8th Grade Mathematics Curriculum

Transcription

1 8th Grade Mathematics Curriculum Course Summary: In Grade 8, instructional time will focus on three critical areas: () formulating and reasoning about expressions and equations, including modeling and association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem. Scope and Sequence: Time Frame Unit 34 Days Number Sense, Expressions, and Equations 68 Days Functions and Linear Relationships 27 Days Transformations and Transversals 35 Days Exponential Functions, Pythagorean Theorem, and Volume

2 Curriculum Revision Tracking Changes made in April, 206: Unit : o Pacing was adjusted from 32 to 34 days o Sequence of Topics 6, 4, and 5 was changed. 2 Page

3 Unit : Number Sense, Expressions and Equations Subject: Mathematics Grade: 8th Grade Name of Unit: Number Sense, Expressions, and Equations Length of Unit: 34 days Overview of Unit: Students will understand that there are numbers which are not rational and approximate them by rational numbers. Students will also analyze and solve linear equations. Priority Standards for unit: MA.8.NS.A.: Explore the real number system. a. Know the differences between rational and irrational numbers. b. Understand that all rational numbers have a decimal expansion that terminates or repeats. c. Convert decimals which repeat into fractions and fractions into repeating decimals. d. Generate equivalent representations of rational numbers. Supporting Standards for unit: MA.8.NS.A.2: Estimate the value and compare the size of irrational numbers and approximate their locations on a number line. For example, by truncating the decimal expansion of 2, show that 2 is between and 2, then between.4 and.5, and explain how to continue on to get better approximations. MA.8.EEI.C.: Solve linear equations and inequalities in one variable. a. Create and identify linear equations with one solution, infinitely many solutions or no solutions. b. Solve linear equations and inequalities with rational number coefficients, including equations and inequalities whose solutions require expanding expressions using the distributive property and combining like terms. ISTE-EMPOWERED LEARNER : Students leverage technology to take an active role in choosing, achieving and demonstrating competency in their learning goals, informed by the learning sciences. ISTE-KNOWLEDGE COLLECTOR.3: Students critically curate a variety of resources using digital tools to construct knowledge, produce creative artifacts and make meaningful learning experiences for themselves and others. ISTE-INNOVATIVE DESIGNER.4: Students use a variety of technologies within a design process to identify and solve problems by creating new, useful or imaginative solutions. ISTE-COMPUTATIONAL THINKER.5: Students develop and employ strategies for understanding and solving problems in ways that leverage the power of technological methods to develop and test solutions. 3 Page

4 Standard MA.8.NS.A. MA.8.NS.A. MA.8.NS.A. MA.8.NS.A. Unwrapped Skills Unwrapped Concepts (Students (Students need to Bloom s Taxonomy need to know) be able to do) Levels differences between rational and irrational numbers. Know Remember all rational numbers have a decimal expansion that terminates Webb's DOK or repeats. Understand Understand 2 decimals which repeat into fractions and fractions into repeating decimals Convert Apply 2 equivalent representations of rational numbers Generate Create 2 Essential Questions:. In earlier courses you studied rational numbers. What other types of numbers are there? 2. In earlier courses you studied rational numbers. Why do you need them? 3. Why do you write equations? Enduring Understanding/Big Ideas:. There are rational and irrational numbers in the real number system. 2. Know the differences between them can help you understand if a fraction can be made from the number, or whether or not a decimal and be derived from a fraction or square roots. 3. Complex questions can be solved using the structure of an equation and the process of inverse operations to isolate variables. Unit Vocabulary: Academic Cross-Curricular Words Ratios Percents Content/Domain Specific Topic Irrational Numbers Perfect Square Real Number Repeating Decimal Square Root Terminating Decimal Resources for Vocabulary Development: Use quality tools (See Adult Learning Framework handbook) 4 Page

