12th Grade Math

 

Measurement Geometry and Spatial Sense Patterns, Functions and Algebra Data analysis and Probability


 

Number, Number Sense and Operations

(Based on State of Ohio
Curriculum Standards)

1. Determine what properties (closure, identity, inverse, commutative and associative) hold for operations with complex numbers.
 
  1. Math Dictionary animation for kids  This is an outstanding website allowing you to explore a comprehensive view of math with many examples  4 Star
2. Apply combinations as a method to create coefficients for the Binomial Theorem, and make connections to everyday and workplace problem situations.
  1. Binomial Probabilities Find the probability of a number of successes or failures in a binomial experiment using a tree diagram, a bar graph, and direct calculation.
  2. Permutations and Combinations Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle.

Measurement

1. Solve problems involving derived measurements; e.g., acceleration and pressure.  
2. Use radian measures in the solution of problems involving angular velocity and acceleration.  
3. Apply informal concepts of successive approximation, upper and lower bounds, and limits in measurement situations; e.g., measurement of some quantities, such as volume of a cone, can be determined by sequences of increasingly accurate approximations.
  1. Pyramids and Cones - Activity AVary the height and base‑edge or radius length of a pyramid or cone and examine how its three‑dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone.

Geometry and Spatial Sense

1. Use matrices to represent translations, reflections, rotations, dilations and their compositions.  
2. Derive and apply the basic trigonometric identities; i.e., angle addition, angle subtraction and double angle.
  1. Simplifying Trigonometric Expressions    Choose the correct steps to simplify a trigonometric function. Use step-by-step feedback to diagnose incorrect steps.
  2. Sum and Difference Identities for Sine and Cosine Choose the correct steps to evaluate a trigonometric expression using sum and difference identities. Use step‑by‑step feedback to diagnose incorrect steps.
3. Relate graphical and algebraic representations of lines, simple curves and conic sections.
  1. Circles Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response.
  2. Ellipse - Activity A   Compare the equation of an ellipse to its graph. Vary the terms of the equation of the ellipse and examine how the graph changes in response. Drag the vertices and foci, explore their Pythagorean relationship, and discover the string property.
  3. Hyperbola - Activity A Compare the equation of a hyperbola to its graph. Vary the terms of the equation of the hyperbola. Examine how the graph of the hyperbola and its asymptotes changes in response.
4. Recognize and compare specific shapes and properties in multiple geometries; e.g., plane, spherical and hyperbolic.
  1. Platonic Solids - Virtual Manipulative  This online activity allows you to experiment with five platonic solids, counting their faces, edges, and vertices.
  2. Shapes   This website will allow your students to learn all about shapes and have fun at the same time
     

Patterns, Functions and Algebra

1. Analyze the behavior of arithmetic and geometric sequences and series as the number of terms increases.
  1. Arithmetic Sequences    Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response.
  2. Arithmetic and Geometric Sequences   Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response.
  3. Geometric Sequences   Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas.
2. Translate between the numeric and symbolic form of a sequence or series.
  1. Arithmetic Sequences    Find the value of individual terms in arithmetic sequences using graphs of the sequences and direct computation. Vary the common difference and examine how the sequences change in response.
  2. Arithmetic and Geometric Sequences   Find the value of individual terms in an arithmetic or geometric sequence using graphs of the sequence and direct computation. Vary the common difference and common ratio and examine how the sequence changes in response.
  3. Geometric Sequences   Explore geometric sequences by varying the initial term and the common ratio and examining the graph. Compute specific terms in the sequence using the explicit and recursive formulas.
 
3. Describe and compare the characteristics of transcendental and periodic functions; e.g., general shape, number of roots, domain and range, asymptotic behavior, extrema, local and global behavior.
  1. Cosine Function Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle.
  2. Exponential Functions - Activity A  Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function.
  3. Logarithmic Functions - Activity A Compare the equation of a logarithmic function to its graph. Change the base of the logarithmic function and examine how the graph changes in response. Use the line y = x to compare the associated exponential function.
  4. Logarithmic Functions: Translating and Scaling Vary the values in the equation of a logarithmic function and examine how the graph is translated or scaled. Connect these transformations with the domain of the function, and the asymptote in the graph.
  5. Sine Function Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle.
  6. Tangent Function Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle.
  7. Translating and Scaling Sine and Cosine Functions - Activity A  Experiment with the graph of a trigonometric function of the form y = a sin[b (x ? c)] + d. Relate the equation and graph to amplitude, period, and frequency.
4. Represent the inverse of a transcendental function symbolically.  
5. Set up and solve systems of equations using matrices and graphs, with and without technology. Matrices: Equations and Systems of Equations
This study guide from Encyclopedia Britannica covers a discussion of inverse matrices, determinants, matrix equations, and simultaneous equations.
6. Make arguments about mathematical properties using mathematical induction.
  1. Mathway This a step by step math solver for General Math, Geometry, Algebra, Pre Algebra, Trigonometry, Pre-calculus, Calculus.  A great program to show students step by step directions and also allow a teacher to create a presentation to be used on their LSD projector.  This is a great tool for facilitating and allowing at teacher to better present their instruction.   4 Star
7. Make mathematical arguments using the concepts of limit.  
8. Compare estimates of the area under a curve over a bounded interval by partitioning the region with rectangles; e.g., make successive estimates using progressively smaller rectangles.  
9. Translate freely between polar and Cartesian coordinate systems.
  1. Points in Polar Coordinates  Identify the polar coordinates of a point. Drag the point in the plane and investigate how its r and theta coordinates change in response. Compare its Cartesian coordinates.
10. Use the concept of limit to find instantaneous rate of change for a point on a graph as the slope of a tangent at a point.  

Data Analysis and Probability

1. Identify and use various sampling methods (voluntary response, convenience sample, random sample, stratified random sample, census) in a study.  
2. Transform bi-variate data so it can be modeled by a function; e.g., use logarithms to allow nonlinear relationship to be modeled by linear function.  
3. Describe the shape and find all summary statistics for a set of univariate data, and describe how a linear transformation affects shape, center and spread.  
4. Apply the concept of a random variable to generate and interpret probability distributions, including binomial, normal and uniform.
  1. Binomial Probabilities  Find the probability of a number of successes or failures in a binomial experiment using a tree diagram, a bar graph, and direct calculation.
5. Use sampling distributions as the basis for informal inference.  
6. Use theoretical or experimental probability, including simulations, to determine probabilities in real-world problem situations involving uncertainty, such as mutually exclusive events, complementary events, and conditional probability.