Unit: 2.1 Numbers, Number Systems, and Number Relationships Unit Outcomes: Eighth grade students will demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers, and number systems. A. 2.1.8.B Represent numbers in equivalent forms A. Students will convert numbers between integers, fractions, decimals, and percents. Students will convert numbers between exponential form and standard form. Students will calculate square roots and absolute value. Enrichment: Higher level thinking problems involving large numbers, negative exponents, and open-ended questions B. 2.1.8.D Extend place value concepts to represent large numbers using exponential, scientific, and calculator notation B. Students will perform operations with numbers in exponential, scientific, and calculator notation. Students will use numbers in exponential, scientific, and calculator notation to make estimates.
Enrichment: Higher level thinking problems involving students solving problems using negative exponents and open ended questions C. 2.1.8.F Use all concepts of exponents and roots to determine unknown quantities in equations C. Students will work with radicals and integer exponents. Students will use square root and cube root symbols to represent solutions to equations. Students will evaluate square roots and cube roots of perfect squares and perfect cubes. Remediation: Classroom remediation, morning enrichment group, worksheets, games small group instruction, one-on-one instruction, and grade level remediation teacher Enrichment: Higher level thinking problems involving real life situations, multiple step problems, open-ended questions, and web-quests Assessment Criteria: Homework, quizzes, tests, open-ended questions, PA Benchmark Vocabulary: absolute value, cube root, exponential form, integer, negative exponents, perfect square, scientific notation, and square root
Unit: 2.2 Computation and Estimation Unit Outcomes: Eighth grade students will estimate the values of irrational numbers basic operations of fractions and percents. Students will be able to check the reasonableness of estimated answers. A. 2.2.8.D Basic functions and reasonableness of answers A. Students will know the difference between rational and irrational numbers. Students will understand that every number has a decimal expansion. Students will convert a decimal expansion into a rational number. Enrichment: Higher level thinking problems involving conversion of repeating (non-terminating) decimals into rational numbers Assessment Criteria: Homework, quizzes, tests, open-ended questions, PA Benchmark Vocabulary: Irrational number and rational number
Unit: 2.4 Mathematical Reasoning and Connections Unit Outcomes: Eighth grade students will solve mathematical situations through reasoning skills. A. 2.4.8.A Draw inductive and deductive conclusions A. Students will know the difference between inductive and deductive reasoning, and determine usage of each. Students will solve problems using inductive and deductive reasoning. Enrichment: Higher level thinking problems involving real world situations and applications. B. 2.4.8.B Use if then statements to construct valid arguments B. Students will solve open-ended problems by implementing if then statements. Students will orally defend arguments using if then statements. Enrichment: Higher level thinking problems involving construction of if then statements based on personal connections Assessment Criteria: Homework, quizzes, tests, open-ended questions, PA Benchmark
Vocabulary: Deductive reasoning and inductive reasoning
Unit: 2.5 Mathematical Problem Solving and Communication Unit Outcomes: Eighth grade students will develop and analyze a plan to problem solve. A. 2.5.8.A Develop problem solving strategies A. Students will identify information needed to solve a problem. Students will apply estimation skills in problem solving when appropriate. Students will develop and carry out a problem solving plan. Students will check validity of the plan and explain how the problem was solved. Enrichment: Higher level activities involving multiple step problems, and open-ended questions B. 2.5.8.B Use precise mathematical language to explain and interpret results B. Students will use graphs, tables, charts, and diagrams to analyze results. Students will use algebraic equations and formulas to explain outcomes. Enrichment: Higher level thinking problems involving the creation of original tables, graphs, charts, and equations used to interpret data
Assessment Criteria: Homework, quizzes, tests, open-ended questions, PA Benchmark Vocabulary: algebraic equation
Unit: 2.6 Statistics and Data Analysis Unit Outcomes: Eighth grade students will construct and interpret information using different data displays. A. 2.6.8.B Organize and display one and two variable data A. Students will construct and interpret stem-and-leaf plots. Students will construct and interpret box-and-whisker plots. Students will construct and interpret two variable scatter plots. Enrichment: Higher level thinking problems involving collecting, constructing, and interpreting original data B. 2.6.8.C Describe relationship for two-variable data displays B. Students will describe patterns such as clustering, outliers, positive and negative association, and linear and nonlinear association. Students will investigate patterns of association in two-variable data displays. Enrichment: Higher level thinking problems involving comparing and contrasting multiple data sources
Assessment Criteria: Homework, quizzes, tests, open-ended questions, PA Benchmark Assessment Test, and classroom activities Vocabulary: correlation, linear relationship, nonlinear relationship, outliers, and quartiles
Unit: 2.8 Algebra and Functions Unit Outcomes: Eighth grade students will evaluate and simplify algebraic expressions and solve and graph linear equations and inequalities. A. 2.8.8.B Solve linear equations with one, infinite, or no solutions A. Students will analyze and solve linear equations. Students will solve linear equations with one variable. Students will give examples of linear equations with one solution, many solutions, or no solution. Students will give examples of non-linear equations. Enrichment: Solve multiple linear equations and graph their solutions. Compare and contrast the outcomes of each graph B. 2.8.8.D Create a table or graph from a function rule B. Students will define, evaluate, and compare functions. Students will understand that a function is a rule that states for every input there is exactly one output.