5 digits Topic : Rational & Irrational Numbers Standard Topic & Section Suggested # of Days Notes MA.8.NS.A..: Expressing Rational Numbers and Decimal Expansion MA.8.NS.A..2: Exploring Rational Numbers MA.8.NS.A. MA.8.NS.A.2.3: Approximating Rational Numbers.4: Comparing and Ordering Rational and Irrational Numbers MA.8.NS.A. MA.8.NS.A.2.5: Problem Solving Review Day.5 Review, Look Over and Test within a three day period Test.5 (suggested) 5 Page

6 digits Topic 2: Linear Equations in One Variable Standard Topic & Section Suggested # of Days Notes Add/Subtract/Multiply/Divide Integers 2 Supplement Algebra 2.5 and 2.6 as needed Intervention Clusters 0, and 2. Fractions Approx. 4 as needed Use Intervention Lessons, Journal Entries and Intervention HW assignments as needed Supplement Distributive Property Supplement Simplifying Expressions (Combining Like Terms) Supplement May need to create own practice Supplement May need to create own practice Intervention Cluster 25 Expressions and Equations Approx. 4 as needed Use Intervention Lessons, Journal Entries and Intervention HW assignments as needed MA.7.EEI.B. 2.: Solving Two-Step Equations Algebra MA.7.EEI.B. MA.7.EEI.B.2 2.2: Solving Equations with Variables on Both Sides 2.3: Solving Equations Using the Distributive Property Algebra Algebra REVIEW Solving Equations Quiz Solving Equations MA.7.EEI.B.2 2.4: Solutions - One, None, or Infinitely Many MA.7.EEI.B.2 2.5: Problem Solving Review Topic 2.5 Test Topic Page

7 Unit 2: Functions and Linear Relationships Subject: Mathematics Grade: 8th Grade Name of Unit: Functions and Linear Relationships Length of Unit: 68 Days Overview of Unit: Students will understand the concepts related to identifying, creating, manipulating and solving functions and systems of equations. Students will also understand the concepts of using and creating systems of categorical data. Priority Standards for unit: 8.EEI.B.: Graph proportional relationships. a. Interpret the unit rate as the slope of the graph. b. Compare two different proportional relationships. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. 8.EEI.B.2: Apply concepts of slope and y-intercept to graphs, equations and proportional relationships. a. Explain why the slope (m) is the same between any two distinct points on a non-vertical line in the Cartesian coordinate plane. b. 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.EEI.C.: Solve linear equations and inequalities in one variable. a. Create and identify linear equations with one solution, infinitely many solutions or no solutions. b. Solve linear equations and inequalities with rational number coefficients, including equations and inequalities whose solutions require expanding expressions using the distributive property and combining like terms. 8.EEI.C.2: Analyze and solve systems of linear equations. a. Graph systems of linear equations and recognize the intersection as the solution to the system. b. Explain why solution(s) to a system of two linear equations in two variables correspond to point(s) of intersection of the graphs. c. Explain why systems of linear equations can have one solution, no solution or infinitely many solutions. d. Solve systems of two linear equations. 8.F.A.3: Investigate the differences between linear and nonlinear functions. a. Interpret the equation y = mx + b as defining a linear function, whose parameters are the slope (m) and the y-intercept (b). b. Recognize that the graph of a linear function has a constant rate of change c. Give examples of nonlinear functions. 7 Page

8 Supporting Standards for unit: 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.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 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.DSP.A.: Construct and interpret scatter plots of bivariate measurement data to investigate patterns of association between two quantities. 8.DSP.A.2: Generate and use a trend line for bivariate data, and informally assess the fit of the line. 8.DSP.A.3: Interpret the parameters of a linear model of bivariate measurement data to solve problems. 8.DSP.A.4: Understand the patterns of association in bivariate categorical data displayed in a two-way table. a. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. b. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. 8.F.A.: Explore the concept of functions. (The use of function notation is not required.) a. Understand that a function assigns to each input exactly one output. b. Determine if a relation is a function. c. Graph a function. 8.F.A.2: Compare characteristics of two functions each represented in a different way. 8.F.B.: Use functions to model linear relationships between quantities. a. Explain the parameters of a linear function based on the context of a problem. b. Determine the parameters of a linear function. c. Determine the x-intercept of a linear function. 8.F.B.2: Describe the functional relationship between two quantities from a graph or a verbal description. ISTE-EMPOWERED LEARNER : Students leverage technology to take an active role in choosing, achieving and demonstrating competency in their learning goals, informed by the learning sciences. 8 Page

