232




http://insidemathematics.org/problems-of-the-month/pom-theshapeofthings.pdf

http://www.mathsmate.com/WebPages/usa/usaDownloads/usaPDFsbBG/SB%2025.pdf




Reflection: A reflection is a transformation that flips an object across a line of reflection (in a coordinate grid the line of reflection may be the x- or y-axis). In a rotation, the rotated object is congruent to its pre-image.

Practice (continued) 8.G.A.2 Math’s Mate Skill Builder Blue/Green • 25.6 Recognizing Congruence of Two-

Dimensional Shapes (P)

8.G.A.3 Math’s Mate Skill Builder Blue/Green • 25.7 Recognizing Similarity of Two-

Dimensional Shapes (P) Assessments

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When an object is reflected across the y-axis, the reflected x-coordinate is the opposite of the pre-image x-coordinate.

Rotation: A rotated figure is a figure that has been turned about a fixed point. This is called the center of rotation. A figure can be rotated up to 360˚. Rotated figures are congruent to their pre-image figures. Consider when is rotated 180˚ clockwise about the origin. The coordinates of are D(2,5), E(2,1), and F(8,1). When rotated 180˚, has new coordinates D’(-2,-5), E’(-2,-1) and F’(-8,-1). Each coordinate is the opposite of its pre-image.

DEF∆DEF∆

''' FED∆

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Common Core State Standards Explanations/Examples Resources 8.G.A.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

8.G.A.4 • Is Figure A similar to Figure A’? Explain how you

know.

• Describe the sequence of transformations that

results in the transformation of Figure A to Figure A’.

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Unit 1: Geometry Sub-Unit B: Angle Relationships

September 15, 2014 – September 26, 2014 Common Core State Standards Explanations/Examples Resources

8.G.A: Understand congruence and similarity using physical models, transparencies, or geometry software. 8.G.A.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals as to why this is so.

8.G.A.5 • Students can informally prove relationships with

transversals.

Show that 𝑚𝑚∠3+ 𝑚𝑚∠4+ 𝑚𝑚∠5 = 180° if ℓ and m are parallel lines and t1 & t2 are transversals. 𝑚𝑚∠1+ 𝑚𝑚∠2+ 𝑚𝑚∠3 = 180°. Angle 1 and Angle 5 are congruent because they are corresponding angles (∠5 ≅ ∠1). can be substituted for . ∠4 ≅ ∠2 : because alternate interior angles are congruent. can be substituted for Therefore 𝑚𝑚∠3 + 𝑚𝑚∠4+ 𝑚𝑚∠5 = 180°

Lessons Tasks 8.G.A.5 Illustrative Mathematics • A Triangle’s Interior Angles (C) • Find the Angle (A) • Find the Missing Angle (A) • Tiles Patterns 1: Octagons and

Squares (C, A)

Activities Practice 8.G.A.5 Math’s Mate Skill Builder Blue/Green • 24.11 Finding the Size of Angles

Inside a Triangle (P) Assessments

1∠5∠

4∠ 2∠

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Unit 2: Solving Equations

Students will be able to solve linear equations in one variable, expanding upon their understanding of combining like terms and the distributive property. They will be able to analyze equations to give an example for the number of possible solutions: one solution, no solutions, or infinitely many solutions.

8.EE.C.7

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Unit 2: Solving Equations September 29, 2014 – October 31, 2014

Common Core State Standards Explanations/Examples Resources 8.EE.C: Analyze and solve linear equations and pairs of simultaneous linear equations.

8.EE.C.7 Solve linear equations in one variable. a. Give examples of linear equations in one

variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

8.EE.C.7 As students transform linear equations in one variable into simpler forms, they discover the equations can have one solution, infinitely many solutions, or no solutions. When the equation has one solution, the variable has one value that makes the equation true as in 12 − 4𝑦𝑦 = 16. The only value for y that makes this equation true is -1. When the equation has infinitely many solutions, the equation is true for all real numbers as in 7x + 14 = 7 (x+2). This equation simplifies to 14 = 14 or 0 = 0. Since the expressions are equivalent, the value for the two sides of the equation will be the same regardless which real number is used for the substitution. When an equation has no solutions it is also called an inconsistent equation. This is the case when the two expressions are not equivalent as in 5𝑥𝑥 − 2 = 5(𝑥𝑥 + 1). When simplifying this equation, students will find that the solution appears to be two numbers that are not equal or -2 = 1. In this case, regardless which real number is used for the substitution, the equation is not true and therefore has no solution.

Lessons CMP • Moving Straight Ahead (2nd ed)

o Investigation 3.1-3.5 (C, P, A)

MARS Shell Center • Building and Solving Equations 1 (P) • Solving Real-Life Problems: Baseball

Jerseys (A)

Mathalicious • Domino Effect (A)

Tasks Illustrative Mathematics • Solving Equations (C) • The Sign of Solutions (C)

Activities Practice Math’s Mate Skill Builder Blue/Green • Equations (P) Assessments

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http://map.mathshell.org/materials/lessons.php?taskid=433&subpage=problem

http://map.mathshell.org/materials/lessons.php?taskid=433&subpage=problem

http://www.mathalicious.com/lesson/domino-effect/





Unit 2: Solving Equations September 29, 2014 – October 31, 2014

Common Core State Standards Explanations/Examples Resources 8.EE.C.7 (continued) 8.EE.C.7 (continued)

• Solve: o o o o

o

4)7(3 =+− x8483 −=− xx

235)1(3 −=−+ xx7)3(7 =−m

yy31

43

32

41

−=−

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Unit 3: Linear Relationships

Students will define a function, understanding the correlation between domain and range. Students will be able to analyze the connections between a graph, tables of values, equation and story problem of a linear function. Students will explore the slope of an equation using similar triangles, for any two points along a line. Students will build upon their knowledge of proportional relationships (7.RP.2) from 7th grade to interpret the unit rate as the slope of the graph. Students will compare and contrast linear and non-linear models along all four faces of a function. They will be able to interpret the slope and beginning value, constructing a linear model, given any one of the three remaining faces. Students will expand upon their work with linear equations to solve systems of simultaneous linear equations.

