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C O M S E T L G Y V anB ureT cholgyC t N ovem br,206 M ichgantem sH S olC E xpectains T hefolw ingsatM m coeidnfbythC T aIegrdM E instucoahV B reT nlgyC t. ALGEBRA 1 H C S E C ode L1.1 L1.1.3 L1.1.4 L1.2.4 L2.1.5 L2.1.6 L3.1.2 A1.1.1 A1.2.1 A2.2.2 A2.2.3 A2.7.2 E xpectaion Number Systems and Number Sense Explain how the properties of associativity, commutativity, and distributivity, as well as identity and inverse elements, are used in arithmetic and algebraic calculations. Describe the reasons for the different effects of multiplication by, or exponentiation of, a positive number less than 0, a number between 0 and 1, and a number greater than 1. Organize and summarize a data set in a table, plot, chart, or spreadsheet; find patterns in a display of data; understand and critique data displays in the media. Add, subtract, and multiply complex numbers. Use conjugates to simplify quotients of complex numbers. Recognize when exact answers aren’t always possible or practical. Use appropriate algorithms to approximate solutions to equations (e.g., to approximate square roots). Describe and interpret logarithmic relationships in such contexts as the Richter scale, the pH scale, or decibel measurements (e.g., explain why a small change in the scale can represent a large change in intensity). Solve applied problems. Give a verbal description of an expression that is presented in symbolic form, write an algebraic expression from a verbal description, and evaluate expressions given values of the variables. Write and solve equations and inequalities with one or two variables to represent mathematical or applied situations. Apply given transformations (e.g., vertical or horizontal shifts, stretching or shrinking, or reflections about the xand y-axes) to basic functions and represent symbolically. Recognize whether a function (given in tabular or graphical form) has an inverse and recognize simple inverse pairs (e.g., f (x) = x3 and g(x) = x1/3). Express direct and inverse relationships as functions (e.g., y = kxn and y = kx-n, n > 0) and recognize their characteristics (e.g., in y = x3, note that doubling x results in multiplying y by a factor of 8). C om ent Cost comparisons – break point GEOMETRY J:\OFFICE\SVernon\SusanW\HSCE Web Files\VAN BUREN MATH HIGH SCHOOL CONTENT STANDARDS\COSMETOLOGY MATH.doc C O M S E T L G Y V anB ureT cholgyC t N ovem br,206 M ichgantem sH S olC E xpectains H C S E C ode L3.1.1 E xpectaion Convert units of measurement within and between systems; explain how arithmetic operations on measurements affect units, and carry units through calculations correctly. Differentiate between statistical arguments (statements verified empirically using examples or data) and logical arguments based on the rules of logic. Solve multistep problems and construct proofs involving vertical angles, linear pairs of angles, supplementary angles, complementary angles, and right angles. Solve multistep problems and construct proofs involving corresponding angles, alternate interior angles, alternate exterior angles, and same-side (consecutive) interior angles. Prove that the angle sum of a triangle is 180° and that an exterior angle of a triangle is the sum of the two remote interior angles. Construct and justify arguments and solve multistep problems involving angle measure, side length, perimeter, and area of all types of triangles. Solve multistep problems involving circumference and area of circles. Solve multistep problems involving surface area and volume of pyramids, prisms, cones, cylinders, hemispheres, and spheres. Identify symmetries of pyramids, prisms, cones, cylinders, hemispheres, and spheres. Identify or sketch a possible three-dimensional figure, given two-dimensional views (e.g., nets, multiple views). Create a two-dimensional representation of a three-dimensional figure. Identify or sketch cross sections of three-dimensional figures. Identify or sketch solids formed by revolving twodimensional figures around lines. Know the definition of dilation and find the image of a figure under a given dilation. L4.1.2 G1.1.1 G1.1.2 G1.2.1 G1.2.2 G1.6.1 G1.8.1 G1.8.2 G2.2.1 G2.2.2 G3.2.1 C om ent Styling ALGEBRA II H C S E C ode L3.2.1 E xpectaion C om ent Determine what degree of