9 Standard Unwrapped Concepts (Students need to know) Unwrapped Skills (Students need to be able to do) Bloom s Taxonomy Levels Webb's DOK 8.EEI.B. Proportional relationships Graph Apply 2 8.EEI.B. Unit rate as the slope of the graph Interpret Understand 2 8.EEI.B. Two different proportional relationships Compare Analyze 2 Concepts of slope and y- intercept to graphs, equations Apply 8.EEI.B.2 and proportional relationships Apply 2 8.EEI.B.2 why the slope (m) is the same between any distinct points on a non-vertical line in the Cartesian coordinate plane. Explain Understand 3 8.EEI.B.2 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. Derive Create 2 8.EEI.C. Systems linear equations in and inequalities in one variable Solve Apply 2 8.EEI.C. linear equations with one solution, infinitely many solutions or no solution Create Create 3 8.EEI.C. linear equations with one solution, infinitely many solutions or no solution Identify Remember 8.EEI.C. linear equations and inequalities with rational number coefficients, including equations and inequalities whose solutions require expanding expressions using the distributive property and combining like terms Solve Apply 2 8.EEI.C.2 Systems of Linear Equations Analyze Analyze 2 8.EEI.C.2 Systems of Linear Equations Solve Apply 2 8.EEI.C.2 systems of linear equations and recognize the intersection as the solution to the system. Graph Apply 2 9 Page

10 8.EEI.C.2 why solution(s) to a system of two linear equations in two variables correspond to point(s) of intersection of the graphs Explain Understand 3 8.EEI.C.2 why systems of linear equations can have one solution, no solution or infinitely many solutions. Explain Understand 3 8.EEI.C.2 systems of two linear equations Solve Apply 2 8.F.A.3 the differences between linear and nonlinear functions. Investigate Understand 8.F.A.3 the equation y = mx + b as defining a linear function, whose parameters are the slope (m) and the y-intercept (b). Interpret Analyze 2 8.F.A.3 that the graph of a linear function has a constant rate of change Recognize Understand 8.F.A.3 examples of nonlinear functions. Give Understand 2 8.DSP.A. scatter plots of bivariate measurement data to investigate patterns of association between two quantities. Construct Apply 2 8.DSP.A. scatter plots of bivariate measurement data to investigate patterns of association between two quantities. Interpret Analyze 3 8.DSP.A.2 trend line for bivariate data, and informally assess the fit of the line. Generate Create 2 8.DSP.A.2 trend line for bivariate data, and informally assess the fit of the line. Use Understand 2 8.DSP.A.3 parameters of a linear model of bivariate measurement data to solve problems. Interpret Understand 2 8.DSP.A.4 patterns of association in bivariate categorical data displayed in a two-way table. Understand Understand 2 two-way table summarizing data on two categorical variables 8.DSP.A.4 collected from the same subjects. Construct Create 2 8.DSP.A.4 two-way table summarizing data Interpret Analyze 2 0 Page