Sub-Unit A: Linear

Functions

8.F.A.1

8.F.B.5

8.EE.B.6

8.F.A.3

8.EE.B.5

8.F.B.4

8.F.A.2

Sub-Unit B:

Systems of Linear

Equations

8.EE.C.8

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Unit 3: Linear Relationships Sub-Unit A: Linear Functions

November 3, 2014 – December 19, 2014 Common Core State Standards Explanations/Examples Resources

8.F.A: Define, evaluate, and compare functions. 8.F.A.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

8.F.A.1 • The rule that takes x as input and gives x2 + 5x+ 4 as

output is a function. Using y to stand for the output we can represent this function with the equation y = x2 + 5x + 4, and the graph of the equation is the graph of the function. Students are not yet expected use function notation such as f(x) = x2 + 5x + 4.

Lessons 8.F.A.1 CMP • Common Core Additional

Investigations (8) o Investigation 2

Tasks 8.F.A.1 Howard County • Earning Incentives • Towering Numbers

Illustrative Mathematics • Foxes and Rabbits • Function Rules • US Garbage

8.F.A.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

8.F.A.2 • Compare the two linear functions listed below and

determine which equation represents a greater rate of change. Function 1:

Function 2: The function whose input x and output y are related by

y = 3x + 7

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https://grade8commoncoremath.wikispaces.hcpss.org/Unit+3+Analyzing+Functions+and+Equations








8.F.A.2 (continued) 8.F.A.2 (continued) • Compare the two linear functions listed below and

determine which has a negative slope.

Function 1: Gift Card

Samantha starts with $20 on a gift card for the book store. She spends $3.50 per week to buy a magazine. Let y be the amount remaining as a function of the number of weeks, x.

x y 0 20 1 16.50 2 13.00 3 9.50 4 6.00

Function 2: Calculator Rental

The school bookstore rents graphing calculators for $5 per month. It also collects a non-refundable fee of $10.00 for the school year. Write the rule for the total cost (c) of renting a calculator as a function of the number of months (m).

Tasks (continued) 8.F.A.1 (continued) Inside Mathematics • Between the Lines • Circular Reasoning • Cut it Out • Miles of Tiles • Surrounded and Covered

MARS Shell Center • Functions

8.F.A.2 Howard County • Music Dilemma

Illustrative Mathematics • Battery Charging

8.F.A.3 Illustrative Mathematics • Introduction to Linear Functions

Inside Mathematics • Surrounded and Covered

MARS Shell Center • Meal Out

Activities

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http://insidemathematics.org/problems-of-the-month/pom-betweenthelines.pdf

http://insidemathematics.org/problems-of-the-month/pom-circularreasoning.pdf

http://insidemathematics.org/problems-of-the-month/pom-cutitout.pdf

http://insidemathematics.org/problems-of-the-month/pom-milesoftiles.pdf

http://insidemathematics.org/problems-of-the-month/pom-surroundedandcovered.pdf






http://map.mathshell.org/materials/download.php?fileid=1114




8.F.A.2 (continued) 8.F.A.2 (continued) Solution:

Function 1 is an example of a function whose graph has negative slope. Samantha starts with $20 and spends money each week. The amount of money left on the gift card decreases each week. The graph has a negative slope of -3.5, which is the amount the gift card balance decreases with Samantha’s weekly magazine purchase. Function 2 is an example of a function whose graph has positive slope. Students pay a yearly nonrefundable fee for renting the calculator and pay $5 for each month they rent the calculator. This function has a positive slope of 5, which is the amount of the monthly rental fee. An equation for Example 2 could be c = 5m + 10.

Practice 8.F.A.1/8.F.A.2 Math’s Mate Skill Builder Mauve/Lime • 19.3 Graphing Vertical and Horizontal

Lines on a Coordinate Plane (P) • 19.4 Graphing Linear Equations on a

Coordinate Plane by First Completing a Table of Values (P)

• 19.16 Completing a Table of Values for a Non-linear Function (P)

• 19.17 Graphing Non-linear Functions on a Coordinate Plane by First Completing a Table of Values (P)

Assessments 8.F.A.1 Inside Mathematics • House Prices • Party

8.F.A.3 Interpret the equation 𝑦𝑦 = 𝑚𝑚𝑥𝑥 + 𝑏𝑏 as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function 𝐴𝐴 = 𝑠𝑠2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1, 1), (2, 4), and (3, 9), which are not on a straight line.

8.F.A.3 • Determine which of the functions listed below are

linear and which are not linear and explain your reasoning.

o y = -2x2 + 3 non linear

o y = 2x linear

o A = πr2 non linear

o y = 0.25 + 0.5(x – 2) linear

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http://insidemathematics.org/common-core-math-tasks/8th-grade/8-2007%20House%20Prices.pdf

http://insidemathematics.org/common-core-math-tasks/8th-grade/8-2004%20Party.pdf




8.F.B: Use functions to model relationships between quantities. 8.F.B.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from the description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

8.F.B.4 • The table below shows the cost of renting a car. The

company charges $45 a day for the car as well as charging a one-time $25 fee for the car’s navigation system (GPS). Write an expression for the cost in dollars, c, as a function of the number of days, d.

Students might write the equation c = 45d + 25 using the verbal description or by first making a table.

Days (d)

Cost (c) in dollars

1 70 2 115 3 160 4 205

Students should recognize that the rate of change is 45 (the cost of renting the car) and that initial cost (the first day charge) also includes paying for the navigation system. Classroom discussion about one time fees vs. recurrent fees will help students model contextual situations.

• When scuba divers come back to the surface of the water, they need to be careful not to ascend too quickly. Divers should not come to the surface more quickly than a rate of 0.75 ft per second. If the divers start at a depth of 100 feet, the equation d = 0.75t – 100 shows the relationship between the time of the ascent in seconds (t) and the distance from the surface in feet (d).

Lessons 8.F.B.4/8.F.B.5 CMP • Thinking with Mathematical Models

(2nd ed) o Investigation 1 o Investigation 2

Prentice Hall • PH A1

o Ch 5.1 o Ch 6.1-6.3

Tasks 8.F.B.4 Illustrative Mathematics • Baseball Card (C) • Video Streaming (P, A)

Inside Mathematics • Circular Reasoning (C) • Measuring Up (C) • Surrounded and Covered (C)

MARS Shell Center • Baseball Jerseys

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http://insidemathematics.org/problems-of-the-month/pom-circularreasoning.pdf

http://insidemathematics.org/problems-of-the-month/pom-measuringup.pdf






8.F.B.4 (continued) 8.F.B.4 (continued) o Will they be at the surface in 5 minutes? How

long will it take the divers to surface from their dive?

o Make a table of values showing several times and the corresponding distance of the divers from the surface. Explain what your table shows. How do the values in the table relate to your equation?

