CARLISLE AREA SCHOOL DISTRICT Carlisle, PA Standards Math 12 GRADE 12

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1 CARLISLE AREA SCHOOL DISTRICT Carlisle, PA Standards Math 12 GRADE 12 Date of Board Approval: April 21, 2011

2 CARLISLE AREA SCHOOL DISTRICT PLANNED INSTRUCTION COVER PAGE Title of Course: _Standards Math 12 Subject Area:_Mathematics Grade Level: _12 Course Length: (Semester/Year): _Year Duration: _50 minutes Frequency: _2 days per week Prerequisites: _Basic or Below Basic on 11 th Grade Math PSSA Credit: _.4 Level: _Not Applicable Course Description/Objectives: The district shall provide for attainment of the academic standards per Chapter 4, Section Each student shall demonstrate proficiency in the following areas: Numbers and Operations, Measurement, Geometry, Algebraic concepts and Data Analysis and Probability. Major Text(s)/Resources: PSSA Coach Workbook Curriculum Writing Committee: Kelly Brent Jennifer Barnhart 1

3 Unit 1: Test Taking Strategies Subject Area: Standards Math 12 Grade:12 2.5A Select and use appropriate mathematical concepts and techniques from different areas of mathematics and apply them to solving non-routine and multi-step problems. 2.5A Select and use appropriate mathematical concepts and techniques from different areas of mathematics and apply them to solving non-routine and multi-step problems. 2.5A Select and use appropriate mathematical concepts and techniques from different areas of mathematics and apply them to solving non-routine and multi-step problems. Use a graphing calculator to provide insight into problems when the mathematical procedure to find the correct answer cannot be recalled. Work backwards to determine which multiple choice answer is correct. Make diagrams to illustrate a problem and provide insight into the solution. Use formulas provided on reference sheets for high stakes tests. 2.5 C Present mathematical procedures and results clearly, systematically, succinctly and correctly. Write answers to open-ended questions graded on a rubric. 2.5 D Conclude a solution process with a summary of results and evaluate the degree to which the results obtained represent an acceptable response to the initial problem and why the reasoning is valid. Check answers to multiple choice questions for reasonableness and eliminate unreasonable responses. 2

4 Unit 2: Numbers and Operations Subject Area: Standards Math 12 Grade:12 2.1A Use operations (e.g., opposite, reciprocal, absolute value, raising to a power, finding roots, finding logarithms). 2.1A Use operations (e.g., opposite, reciprocal, absolute value, raising to a power, finding roots, finding logarithms). 2.1A Use operations (e.g., opposite, reciprocal, absolute value, raising to a power, finding roots, finding logarithms Find the square root of an integer to the nearest tenth using either a calculator or estimation. PSSA M11.A Express numbers and/or simplify expressions using scientific notation (including numbers less than 1). PSSA M11.A Simplify square roots.(e.g, ) PSSA M11.A A Use operations (e.g., opposite, reciprocal, absolute value, raising to a power, finding roots, finding logarithms Find the Greatest Common Factor (GCF) and/or the Least Common Multiple (LCM) for sets of monomials. PSSA M11.A A Use operations (e.g., opposite, reciprocal, absolute value, raising to a power, finding roots, finding logarithms Locate/identify irrational numbers at the approximate location on a number line. PSSA M11 A Compare and/or order any real numbers (rational and irrational may be mixed). PSSA M11.A

5 Unit 2: Numbers and Operations Subject Area: Standards Math 12 Grade: A Use operations (e.g., opposite, reciprocal, absolute value, raising to a power, finding roots, finding logarithms 2.1A Use operations (e.g., opposite, reciprocal, absolute value, raising to a power, finding roots, finding logarithms 2.2A Develop and use computation concepts, operations and procedures with real numbers in problem-solving situations. 2.2A Develop and use computation concepts, operations and procedures with real numbers in problem-solving situations. 2.2A Develop and use computation concepts, operations and procedures with real numbers in problem-solving situations. Simplify/evaluate expressions involving positive and negative exponents, roots and/or absolute value (may contain all types of real numbers - exponents should not exceed power of 10). PSSA M11.A Simplify/evaluate expressions involving multiplying with exponents (e.g. x 6 x 7 = x 13 ), powers of powers (e.g., (x 6 ) 7 =x 42 ) and powers of products (2x 2 ) 3 =8x 6 (positive exponents only PSSA M11.A Solve problems using operations with rational numbers including rates and percents (single and multi-step and multiple procedure operations) (e.g., distance, work and mixture problems, etc.). PSSA M Solve problems using direct and inverse proportions. PSSA M11.A Identify and/or use proportional relationships in problem solving settings PSSA M11.A Simplify/evaluate expressions using the order of operations to solve problems (any rational numbers may be used). PSSA M11.A Use estimation to solve problems PSSA M11.A