11 on two categorical variables collected from the same subjects. 8.DSP.A.4 relative frequencies calculated for rows or columns to describe possible association between the two variables. Use Understand 2 8.F.A. the concept of functions Explore Evaluate 3 8.F.A. a function assigns to each input exactly one output Understand Understand Determine 8.F.A. if a relation is a function Understand 2 8.F.A. a function Graph Apply 2 8.F.A.2 characteristics of two functions each represented in a different way. Compare Analyze 3 8.F.B. functions to model linear relationships between quantities. Use Understand 3 8.F.B. the parameters of a linear function based on the context of a problem Explain Understand 3 8.F.B. the parameters of a linear function Determine Understand 2 8.F.B. the x-intercept of a linear function Determine Understand 3 8.F.B.2 the functional relationship between two quantities from a graph or a verbal description. Describe Evaluate 3 Essential Questions:. What is a function? How are functions used? Enduring Understanding/Big Ideas:. A function is a relationship between x and y, such that for every x input there is one and only one y output. Functions are used to describe and predict relationships between bivariate sets of data. Unit Vocabulary: Academic Cross-Curricular Words Scatter Plot Initial Values Content/Domain Specific Topic 7 Function Page

12 Trend Line Outlier Cluster Bivariate Data Independent Variable Dependent Variable Experiment Group Control Group Relationship Linear Function Non-Linear Function Interval Rate of Change Relation Vertical Line Test Topic 5 Linear Equation Slope Slope of a line y-intercept Proportional Relationship Rate of Change Topic 8 Linear Function Rule Initial Value Unit Rate Topic 4 Cluster Gap Outlier Scatter Plot Trend Line Positive or Negative Association Linear or Nonlinear Association Topic 6 Solution of a System of Linear Equations System of Linear Equations Topic 5 Bivariate Categorical Data Bivariate Data Categorical Data Measurement Data Two-way Frequency Table Two-way Relative Frequency Table Resources for Vocabulary Development: Use quality tools (See Adult Learning Framework handbook) 2 Page

13 digits Topic 7: Defining & Comparing Functions Standard Topic & Section Suggested # of Days Notes 8.F.A. 7.: Recognizing a Function 8.F.A. 7.2: Representing a Function 8.F.A.2 7.3: Linear Functions 8.F.A.2 7.4: Nonlinear Functions 8.F.A.3 7.5: Increasing and Decreasing Intervals 8.F.A. 7.6: Sketching a Function Graph 8.F.A. 8.F.A.2 8.F.A.3 7.6: Problem Solving Review.5 Test.5 3 Page

14 digits Topic 5: Proportional Relationships, Lines, & Linear Equations digits Topic 8: Linear Functions Standard Topic & Section Suggested # of Days Notes MA.8.EEI.B. 8.F.A.2 5.: Graphing Proportional Relationships 8.: Defining a Linear Function Rule Algebra as needed Algebra 4.5 as needed MA.8.EEI.B.2 5.2: Linear Equations y = mx Algebra as needed 8.F.A.2 8.2: Rate of Change Algebra 4.4 as needed MA.8.EEI.B. 5.3: Slope of a Line Algebra 4.4 as needed MA.8.EEI.B. 5.4: Unit Rates and Slope Algebra 4.4 as needed 8.F.A.2 8.F.A.3 8.3: Initial Value Algebra 4.5 as needed MA.8.EEI.B.2 5.5: Y-intercept of a Line Algebra 4.5 as needed MA.8.EEI.B.2 5.6: Linear Equations: y = mx + b Algebra as needed MA.8.EEI.C. 8.4: Comparing Two Linear Functions MA.8.EEI.C. 5.7: Problem Solving 8.F.A.2 8.F.A.3 8.6: Problem Solving Topic 8 Review 2 Test Topic Page

15 digits Topic 6: Systems of Two Linear Equations Standard Topic & Section Suggested # of Days Notes 8.EEI.C.2 8.EEI.C.2 8.EEI.C.2 8.EEI.C.2 8.EEI.C.2 8.EEI.C.2 6.: What is a System of Linear Equations in Two Variables 6.2: Estimating Solutions of Linear Systems by Inspection 6.3: Solving Systems of Linear Equations by Graphing 6.4: Solving Systems of Linear Equations using Substitutions 6.5: Solving Systems of Linear Equations using Elimination (Addition) 6.6: Solving Systems of Linear Equations using Elimination (Subtraction) 2 2 Algebra 7.5 as needed 2 Algebra 7. as needed 2 Algebra 7.2 as needed 2 Algebra 7.3 as needed 2 Algebra 7.3 as needed 8.EEI.C.2 Problem Solving 2 Review 2 Test 2 5 Page

