Scholastic Area that Course Is Active In: Mathematics
Students will explore exponential functions.
Extend properties of exponents to include all integer exponents.
Investigate and explain characteristics of exponential functions, including domain and range, asymptotes, zeros, intercepts, intervals of increase and decrease, rates of change, and end behavior.
Graph functions as transformations of f(x) = ax.
Solve simple exponential equations and inequalities analytically, graphically, and by using appropriate technology.
Understand and use basic exponential functions as models of real phenomena.
Understand and recognize geometric sequences as exponential functions with domains that are whole numbers.
Interpret the constant ratio in a geometric sequence as the base of the associated exponential function.
Students will explore inverses of functions.
Discuss the characteristics of functions and their inverses, including one-to-oneness, domain and range.
Determine inverses of linear, quadratic, and power functions and functions of the form f(x) =
a/x, including the use of restricted domains.
Explore the graphs of functions and their inverses.
Use composition to verify that functions are inverses of each other.
Strand: Data Analysis and Probability
Using sample data, students will make informal inferences about population means and standard deviations.
Pose a question and collect sample data from at least two different populations.
Understand and calculate the means and standard deviations of sets of data.
Use means and standard deviations to compare data sets.
Compare the means and standard deviations of random samples with the corresponding population parameters, including those population parameters for normal distributions. Observe that the different sample means vary from one sample to the next. Observe that the distribution of the sample means has less variability than the population distribution.
Students will investigate properties of geometric figures in the coordinate plane.
Determine the distance between two points.
Determine the distance between a point and a line.
Determine the midpoint of a segment.
Understand the distance formula as an application of the Pythagorean theorem.
Use the coordinate plane to investigate properties of and verify conjectures related to triangles and quadrilaterals.
Students will understand and use the language of mathematical argument and justification.
Use conjecture, inductive reasoning, deductive reasoning, counterexamples, and indirect proofs as appropriate.
Understand and use the relationships among a statement and its converse, inverse, and contrapositive.
Students will discover, prove, and apply properties of triangles, quadrilaterals, and other polygons.
Determine the sum of interior and exterior angles in a polygon.
Understand and use the triangle inequality, the side-angle inequality, and the exterior-angle inequality.
Understand and use congurence postulates and theorems for triangles (SSS, SAS, ASA, AAS, HL).
Understand, use, and prove properites of and relationship among special quadrilaterals: parallelogram, rectangle, rhombus, square, trapezoid, and kite.
Find and use points of concurrency in triangles: incenter, orthocenter, circumcenter, and centroid.
Students will identify and use special right triangles.
Determine the lengths of sides of 30°-60°-90° triangles.
Determine the lengths of sides of 45°-45°-90° triangles.
Students will define and apply sine, cosine, and tangent ratios to the right triangles.
Discover the relationship of the trigonometric ratios for similar triangles.
Explain the relationship between the trigonometric ratios of complementary angles.
Solve applications problems using the trigonometric ratios.
Students will understand the properties of circles.
Understand and use properties of chords, tangents, and secants as an application of triangle similarity.
Understand and use properties of central, inscribed, and related angles.
Use the properties of circles to solve problems involving the length of an arc and the area of a sector.
Justify measurements and relationships in circles using geometric and algebraic properties.
Students will find and compare the measures of spheres.
Use and apply surface area and volume of a sphere.
Determine the effect on surface area and volume of changing the radius or diameter of a sphere.
Strand: Process Standards
Students will solve problems using appropriate technology.
Build new mathematical knowledge through problem solving.
Solve problems that arise in mathematics and in other contexts.
Apply and adapt a variety of appropriate strategies to solve problems.
Monitor and reflect on the process of mathematical problem solving.
Students will reason and evaluate mathematical arguments.
Recognize reasoning and proof as fundamental aspects of mathematics.
Make and investigate mathematical conjectures.
Develop and evaluate mathematical arguments and proofs.
Select and use various types of reasoning and methods of proof.
Students will communicate mathematically.
Organize and consolidate their mathematical thinking through communication.
Communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
Analyze and evaluate the mathematical thinking of stratgies of others.
Use the language of mathematics to express mathematical ideas precisely.
Students will make connections among mathematical ideas and to other disciplines.
Recognize and use connections among mathematical ideas.
Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
Recognize and apply mathematics in contexts outside of mathematics.
Students will represent mathematics in multiple ways.
Create and use representations to organize, record and communicate mathematical ideas.
Select, apply, and translate among mathematical representations to solve problems.
Use representations to model and interpret physical, social, and mathematical phenomena.
The Guiding Sub-questions are related, relevant, and connected to exploring the Essential Question. They are higher level questions and are specific enough to guide the work of the unit. (Subquestions must be entered one at a time and updated . . . they are numbered automatically.)
Begin writing a unit by establishing what you want students to know and be able to do and planning how you will know "what they know". This Assessment Plan is a general plan (specific assessment instruments are in the teaching procedures); this section should both help you to plan and to give teachers an idea of the varied types of assessment that will be used in the unit. Be sure to include informal checks of understanding, student self-assessment, and authentic assessment. Include pre and post assessment.
Preparation for students includes notes on preparing the learner such as possible misconceptions students may have, ideas of pre-exposure for learners, and prerequisite lessons. It includes ideas for accelerated learning.
Unit Resources include general, global resources that might include bookmarks, books, periodicals, media and software. URLs need to be provided for each resource to identify a source from which it can be obtained. Resources might include those purchased as part of an adoption. More specific resources will be referenced within the teaching procedures.