6 Unit 3: Measurement Subject Area: Standards Math 12 Grade:12 2.3B Measure and compare angles in degrees and radians 2.3C Demonstrate the ability to produce measures with specified levels of precision. 2.3C Demonstrate the ability to produce measures with specified levels of precision. 2.3C Demonstrate the ability to produce measures with specified levels of precision. 2.3A Select and use appropriate units and tools to measure to the degree of accuracy required in particular measurement situations. Measure and/or compare angles in degrees (up to 360 ) (protractor must be provided or drawn). (PSSA M11.B.2.1.1) Calculate the surface area of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheet. (PSSA-M11.B.2.2.1) Calculate the volume of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheet. (PSSA- M11.B.2.2.2) Estimate area, perimeter or circumference of an irregular figure. (PSSA- M11.B.2.2.3) Find the measurement of a missing length given the perimeter, circumference, area or volume. (PSSA- M11.B.2.2.4) Describe how a change in the linear dimension of a figure affects its perimeter, circumference, area or volume. (PSSA M11.B.2.3.1) 5

7 Unit 3: Measurement Subject Area: Standards Math 12 Grade:12 2.9F Use the properties of angles, arcs, chords, tangents and secants to solve problems involving circles. 2.9F Use the properties of angles, arcs, chords, tangents and secants to solve problems involving circles. 2.9C Identify and prove the properties of quadrilaterals involving opposite sides and angles, consecutive sides and angles and diagonals using deductive proofs. 2.9C Identify and prove the properties of quadrilaterals involving opposite sides and angles, consecutive sides and angles and diagonals using deductive proofs. Identify and/or use the properties of a radius, diameter and/or tangent of a circle (given numbers should be whole.) (PSSA- M11.C.1.1.1) Identify and/or use the properties of arcs, semicircles, inscribed angles and/or central angles. (PSSA- M11.C.1.1.2) Identify and/or use properties of triangles (e.g., medians, altitudes, angle bisectors, side/angle relationships, Triangle Inequality Theorem). (PSSA - M11.C.1.2.1) Identify and/or use properties of quadrilaterals (e.g., parallel sides, diagonals, bisectors, congruent sides/angles and supplementary angles). (PSSA - M11.C.1.2.2) 2.9C Identify and prove the properties of quadrilaterals involving opposite sides and angles, consecutive sides and angles and diagonals using deductive proofs. Identify and/or use properties of isosceles and equilateral triangles (PSSA - M11.C.1.2.3) 6

8 Unit 4: Geometry Subject Area: Standards Math 12 Grade:12 2.9B Prove that two triangles or two polygons are congruent or similar using algebraic, coordinate and deductive proofs. 2.10B Identify, create and solve practical problems involving right triangles using the trigonometric functions and the Pythagorean Theorem. 2.9G Solve problems using analytic geometry 2.9G Solve problems using analytic geometry Identify and/or use properties of congruent and similar polygons or solids. (PSSA - M11.C.1.3.1) Find the measure of a side of a right triangle using the Pythagorean Theorem (Pythagorean Theorem included on the reference sheet). (PSSA - M11.C.1.4.1) Calculate the distance and/or midpoint between 2 points on a number line or on a coordinate plane (formula provided on the reference sheet). (PSSA - M11.C Relate slope to perpendicularity and/or parallelism (limit to linear algebraic expressions; slope formula provided on the reference sheet). (PSSA - M11.C.3.1.2) 7

