Math 8 Honors Common Core Mathematics
Prince George’s County Public Schools
2014 - 2015
Course Code: Prerequisites: Successful completion of Math 7 Common Core or Math 7 Common Core Honors This course continues the trajectory towards a more formalized understanding of mathematics that occurs at the high school level that was begun in Math 6 and 7 Common Core. Students extend their understanding of rational numbers to develop an understanding of irrational numbers; connect ratio and proportional reasoning to lines and linear functions; define, evaluate, compare, and model with functions; build understanding of congruence and similarity; understand and apply the Pythagorean Theorem; and extend their understanding of statistics and probability by investigating patterns of association in bivariate data. The course is extended with learning objectives aligned to High School Mathematics Common Core Standards. In all mathematics courses, the Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.
INTRODUCTION:
Typically in a Math class, to understand the majority of the information it is necessary to continuously practice your skills. This requires a tremendous amount of effort on the student’s part. Each student should expect to dedicate 2 - 3 hours of studying for every hour in class. Some hints for success in a Math class include: attending class daily, asking questions in class, and thoroughly completing all homework problems with detailed solutions as soon as possible after each class session.
INSTRUCTOR INFORMATION: Name: E-Mail: Planning: Phone:
CLASS INFORMATION:
COURSE NUMBER: CLASS MEETS: ROOM: TEXT: Big Ideas (Blue), Holt McDougal
CALCULATORS:
For Math 8, a scientific calculator is required. The use of graphing calculators is not allowed.
GRADING: Middle School Mathematics
Overview: The goal of grading and reporting is to provide the students with feedback that reflects their progress towards the mastery of the content standards found in the Math 8 Common Core Curriculum Framework Progress Guide. Factors
Classwork
Homework
Assessment
Brief Description This includes all work completed in the classroom setting. Including: Group participation Notebooks Vocabulary Written responses Group discussions Active participation in math projects Completion of assignments This includes all work completed outside of the classroom and student’s preparation for class (materials, supplies, etc.) Assignments can included, but not limited to: Problem of the Week Performance Tasks This category entails both traditional and alternative methods of assessing student learning: Group discussions Performance Tasks Problem Based Assessments Exams Quizzes Research/Unit Projects Portfolios Oral Presentations Surveys An instructional rubric should be created to outline the criteria for success for each alternative assessment.
Your grade will be determined using the following scale: 90% - 100% A 80% - 89% B 70% - 79% C 60% - 69% D 59% and below E
Grade Percentage Per Quarter
30%
20%
50%
Math 8 Honors Common Core Curriculum Map Standards for Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics.
5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Quarters 1
Unit 1 Radicals and Irrational Numbers Rational and Irrational Numbers 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 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. Understanding the Pythagorean Theorem 8.G.6: Explain a proof of the Pythagorean Theorem and its converse.
Unit 2 Exponents Radicals and Integers Exponents 8.EE.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions 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. 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. 8.G.9: Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
Applying the Pythagorean Theorem 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 8.G.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
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HONORS EXTENSIONS Additional Student Learning Objectives Students will… Reduce irrational numbers to simplest radical form. √ N.RN.2)
Students will… √ . (Algebra I -
Identify real and complex numbers through the introduction of (Algebra II - N.CN.1)
Rationalizing fractions with a square root in the denominator. (Algebra I - N.RN.2)
Derive (and use) the distance formula from the Pythagorean Theorem using the hypotenuse of a triangle. (extension of 8.G.8)
√
.
Multiply and divide monomials. (Algebra I – APR.A.1)
Determine the volume of composite figures such as determining how much rubber is needed to make a tennis ball by taking the outer sphere volume minus the inner sphere volume or determining how much grain will fit in a cylindrical silo with a conical top. (Geometry – GMD.A.3)
or
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Standards for Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics.
5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Quarters 2
Unit 3 Geometry
Unit 4 Functions
Congruence and Similarity Transformations 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.
Introduction to Functions 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.G.1: Verify experimentally the properties of rotations, reflections, and translations. 1a. Lines are taken to lines, and line segments to line segments of the same length.
8.F.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.
1b. Angles are taken to angles of the same measure. 1c. Parallel lines are taken to parallel lines. 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. 8.G.3: Describe the effect of dilations, translations, rotations, and reflections on twodimensional figures using coordinates. 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.
Linear Functions. 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. 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.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.
Linear Models 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.
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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.
HONORS EXTENSIONS Additional Student Learning Objectives Students will…
Students will…
Find angle measures and patterns created by transversals with non-parallel lines.
Explain when an equation is not a function for all real values of equations.(Algebra 1 – F.IF.A.1)
Find the vertices of the original pre-image given an image and a series of transformations that had been performed. (Geometry – G.CO.A.5)
Restrict the domain of those same equations so that each equation becomes a function. (Algebra 1 – F.IF.A.1)
Use function notation. (Algebra 1 – F.IF.A.2)
Discuss maxima/minima and local maxima/minima of a function. (Algebra 1 – F.IF.B.4, F.IF.C.7.A)
given certain
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Standards for Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics.
5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Quarters 3 & 4
Unit 5 Equations Solving Equations. 8.EE.7: Solve linear equations in one variable 7a. 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 (a and b are different numbers). 7b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
Solving Systems of Equations. 8.EE.8: Analyze and solve pairs of simultaneous linear equations 8a. 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.
Unit 6 Bivariate Data and Models Investigate patterns of association in bivariate data. 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. 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.
8a. 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. 8b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. 8c. Solve real-world and mathematical problems leading to two linear equations in two variables.
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HONORS EXTENSIONS Additional Student Learning Objectives Students will…
Students will…
Create and solve inequality representations of real-life situations. (i.e. The school band sells shirts for $10 each. It costs them $3 per shirt to buy each shirt and $2 per shirt to have the logo printed. There was also a $1,000 printer set-up fee. If they want to have a profit of at least $4 per shirt sold, how many shirts do they need to sell?) (Algebra I – A.CED.A.1) Solve simple quadratic equations of the form A.REI.B.4)
. (Algebra I –
Explain why some points on a scatter plot would not be chosen to write an equation that represents the data. (Algebra I – S.ID.B.6)
Collect their own data, graph, interpret, and then make predictions using linear extrapolation and interpolation. (Algebra I – S.ID.B.6)
Use linear regression to generate the line of best fit. (Algebra I – S.ID.B.6)
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