images.pcmac.orgimages.pcmac.org/Uploads/Fayette/Fayette/Divisions... · Web viewCCRS QUALITY CORE CONTENT STANDARDS EVIDENCE OF STUDENT ATTAINMENT RESOURCES FIRST SIX WEEKS RVW 7th

COURSE CONTENTMATHEMATICS

EIGHTH GRADE

CCRS QUALITYCORE CONTENT STANDARDS EVIDENCE OF STUDENT

ATTAINMENT RESOURCES

FIRST SIX WEEKSRVW 7th Grade Standards *Glencoe Pre-Alegbra Book

Chapter 2 (Pg. 59-117)Operations with integersPg. 61-102

1 [8.NS.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.

Students:Given a variety of numbers,

Categorize the numbers as rational and irrational and defend the placement.

Given a rational number in fraction form,

Provide the decimal representation showing the repeating nature of the decimal expansion.

Given a repeating decimal expansion,

Produce the rational representation in the form a/b.

Chapter 3 (Pg. 119-169)Pge. 123-135

RVW 7th Grade Standards Pg. 136-160

RVW 7th Grade Standards Chapter 4 (Pg. 173-219)

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Expressions and EquationsPg. 173-185

9 [8.EE.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 bare 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.

Students:

Solve linear equations in one variable including when manipulation of the expressions in the equation becomes necessary to obtain a solution, if one exists,

Provide examples of linear equations which have one solution, infinitely many solutions, or no solutions and use these to describe the characteristics of such equations.

Pg. 186-211

SECOND SIX WEEKSRVW 7th Grade Standards Chapter 5 (pg. 221-263)

Multi-step equations and inequalitiesPg. 223-228

9 [8.EE.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 bare 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.

Students:

Solve linear equations in one variable including when manipulation of the expressions in the equation becomes necessary to obtain a solution, if one exists,

Provide examples of linear equations which have one solution, infinitely many solutions, or no solutions and use these to describe the characteristics of such

Pg. 231-255

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EIGHTH GRADE

equations.

RVW

RVW

7th Grade Standards

To be included with Chaper 11

7th Grade Standards

Chapter 6 (pg. 265-331)Ratio, Proportions, and Similar Figures

Pg. 311-316

Chapter 7 (pg. 335-395)Fractions and Percents

THIRD SIX WEEKS11 [8.F.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.1

(1Function notation is not required in Grade 8.)

Students:Given input/output relations between two variables in graphical form, verbal description, set of ordered pairs, or an algebraic model,

Distinguish between those that are functions and non-functions.

Chapter 8 (pg. 397-475)Linear Functions and Graphing

Pg. 399-404

13 [8.F.3] Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. Example: The function A = s2 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.3] Interpret the equation y = mx + b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. Example: The function A = s2 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.

14 [8.F.4] Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a 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.

Students:Given representations of functions in non-equation form,

Interpret the properties of the relationship from the representation and use the interpretation to represent the

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EIGHTH GRADE

function in algebraic form, Communicate the

relationships among the representations (tables, graphs, and equations) including the rate of change and initial value.

15 [8.F.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.

Students:Given graphical representations of functions,

Use mathematical reasoning to analyze the graphs and describe the functional relationships between the quantities.Given verbal descriptions of functions,

Use mathematical reasoning and understandings of functions to sketch graphs that exhibit the features from the descriptions.

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Example: Tides Battery Charging

12 [8.F.2] Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). 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.

Students: Given two functions in a contextual situation that are represented in different ways (algebraically, graphically, numerically in tables, or by verbal descriptions),

Use logical reasoning and mathematical vocabulary to interpret the context and compare and contrast the properties of the functions,

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EIGHTH GRADE

(e.g., rate of change or slope).

8 [8.EE.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 equationy = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Students:

Create two different slope triangles (the triangle formed by the segment defined by the two points, the vertical segment from the first point to the horizontal line through the second, and the horizontal line segment from this point to the second point) for the same line, conjecture about the ratio of the vertical change to the horizontal change when such triangles are created, and justify this conjecture through the relationship of proportional sides in similar triangles,

Justify the relationship that all slope triangles formed on the same line are similar in order to derive the equations y = mx for a line going through a point (x,y) and the point (0,0), and y = mx + b for a line through (x, y) and the point (0,b), having y-intercept b.

Pg. 439-444

10 [8.EE.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

Students:Given two linear equations in graphical or algebraic form,

Produce the coordinates of the point of intersection of the two


Example: Kimi and Jordan Fixing the Furnace

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EIGHTH GRADE

estimate solutions by graphing the equations. Solve simple cases by inspection. Example: 3x + 2y= 5 and 3x + 2y = 6 have no solution because 3x + 2ycannot simultaneously be 5 and 6.

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

lines and explain the relationship of this point to the two equations when taken simultaneously.