Tasks (continued) 8.F.B.5 Illustrative Mathematics • Bike Race (C) • Tides (C) • Velocity vs. Distance (C)

Inside Mathematics • Growing Staircases (C)

Activities Practice 8.F.B.4 Math’s Mate Skill Builder Mauve/Lime • 19.13 Writing the Equations of a

Straight Line when Two Points are Given (P)

Assessments 8.F.B.4 Inside Mathematics • House Prices (P, A) • Vincent’s Graphs (C, A)

8.F.B.5 Inside Mathematics • Party (A)

8.F.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

8.F.B.5 • The graph below shows a student’s trip to school.

This student walks to his friend’s house and, together, they ride a bus to school. The bus stops once before arriving at school.

Describe how each part A-E of the graph relates to the story.

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http://insidemathematics.org/problems-of-the-month/pom-growingstaircases.pdf




http://insidemathematics.org/common-core-math-tasks/8th-grade/8-2007%20House%20Prices.pdf

http://insidemathematics.org/common-core-math-tasks/8th-grade/8-2009%20Vincent's%20Graphs.pdf

http://insidemathematics.org/common-core-math-tasks/8th-grade/8-2004%20Party.pdf




8.EE.B: Understand the connections between proportional relationships, lines, and linear equations. 8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

8.EE.B.5 Using graphs of experiences that are familiar to students increases accessibility and supports understanding and interpretation of proportional relationship. Students are expected to both sketch and interpret graphs. • Compare the scenarios to determine which

represents a greater speed. Include a description of each scenario including the unit rates in your explanation.

Scenario 1: Scenario 2:

Lessons 8.EE.B.5 CMP • Common Core Additional

Investigations (7) o Investigation 1 (C, P)

• Comparing and Scaling o Investigation 1.1-1.2 (1st ed)

(C, P) o Investigation 3.1-3.3 (1st ed)

(C , A) o Investigation 4.1 (1st ed) (C, A) o Investigation 4.3 (1st ed) (A) o Investigation 2.3 (2nd ed) (P, A) o Investigation 3.3-3.4 (2nd ed)

(P, A) • Moving Straight Ahead (1st ed)

o Investigation 1 (C) o Investigation 2 (P, A) o Investigation 3.2 (P) o Investigation 3.4 (C, A) o Investigation 5 (C, P, A)

Capella Server • 22 Minutes (C, P)

Howard County • Hair and Nails (C)

MARS Shell Center • Proportion or Not? (C, P)

y = 50x x is time in hours y is distance in miles

Page | 22

https://grade7commoncoremath.wikispaces.hcpss.org/Unit+2+Ratios+and+Proportional+Relationships

http://map.mathshell.org/materials/lessons.php?taskid=483




8.EE.B.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

8.EE.B.6 • Explain why ∆𝐴𝐴𝐴𝐴𝐴𝐴 is similar to ∆𝐷𝐷𝐷𝐷𝐷𝐷, and deduce

that has the same slope as . Express each line as an equation.

Lessons (continued) 8.EE.B.5 (continued) Mathalicious • Pizza Pi (C, A)

8.EE.B.6 CMP • Moving Straight Ahead (1st ed)

o Investigation 5 (C, P, A) NCTM Illuminations • Rise-Run, Triangles (C, P)

Tasks 7.RP.A.1/7.RP.A.2/8.EE.B.5 Capella Server • Mullet Ratio (C)

Howard County • Apple Pie Bake Sale (C) • Mandarin Orange Cake Recipes (C) • Photo Sizes (C) • Popping Corn (A)

AB BE

Page | 23

http://www.mathalicious.com/lesson/pizza-pi/

http://illuminations.nctm.org/LessonDetail.aspx?id=L728








Tasks (continued) 8.EE.B.5 (continued) Illustrative Mathematics • Art Class (A) • Buying Bananas (C) • Coffee by the Pound (A) • Comparing Speeds in Graphs and

Equations (C) • Peaches and Plums (C) • Robot Races (C) • Sore Throats, Variation 2 (A) • Track Practice (C) • Walk-A-Thon 2 (A) • Who Has the Best Job? (C, A)

Inside Mathematics • First Rate (A)

Irvine Mathematics Project • Jumping Jacks (C, P)

MARS Shell Center • A Golden Crown (C) • Bike Ride (C) • Buses (P) • Journey (A) • Shelves (A)

NCTM Illuminations • Feeding Frenzy (P, A)

Page | 24












http://insidemathematics.org/problems-of-the-month/pom-firstrate.pdf

http://sites.uci.edu/irvinemathproject/files/2013/04/2_1Jumping-Jacks.pdf










Activities 8.EE.B.5 NCTM Illuminations • Barbie Bungee (C) • Bouncing Tennis Balls (C)

Practice 8.EE.B.5 Math’s Mate Skill Builder Blue/Green • 14.9 Finding Other Rates (P, A)

Assessments 8.EE.B.5 Inside Mathematics • Cereal (C) • Lawn Mowing (A)

Page | 25




http://insidemathematics.org/common-core-math-tasks/7th-grade/7-2004%20Cereal.pdf

http://insidemathematics.org/common-core-math-tasks/7th-grade/7-2005%20Lawn%20Mowing.pdf


Unit 3: Linear Relationships Sub-Unit B: Systems of Linear Equations

January 6, 2015 – January 23, 2015 Common Core State Standards Explanations/Examples Resources

8.EE.C: Analyze and solve linear equations and pairs of simultaneous linear equations. 8.EE.C.8 Analyze and solve pairs of simultaneous linear equations. a. Understand that solutions to a system of

two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3𝑥𝑥 + 2𝑦𝑦 = 5 and 3𝑥𝑥 + 2𝑦𝑦 = 6 have no solution because 3𝑥𝑥 + 2𝑦𝑦 cannot simultaneously be 5 and 6.

c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second par.

8.EE.C.8 Systems of linear equations can also have one solution, infinitely many solutions or no solutions. Students will discover these cases as they graph systems of linear equations and solve them algebraically.

A system of linear equations whose graphs meet at one point (intersecting lines) has only one solution, the ordered pair representing the point of intersection. A system of linear equations whose graphs do not meet (parallel lines) has no solutions and the slopes of these lines are the same. A system of linear equations whose graphs are coincident (the same line) has infinitely many solutions, the set of ordered pairs representing all the points on the line.

By making connections between algebraic and graphical solutions and the context of the system of linear equations, students are able to make sense of their solutions. Students need opportunities to work with equations and context that include whole number and/or decimals/fractions.

