9-12 Grade Math
by Andrea Anderson
March 22, 2005
12.1.1 By the end of the twelfth grade, students will describe and compare the relationships between subsets of real numbers.
Draw Venn diagrams including but not limited to natural, whole, integer, rational, irrational, and real numbers. (Alg I and AMII)
Find intersection and union of two sets of numbers. (Alg I & AMII)
Given a number, identify which subsets it belongs. (Alg I & AMII)
Distinguish between rational and irrational numbers expressed in various forms.(Alg I & AMII)
Identify numbers from every subset of real numbers. (Alg I & AMII)
List Criteria of each subset of real numbers. (Alg I & AMII)
Determine the domain of different kinds of functions. (Alg II)
12.1.2 By the end of the twelfth grade, students will express the equivalent forms of numbers using exponents, radicals, scientific notation, absolute values, fractions, decimals, and percents.
Convert from scientific notation to standard notation. (Alg I & AMI)
Convert from standard notation to scientific notation. (Alg I & AMI)
Convert between fractions, decimals, and percents using appropriate notation. (Alg I & AMI)
Recognize radicals that are integers. (Alg I & AMII)
Recognize a radical falling between two whole numbers. (Alg I & AMII)
Express numbers using positive integers in exponents, expanded and standard notation. (Alg I & AMII)
Convert absolute value to standard form. (Alg I & AMI)
Computation/Estimation
12.2.1 By the end of the twelfth grade, students will solve theoretical and applied problems using numbers in equivalent forms, radicals, exponents, scientific notation, absolute values, fractions, decimals, and percents, ratios and proportions, order of operations, and properties of real numbers.
Compute using numbers in equivalent forms, radicals, exponents, scientific notation and absolute values. (Alg II & AMII)
Apply the properties of real numbers to numerical expressions. (Alg II & AMII)
Simplify numbers in equivalent forms, radicals, exponents, scientific notation, absolute values, and order of operations. (Alg II & AMII)
Solve equations using numerical properties. (Alg II & AMII)
12.2.2 By the end of the twelfth grade, students will justify solutions to mathematical problems.
Write an explanation based on the context of the problem stating why the solution is reasonable. (Alg I & AMII)
Determine the reasonableness of a solution by checking. (Alg I and AMII)
12.2.3 By the end of the twelfth grade, students will perform estimations and computations of real numbers mentally, with paper and pencil and with technology.
Perform computations with technology. (Alg I & AMI)
Compute and estimate computations mentally. (Alg I & AMI)
Compute and estimate with paper and pencil. (Alg I & AMI)
Estimate to determine reasonableness of a computation. (Alg I & AMI)
MEASUREMENT
12.3.1 By the end of the twelfth grade, students will select and use measuring units, tools and/or technology and explain the degree of accuracy and precision of measurements.
Explain the accuracy of the measurement (AMI & Alg I)
Explain the precision of the measurement tool (AMI & Alg I)
Select appropriate measuring units to achieve a specified degree of accuracy and precision. (AMI & Alg I)
Select appropriate tools and/or technology to achieve a specified degree of accuracy and precision. (AMI & Alg I)
Measure to a specified degree of accuracy (closest to true value). (AMI & Alg I)
12.3.2 By the end of the twelfth grade, students will convert between metric and standard units of measurement given conversion factors.
Convert measurements between the metric system and standard system of measurement. (7th grade)
Use unit analysis to check measurement computations (miles/hr to ft/sec).
GEOMETRY/SPATIAL CONCEPT
12.4.1 By the end of the twelfth grade, students will calculate perimeter and area of two-dimensional shapes and surface area and volume of three-dimensional shapes.
Calculate perimeter for any two-dimensional shape. (Geometry & AMI)
Calculate surface area for two and three-dimensional shapes. (Geometry & AMI)
Calculate the volume for three-dimensional shapes. (Geometry & AMI)
Calculate the area of a shaded region. (Geometry and AMI)
12.4.2 By the end of the twelfth grade, students will create geometric models to describe the physical world.
Create perspective drawings. (Geometry & AMI)
Create scale models. (Geometry & AMI)
Describe the physical world using geometric relationships. (Geometry & AMI)
Describe the real world using geometric terms. (Geometry & AMI)
12.4.3 By the end of the twelfth grade, students will evaluate characteristics and properties of two and three-dimensional geometric shapes.
Classify and compare attributes of two- and three-dimensional shapes. (Geometry & AMI)
Determine the effects of changing dimensions on perimeter, area, and volume. (Geometry and AMI)
Investigate and deduce geometric properties using transformations such as translations, rotations, and reflections. (Geometry & AMI)
Analyze characteristics of two- and three-dimensional figures. (Geometry and AMI)
Analyze figures in terms of congruence. (Geometry & AMI)
Analyze figures in terms of similarity. (Geometry and AMI)
12.4.4 By the end of the twelfth grade, students will apply coordinate geometry to locate and describe objects algebraically.
Graph a geometric shape and determine the slope of the sides. (Alg I and AMII)
Identify the missing vertices of a polygon. (Alg I and AMII)
Apply coordinate geometry to locate objects on a coordinate plane. (Alg I & AMII)
Apply coordinate geometry to analyze figures using slope. (Alg I and AMII)
Apply coordinate geometry to analyze figures using the distance formula. (Alg I & AMII)
Apply the relationship between parallel and perpendicular lines. (Alg I and AMII)
12.4.5 By the end of the twelfth grade, students will apply right triangle trigonometry to find length and angle measure.