Given a real world or mathematical situation involving two linear relationships,

Model the situation with linear equations, find the intersection point of the two lines, and interpret this point in terms of the original context.

FOURTH SIX WEEKS

3 [8.EE.1] Know and apply the properties of integer exponents to generate equivalent numerical expressions. Example: 32 x 3-5 = 3-3 =1/3

3 = 1/27.

Students:Given exponential expressions with integer exponents,

Produce equivalent expressions that are useful for different mathematical situations,

Justify, through application, the equivalence of exponential expressions using properties of exponents.

Chapter 9 (pg. 477-549)Powers and Nonlinear functions

Pg. 481-485

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RVW 7th Grade Standards Pg. 486-4903 [8.EE.1] Know and apply the properties of integer exponents to generate equivalent

numerical expressions. Example: 32 x 3-5 = 3-3 =1/3

3 = 1/27.

Students:Given exponential expressions with integer exponents,

Produce equivalent expressions that are useful for different mathematical situations,

Justify, through application, the equivalence of exponential expressions using properties of exponents.

Pg. 495-505

5 [8.EE.3] Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. Example: Estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger.

Students:Given real-world or mathematical contexts,

Estimate very small or very large quantities from the contexts as a single digit times a whole-number power of 10.

Given two very small or very large related quantities in the form of a single digit times a whole-number power of 10,

Determine the relative size of each number and approximate how many times as much one is than the other using power of ten representations.

Pg. 507-514

Chapter 10 (pg. 551-613)

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EIGHTH GRADE

Real numbers and Right Triangles6 [8.EE.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.

Students:

Interpret scientific notation that has been generated by technology.

Given any context where scientific notation is present including situations where both scientific and decimal notation are present,

Add, subtract, multiply, and divide these numbers expressing numerical answers with a degree of precision appropriate for the problem context (including choice of units) and explain the meaningfulness of the results related to the original context.

7 [8.EE.5] Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. Example: Compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

Students: Given real-world or mathematical contexts involving proportional relationships,

Graph the relationships from the contexts and use mathematical language to explain the connection between the slope of the line and the unit rate for the proportion.

Given contextual situation involving two different proportional relationships

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EIGHTH GRADE

represented in different ways, (e.g., one graph and one table),

Use the common concept of unit rate to make comparisons between the two different proportional relationships.

1 [8.NS.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.

Students:Given a variety of numbers,

Categorize the numbers as rational and irrational and defend the placement.

Given a rational number in fraction form,

Provide the decimal representation showing the repeating nature of the decimal expansion.

Given a repeating decimal expansion,

Produce the rational representation in the form a/b.

Pg. 555-570

2 [8.NS.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). 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.

Students:

Place irrational numbers on a number line by using known relationships about the number

Pg. 555-570

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EIGHTH GRADE

to approximate the size of an irrational number by manipulating (dividing, multiplying, squaring) numbers until the desired approximation is determined, strategically using technology when appropriate.

4 [8.EE.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.

Students: When presented with an equation of the form x2= p,

Translate this to the form x = plus or minus square root p and evaluate the expression when pis a perfect square.

When presented an equation in the form x3 = p,

Translate this into the form X = cube root p and evaluate the expression when pis a perfect cube,

Critique why the following (or other proof) means √2 must be irrational: If the square root of 2 is rational it may be written as square root 2 = p/q. This means that 2 = p2/q2and therefore 2q2 = p. Since p2 has as its prime factorization two sets of factors of p, it has an even number of factors. The same is true of q2. Therefore, 2q2 has an odd number of prime factors. It is impossible for an even number of prime factors to equal

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EIGHTH GRADE

an odd number of prime factors. Therefore, square root 2 cannot equal p/q and cannot be rational.

20 [8.G.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. 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 why this is so.

Students:Use knowledge of straight angles and mathematical reasoning to,

Create informal arguments concerning: facts about the angle sum and exterior angle of triangles, facts about the angles created when parallel lines are cut by a transversal, and angle-angle criterion for similarity of triangles.

Pg. 572-600

22 [8.G.7] Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Students:Given real-world and mathematical problems in two and three dimensions,

Apply the Pythagorean Theorem in order to solve problems and justify solutions and solution paths for finding side lengths in right triangles within the problem contexts.

21 [8.G.6] Explain a proof of the Pythagorean Theorem and its converse. Students:Given a proof of the Pythagorean Theorem,

Use mathematical reasoning and vocabulary to verbally explain the theorem and its converse.

Pg. 584

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EIGHTH GRADE

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

Students:Given real-world and mathematical problems that can be represented on a coordinate plane,

Apply the Pythagorean Theorem in order to solve problems and justify solutions and solution paths for finding side lengths (distances between points) in right triangles within the problem contexts.


Example: Finding isosceles triangles

FIFTH SIX WEEKS

20 [8.G.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. 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 why this is so.