16 digits Topic 4: Scatter Plots Standard Topic & Section Suggested # of Days Notes 8.DSP.A. 4. Interpreting Scatter Plots 8.DSP.A. 4.2 Constructing Scatter Plots 8.DSP.A. 8.DSP.A. 8.DSP.A.2 8.DSP.A Investigating Patterns: Clustering and Outliers 4.4 Investigating Patterns: Association 4.5 Linear Models- Fitting a Straight Lines 4.6 Using the Equation of a Linear Model 8.DSP.A Problem Solving Review.5 Topic 4 TEST.5 6 Page

17 digits Topic 5: Analyzing Categorical Data *This unit is considered modular, and may be moved to a different time of the year to accommodate time and testing constraints. Standard Topic & Section Suggested # of Days Notes MA.8.DSP.A.4 5.: Bivariate Categorical Data MA.8.DSP.A.4 MA.8.DSP.A.4 MA.8.DSP.A.4 MA.8.DSP.A.4 5.2: Constructing Two-way Frequency Tables 5.3: Constructing Two-way Relative Frequency Tables 5.4: Constructing Two-way Relative Frequency Tables 5.5: Interpreting Two-way Relative Frequency Tables MA.8.DSP.A.4 5.6: Choosing a Measure of Frequency MA.8.DSP.A.3 MA.8.DSP.A.4 5.7: Problem Solving Review.5 Test.5 7 Page

18 Unit 3: Transformations and Transversals Subject: Mathematics Grade: 8th Grade Name of Unit: Transformations and Transversals Length of Unit: 27 Days Overview of Unit: Students will understand the concepts of identifying similar figures and translating those figures on the coordinate plane. Priority Standards for unit: MA.8.GM.A.: Verify experimentally the congruence properties of rigid transformations. a. Verify that angle measure, betweeness, collinearity and distance are preserved under rigid transformations. b. Investigate if orientation is preserved under rigid transformations. MA.8.GM.A.2: Understand that two-dimensional figures are congruent if a series of rigid transformations can be performed to map the pre-image to the image. a. Describe a possible sequence of rigid transformations between two congruent figures. MA.8.GM.A.3: Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. MA.8.GM.A.4: Understand that two-dimensional figures are similar if a series of transformations (rotations, reflections, translations and dilations) can be performed to map the pre-image to the image. a. Describe a possible sequence of transformations between two similar figures. MA.8.GM.A.5: Explore angle relationships and establish informal arguments. a. Derive the sum of the interior angles of a triangle. b. Explore the relationship between the interior and exterior angles of a triangle. c. Construct and explore the angles created when parallel lines are cut by a transversal. d. Use the properties of similar figures to solve problems. Supporting Standards for unit: MA.8.GM.A. Verify experimentally the congruence properties of rigid transformations. a. Verify that angle measure, betweeness, collinearity and distance are preserved under rigid transformations. b. Investigate if orientation is preserved under rigid transformations. MA.8.GM.A.2 Understand that two-dimensional figures are congruent if a series of rigid transformations can be performed to map the pre-image to the image. MA.8.GM.A.4 Understand that two-dimensional figures are similar if a series of transformations (rotations, reflections, translations and dilations) can be performed to map the pre-image to the image. 8 Page

