Mathematics Scope & Sequence MMA

Transcription

1 Mathematics Scope & Sequence MMA Revised: May 2011 First Six Weeks (29 ) Essential Algebra M.1.A compare and analyze various methods for solving a real-life problem methods) to solve problems from a variety M.1.C select a method to solve a problem, defend the method, and justify the reasonableness of the results Represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions and equations Translate verbal statements into algebraic equations Evaluate expressions for a given value Use the distributive property to solve equations involving grouping symbols Solve multi-step equations with variables on both sides Solve a formula for a specific variable 8-9 Recognize patterns to make a prediction and justify why the prediction is reasonable Use basic principles of algebra to solve real world problems Textbook Sections: 1.7, 2.4, 2.5 M.1.A compare and analyze various methods for solving a real-life problem Solve one-step, two-step, and multi-step inequalities in one variable Inequalities methods) to solve problems from a variety M.1.C select a method to solve a problem, defend the method, and justify the reasonableness of the results M.2.A interpret information from various graphs, including line graphs,... to draw conclusions from data Graph an inequality in one variable Write an inequality in one variable representing a given graph Write an inequality in one variable for a real world situation Write a compound inequality describing a given graph Write and graph a compound inequality for a real world situation 5-7 Wk 3/4 CCA Sept 5-16 Textbook Sections: 2.6 First six weeks curriculum continued on next page

2 M.9.A use geometric transformations, symmetry, and perspective drawings to structure in art and architecture Identify, name, and draw points, lines, segments, rays and planes Solve application problems using the midpoint and Segment Addition Postulate, including algebraic expressions representing dimensions Classify and measure angles Geometry and Reasoning Name congruent, adjacent, complementary, supplementary, linear pairs, and vertical angles in complex figures Solve application problems involving vertical angles, bisected angles, linear pairs, complementary angles, and supplementary angles, including algebraic expressions representing dimensions Solve application problems using the Angle Addition Postulate, including algebraic expressions representing dimensions Solve application problems using the relationships between angles formed when transversals cross parallel lines 7-8 Wk 6 DCA Sept Use inductive reasoning to make conjectures from number and picture patterns, specific examples, or events Recognize patterns to make a prediction and justify why the prediction is reasonable Textbook Sections: 3.1, 3.2, 3.3, 3.4, 3.5

3 Second Six Weeks (29 ) M.5.A use rates, linear functions, and direct variation to solve problems involving personal finance and budgeting, including compensations and deductions M.8.C use direct and inverse variation to describe physical laws such as Hook s, Newton s, and Boyle s laws Determine the average rate of change Interpret slope as an average rate of change Determine the slope of the line drawn through two points Identify increasing and decreasing linear functions Determine the slope and y-intercept of a line algebraically and graphically Identify whether a situation can be modeled by a linear function Identify independent and dependent variables in real world situations Identify the practical meaning of x- and y-intercepts Write and graph linear functions in slope-intercept form Linear Equations Interpret the slope and y-intercept of linear functions in contextual situations Use the slope-intercept form of linear equations to solve problems Determine the equation for a linear function given its slope and y-intercept Determine the equation for a linear function that includes two given points 9-10 Wk 9 CCA Oct Determine a line of best fit with a straightedge Determine the regression equation to interpolate and extrapolate Recognize the equivalent forms of the direct variation statement Determine the constant of proportionality in direct variation problems Recognize equations of the form xy=k as inverse variations Graph inverse variation relationship from symbolic rules Apply direct variation and inverse variation to physical laws ( Hook s, Newton s, and Boyle s) Apply direct and inverse variation to solve real-world problems Textbook Sections: 6.1, 6.2, 6.3, 13.5, 13.6 Second six weeks curriculum continued on next page.

