Sevier County School System Math Correlations/Pacing Guide Grade 8

Eighth Grade

Sevier County School System

TNReady Blueprint

Math Correlations/Pacing Guide 2016-2017

This pacing guide was designed to correlate with the TNReady Blueprint Assessment.

The following pages are a recommended pacing guide for mathematics. This pacing guide is designed to assist the teacher in planning for the entire school year and to complete the necessary Tennessee State Standards required for eighth grade. All topics and lessons are listed in an order that is conducive to completing necessary skills prior to testing for eighth grade.

The last day of the 5th six weeks will be April 11, 2017. You need to be finished with instruction by this date in order to have time for TNReady review. There are six total units in the 8th Go Math series, each unit is made up of roughly 3-5 modules.

●Curriculum standards drive the instruction, not the textbook. In the pacing guide, you will find the standards are not taught in consecutive order. The textbook is a resource to assist you in meeting the needs of your students, but may not correlate with our current standards or go into depth in the coverage of the content as it should to adequately prepare students for the rigor associated with the new tests. This guide will ensure the standards are taught prior to the TNReady assessment.

●Please use the resources listed to supplement the textbook.

●With the changes with TN Ready Assessment and the item types, incorporating math tasks will be critical in your instruction.

Livebinder also has many resources for tasks.

(Access key: seviermath)

●The orange highlighted TN State Standard is the fluency standard. Whenever the word fluently appears in the content standard, the word means quickly and accurately. To be fluent is to flow: Fluent isn’t halting, stumbling, or reversing oneself. The key components of fluency are efficiency, understanding, and flexibility. Fluency in this sense is not something that happens all at once in a single grade but requires attention to students understanding along the way. It is important to ensure that sufficient practice and extra support are provided at each grade to allow all students to meet the standards that call explicitly for fluency. It is important to provide the conceptual building blocks that develop understanding in tandem with skill along the way to fluency.

Eighth grade fluency expectations:

8.EE.7- Solve one-variable linear equations, including cases with infinitely many solutions or no solutions.

8.G.9-Solve problems involving volumes of cones, cylinders, and spheres together with previous geometry work, proportional reasoning and multi-step problem solving in grade 7.

These standards will need to be frequently revisited throughout the school year using tasks and additional resources.

●The Standards for Mathematical Practice should be taught simultaneously with the Common Core State Standards. Students should be familiar with the technical terminology used. Please go to key: seviermath) for math practice posters.

●It is imperative to incorporate Accountable Talk and Number Talks into weekly lesson planning and student activities. For more information on Number Talks, please research Number Talks by Marilyn Burns via website access to downloadable content at : In order to extend number talks practice, refer to Extending Number Talks.

●Math Journal Tasks can be found at (Access key: seviermath). These are suggested tasks that match the Common Core Standards. For a complete listing of math journal tasks, please refer to pages 9-14 of the Journal e-book.

Livebinder will have resources for tasks, standards, and strategies etc. Please visit as a resource.

The books listed in red are from the Kathryn Dillard training in June 2015. They are listed in Livebinder.

●Access key: seviermath

●Click here for the Tennessee ToolBox for 8th Math

Standards for Mathematical Practice

Math Practices / Explanations and Examples

Make sense of problems and persevere in solving them.

/ In grade 8, students solve real world problems through the application of algebraic and geometric concepts. Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may check their thinking by asking themselves, “What is the most efficient way to solve the problem?”, “Does this make sense?”, and “Can I solve the problem in a different way?”

Reason abstractly and quantitatively.

/ In grade 8, students represent a wide variety of real world contexts through the use of real numbers and variables in mathematical expressions, equations, and inequalities. They examine patterns in data and assess the degree of linearity of functions. Students contextualize to understand the meaning of the number or variable as related to the problem and decontextualize to manipulate symbolic representations by applying properties of operations.

Construct viable arguments and critique the reasoning of others.

/ In grade 8, students construct arguments using verbal or written explanations accompanied by expressions, equations, inequalities, models, and graphs, tables, and other data displays (i.e. box plots, dot plots, histograms, etc.). They further refine their mathematical communication skills through mathematical discussions in which they critically evaluate their own thinking and the thinking of other students. They pose questions like “How did you get that?”, “Why is that true?” “Does that always work?” They explain their thinking to others and respond to others’ thinking.

Model with mathematics.