19 ISTE-EMPOWERED LEARNER : Students leverage technology to take an active role in choosing, achieving and demonstrating competency in their learning goals, informed by the learning sciences. ISTE-KNOWLEDGE COLLECTOR.3: Students critically curate a variety of resources using digital tools to construct knowledge, produce creative artifacts and make meaningful learning experiences for themselves and others. ISTE-COMPUTATIONAL THINKER.5: Students develop and employ strategies for understanding and solving problems in ways that leverage the power of technological methods to develop and test solutions. Standards MA.8.GM.A.4 Unwrapped Concepts (Students need to know) two-dimensional figures are similar if a series of transformations (rotations, reflections, translations and dilations) can be performed to map the Unwrapped Skills (Students need to be able to do) Bloom s Taxonomy Levels Webb's DOK pre-image to the image. Understand Understand 2 possible sequence of transformations between two similar figures. Describe Understand 2 MA.8.GM.A.4 angle relationships and establish informal MA.8.GM.A.5 arguments. Explore Understand 3 sum of the interior MA.8.GM.A.5 angles of a triangle. Derive Create 2 relationship between the interior and exterior MA.8.GM.A.5 angles of a triangle Explore Understand 3 the angles created when parallel lines are cut by a MA.8.GM.A.5 transversal Explore Understand 3 properties of similar figures to solve MA.8.GM.A.5 problems. Use Analyze 2 9 Page

20 Essential Questions:. What does it mean for two figures to be identical? 2. How do geometric properties and logical reasoning allow you to form arguments and make conclusions about relationships in geometry? Enduring Understanding/Big Ideas:. Two figures are identical if you can map one to the other by a sequence of rigid motions, such as translations, reflections, and rotations. 2. You can use what you know about transversals, parallel lines, and Pythagorean Theorem to identify, compare, or contrast geometric shapes. Unit Vocabulary: Academic Cross-Curricular Words Flip Turn Slide Enlarge Shrink Increase Decrease Similar Corresponding Interior Exterior Content/Domain Specific Topic 9 Congruent Figures Image Reflection Rigid Motion Rotation Transformation Translation Topic 0 Dilation Enlargement Reduction Scale Factor Similar Figures Topic Alternate Interior Angles Corresponding Angles Deductive reasoning Exterior angle of a triangle Transversal Resources for Vocabulary Development: Use quality tools (See Adult Learning Framework handbook) 20 Page

21 digits Topic 9: Congruence Standard Topic & Section Suggested # of Days Notes MA.8.GM.A. 9.: Translations MA.8.GM.A. 9.2: Reflections MA.8.GM.A. 9.3: Rotations MA.8.GM.A Review QUIZ MA.8.GM.A.2 9.4: Congruent Figures MA.8.GM.A. MA.8.GM.A.2 9.5: Problem Solving Review 2 Topic 9 TEST 2 Page

22 digits Topic 0: Similarity Standard Topic & Section Suggested # of Days Notes MA.8.GM.A.3 0.: Dilations MA.8.GM.A.4 0.2: Similar Figures MA.8.GM.A.4 0.3: Relating Similar Triangles and Slope MA.8.GM.A.3 MA.8.GM.A.4 0.4: Problem Solving 22 Page

23 digits Topic : Reasoning in Geometry Standard Topic & Section Suggested # of Days Notes MA.8.GM.A.5 MA.8.GM.A.5 MA.8.GM.A.5 MA.8.GM.A.5 MA.8.GM.A.5.: Angles, Lines and Transversals.2: Reasoning and Parallel Lines.3: Interior Angles of Triangles.4: Exterior Angles of Triangles.5: Angle to Angle Triangle Similarity MA.8.GM.A.5.6 Problem Solving Review 2 Test Topic 23 Page