accuracy is reasonable for measurements in a given situation; express accuracy through use of significant digits, error tolerance, or percent of error; describe how errors in measurements are magnified by computation; recognize accumulated error in applied situations. J:\OFFICE\SVernon\SusanW\HSCE Web Files\VAN BUREN MATH HIGH SCHOOL CONTENT STANDARDS\COSMETOLOGY MATH.doc C O M S E T L G Y V anB ureT cholgyC t N ovem br,206 M ichgantem sH S olC E xpectains ALGEBRA II (Continued) Identify possible sources of bias in data collection and sampling methods and simple experiments; describe how such bias can be reduced and controlled by random sampling; explain the impact of such bias on conclusions made from analysis of the data; and know the effect of replication on the precision of estimates. Distinguish between an observational study and an experimental study, and identify, in context, the conclusions that can be drawn from each. Design simple experiments or investigations to collect data to answer questions of interest; interpret and present results. (Recommended) Understand methods of sampling, including random sampling, stratified sampling, and convenience samples, and be able to determine, in context, the advantages and disadvantages of each. (Recommended) Explain the basic ideas of statistical process control, including recording data from a process over time. (Recommended) S3.1.2 S3.1.3 S3.1.4* S3.1.5* S3.2.1* OTHER MATH G C L E C ode A.FO. 06.06 G.GS. 06.01 N.MR. 06.01 N.ME. 06.11 N.FL. 06.12 N.MR. 06.13 E xpectaion C om ent Represent information given in words using algebraic expressions and equations. Understanding and apply basic properties of lines, angles, and triangles, including: •triangle inequality •relationships of vertical angles, complementary angles, supplementary angles •congruency of corresponding and alternate interior angles when parallel lines are cut by a transversal, and that such congruencies imply parallel lines •locate interior and exterior angles of any triangle, and use the property that an exterior angle of a triangle is equal to the sum of the remote (opposite) interior angles •know that the sum of the exterior angles of a convex polygon is 360° Understand division of fractions as the inverse of multiplication, e.g., if 4/5 ÷ 2/3 = , the 2/3 • = 4/5, so = 4/5 • 3/2 = 12/10. Find equivalent ratios by scaling up or scaling down. Calculate part of a number given the percentage and the number. Solve contextual problems involving percentages such as sales taxes and tips.* J:\OFFICE\SVernon\SusanW\HSCE Web Files\VAN BUREN MATH HIGH SCHOOL CONTENT STANDARDS\COSMETOLOGY MATH.doc C O M S E T L G Y V anB ureT cholgyC t N ovem br,206 M ichgantem sH S olC E xpectains A.PA. 07.11 N.MR. 07.04 N.FL. 07.05 N.FL. 07.09 G.SR. 07.01 G.TR. 07.03 G.TR. 07.04 N.MR. 08.07 N.MR. 08.08 N.FL. 08.11 OTHER MATH (Continued) Understand and use basic properties of real numbers; additive and multiplicative identifies additive and multiplicative inverses, commutativity, associativity, and the distributive property of multiplication over addition. Convert ratio quantities between different systems of units, such as feet per second to miles per hour. Solve proportion problems using such methods as unit rte, scaling, finding equivalent fractions, and solving the proportion equation a/b = c/d; know how to see patterns about proportional situations in tables.* Estimate results of computations with rational numbers. Use a ruler and other tools to draw squares, rectangles, triangles, and parallelograms with specified dimensions. Understand that in similar polygons, corresponding angles are congruent and the ratios of corresponding sides are equal; understand the concepts of similar figures and scale factor. Solve problems about similar figures and scale drawings. Understand percent increase and percent decrease in both sum and product form, e.g., 3% increase of a quantity x is x + .03x = 1.03x. Solve problems involving percent increases and decreases. Solve problems involving ratio units, such as miles per hour, dollars per pound, or persons per square mile.* Scale drawings of business plan Scale model salon Business Math Business Math J:\OFFICE\SVernon\SusanW\HSCE Web Files\VAN BUREN MATH HIGH SCHOOL CONTENT STANDARDS\COSMETOLOGY MATH.doc