Idempotent

This activity teaches calculus AB or BC students to use integrals as the dot product operation on functions, treating functions as vectors and performing orthogonal projection on them. The result is a method for approximating functions with polynomials which is different from Taylor series. BC calculus students will also do a quick exploration of Fourier series. Pre-planning: 1 period for AB version ; 2 periods for BC version decide whether activity will be group based or individual minimum on

Teachers frequently get questions from students who are very astute or just curious. A math question that seems simple may have a difficult answer or the answer may connect in unexpected ways to other ideas. This text aims to address commonly asked questions about the algebra curriculum that require expert knowledge to answer. Questions addressed: I don't understand the "machine" analogy for functions.Why does a function have to pass the vertical line test?How is a sequence different from a

AP Calculus teachers need something to teach after the AP test in May. If your students are serious about learning and you are serious about teaching, why not get them started learning quantum mechanics? Seriously. This resource includes three activities, each with three parts which explore wavefunctions and the Schrodinger equation. Students will solve differential equations, find quantized energy levels, approximate solutions with power series, and generally be amazed at the power of calcu

Geometric mean is a topic in geometry that is only used to calculate a pointless length in right triangles. It is a throwaway topic, right? If your students are tired of having their time wasted memorizing calculations they will never use again, they will be demanding to know why they should learn about the geometric mean. Included are three mini-lessons -- one each for geometry honors, precalculus honors, BC calculus. You are saying, "But I only teach, geometry. Why would I bother paying f

Included are two versions of a semester 1 final exam for a standard AB Calculus curriculum. The first version consists of the simple versions of standard questions; the second version consists of challenging versions of standard questions. They can be used as tests or practice tests. The tests can be finished without a calculator. The questions assume the student is familiar with the derivatives of all elementary functions. A brief introduction to anti-derivatives is optional and those ques

Self-executing lessons are ideal for sub-plans, as supplemental material for "flipped" classrooms, or for any teacher wanting to leverage their limited instructional time. The learning of basic notation and rules is accomplished via pattern recognition. Though they appear to be standard worksheets, self-executing lessons have an organizational structure distinguishing them from the random assortment of problems one typically finds in a worksheet. The concepts, examples, and exercises are caref

After ten years of math class, many students have surprisingly not learned math, but they have learned to hate math. This is the opposite of what we want to happen. This activity is for all students, especially the ones who say they hate math and like art. Even though math is a form of art. I know, I know, just humor them . . . Students will learn to draw using the graphing calculator at www.geogebra.org and their knowledge of graph transformations. The instructions include simple examples

It is not always possible to know what a student has learned from previous math classes. This is particularly true if the school year has been disrupted or the student's learning has changed formats. Intervention specialists and special education teachers will find this diagnostic more useful than the standardized tests given to students every year by the state or district. Let's be honest, if you can figure out what a score of "low average" in "operations and algebraic thinking" on the NWEA

It is not always possible to know what a student has learned from previous math classes. This is particularly true if the school year has been disrupted or the student's learning has changed formats. Intervention specialists and special education teachers will find this diagnostic more useful than the standardized tests given to students every year by the state or district. Let's be honest, if you can figure out what a score of "low average" in "operations and algebraic thinking" on the NWEA

Self-executing lessons are ideal for sub-plans, as supplemental material for "flipped" classrooms, or for any teacher wanting to leverage their limited instructional time. The learning of basic notation and rules is accomplished via pattern recognition. This self-executing lesson will get precalculus students started learning calculus over the summer so that next year begins smoothly. It would be particularly useful for calculus teachers needing to accelerate the pacing of their curriculum. DA

If your students are the kind who rebel against memorizing pointless formulae without an explanation of where they come from, they will be infuriated by the topic of rotated conic sections as presented in the textbook. The presentation in this text uses linear algebra, in particular, vectors and matrices in 2D, especially the rotation matrix. These explanations will require predigestion by the instructor. A mastery of vector and matrix multiplication in 2D is necessary. It will be most benefi

Series convergence is a difficult topic because there are so many possible tests and multiple intermediate steps for each test and sometimes multiple tests that all have to be executed in the correct order. Biologists use a tool called a dichotomous key to classify organisms that look similar. This is a dichotomous key for classifying a series as absolutely convergent, conditionally convergent, or divergent. On each page is a question and, depending on the answer, instructions to go to another

This is a short guide for calculus students (and teachers) for the topic of series convergence tests. It explains in simple language how the three possible classifications of a series -- absolutely convergent, conditionally convergent, divergent -- are related to the three main tests -- Integral Test, Alternating Series Test, Series Divergence Test. All other tests are shortcuts based on these three to be used with specific types of series. Instructors and curious students will be pleased to g

Multi-step word problems with the steps separated out into sub-questions to support students who struggle with planning multiple steps. The first page is a review of dot product properties. Topics include lines, planes, work, torque, special relativity, and the proof of the law of cosines. Choose any or all to use with a class according to their interests. It is assumed that students know the mechanics of addition, scalar multiplication, dot product, and cross product. An answer key is not in

This text seeks to give a succinct conceptual explanation of half of the math that most people will ever learn. A successful reading of it will leave the reader with a mental structure into which to place their existing and future math knowledge. It will not be teaching mechanical skills such as the division algorithm or logarithm laws. We hope that it brings clarity to the teaching and learning of math which too often gets bogged down in memorizing seemingly arbitrary rules.

Six multi-part word problems with diagrams to practice trigonometry. Answer Key included. Diagrams are drawn for the students already. The two major skills necessary for word problems are turning the statement into a diagram and turning the diagram into equations. Making students practice both simultaneously causes frustration and little learning. You will want to have them practice making labelled diagrams on a different assignment. Topics: (1) right triangle trig, geometry of triangles (

Proving trig identities is, for most Algebra2/Precalculus students, the most difficult problem type in the course. The difficulty arises from the multitude of possible steps to take. Years of experience have produced this ordered list of six actions. The way to use the list is to start at the top and go down the list until you hit an action that is possible. In almost all cases, if the action is possible, then it is the right one to take. This takes the guesswork out of the solution. Includ

Teachers frequently get questions from students who are very astute or just curious. A math question that seems simple may have a difficult answer or the answer may connect in unexpected ways to other ideas. This text aims to address commonly asked questions about the middle school math curriculum that require expert knowledge to answer. Questions addressed:Why is 1 not a prime integer?How many prime integers are there?Why is 0 times 7 equal to 0?Why is -1 times 2 equal to -2?Is 2 + 2 always e

Honestly, I'm just tired of hearing the wrong definition for continuity from teachers and textbooks alike. It is time for us as a species to move on from pretending that continuity is about "drawing a graph without picking up your pencil." Technically, that property is 'path connectedness.'

The Lissajous Lab is a quick activity to summarize what students have learned about transforming trig functions. Students also learn a bit about how to use the free, online graphing calculator application at www.desmos.com to create parameterized curves and sliders. It can give the overworked teacher a day to relax while they grade or lesson plan or a subplan that requires little math expertise.