• Find x and y using elimination and then using substitution.

o 3x + 4y = 7

o -2x + 8y = 10

Lessons Tasks 8.EE.C.8 Illustrative Mathematics • Cell Phone Plans • Fixing the Furnace • How Many Solutions • Kimi and Jordan • Quinoa Pasta 1 • Summer Swimming • The Intersection of Two Lines

Inside Mathematics • Miles of Tiles • On Balance • The Wheel Shop

Activities Practice Assessments 8.EE.C.8 Inside Mathematics • Picking Apples

Page | 26








http://insidemathematics.org/problems-of-the-month/pom-milesoftiles.pdf

http://insidemathematics.org/problems-of-the-month/pom-onbalance.pdf

http://insidemathematics.org/problems-of-the-month/pom-thewheelshop.pdf

http://insidemathematics.org/common-core-math-tasks/8th-grade/8-2005%20Picking%20Apples.pdf




8.EE.C.8 (continued)

8.EE.C.8 (continued) • Plant A and Plant B are on different watering

schedules. This affects their rate of growth. Compare the growth of the two plants to determine when their heights will be the same.

Let W = number of weeks

Let H = height of the plant after W weeks

Plant A Plant B W H W H 0 4 (0,4) 0 2 (0,2) 1 6 (1,6) 1 6 (1,6) 2 8 (2,8) 2 10 (2,10) 3 10 (3,10) 3 14 (3,14)

• Given each set of coordinates, graph their

corresponding lines.

Solution:

Page | 27




8.EE.C.8 (continued) 8.EE.C.8 (continued) • Write an equation that represent the growth rate of

Plant A and Plant B.

Solution:

Plant A H = 2W + 4

Plant B H = 4W + 2

• At which week will the plants have the same height?

Solution:

The plants have the same height after one week.

Plant A: H = 2W + 4 Plant B: H = 4W + 2

Plant A: H = 2(1) + 4 Plant B: H = 4(1) + 2

Plant A: H = 6 Plant B: H = 6

After one week, the height of Plant A and Plant B are both 6 inches.

Page | 28



In this unit students will expand upon their understanding of rational numbers, with integer exponents, developed in 7th grade, to analyze properties of exponents. Students will explore beyond the rational numbers to investigate irrational numbers, including square and cube roots. Students will build upon their knowledge of exponents to generate equivalent exponential expressions. They will apply their understanding of exponents to estimate small and large numbers using scientific notation. Students will analyze their answer using appropriate units of measure. Students will conceptually understand the similarities and differences between rational and irrational numbers. They will be able to create a rational approximation for irrational numbers, including square and cube roots, and locate them on a number line. Building upon their understanding of square roots, students will solve simple square and cube root equations. They will then apply their understanding of irrational numbers and solving square root equations to the Pythagorean Theorem. Students will be able to prove the Pythagorean Theorem and its converse, applying it to two- and three-dimensions.

Sub-Unit A: Exponents

8.EE.A.1

8.EE.A.3

8.EE.A.4

Sub-Unit B:

Pythagorean Theorem

8.NS.A.1

8.NS.A.2

8.EE.A.2

8.G.B.6

8.G.B.7

8.G.B.8

Page | 29


Unit 4: (E3) Exponential Expressions and Equations Sub-Unit A: Exponents

January 26, 2015 – February 20, 2015 Common Core State Standards Explanations/Examples Resources

8.EE.A: Work with radicals and integer exponents. 8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32×3–5 = 3–3 = 1/33 = 1/27.

8.EE.A.1 • 43

52= 64

25

• 43

47= 43−7 = 4−4 = 1

44= 1

256

• 4−3

52= 4−3 × 1

52= 1

43× 1

52= 1

64× 1

25= 1

16,000

Lessons 8.EE.A.1 CMP • Common Core Additional

Investigations (8) o Investigation 1.1 (C, P)

8.EE.A.3 CMP • Data Around Us (1st ed)

o Investigation 4 (C, P)

Tasks 8.EE.A.1 Illustrative Mathematics • Extending the Definitions of

Exponents (C)

Inside Mathematics • Tri-Triangles (C)

8.EE.A.3 Illustrative Mathematics • Ant and Elephant (A) • Pennies to Heaven (A)

8.EE.A.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3×108 and the population of the world as 7×109, and determine that the world population is more than 20 times larger.

8.EE.A.3 Estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times larger.

8.EE.A.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

8.EE.A.4 Students can convert decimal forms to scientific notation and apply rules of exponents to simplify expressions. In working with calculators or spreadsheets, it is important that students recognize scientific notation. Students should recognize that the output of 2.45E23 is 2.45 x 1023 and 3.5E-4 is 3.5 x 10-4. Students enter scientific notation using E or EE (scientific notation), × (multiplication), and ^ (exponent) symbols.

Page | 30



http://insidemathematics.org/problems-of-the-month/pom-tritriangles.pdf




Unit 4: (E3) Exponential Expressions and Equations Sub-Unit A: Exponents

January 26, 2015 – February 20, 2015 Common Core State Standards Explanations/Examples Resources

Tasks (continued) 8.EE.A.4 Illustrative Mathematics • Ant and Elephant (C, A) • Ants Versus Humans (C, A) • Giantburgers (A) • Pennies to Heaven (C, A)

MARS Shell Center • 100 People (A) • A Million Dollars (A)

Activities 8.EE.A.3 YouTube • Powers of Ten (C, P, A) Practice 8.EE.A.3 Math’s Mate Skill Builder Blue/Green • 17.8-17.9 Scientific Notation (P)

Assessments 8.EE.A.1 MARS Shell Center • Generalizing Patterns: The Difference

of Two Squares (C) 8.EE.A.3 MARS Shell Center • Estimating Length Using Scientific

Notation (P)

Page | 31







http://www.youtube.com/watch?v=0fKBhvDjuy0&noredirect=1








Sub-Unit B: Pythagorean Theorem February 23, 2015 – April 3, 2015

Common Core State Standards Explanations/Examples Resources 8.NS.A: Know that there are numbers that are not rational, and approximate them by rational numbers.

8.NS.A.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion, which repeats eventually into a rational number.

8.NS.A.1 Students can use graphic organizers to show the relationship between the subsets of the real number system.

Lessons 8.NS.A.1 CMP • Looking for Pythagoras

o Investigation 5 (1st ed) (C, P)

MARS Shell Center • Repeating Decimals (C, P)

8.NS.A.2 CMP • Looking for Pythagorus

o Investigation 4.1 (2nd ed) (C)

Tasks 8.NS.A.1 Illustrative Mathematics • Identifying Rational Numbers (A)

8.NS.A.2 Illustrative Mathematics • Comparing Rational and Irrational

Numbers (A) • Irrational Numbers on the Number

Line (A) • Placing a Square Root on the Number

Line (A)

8.NS.A.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π2). For example, by truncating the decimal expansion of√2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.