Students:Use knowledge of straight angles and mathematical reasoning to,

Create informal arguments concerning: facts about the angle sum and exterior angle of triangles, facts about the angles created when parallel lines are cut by a transversal, and angle-angle criterion for similarity of triangles.

Chapter 11 (Pg. 615-701)Distance and angle

Pg. 619-625

17 [8.G.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.

Students:Given a variety of 2-D shapes,

Identify congruent shapes, Prove the congruence of two

shapes by modeling the sequence of translations,

Pg. 630-638

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EIGHTH GRADE

rotations and reflections, necessary to map one object to the other.

16 [8.G.1] Verify experimentally the properties of rotations, reflections, and translations:

a. Lines are taken to lines, and line segments are taken 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.

Students:Given geometric constructions, (e.g., lines, line segments, angles, parallel lines) and possible rotations, reflections, and translations,

Use logical reasoning to conjecture about the effects of rotations, reflections, and translations on the shapes,

Test conjectures using a variety of models, (e.g., physical models, replications on transparency sheets, or replications on geometry software),

Use the results of model manipulation to generalize properties of rotations, reflections, and translations.

Pg. 639-644

Also include pg. 311-316 from Ch. 6

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

Students:Given a variety of sequences of dilations, translations, rotations, and reflections,

Use a coordinate plane to model and describe the effects of the transformational geometry sequences on given shapes and the corresponding coordinates,

Compare the properties of the original figure to the newly created figures to determine

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EIGHTH GRADE

similarity and congruence.

19 [8.G.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.

Students:Given a variety of 2-D shapes,

Identify similar shapes, Prove the similarity of two

shapes by modeling the sequence of rotations, reflections, translations, and dilations necessary to map one object to the other.

RVW 7th Grade Geometry Standards Pg. 646-68316 [8.G.1] Verify experimentally the properties of rotations, reflections, and

translations:

a. Lines are taken to lines, and line segments are taken 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.

Students:Given geometric constructions, (e.g., lines, line segments, angles, parallel lines) and possible rotations, reflections, and translations,

Use logical reasoning to conjecture about the effects of rotations, reflections, and translations on the shapes,

Test conjectures using a variety of models, (e.g., physical models, replications on transparency sheets, or replications on geometry software),

Use the results of model manipulation to generalize properties of rotations, reflections, and translations.

Pg. 103-108Pages 639-644

SIXTH SIX WEEKS

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EIGHTH GRADE

RVW 7th Grade Standards Chapter 12 (pg. 703-769)Surface Area and VolumePg. 706-723

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

Students:Given real-world and mathematical problems involving volumes of cones, cylinders, and spheres,

Choose and apply appropriate formulas for finding volume,

Use mathematical language to communicate the relationship between the formula chosen and the problem context.

Pg. 725-730

RVW 7th Grade Standards Pg. 732-749

25 [8.SP.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.

Students:Given sets of bivariate measurement data or contextual situations in which bivariate measurement data must be collected,

Construct and interpret scatter plots,

Describe visual patterns observed, (e.g., clustering, outliers, positive or negative association, linear, and non-linear association).

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EIGHTH GRADE

26 [8.SP.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.

Reference pages 454-455Line of best fit in text book

27 [8.SP.3] Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. 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.

Students:Given a contextual or mathematical situation involving bivariate measurement data,

Represent the situation graphically and algebraically, describe the relationship between the two models, and interpret the slope and/or the intercept of the line in order to find answers to questions.

Statistics and Probability

Illustrative MathematicsIllustrativematematics.com

Examples: Airports Favorite Subject

28 [8.SP.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. 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?

Students:Given a contextual or mathematical situation involving bivariate categorical data,

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.

ADDITONAL RESOURCES Master resources that

accompany the Glencoe Textbook are a good place for

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EIGHTH GRADE

intervention work Chapter resource materials

also provide word problem examples from which to draw

Illustrative Math Ed Helper Worksheetswork.com Mathisfun.com www.coolmath.com/

algebra/Algebra1/ www.illustrativematics.org/

standards/k8 http://play.ccssgames.com/

faq-page mangahigh.com puzzmath.com TI-79 airsedu.org performanceseries.org NCTM illuminations Thinking blocks Dan Meyer 3 Act Math Tasks IXL (30 day free trial) Buzzmath opusmath.com khanacademy.com studyisland.com

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http://www.illustrativmatiematics.org/standards/k8

http://www.illustrativmatiematics.org/standards/k8

http://www.coolmath.com/algebra/Algebra1/

http://www.coolmath.com/algebra/Algebra1/

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images.pcmac.orgimages.pcmac.org/Uploads/Fayette/Fayette/Divisions... · Web viewCCRS QUALITY CORE CONTENT STANDARDS EVIDENCE OF STUDENT ATTAINMENT RESOURCES FIRST SIX WEEKS RVW 7th