24 Unit 4: Exponential Functions, Pythagorean Theorem and Volume Subject: Mathematics Grade: 8th Grade Name of Unit: Exponential Functions, Pythagorean Theorem and Volume Length of Unit: 35 Days Overview of Unit: Students will work with radicals and integer exponents and understand the concepts of geometric reasoning as it relates to the Pythagorean Theorem. Students will also solve real-world and mathematical problems involving volume. Priority Standards for unit: MA.8.GM.B. Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. MA.8.GM.C. Solve problems involving volume of cones, pyramids and spheres. MA.8.EEI.A. Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, = 3 3 = /33 = /27. Supporting Standards for unit: MA.8.GM.B. Explain a proof of the Pythagorean Theorem and its converse. MA.8.GM.B.3 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. MA.8.GM.C. Solve problems involving surface area and volume. a. Understand the concept of surface area and find surface area of pyramids. b. Understand the concepts of volume and find the volume of pyramids, cones and spheres. MA.8.EEI.A.2 Solve equations of the form x 2 = p and x 3 = p, where p is a positive rational number. MA.8.EEI.A.2 Evaluate square roots of perfect squares less than or equal to 625 and cube roots of perfect cubes less than or equal to 000. MA.8.EEI.A.2 Recognize that square roots of non-perfect squares are irrational. MA.8.EEI.A.4: Use scientific notation to solve problems. a. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. b. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. ISTE-EMPOWERED LEARNER : Students leverage technology to take an active role in choosing, achieving and demonstrating competency in their learning goals, informed by the learning sciences. 24 Page

25 ISTE-KNOWLEDGE COLLECTOR.3: Students critically curate a variety of resources using digital tools to construct knowledge, produce creative artifacts and make meaningful learning experiences for themselves and others. ISTE-INNOVATIVE DESIGNER.4: Students use a variety of technologies within a design process to identify and solve problems by creating new, useful or imaginative solutions. ISTE-COMPUTATIONAL THINKER.5: Students develop and employ strategies for understanding and solving problems in ways that leverage the power of technological methods to develop and test solutions. Standards Unwrapped Concepts (Students need to know) Unwrapped Skills (Students need to be able to do) Bloom s Taxonomy Levels Webb's DOK MA.8.EEI.A. the properties of integer exponents to generate equivalent numerical expressions Know Remember MA.8.EEI.A. the properties of integer exponents to generate equivalent numerical expressions Apply Apply 2 A.8.GM.B. models to demonstrate a proof of the Pythagorean Theorem and its converse Use Apply 2 MA.8.GM.B.2 the Pythagorean Theorem to determine unknown side lengths in right triangles in problems in two- and threedimensional contexts. Use Apply 2 A.8.GM.C. problems involving surface area and volume. Solve Apply 2 scientific notation and choose units of appropriate size for measurements of very large or 2 MA.8.EEI.A.4 very small quantities. Use Apply MA.8.EEI.A.4 scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Use Apply 2 25 Page

26 Essential Questions:. How do geometric properties and logical reasoning allow you to form arguments and make conclusions about relationships in geometry? 2. Measurements frequently involve very large or very small numbers. How can you make such measurements easy to use and compare? 3. How can you tell whether a linear equation models a proportional relationship? 4. What methods can you use to solve pairs of simultaneous linear equations in two variables? Enduring Understanding/Big Ideas:. You can use what you know about Pythagorean Theorem to identify, compare, or contrast geometric shapes. 2. The process of scientific notation can be used to work with and express extreme values. 3. Understanding the forms of linear equations such as y = mx + b can give you the ability to determine the type of line presented in equation form. 4. You may use graphing, substitution or elimination to determine if a solution exists and then to find the solution to set of equations. Unit Vocabulary: Academic Cross-Curricular Words Content/Domain Specific Topic 3 Cube Root Negative Exponent Property Perfect Cube Zero Exponent Property Topic 4 Scientific Notation Topic 2 Proof Theorem Hypotenuse Leg of a Right Triangle Pythagorean Theorem Converse of Pythagorean Theorem Topic 3 Base Cone Cylinder Height 26 Page

27 Lateral Area Lateral Surface Radius Right Cone Right Cylinder Slant Height Sphere Surface Area Vertex Volume Resources for Vocabulary Development: Use quality tools (See Adult Learning Framework handbook) 27 Page