8.NS.A.2 Students can approximate square roots by iterative processes. • Approximate the value of √5 to the nearest

hundredth.

Page | 32










Unit 4: (E3) Exponential Expressions and Equations Sub-Unit B: Pythagorean Theorem February 23, 2015 – April 3, 2015

Common Core State Standards Explanations/Examples Resources 8.NS.A.2 (continued) 8.NS.A.2 (continued)

Solution: Students start with a rough estimate based upon perfect squares. √5 falls between 2 and 3 because 5 falls between 22 = 4 and 32 = 9. The value will be closer to 2 than to 3. Students continue the iterative process with the tenths place value. √5 falls between 2.2 and 2.3 because 5 falls between 2.22 = 4.84 and 2.32 = 5.29. The value is closer to 2.2. Further iteration shows that the value of √5 is between 2.23 and 2.24 since 2.232 is 4.9729 and 2.242 is 5.0176.

• Compare √2 and √3 by estimating their values, plotting them on a number line, and making comparative statements.

Solution: Statements for the comparison could include: √2 is approximately 0.3 less than √3 √2 is between the whole numbers 1 and 2 √3 is between 1.7 and 1.8

Activities NCTM Illuminations • Square Roots Go Rational (C, P) Practice Assessments

Page | 33




Common Core State Standards Explanations/Examples Resources 8.EE.A: Work with radicals and integer exponents.

8.EE.A.2 Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

8.EE.A.2 • 32 = 9 and √9 = ±3

• �13�3

= �13

33� = 1

27 and � 1

273

= √13

√273 = 13

• Solve:

Solution: 𝑥𝑥2 = 9√𝑥𝑥2 = √9𝑥𝑥 = ±3

• Solve

Solution: 𝑥𝑥3 = 8√𝑥𝑥33 = √83

𝑥𝑥 = 2

Lessons 8.EE.A.2 CMP • Common Core Additional

Investigations (8) o Investigation 1.2 (C, P)

• Looking for Pythagoras (1st ed) o Investigation 2.2-2.3 (C)

Tasks 8.EE.A.2 Inside Mathematics • Polly Gone (C) Activities Practice Assessments

8.G.B: Understand and apply the Pythagorean Theorem. 8.G.B.6 Explain a proof of the Pythagorean Theorem and its converse.

8.G.B.6 Students should verify, using a model, that the sum of the squares of the legs is equal to the square of the hypotenuse in a right triangle. Students should also understand that if the sum of the squares of the 2 smaller legs of a triangle is equal to the square of the third leg, then the triangle is a right triangle.

Lessons 8.G.B CMP • Looking for Pythagoras (2nd ed)

o Investigation 3 8.G.B.6/8.G.B.7 Howard County • Pythagorean Theorem

92 =x

83 =x

Page | 34

http://insidemathematics.org/problems-of-the-month/pom-pollygone.pdf

https://grade8commoncoremath.wikispaces.hcpss.org/Unit+2+Geometry



Common Core State Standards Explanations/Examples Resources 8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

8.G.B.7 Through authentic experiences and exploration, students should use the Pythagorean Theorem to solve problems. Problems can include working in both two and three dimensions. Students should be familiar with the common Pythagorean triplets.

Tasks 8.G.B.6 Illustrative Mathematics • Converse of the Pythagorean

Theorem 8.G.B.7 Howard County • Curb Appeal

Inside Mathematics • First Rate • Patterns in Prague

8.G.B.8 Howard County • Amazing Amusement Park

Activities Practice 8.G.B.7 Math’s Mate Skill Builder Mauve/Lime • 28.5 Applying Pythagorean Theorem

(A)

8.G.B.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

8.G.B.8 • Students will create a right triangle from the two

points given (as shown in the diagram below) and then use the Pythagorean Theorem to find the distance between the two given points.

Page | 35

http://s3.amazonaws.com/illustrativemathematics/illustration_pdfs/000/000/724/original/illustrative_mathematics_724.pdf?1350316862

http://s3.amazonaws.com/illustrativemathematics/illustration_pdfs/000/000/724/original/illustrative_mathematics_724.pdf?1350316862


http://insidemathematics.org/problems-of-the-month/pom-firstrate.pdf

http://www.insidemathematics.org/pdfs/eighth-grade/patterns-in-prague/task.pdf





Common Core State Standards Explanations/Examples Resources Practice (continued) 8.G.B.8 Math’s Mate Skill Builder Mauve/Lime • 28.10 Applying Pythagorean Theorem

to Find the Distance Between Two Points Located on a Coordinate Plane (P)

Assessments

Page | 36





Unit 5: Volume

Students will apply their understanding of volume to cylinders, cones, and spheres. Students will know and apply the formulas for volume to real-world and mathematical problems.

Volume

8.G.C.9

Page | 37


Unit 5: Volume April 6, 2015 – April 24, 2015

Common Core State Standards Explanations/Examples Resources 8.G.C: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

8.G.C.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

8.G.C.9 • James wanted to plant pansies in his new planter.

He wondered how much potting soil he should buy to fill it. Use the measurements in the diagram below to determine the planter’s volume.

Lessons 8.G.C.9 CMP • Filling and Wrapping (1st ed)

o Investigation 4 (C) o Investigation 5 (C)

NCTM Illuminations • Popcorn, Anyone? (C, P, A)

Tasks 8.G.C.9 Illustrative Mathematics • Comparing Snow Cones (A) • Flower Vases (A) • Glasses (A) • Shipping Rolled Oats (A)

Activities Practice Assessments

Page | 38







Unit 6: Data Analysis

Students will build upon their previous understanding of samples and populations, creating data displays and making conjectures about the data. Students will investigate patterns such as clustering, outliers, positive or negative association, linear and non-linear association for bivariate data. Students will fit linear models to scatter plots and make conjectures about the data using the equations. Students will use two-way tables to analyze frequencies and describe a possible association between the variables.

Data Analysis

8.SP.A.1

8.SP.A.2

8.SP.A.3

8.SP.A.4


Unit 6: Data Analysis April 27, 2015 – May 15, 2015

Common Core State Standards Explanations/Examples Resources 8.SP.A: Investigate patterns of association in bivariate data.