4 Linear Systems of Equations M.5.A use rates, linear functions, and direct variation to solve problems involving personal finance and budgeting, including compensations and deductions Define variables and write systems of equations with two variables from a problem situation Solve a system of two linear equations graphically, including systems with no solution and infinitely many solutions Solve a system of two linear equations by substitution, elimination, and by using matrices, including systems with no solution and infinitely many solutions Relate the algebraic, graphic, and tabular solution to a system of two linear equations Read, interpret, and analyze the solution to a system of equations to determine if it is a reasonable solution to an application problem situation 8-9 Wk 11 OER Oct 31- Nov 4 Textbook Sections: 6.4, 6.5, 6.6, 6.7 Solve linear inequalities numerically and graphically Determine if an ordered pair is a solution to a system of inequalities Linear Inequalities M.5.A use rates, linear functions, and direct variation to solve problems involving personal finance and budgeting, including compensations and deductions Use properties of inequalities to solve linear inequalities algebraically Define variables and write systems of inequalities with two variables from a problem situation Solve systems of inequalities with two variables graphically Analyze the graphs of a system of inequalities and identify the solution(s) Generate a table of values and analyze to find the point(s) of intersection (solutions) 6-7 Wk 12 DCA Nov 7-11 Read, interpret, and analyze the solutions(s) to a system of inequalities to determine if it is a reasonable solution to an application problem situation Minimize and maximize an objective function Textbook Sections: 2.6, 6.8, 6.9

5 Third Six Weeks (29 ) Polygons M.1.A compare and analyze various methods for solving a real-life problem M.9.A use geometric transformations, symmetry, and perspective drawings to structure in art and architecture Solve equations using the Triangle Sum Theorem and the Exterior Angle Theorem to find the measure of an angle Use constructions and counter-examples to justify the Triangle Inequality Theorem Solve application problems using the Triangle Inequality Theorem Solve application problems using altitudes, medians and perpendicular bisectors, including algebraic expressions representing dimensions Classify polygons based on their sides and angles, including regular/irregular and concave/convex Find angle sums or missing angle measures using Polygon Angle Sum and Polygon Exterior Angle Sum theorems 9-10 Wk 15 CCA Dec 5-9 Solve application problems using Polygon Angle Sum Theorem and Polygon Exterior Angle Sum Theorem, including algebraic expressions representing dimensions Apply properties of parallelograms to find missing lengths and angle measures Solve application problems using the properties of quadrilaterals (parallelogram, rectangle, square, rhombus, and trapezoids), including algebraic expressions representing dimensions Textbook Sections: 4.1, 4.4, 4.6, 4.7, 4.8, 4.9 M.1.C select a method to solve a problem, defend the method, and justify the reasonableness of the results Use the coordinate plane to find the distance between two points Solve application problems involving the distance formula Relate the distance formula to the Pythagorean Theorem Right Triangles M.9.A use geometric transformations, symmetry, and perspective drawings to structure in art and architecture Use the Pythagorean Theorem to solve real-world problems Use an equilateral triangle and the Pythagorean Theorem to develop the right triangle relationships Use a square and the Pythagorean Theorem to develop the right triangle relationships 7-8 Solve application problems using special right triangle relationships in real-world situations Make connections to concrete models, pictures, and figures Find square roots Simplify products and quotients containing radicals Textbook Sections: 10.1, 10.2, 10.3, 12.6 Third six weeks curriculum continued on next page.

6 Exponent Rules Textbook Sections: 1.8 Simplify expressions using laws of exponents, including zero and negative exponents 1 Day Wk 18 DCA Jan 9-13

7 Exponential and Logarithmic Functions Fourth Six Weeks (29 ) M.2.D use regression methods available through technology to describe various models for data such as...exponential, etc., select the most appropriate model, and use the model to interpret information M.7.C investigate and compare investment options including stocks, bonds, annuities, and retirement plans Textbook Sections: 13.8, 13.9 Recognize and write an exponential function as a rule for applying a growth factor or a decay factor Recognize exponential functions from equations Graph exponential functions from equations Identify the domain and range of exponential functions Identify the y-intercept of exponential functions Solve real-world problems involving exponential growth and decay Write equivalent forms of exponential and logarithmic functions 7-8 Wk 21 CCA Jan 30- Feb 3 Sketch the graph of a quadratic parent function Connect all quadratic graphs to the parent function Identify the line of symmetry and write its equation Identify maximum or minimum as the vertex Recognize that c is the y-intercept Quadratics Identify domain and range of quadratic functions Be able to describe verbally the changes in the graph when each parameter changes Solve quadratics by graphing Textbook Sections: 12.2, 12.3, 12.4, 12.5, 12.7 Fourth six weeks curriculum continued on next page. Solve quadratics that have two, one, or no solutions Use algebraic methods including factoring, quadratic formula, square roots, and completing the square to solve quadratics Use quadratic regression to write the equation of a quadratic function