9 Unit 5: Algebraic Concepts Subject Area: Standards Math 12 Grade:12 2.8A Analyze a given set of data for the existence of a pattern and represent the pattern algebraically and graphically. 2.8Q Represent functional relationships in tables, charts and graphs. 2.8O Determine the domain and range of a relation, given a graph or set of ordered pairs. Analyze a set of data for the existence of a pattern and represent the pattern algebraically and/or graphically. (PSSA - M11.D.1.1.1) Determine if a relation is a function given a set of points or a graph. (PSSA - M11.D.1.1.2) Identify the domain, range or inverse of a relation (may be presented as ordered pairs or a table). (PSSA - M11.D.1.1.3) 2.8DFormulate expressions, equations, inequalities, systems of equations, systems of inequalities and matrices to model routine and non-routine problem situations. Solve compound inequalities and/or graph their solution sets on a number line (may include absolute value inequalities). (PSSA - M11.D.2.1.1) 2.8DFormulate expressions, equations, inequalities, systems of equations, systems of inequalities and matrices to model routine and non-routine problem situations Write, solve and/or apply a linear equation (including problem situations). (PSSA - M11.D.2.1.3) 8

10 Unit 5: Algebraic Concepts Subject Area: Standards Math 12 Grad e:12 2.8K Select, justify and apply an appropriate technique to graph a linear function in two variables, including slopeintercept, x- and y-intercepts, graphing by transformations and the use of a graphing calculator. 2.8K Select, justify and apply an appropriate technique to graph a linear function in two variables, including slopeintercept, x- and y-intercepts, graphing by transformations and the use of a graphing calculator. 2.8H Select and use an appropriate strategy to solve systems of equations and inequalities using graphing calculators, symbol manipulators, spreadsheets and other software. Identify or graph functions, linear equations or linear inequalities on a coordinate plane. (PSSA - M11.D.2.1.2) Match the graph of a given function to its table or equation. (PSSA - M11.D ) Write and/or solve systems of equations using graphing, substitution and/or elimination (limit systems to 2 equations). (PSSA - M11.D.2.1.4) 2.8NSolve linear, quadratic and exponential equations both symbolically and graphically. 2.8S Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic). Solve quadratic equations using factoring (integers only not including completing the square or the Quadratic Formula). (PSSA - M11.D.2.1.5) Add, subtract and/or multiply polynomial expressions (express answers in simplest form nothing larger than a binomial multiplied by a trinomial). (PSSA - M11.D.2.2.1) 9

11 Unit 5: Algebraic Concepts Subject Area: Standards Math 12 Grade: S Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic). 2.8S Analyze properties and relationships of functions (e.g., linear, polynomial, rational, trigonometric, exponential, logarithmic). 2.8R Create and interpret functional models Factor algebraic expressions, including difference of squares and trinomials (trinomials limited to the form ax 2 +bx+c where a is not equal to 0). (PSSA - M11.D.2.2.2) Simplify algebraic fractions (PSSA - M11.D.2.2.3) Identify, describe and/or use constant or varying rates of change. (PSSA - M11.D.3.1.1) 2.8R Create and interpret functional models 2.8J Demonstrate the connection between algebraic equations and inequalities and the geometry of relations in the coordinate plane. Determine how a change in one variable relates to a change in a second variable (e.g., y=4/x, if x doubles, what happens to y?). (PSSA - M11.D.3.1.2) Compute the slope and/or y-intercept represented by a linear equation or graph. (PSSA - M11.D.3.2.3) 10

12 Unit 5: Algebraic Concepts Subject Area: Standards Math 12 Grade: L Write the equation of a line when given the graph of the line, two points on the line, or the slope of the line and a point on the line. 2.8L Write the equation of a line when given the graph of the line, two points on the line, or the slope of the line and a point on the line. Apply the formula for the slope of a line to solve problems (formula given on reference sheet). (PSSA - M11.D.3.2.1) Given the graph of the line, 2 points on the line, or the slope and a point on a line, write or identify the linear equation in point-slope, standard and/or slope-intercept form. (PSSA - M11.D.3.2.2) 11