8.SP.A.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

8.SP.A.1

Lessons 8.SP.A CMP • Samples and Populations (2nd ed)

o Investigation 4.1-4.2 8.SP.A.2 Howard County • Line of Best Fit

8.SP.A.3 Prentice Hall • PH A1

o Ch 6.7 Howard County • Interpreting Slope and Y-Int

Tasks 8.SP.A.1 Howard County • What is the Relationship

Inside Mathematics • House Prices • Through the Grapevine

8.SP.A.3 Howard County • Obesity Rates

8.SP.A.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

8.SP.A.2 • The capacity of the fuel tank in a car is 13.5 gallons.

The table below shows the number of miles traveled and how many gallons of gas have been used. Describe the relationship between the variables. If the data is linear, determine a line of best fit. Do you think the line represents a good fit for the data set? Why or why not? What is the average fuel efficiency of the car in miles per gallon?

Miles Traveled 0 75 120 160 250 300

Gallons Used 0 2.3 4.5 5.7 9.7 10.7

Page | 40

https://grade8commoncoremath.wikispaces.hcpss.org/Unit+4+Patterns+of+Association



http://insidemathematics.org/index.php/8th-grade

http://insidemathematics.org/index.php/8th-grade




Common Core State Standards Explanations/Examples Resources 8.SP.A.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

8.SP.A.3 • Given data from students’ math scores and

absences, make a scatterplot.

o Draw a line of best fit, paying attention to the closeness of the data points on either side of the line.

Activities Practice Assessments

Page | 41



Common Core State Standards Explanations/Examples Resources 8.SP.A.3 (continued) 8.SP.A.3 (continued)

o From the line of best fit, determine an approximate linear equation that models the given data (about y = 95

325

+− x )

o Students should recognize that 95 represents the y intercept and

325

− represents the slope of

the line.

Students can use this linear model to solve problems. For example, through substitution, they can use the equation to determine that a student with 4 absences should expect to receive a math score of about 62. They can then compare this value to their line.

8.SP.A.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

8.SP.A.4 • The table illustrates the results when 100 students

were asked the survey questions: “Do you have a curfew?” and “Do you have assigned chores?” Is there evidence that those who have a curfew also tend to have chores?

Page | 42



Common Core State Standards Explanations/Examples Resources 8.SP.A.4 (continued) 8.SP.A.4 (continued)

Solution: Of the students who answered that they had a curfew, 40 had chores and 10 did not. Of the students who answered they did not have a curfew, 10 had chores and 40 did not. From this sample, there appears to be a positive correlation between having a curfew and having chores.

Page | 43

Performance Level Descriptors – Grade 8 Mathematics

Grade 8 Math : Sub-Claim A The student solves problems involving the Major Content for grade/course with connections to the Standards

for Mathematical Practice. Level 5: Distinguished

Command

Level 4: Strong Command Level 3: Moderate

Command

Level 2: Partial Command

Expressions and Equations

8 EE.A.1 8 EE.A.2

Evaluates and generates equivalent numerical expressions applying properties of integer exponents.

Solves equations of the form x2 = p and x3 = p, representing solutions using √ or symbols.

Demonstrates a solid understanding of the structure of these properties within a real- world context.


Solves equations of the form x2 = p and x3 = p, representing solutions using √ or symbols.

Demonstrates a general understanding of the structure of these properties within a real- world context.


Solves equations of the form x2 = p, where p is a perfect square and solves equations of the form x3 = p, where p is a perfect cube, by representing the positive solution of the equation.

Evaluates simple numerical expressions using properties of integer exponents.

Partially solves equations of the form x2 = p, where p is a perfect square, by representing the positive solution of the equation.

Scientific Notation 8.EE.A.3 8.EE.A.4-1 8.EE.A.4-2

Using scientific notation, estimates very large and very small quantities and determines how many times as large one number is in relation to another.

Performs operations with numbers expressed in scientific notation, with and without technology.

Using scientific notation, estimates very large and very small quantities and determines how many times as large one number is in relation to another.

Performs operations with numbers expressed in scientific notation, without technology.

Using scientific notation, estimates very large and very small quantities.


Using scientific notation, estimates very large quantities.


Page | 44




Command


Command


Interprets scientific notation that has been generated by technology.

Interprets scientific notation that has been generated by technology.

Proportional Relationships and Linear Equations

8.EE.B.5-1 8.EE.B.5-2 8.EE.B.6-1 8.F.A.3-1

Graphs linear relationships in the form y=mx+b, including proportional relationships.

Interprets the unit rate as the slope of the graph of a proportional relationship and applies these concepts to solve real-world problems.

Compares two different proportional relationships represented in different ways.

Interprets y=mx+b as defining a linear function.

Uses similar triangles to show that the slope is the same between any two distinct points on a non-

Graphs linear relationships in the form y=mx+b, including proportional relationships.



Interprets y=mx+b as defining a linear function.

Graphs linear relationships, in the form y=mx+b, including proportional relationships.



Graphs linear relationships, in the form y=mx+b, including proportional relationships.

Interprets the unit rate as the slope of the graph of a proportional relationship.

Makes some comparisons between two different proportional relationships represented in different ways.

Page | 45




Command


Command


vertical line in the coordinate plane.

Solving Linear Equations

8.EE.C.7 8.EE.C.Int. 1

Solves complex mathematical and real- world linear equations in one variable, with rational number coefficients, including those that require use of the distributive property and combining of like terms.

Solves mathematical and real-world linear equations in one variable, with rational number coefficients, including those that require use of the distributive property or combining of like terms.

Solves linear equations in one variable, with rational number coefficients, including those that require use of the distributive property and combining like terms.

Solves linear equations in one variable, with rational number coefficients, including those that require use of the distributive property or combining like terms.

Simultaneous Linear Equations

8.EE.C.8a 8.EE.C.8b-1 8.EE.C.8b-2 8.EE.C.8b-3

Analyzes and solves mathematical and real- world problems leading to pairs of simultaneous linear equations graphically, algebraically and by inspection.

Understands the relationship between the graphic representation and the algebraic solution to the system. Verifies a solution utilizing multiple methods to prove accuracy.

Analyzes and solves mathematical and real- world problems leading to pairs of simultaneous linear equations graphically, algebraically and by inspection.

Understands the relationship between the graphic representation and the algebraic solution to the system.

Analyzes and solves mathematical problems leading to pairs of simultaneous linear equations graphically and algebraically.

Solves mathematical problems leading to pairs of simultaneous linear equations graphically or by inspection.