8 Use ratios and rates to solve problems Use proportions to solve problems, including the pitch of a vibrating string Measurement M.1.C select a method to solve a problem, defend the method, and justify the reasonableness of the results M.4.A compare theoretical and empirical probability M.4.B use experiments to determine the reasonableness of a theoretical model such as binomial, geometric, etc M.9.B use geometric transformations, proportions, and periodic motion to structure in music Use unit or dimensional analysis to solve problems Recognize perimeter as a geometric property of plane figures Write formulas for and calculate perimeters for squares, rectangles, triangles, parallelograms, trapezoids, and polygons, including figures in the coordinate plane Use unit analysis to solve problems involving perimeter Write and use formulas for the circumference of a circle Calculate perimeters of irregular shapes using formulas and combination of formulas 6-7 Wk 24 DCA Feb Calculate areas of polygons and circles using appropriate formulas Solve application problems involving perimeter and area Determine probabilities using areas in real world situations Describe the effect on perimeter and area when one or more dimensions are changed Textbook Sections: 5.1, 5.2, 5.3, 5.4

9 Fifth Six Weeks (30 ) M.9.A use geometric transformations, symmetry, and perspective drawings to structure in art and architecture Determine names and numbers of faces, edges, vertices and bases of three-dimensional figures; including composite figures Describe a three-dimensional figure given its net Describe cross sections of solids; cross section may be a point, line segment, or region of a plane Find the area of cross sections of prisms Draw orthographic and isometric views from a 3-D view of a model and draw a 3-D view of a model given an orthographic or isometric view Surface Area and Volume Determine a three-dimensional view from a drawing of the top view with number of cubes in each column Write formulas for and calculate lateral and total surface area of prisms, pyramids, cones, cylinders, and spheres Find lateral or total surface area of 3-D figures given a net (with and without dimensions) Solve application problems using surface area of prisms, pyramids, spheres, cones, cylinders and composite figures in real-world situations Describe the effect on surface area when one or more dimensions are changed 7-8 Wk 26 CCA March 5-9 Find volume of prisms, pyramids, cones, and cylinders Find volume of 3-D figures given a net (with and without dimensions) Solve application problems using volume of prisms, pyramids, spheres, cones, cylinders and composite figures in real-world situations Describe the effect on volume when one or more dimensions are changed Textbook Sections: 5.5, 5.6, 5.7 Fifth six weeks curriculum continued on next page.

10 Circles M.1.C select a method to solve a problem, defend the method, and justify the reasonableness of the results M.2.A interpret information from various graphs, including...circle graphs... to draw conclusions from the data Identify tangents, secants, chords, diameters, radii, inscribed angles, central angles, and major/minor arcs Explore the relationships among angles in circles and use these relationships to solve problems (including tangent line to radius, central angles, and inscribed angles) Find the measure of a central angle if a circle were divided into a given number of equal sectors Apply central angles to circle graphs 5-6 Interpret circle graphs and draw conclusions Use proportions to find arc lengths and the area of a sector Textbook Sections: 10.4, 10.5 M.9.A use geometric transformations, symmetry, and perspective drawings to structure in art and architecture Graph translation and reflection images on a coordinate plane Identify and draw translations on a coordinate plane given an algebraic expression, such as (x+2, y-3) 6-7 Transformations Identify and draw rotations about the origin Identify and draw compositions of transformations that include two or more translations, reflections, or rotations Draw dilation images on a coordinate plane Use properties of congruence and transformations to determine if a two-dimensional figure will tessellate on the plane Solve real world problems using properties of transformations, including tessellations Textbook Sections: 8.1, 8.2, 8.3, 8.4 Statistics M.2.A interpret information from various graphs, including...circle graphs... to draw conclusions from the data M.2.B analyze numerical data using measures of central tendency, variability, and correlation in order to make inferences M.2.C analyze graphs from journals, newspapers, and other sources to determine the validity of stated arguments M.3.A formulate a meaningful question, determine the data needed to answer the question, gather the appropriate data, analyze the data, and draw reasonable conclusions Recognize how scaling the axis of a graph can misrepresent the situation Read and interpret information from various graphs including line graphs, bar graphs, circle graphs, scatter plots, line plots, stem and leaf plots, box and whisker plots and histograms Analyze graphs from newspapers and other sources to determine the validity of stated arguments Construct stem and leaf plots, box and whisker plots and histograms Determine mean, median, and mode for a set of data Analyze data in order to draw reasonable conclusions 5-6 Wk 29/30 DCA April 2-13 Textbook Sections: 2.7, 2.8, 2.9