13 Unit 6: Data Analysis and Probability Subject Area: Standards Math 12 Grade: A Design and conduct an experiment using random sampling. Describe the data as an example of a distribution using statistical measures of center and spread. Organize and represent the results with graphs. (Use standard deviation, variance and t-tests.) 2.6A Design and conduct an experiment using random sampling. Describe the data as an example of a distribution using statistical measures of center and spread. Organize and represent the results with graphs. (Use standard deviation, variance and t-tests.) 2.6A Design and conduct an experiment using random sampling. Describe the data as an example of a distribution using statistical measures of center and spread. Organize and represent the results with graphs. (Use standard deviation, variance and t-tests.) 2.6A Design and conduct an experiment using random sampling. Describe the data as an example of a distribution using statistical measures of center and spread. Organize and represent the results with graphs. (Use standard deviation, variance and t-tests.) 2.7ESolve problems involving independent simple and compound events. Create and/or use appropriate graphical representations of data, including box-and-whisker plots, stem-and-leaf plots or scatter plots. (PSSA - M11.E.1.1.1) Analyze data and/or answer questions based on displayed data (box-andwhisker plots, stem-and-leaf plots or scatter plots). (PSSA - M11.E.1.1.2) Calculate or select the appropriate measure of central tendency (mean, mode or median) of a set of data given or represented on a table, line plot or stem-and-leaf plot.(pssa - M11.E Calculate and/or interpret the range, quartiles and interquartile range of data. (PSSA - M11.E.2.1.2) Describe how outliers affect measures of central tendency (PSSA - M11.E.2.1.3) Find probabilities for independent, dependent or compound events and represent as a fraction, decimal or percent). ( PSSA - M11.E.3.1.1) 12

14 Unit 6: Data Analysis and Probability Subject Area: Standards Math 12 Grade: A Compare odds and probability Find, convert and/or compare the probability and/or odds of a simple event. (PSSA - M11.E.3.1.2) 2.4EDemonstrate mathematical solutions to problems (e.g., in the physical sciences). 2.6DMake predictions using interpolation, extrapolation, regression and estimation using technology to verify them. 2.6C Determine the regression equation of best fit (e.g., linear, quadratic, exponential). Determine the number of permutations and/or combinations or apply the fundamental counting principle. (Formula provided on the reference sheet). (PSSA - M11.E.3.2.1) Estimate or calculate to make predictions based on a circle, line, bar graph or given situation. (PSSA - M11.E.4.1.1) Use probability to predict outcomes. (PSSA - M11.E.4.1.2) Draw, find and/or write an equation for a line of best fit for a scatter plot. (PSSA - M11.E.4.2.1) Make predictions using the equations or graphs of best-fit lines of scatter plots. (PSSA - M11.E.4.2.2) 13

15 Adaptations/Modifications for Students with I.E.P.s Adaptations or modifications to this planned course will allow exceptional students to earn credits toward graduation or develop skills necessary to make a transition from the school environment to community life and employment. The I.E.P. team has determined that modifications to this planned course will meet the student s I.E.P. needs. Adaptations/Modifications may include but are not limited to: INSTRUCTION CONTENT - Modification of instructional content and/or instructional approaches - Modification or deletion of some of the essential elements SETTING - Preferential seating METHODS - Additional clarification of content - Occasional need for one to one instruction - Minor adjustments or pacing according to the student s rate of mastery - Written work is difficult, use verbal/oral approaches - Modifications of assignments/testing - Reasonable extensions of time for task/project completion - Assignment sheet/notebook - Modified/adjusted mastery rates - Modified/adjusted grading criteria - Retesting opportunities MATERIALS - Supplemental texts and materials - Large print materials for visually impaired students - Outlines and/or study sheets - Carbonless notebook paper - Manipulative learning materials - Alternatives to writing (tape recorder/calculator) 14

CME Project, Algebra Correlated to: The Pennsylvania Math Assessment Anchors and Eligible Content (Grade 11)

CME Project, Algebra Correlated to: The Pennsylvania Math Assessment Anchors and Eligible Content (Grade 11) M11.A Numbers and Operations M11.A.1 Demonstrate an understanding of numbers, ways of representing numbers, relationships among numbers and number systems. M11.A.1.1 Represent and/or use numbers in equivalent