Page | 46




Command


Command


Functions 8.F.A.1-1 8.F.A.1-2 8.F.A.2 8.F.A.3-2

Understands that a function is a rule assigning to each input exactly one output which can be graphed as a set of ordered pairs.

Compares properties of two functions represented in different ways.

Identifies and proves functions as non-linear.

Understands that a function is a rule assigning to each input exactly one output, which can be graphed as a set of ordered pairs.

Compares properties of two functions represented in different ways.

Identifies functions that are non-linear.

Understands that a function is a rule that assigns to each input exactly one output and can be graphed as a set of ordered pairs.

Compares some of the properties of two functions represented in different ways.

Understands that a function is a rule that assigns to each input exactly one output and can be graphed as a set of ordered pairs.

Congruence and Similarity

8.G.A.1a 8.G.A.1b 8.G.A.1c 8.G.A.2 8.G.A.3 8.G.A.4

Describes the effect of dilations, translations, rotations and reflections on two-dimensional figures with and without coordinates, determines whether two given figures are congruent or similar through one or more transformations and describes multiple sequences of transformations to justify congruence or similarity of two figures.

Describes the effect of dilations, translations, rotations and reflections on two-dimensional figures with and without coordinates, determines whether two given figures are congruent or similar through one or more transformations and describes the sequence of transformations to justify congruence or similarity of two figures.

Describes the effect of dilations, translations, rotations and reflections on two-dimensional figures with and without coordinates, and determines whether two given figures are congruent or similar through one or more transformations.

Describes the effect of translations, rotations and reflections on two- dimensional figures without coordinates and determines whether two given figures are congruent.

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Command


Command


Pythagorean Theorem

8.G.B.7-1 8.G.B.7-2 8.G.B.8

Applies the Pythagorean Theorem in a planar case and to find the distance between two points in a coordinate system and in a three-dimensional case in both mathematical and real- world multi-step problems.

Recognizes situations to apply the Pythagorean Theorem in multi-step problems.

Applies the Pythagorean Theorem in a simple planar case and to find the distance between two points in a coordinate system and in a simple three-dimensional case in both mathematical and real-world problems.

Applies the Pythagorean Theorem in a simple planar case and to find the distance between two points in a coordinate system.

Applies the Pythagorean Theorem in a simple planar case.

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Grade 8 Math: Sub-Claim B The student solves problems involving the Additional and Supporting Content for the grade/course with

connections to the Standards for Mathematical Practice. Level 5: Distinguished

Command Level 4: Strong

Command Level 3: Moderate

Command

Level 2: Partial Command Rational Numbers

8.NS.A.1 8.NS.A.2

Distinguishes between rational and irrational numbers, understands that these numbers have decimal expansions and locates them approximately on a number line, and converts between terminating decimals or repeating decimals and fractional representations of rational numbers.

Analyzes and generalizes patterns and structures of repeating decimals.

Distinguishes between rational and irrational numbers, understands that these numbers have decimal expansions and locates them approximately on a number line, and converts between terminating decimals or repeating decimals and fractional representations of rational numbers.

Distinguishes between rational and irrational numbers, understands that these numbers have decimal expansions and locates them approximately on a number line, and converts between terminating decimals or repeating decimals of the form (0.aaa…) and fractional representations of rational numbers.

Distinguishes between rational and irrational numbers and understands that these numbers have decimal expansions and locates them approximately on a number line.

Modeling with Functions

8.F.B.4 8.F.B.5-1 8.F.B.5-2

Constructs a function to model a linear relationship between two quantities described with or without a context.

Given a description of a relationship or two (x,y) values in a table of values or a graph, determines the rate of change and initial

Constructs a function to model a linear relationship between two quantities described with or without a context.

Given a description of a relationship or two (x,y) values in a table of values or a graph, determines the rate of change and initial

Constructs a function to model a linear relationship between two quantities without a context.

Given two (x,y) values in a table of values or a graph, determines the rate of change and initial value of the function.

Constructs a function to model a linear relationship between two quantities in a table or a graph.

Determines the rate of change and initial value of the function from a table or graph that contains the initial value.

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Command

Level 2: Partial Command value of the function.

Analyzes, describes and contextualizes the functional relationship between two quantities.

Sketches a graph of a function when given a written description.

value of the function.

Analyzes and describes the functional relationship between two quantities.

Sketches a graph of a function when given a written description.

Analyzes the graph of a linear function to describe the functional relationship between two quantities.

Sketches the graph of a function when given a written description.

Analyzes the graph of a linear function to describe the functional relationship between two quantities.

Volume

8.G.C.9

Knows the formulas for the volume of cones, cylinders and spheres, and uses them to find the volume or dimensions of composite solids in mathematical and real-world problems.

Applies these formulas to multiple composite mathematical solids and utilize these formulas within a novel context.

Knows the formulas for the volume of cones, cylinders and spheres, and uses them to find the volume or dimensions of solids in mathematical and real- world problems.

Applies these formulas to multiple composite mathematical solids.

Knows the formulas for the volume of cones, cylinders and spheres, and uses them to find the volume of solids in mathematical and real- world problems.

Knows the formulas for the volume of cones, cylinders and spheres, and uses them to find the volume of solids in mathematical problems.

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Command

Level 2: Partial Command Bivariate Data

8.SP.A.1 8.SP.A.2 8.SP.A.3 8.SP.A.4

Justifies the patterns of association that can be seen in bivariate data by constructing, displaying and interpreting scatter plots and two-way tables.

Uses the equation of a linear model to solve problems in context.

Informally fits a straight line to a scatter plot that suggests a linear association and assesses the model fit.

Compares linear models used to fit the same set of data to determine which is a better fit.

Analyzes and describes the patterns of association that can be seen in bivariate data by constructing, displaying and interpreting scatter plots and two-way tables.


Informally fits a straight line to a scatter plot that suggests a linear association and assesses the model fit.



Informally fits a straight line to a scatter plot that suggests a linear association.


Uses a given equation of a linear model to solve problems in context.

Informally fits a straight line to a scatter plot that suggests a linear association.

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Grade 8: Sub-Claim C The student expresses grade/course-level appropriate mathematical reasoning by constructing viable

arguments, critiquing the reasoning of others and/or attending to precision when making mathematical statements.