/ In grade 8, students model problem situations symbolically, graphically, tabularly, and contextually. Students form expressions, equations, or inequalities from real world contexts and connect symbolic and graphical representations. Students solve systems of linear equations and compare properties of functions provided in different forms. Students use scatterplots to represent data and describe associations between variables. Students need many opportunities to connect and explain the connections between the different representations. They should be able to use all of these representations as appropriate to a problem context.

Use appropriate tools strategically.

/ Students consider available tools (including estimation and technology) when solving a mathematical problem and decide when certain tools might be helpful. For instance, students in grade 8 may translate a set of data given in tabular form to a graphical representation to compare it to another data set. Students might draw pictures, use applets, or write equations to show the relationships between the angles created by a transversal.

Attend to precision.

/ In grade 8, students continue to refine their mathematical communication skills by using clear and precise language in their discussions with others and in their own reasoning. Students use appropriate terminology when referring to the number system, functions, geometric figures, and data displays.

Look for and make use of structure.

/ Students routinely seek patterns or structures to model and solve problems. In grade 8, students apply properties to generate equivalent expressions and solve equations. Students examine patterns in tables and graphs to generate equations and describe relationships. Additionally, students experimentally verify the effects of transformations and describe them in terms of congruence and similarity.

Look for and express regularity in repeated reasoning.

/ In grade 8, students use repeated reasoning to understand algorithms and make generalizations about patterns. Students use iterative processes to determine more precise rational approximations for irrational numbers. They analyze patterns of repeating decimals to identify the corresponding fraction. During multiple opportunities to solve and model problems, they notice that the slope of a line and rate of change are the same value. Students flexibly make connections between covariance, rates, and representations showing the relationships between quantities.

TNReady Blueprint for 8th Grade Mathematics - 1st Six Weeks

Text / Tennessee
Standards / Math Practices / Tasks / Resources
1.1
RATIONAL AND IRRATIONAL NUMBERS
P. 7 / 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.
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 ).
8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = 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. / 2,6,7 / CPALMS: Who Is Being Irrational? In this task, students will be able to explain irrational numbers and how they differ from rational numbers.
CPALMS: Dimensions Needed Task. Students are asked to solve problems involving square roots and cube roots.
CPALMS: Estimating Square Roots Task. Students use the meaning of a square root to find a decimal approximation of a square root of a non-square integer. / CPALMS: Really! I'm Rational. In this lesson students will gain an understanding of how repeating decimals are converted into a ratio.
1.2
SETS OF REAL NUMBERS
P. 15 / 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. / 2,5,6,7
1.3
ORDERING REAL NUMBERS
P. 21 / 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 ). / 2,5,6,7
Ready to Go On?
(Module Quiz) / P. 27 in the student textbook
Module 1
Assessment Readiness / P. 28 in the student textbook
MODULE 1 QUIZ / FOUND IN THE ASSESSMENT RESOURCES BOOKLET
2.1
INTEGER EXPONENTS
P. 33 / 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. / 2,5,6,7 / CPALMS: Equivalent Powers Task. Students are given numerical expressions and asked to use properties of integer exponents to find equivalent expressions. / Why U (video explaining how to raise products and quotients by powers)
Book: One Grain of Rice: A Mathematical Folktale
Demi (author)
2.2
SCIENTIFIC NOTATION WITH POSITIVE POWERS OF 10
P. 39 / 8.EE.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. / 1,2,5,6 / Estimating Length Task. After a whole-class introduction, students work on a collaborative task, matching measurements expressed in decimal and scientific notation. These are then matched to everyday objects. / Scientific Notation: PowerPoint
CPALMS: This tutorial on scientific notation shows the advantage of using scientific notation to representing very small numbers as well as very large numbers.
2.3
SCIENTIFIC NOTATION WITH NEGATIVE POWERS OF 10
P. 45 / 8.EE.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. / 2,5,6,7
2.4
OPERATIONS WITH SCIENTIFIC NOTATIONS
P. 51 / 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. / 2,5,6,7 / CPALMS: Pennies to Heaven Task / Practice: Writing in Scientific Notation and in Standard Form
Ready to Go On?
(Module Quiz) / P. 57 in the student textbook
Module 2
Assessment Readiness / P. 58 in the student textbook
MODULE 2 QUIZ / FOUND IN THE ASSESSMENT RESOURCES BOOKLET
UNIT 1 REVIEW / P.59-61 / PERFORMANCE TASK P.62