Apply right triangle trigonometry to solve problems. (Alg II & AMII)
Use inverse trigonometric functions to find angle measures. (Alg II & AMII)
12.4.6 By the end of the twelfth grade, students will apply geometric properties to solve problems.
Find missing angles and lengths of geometric shapes using geometric properties. (Properties may include but are not limited to similarity, parallel and line transversal). (Geometry & AMI)
Utilize geometric models to solve problems in math and other disciplines. (Geometry and AMI)
Apply the area of a sector formula. (Geometry & AMI)
12.4.7 By the end of the twelfth grade, students will apply deductive reasoning to arrive at a conclusion.
Justify steps when solving an algebraic equation using properties of real numbers. (AMII & Alg I)
Utilize principles of logic to establish valid arguments. (AMII & Alg I)
Find patterns in data. (AMII & Alg I)
Graph compound inequalities. (AMII & Alg I)
DATA ANALYSIS, PROBABILITY, AND STATISTICAL CONCEPTS
12.5.1 By the end of the twelfth grade, students will select a sampling technique to gather data, analyze the resulting data and make inferences.
Choose an appropriate sample size. (Alg II & AMII)
Choose an appropriate method of organizing data. (Alg II & AMII)
Choose an appropriate method of graphing to display data. (Alg II & AMII)
Draw conclusions based on data (Alg II & AMII)
Identify mean, median, and mode of a data set. (Alg II & AMII)
Justify the chosen sampling techniques. (Alg II & AMII)
Use technology to analyze data. (Alg II & AMII)
12.5.2 By the end of the twelfth grade, students will write equations and make predictions from sets of data.
Display data in a scatter plot, describe its shape, and estimate how close the data comes to fitting an equation. (Alg I & AMII)
Relate the slope of a regression line to the rate of change for the data set. (Alg I & AMII)
Determine what the y-intercept or beginning value indicates about the data. (Alg I & AMII)
Determine the validity of predictions made from regression equations. (Alg I & AMII)
Create a scatter plot of data. (Alg I & AMII)
Construct box and wisker plots and stem and leaf plots. (Alg I and AMII)
Distinguish between positive, negative or no correlation from a scatter plot. (Alg I & AMII)
Write an equation for the line of best fit. (Alg I & AMII)
12.5.3 By the end of the twelfth grade, students will apply theoretical probability to represent problems and make decisions.
Interpret theoretical probability to represent real-world problems. ( AMII & Alg I)
Solve theoretical probability problems. (AMII & Alg I)
12.5.4 By the end of the twelfth grade, students will evaluate how transformations on data affect the measures of central tendency and variability.
Describe how adding the same amount to each score changes the mean, median, mode, range, outliers, interquartile points, maximum, and minimum. (FST)
Describe how dropping an outlier changes the other measures. (FST)
Use the measures of central tendency to compare and contrast data sets. (FST)
Determine the effects on the measures of central tendency and variability when a data set is transformed by addition. (FST)
Determine the effects on the measures of central tendency and variability when a data set is transformed by multiplication. (FST)
12.5.5 By the end of the twelfth grade, students will interpret data represented by the normal distribution and formulate conclusions.
Sketch a normal or bell curve, label one and two standard deviations from the mean and fill in approximate percents associated with the deviations. (FST)
Determine factors that will produce a curve that is not normal. (FST)
Describe how sample size is related to a normal curve. (FST)
Recognize a normal distribution. (FST)
Determine whether a normal distribution is skewed left or right. (FST)
Locate the mean of a normal curve. (FST)
12.5.6 By the end of the twelfth grade, students will calculate probabilities of independent events.
Calculate probabilities using the fundamental counting principle and permutations. (Alg I & AMII)
List a sample space. (Alg I & AMII)
Determine the number of outcomes using the basic multiplication counting principle. (Alg I & AMII)
Compute the probability of two independent events. (Alg I & AMII)
ALGEBRAIC CONCEPTS
12.6.1 By the end of the twelfth grade, students will graph and interpret algebraic relations and inequalities.
Describe a graph by identifying intercepts, slope. max, min, increasing, decreasing, parallel, and perpendicular. (Alg I & AMII)
Use families of curves to describe the effect of changing coefficients of an equation. (Alg I & AMII)
Graph algebraic equations. (Alg I & AMII)
Graph algebraic inequalities. (Alg I & AMII)
Describe geometric relationships of algebraic equations with reference to slope and y-intercept. (Alg I & AMII)
12.6.2 By the end of the twelfth grade, students will solve problems involving equations and inequalities.
Use appropriate methods to solve linear and quadratic equations. (Alg I)
Write Algebraic equations and use them to solve problems. (Alg I)
Write algebraic inequalities and use them to solve problems. (Alg I)
Solve equations for a given variable. (Alg I & AMII)
12.6.3 By the end of the twelfth grade, students will solve problems involving systems of two equations, and systems of two or more inequalities.
Write and solve systems by graphing, substitution and elimination. (Alg I)
Write and solve systems of inequalities. (Alg I)
Develop matrices and use them to solve problems. (Alg I & Alg II)
12.6.4 By the end of the twelfth grade, students will solve problems using patterns and functions.
Apply direct or indirect variations. (AMI & Alg II)
Recognize patterns of exponential growth and decay and their significance to real- life situations. (Alg I & Alg II)
Represent a problem in multiple formats (words, tables, graphs, and symbols). (Alg I & Alg II)
Solve problems generalizing patterns (Alg I & Alg II)
Solve problems using algebraic expressions. (Alg I & Alg II)
Solve problems using functions of two variables. (Alg I & Alg II)