Level 5: Distinguished Command

Level 4: Strong Command

Level 3: Moderate Command

Level 2: Partial Command Graphs and Equations

8.C.1.1 8.C.1.2 8.C.2

Clearly constructs and communicates a complete response based on the principle that a graph of an equation in two variables is the set of all its solutions and a given equation or system of equations including:

• a logical approach

based on a conjecture and/or stated assumptions

• a logical and complete progression of steps

• precision of calculation • correct use of grade-

level vocabulary, symbols and labels

• complete justification of a conclusion

• generalization of an argument or conclusion

• evaluating, interprets and critiques the

• validity and efficiency of

Clearly constructs and communicates a complete response based on the principle that a graph of an equation in two variables is the set of all its solutions and a given equation or system of equations including:







• evaluating, interpreting and critiques the validity of other’s responses, approaches, conclusions and reasoning

Constructs and communicates a complete response based on the principle that a graph of an equation in two variables is the set of all its solutions and a given equation or system of equations including:



• a logical, but incomplete, progression of steps

• minor calculation errors • some use of grade-level

vocabulary, symbols and labels

• partial justification of a conclusion

• evaluating the validity of other’s approaches and conclusion

Constructs and communicates an incomplete response based on the principle that a graph of an equation in two variables is the set of all its solutions and a given equation or system of equations including:

• a faulty approach based

on a conjecture and/or stated assumptions

• an illogical or incomplete progression of steps

• major calculation errors • limited use of grade-



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Level 2: Partial Command other’s responses,

approaches and reasoning, conclusions and reasoning and providing a counter- example where applicable

Reasoning

8.C.3.1 8.C.3.2 8.C.3.3 8.C.4.1 8.C.6

Clearly constructs and communicates a complete response based on a chain of reasoning to justify or refute algebraic, function or linear-equation propositions or conjectures including:






Clearly constructs and communicates a complete response based on a chain of reasoning to justify or refute algebraic, function or linear-equation propositions or conjectures including:






Constructs and communicates a complete response based on a chain of reasoning to justify or refute algebraic, function or linear-equation propositions or conjectures including:





vocabulary, symbols

Constructs and communicates an incomplete response based on a chain of reasoning to justify or refute algebraic, function or linear-equation propositions or conjectures including:


on a conjecture and/or stated assumptions

• an illogical and incomplete progression of steps



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Level 2: Partial Command • complete justification of

a conclusion • generalization of an

argument or conclusion • evaluating, interpreting

and critiquing the validity and efficiency of other’s responses, approaches, conclusions and reasoning, and providing a counter- example where applicable


• evaluating, interpreting and critiquing the validity of other’s responses, approaches, conclusions and reasoning

and labels • partial justification of a

conclusion • evaluating the validity

of other’s approaches and conclusions

• partial justification of a conclusion.

Geometric Reasoning

8.C.5.1 8.C.5.2 8.C.5.3

Clearly constructs and communicates a complete response based on applying geometric reasoning in a coordinate setting and/or use coordinates to draw geometric conclusions including:


based on a conjecture

Clearly constructs and communicates a complete response based on applying geometric reasoning in a coordinate setting and/or use coordinates to draw geometric conclusions including:



Constructs and communicates a complete response based on applying geometric reasoning in a coordinate setting and/or use coordinates to draw geometric conclusions including:



Constructs and communicates an incomplete response based on applying geometric reasoning in a coordinate setting and/or use coordinates to draw geometric conclusions including:


on a conjecture and/or

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and/or stated assumptions





• generalization of an argument or conclusion

• evaluating, interpreting and critiquing the validity and efficiency of other’s responses, approaches and reasoning, and providing a counter- example where applicable

• identifying and describing errors in solutions and presenting correct solutions

• distinguishing correct






• evaluating, interpreting and critiquing the validity of other’s responses, approaches, conclusions and reasoning

• identifying and describing errors in solutions and presenting correct solutions




vocabulary, symbols and labels


• evaluating the validity of other’s approaches and conclusion

• identifying and describing errors in solutions

stated assumptions • an illogical and

incomplete progression of steps




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Level 2: Partial Command explanation/reasoning

from that which is flawed. If there is a flaw, presents correct reasoning.

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Grade 8: Sub-Claim D The student solves real-world problems with a degree of difficulty appropriate to the grade/course by applying knowledge and skills articulated in the standards for the current grade/course (or for more complex problems,

knowledge and skills articulated in the standards for previous grades/courses), engaging particularly in the Modeling practice, and where helpful making sense of problems and persevering to solve them, reasoning abstractly, and quantitatively, using appropriate tools strategically, looking for the making use of structure

and/or looking for and expressing regularity in repeated reasoning. Level 5: Distinguished

Command


Command


Modeling

8.D.1 8.D.2 8.D.3 8.D.4

Devises a plan to apply mathematics in solving problems arising in everyday life, society and the workplace by:

• using stated

assumptions and making assumptions and approximations to simplify a real-world situation

• mapping relationships between important quantities by selecting appropriate tools to create models

• analyzing relationships mathematically between important quantities to draw conclusions

• writing a complete, clear and correct


• using stated

assumptions and making assumptions and approximations to simplify a real-world situation

• mapping relationships between important quantities by selecting appropriate tools to create models


• writing a complete, clear and correct


• using stated

assumptions and approximations to simplify a real-world situation

• illustrating relationships between important quantities by using provided tools to create models


• writing an incomplete algebraic expression or equation to describe a


• using stated

assumptions and approximations to simplify a real-world situation

• identifying important quantities using provided tools to create models

• analyzing relationships mathematically to draw conclusions

• writing an incomplete algebraic expression or equation to describe a situation

• applying proportional reasoning

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Command


Command


algebraic expression or

equation to describe a situation


• writing/using functions to describe how one quantity of interest depends on another

• using reasonable estimates of known quantities in a chain of reasoning that yields an estimate of an unknown quantity

• reflecting on whether the results make sense

• improving the model if it has not served its purpose

• interpreting mathematical results in the context of the situation

algebraic expression or equation to describe a situation


• writing/using functions to describe how one quantity of interest depends on another



• improving the model if it has not served its purpose

• interpreting mathematical results in the context of the situation

situation • applying proportional

reasoning • writing/using functions

to describe how one quantity of interest depends on another



• modifying the model if it has not served its purpose

• interpreting mathematical results in a simplified context

• using functions to describe how one quantity of interest depends on another

• using unreasonable estimates of known quantities in a chain of reasoning that yields an estimate of an unknown quantity

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Command


Command


• analyzing and/or creating

constraints, relationships and goals analyzing, justifying and defending models which lead to a conclusion

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8th Grade Standards Aligned With the 8 Grade PARCC … · 2017. 7. 19. · Curriculum Guide...

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Transcript of 8th Grade Standards Aligned With the 8 Grade PARCC … · 2017. 7. 19. · Curriculum Guide...