TNReady Blueprint for 8th Grade Mathematics - 2nd Six Weeks

Text / Tennessee
Standards / Math Practices / Tasks / Resources
3.1
REPRESENTING PROPORTIONAL RELATIONSHIPS
P .71 / 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 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.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. / 1-8 / Proportional Word Problems
CPALMS: Compare Slopes Task. Students compare the slopes of two proportional relationships. / Book:
Space Word Problems Starring Ratios and Proportions
Rebecca Wingard-Nelson (author)
Book:
George Shrinks
William Joyce (author)
3.2
RATE OF CHANGE AND SLOPE
P. 77 / 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. / 1-8 / CPALMS: Students are asked to derive the general equation of a line containing the origin, / Book:
A Fly On The Ceiling
Julie Glass and Richard Walz (authors)
3.3
INTERPRETING THE UNIT RATE AS SLOPE
P. 83 / 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. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.
8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). 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.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. / 1-8 / CPALMS: Bacterial Growth Graph Task. Create and interpret various types of graphed relationships
EduToolBox Task: T-shirt / Distance, Rate, and Time Practice Sheet
Ready to Go On?
(Module Quiz) / P. 89 in the student textbook
Module 3
Assessment Readiness / P. 90 in the student textbook
MODULE 3 QUIZ / FOUND IN THE ASSESSMENT RESOURCES BOOKLET
4.1
REPRESENTING LINEAR NON PROPORTIONAL RELATIONSHIPS
P. 95 / 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. / 1-8 / CPALMS: Competing Functions Task. Students are asked to recognize and compare the initial values of two functions represented in different ways.
4.2
DETERMINING SLOPE AND Y-INTERCEPT
P. 101 / 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 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.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. / 1-8 / CPALMS: Deriving Lines, Task 2. Students are asked to derive the general equation of a line with a y-intercept of (0, b). / Series of videos from Khan Academy discussing Slope-Intercept Form
4.3
GRAPHING LINEAR NON PROPORTIONAL RELATIONSHIPS USING SLOPE AND Y-INTERCEPT
P. 107 / 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.
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. / 1-8
4.4
PROPORTIONAL AND NON PROPORTIONAL SITUATIONS
P. 113 / 8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
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.
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. / 1-8 / Learner.Org (Two tasks where students simulate real-world situations to model direct and inverse variations. / "Math is Fun" webpage. Does a good job discussing Directly and Inversely proportional relationships
Khan Academy video: How to recognize the different functions
Ready to Go On?
(Module Quiz) / P. 121 in the student textbook
Module 4
Assessment Readiness / P. 122 in the student textbook
MODULE 4 QUIZ / FOUND IN THE ASSESSMENT RESOURCES BOOKLET
5.1
WRITING LINEAR EQUATIONS FROM SITUATIONS AND GRAPHS
P. 127 / 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. / 1-4, 6-8
5.2
WRITING LINEAR EQUATIONS FROM A TABLE
P. 133 / 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. / 1-4, 6-8
5.3
LINEAR RELATIONSHIPS AND BIVARIATE DATA
P. 139 / 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.
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.
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. / 1-4, 6-8
Ready to Go On?
(Module Quiz) / P. 147 in the student textbook
Module 5
Assessment Readiness / P. 148 in the student textbook
MODULE 5 QUIZ / FOUND IN THE ASSESSMENT RESOURCES BOOKLET
6.1
IDENTIFYING AND REPRESENTING FUNCTIONS
P. 153 / 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. (Function notation is not required in Grade 8.) / 1-8 / Illuminations: Printing Books Task. Students are challenged to select the most cost-effective option for printing a school district's new algebra textbooks. / Why U (6 min. video that discusses functions, domain, range, input, output, and function notation.)
Book:
Two of Everything
Lily Toy Hong (author)
6.2
DESCRIBING FUNCTIONS
P. 161 / 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. (Function notation is not required in Grade 8.)
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. / 1-4, 6-8
6.3
COMPARING FUNCTIONS
P. 167 / 8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
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.
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. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. / 1-3, 6-8 / EduToolBox Task: Workers and Earnings
6.4
ANALYZING GRAPHS
P. 173 / 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. / 1-3, 6-8 / EduToolBox Task: Flower Pot
Ready to Go On?
(Module Quiz) / P. 179 in the student textbook
Module 6
Assessment Readiness / P. 180 in the student textbook
MODULE 6 QUIZ / FOUND IN THE ASSESSMENT RESOURCES BOOKLET
UNIT 2 REVIEW / P.181 - 187 / PERFORMANCE TASK P.188

TNReady Blueprint for 8th Grade Mathematics - 3rd Six Weeks