28 digits Topic 3: Integer Exponents Standard Topic & Section Suggested # of Days Notes MA.8.EEI.A.2 MA.8.EEI.A. 3.: Perfect Squares, Square Roots, and Equations of the form x 2 = p 3.2: Perfect Cubes, Cube Roots, and Equations of the form x 3 = p MA.8.EEI.A. 3.3: Exponents and Multiplication MA.8.EEI.A. 3.4: Exponents and Division MA.8.EEI.A. 3.5: Zero and Negative Exponents MA.8.EEI.A. 3.6: Comparing Expressions with Exponents MA.8.EEI.A. 3.7: Problem Solving Review Topic 3.5 TEST Topic Page

29 digits Topic 2: Using the Pythagorean Theorem Standard Topic & Section Suggested # of Days Notes MA.8.GM.B. 2.: Reasoning and Proof MA.8.GM.B. MA.8.GM.B.2 2.2: Pythagorean Theorem MA.8.GM.B.2 MA.8.EEI.A. 2.3: Finding Unknown Leg Lengths MA.8.GM.B. MA.8.GM.B.3 2.4: Converse of Pythagorean Theorem 2.5: Distance in the Coordinate Plane MA.8.GM.B. MA.8.GM.B.2 2.6: Problem Solving 2 Review.5 Topic 2 TEST.5 29 Page

30 digits Topic 3: Surface Area and Volume Standard Topic & Section Suggested # of Days Notes A.8.GM.C. 3.2: Volume of Cylinders A.8.GM.C. 3.4: Volume of Cones A.8.GM.C. 3.6: Volume of Spheres A.8.GM.C. 3.7: Problem Solving Review.5 Topic 3 QUIZ.5 30 Page

31 digits Topic 4: Scientific Notation Standard Topic & Section Suggested # of Days Notes MA.8.EEI.A.3 4. Exploring Scientific Notation MA.8.EEI.A.3 MA.8.EEI.A.3 MA.8.EEI.A Using Scientific Notation to Describe Very Large Quantities 4.3 Using Scientific Notation to Describe Very Small Quantities 4.4 Operating with Numbers Expressed in Scientific Notation MA.8.EEI.A.3 MA.8.EEI.A Problem Solving Review.5 Topic 4 TEST.5 3 Page

32 Unit of Study Terminology Appendices: All Appendices and supporting material can be found in this course s shell course in the District s Learning Management System. Assessment Leveling Guide: A tool to use when writing assessments in order to maintain the appropriate level of rigor that matches the standard. Big Ideas/Enduring Understandings: Foundational understandings teachers want students to be able to discover and state in their own words by the end of the unit of study. These are answers to the essential questions. Engaging Experience: Each topic is broken into a list of engaging experiences for students. These experiences are aligned to priority and supporting standards, thus stating what students should be able to do. An example of an engaging experience is provided in the description, but a teacher has the autonomy to substitute one of their own that aligns to the level of rigor stated in the standards. Engaging Scenario: This is a culminating activity in which students are given a role, situation, challenge, audience, and a product or performance is specified. Each unit contains an example of an engaging scenario, but a teacher has the ability to substitute with the same intent in mind. Essential Questions: Engaging, open-ended questions that teachers can use to engage students in the learning. Priority Standards: What every student should know and be able to do. These were chosen because of their necessity for success in the next course, the state assessment, and life. Supporting Standards: Additional standards that support the learning within the unit. Topic: These are the main teaching points for the unit. Units can have anywhere from one topic to many, depending on the depth of the unit. Unit of Study: Series of learning experiences/related assessments based on designated priority standards and related supporting standards. Unit Vocabulary: Words students will encounter within the unit that are essential to understanding. Academic Cross-Curricular words (also called Tier 2 words) are those that can be found in multiple content areas, not just this one. Content/Domain Specific vocabulary words are those found specifically within the content. Symbols: This symbol depicts an experience that can be used to assess a student s 2st Century Skills using the rubric provided by the district. This symbol depicts an experience that integrates professional skills, the development of professional communication, and/or the use of professional mentorships in authentic classroom learning activities. 32 Page