11 Sixth Six Weeks (33 ) Similar Figures M.9.A use geometric transformations, symmetry, and perspective drawings to structure in art and architecture Determine if two given figures are similar Determine the measures of perimeter or area provided with some of the dimensions of similar figures 1-2 Textbook Sections: Closing the Distance Grade 11 Personal Income M.3.C determine the appropriateness of a model for making predictions from a given set of data M.5.A use rates, linear functions, and direct variation to solve problems involving personal finance and budgeting, including compensations and deductions M.5.B solve problems involving personal taxes M.5.C analyze data to make decisions about banking M.7.A analyze types of savings options involving simple and compound interest and compare relative advantages of these options M.7.B analyze and compare coverage options and rates in insurance use a linear model to determine simple interest use a linear model to identify the meaning of the slope and y-intercept in the context of the problem use a table to calculate hourly, weekly, monthly, and yearly earnings use a federal income tax table to determine withholding tax use scatter plots to estimate withholding tax use social security tax and Medicare tax percents to calculate deductions use tables and graphs to develop and test algebraic models for the calculation of taxes use function rules to find ending balance for personal checking account 6-7 Textbook Sections: 7.1, 7.2, 7.3, 7.4, 7.5 Sixth six weeks curriculum continued on next page.

12 Investment Options M.2.C analyze graphs from journals, newspapers, and other sources to determine the validity of stated arguments M.3.C determine the appropriateness of a model for making predictions from a given set of data M.5.C analyze data to make decisions about banking M.7.A analyze types of saving options involving simple and compound interest and compare relative advantages of these options M.7.C investigate and compare investment options including stocks, bonds, annuities, and retirement plans M.8.A use geometric models available through technology to model growth and decay in areas such as population, biology, and ecology Use tables and graphs to investigate simple and compound interest Use a given set of data to make predictions Measure inflation using CPI Calculate account balances with one initial deposit earning interest of different compounding periods using tables Calculate account balances using compound interest formula Calculate account balances where deposits are being made while interest is being earned Apply the compound interest formula to determine the future value of a lump-sum investment earning compound interest Apply present value formula in a given situation involving compound interest Solve problems involving annuities 6-7 Compare investment options including stocks, bonds, annuities, and retirement plans Textbook Sections: 7.6, 7.7, 7.8, 7.9, 7.10 Credit M.3.C determine the appropriateness of a model for making predictions from a given set of data M.6.A analyze methods of payment available in retail purchasing and compare relative advantages and disadvantages of each option M.6.B use amortization models to investigate home financing and compare buying and renting a home M.6.C use amortization models to investigate automobile financing and compare buying and leasing a vehicle M.7.B analyze and compare coverage options and rates in insurance M.8.A use geometric models available through technology to model growth and decay in areas such as population, biology, and ecology Determine the interest on a credit card account using the average daily balance method Calculate the value of a car with linear depreciation Calculate the value of a car with exponential depreciation Calculate the total cost of a loan Calculate the amount of principal and the amount of interest paid each month on a loan Determine the value of a car after a certain amount of time Compare buying a car with leasing a car Compare different types of mortgages when purchasing a home 6-7 Textbook Sections: 7.11, 7,12, 7.13, 7.14, 7.15