Enrichment: Given a linear equation, students will create their own function table C. 2.8.8.E Create expressions and equations with one or two variables C. Students will use equations and expressions to model relationships between quantities. Students will determine rate of change and initial value of a function. Enrichment: Higher level thinking problems involving real world situations and applications D. 2.8.8.F Solve one and two variable equations, as well as one variable inequalities. D. Students will be able to write and solve an equation for a given problem. Students will be able to match a written situation to its numeric or algebraic expression, equation, or inequality. Enrichment: Create equations based on the features of a given function and describe it verbally Assessment Criteria: Homework, quizzes, tests, open-ended questions, PA Benchmark Vocabulary: equation, expression, function, inequality, linear equation, non-linear equation, and rational number
Unit: 2.9 Geometry Unit Outcomes: Eighth grade students will name, describe and apply geometric relations for one and two dimensional shapes, and three dimensional solids. A. 2.9.8.A Identify and describe rotations, reflections, and translations and be able to use formulas for volume A. Students will understand congruent and similar figures and determine missing side lengths in two dimensional shapes. Students will verify the properties of rotations, reflections, and translations. Enrichment: Real world mathematical problems involving volume of cones, cylinders, spheres B. 2.9.8.B Predict and describe the result of a translation, rotation, or reflection of a three-dimensional shape B. Students will describe the effect of translations, rotations, and reflections using coordinate points. Enrichment: Higher level thinking problems and open-ended questions involving ordered pair relationships
C. 2.9.8.C Plot, locate, and identify ordered pairs on a coordinate system C. Students will plot and identify ordered pairs located in all four quadrants of the coordinate plane. Enrichment: When given two ordered pairs of points, students will be able to determine whether a line passes through both pairs Assessment Criteria: Homework, quizzes, tests, open-ended questions, PA Benchmark Vocabulary: congruent, dilation, quadrant, reflection, rotation, and translation
Unit: 2.10 Trigonometry Unit Outcomes: Eighth grade students will compute measures of sides and angles using proportions, the Pythagorean Theorem, and right triangle relationships. A. 2.10.8.A Understand and apply Pythagorean Theorem A. Students will analyze and explain a proof of the Pythagorean Theorem and its converse. Students will apply the Pythagorean Theorem to determine unknown side lengths in right triangles. Students will apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Enrichment: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions Assessment Criteria: Homework, quizzes, tests, open-ended questions, PA Benchmark Vocabulary: hypotenuse, proportion, and Pythagorean Theorem
Unit: 2.11 Concepts of Calculus Unit Outcomes: Eighth grade students will describe the concept of unit rate, ratio, slope, and rate of change. A. 2.11.8.B Understand the connections between proportional relationships, lines, and linear equations. A. Students will graph proportional relationships. Students will interpret the unit rate as the slope of the graph. Students will compare two different proportional relationships. Students will use similar triangles to explain why the slope is the same between any two distant points. Enrichment: Compare a distance-time graph to a distance-time equation to determine which two moving objects has the greater speed Assessment Criteria: Homework, quizzes, tests, open-ended questions, PA Benchmark Vocabulary: proportional relationship, rate of change, and unit rate