Introduction to Point-Slope Form

I created this Desmos activity to help students understand point-slope form of a linear equation, both how it relates to the equation for calculating the slope between two points and why it might be useful even if you're already good at slope-intercept form. It also introduces the idea of calling the change in x by the name h.

SolveMe Mobiles

The puzzles at SolveMe Mobiles are linear equations disguised as perfectly balanced mobiles. The early puzzles are simple while the later ones require solving systems of equations. The interface is elegant. Drag a beam to have the corresponding equation appear. Drag a shape that's on both sides of an equation to subtract it. Drag a common factor to divide by it. Substitute by dragging a shape that you've isolated on one side of an equation to somewhere else it appears. Create your own mobiles. Play without creating an account or create an account to save your progress and creations. (No email is required to create an account, though those over 13 may include an email for the purposes of password reset.)

Observe and Ask

This simple Desmos sketch is designed to elicit observations and questions that will lead naturally to an introduction of the ideas of domain and range and an exploration of power functions. I show it to a class without any explanation and as I move the a-slider I ask for questions (which I write on the board, but don't answer). If students want the k-slider moved or if they want to see a particular value of a or k, I oblige. Eventually I ask students to begin trying to answer some of the questions and see where that takes us.

Puzzle

Can you figure out how the p and q sliders control the lines? To check your answer, try typing in equations of the lines (in terms of p and q) in the blank rows underneath the sliders and see if the lines that your equations produce match the lines that are already there. (When you've found something that works--but not before, that's cheating!--you can scroll down to rows below the blank ones to see if your equations are the same as the ones that were actually used to produce the lines.)

Operations on functions graphically

A.B. Cron has created a series of GeoGebra applets that demonstrate operations on functions graphically. You can enter any two functions (f and g) and then, from their graphs, determine points that will be on the graph of, for example, h = f + g. After plotting a number of points, you can check the box to show the graph of h to check your work. The adding functions applet has links to the applets for subtracting, multiplying, dividing, and composition.

(Links updated 7/30/2016)

Finding logs

This is a clean, simple applet by Michael Borcherds that provides practice finding logs. It keeps track of how many you got right on the first try and how much time you've spent. To restart the count, refresh the page.

Mathmo

Mathmo is a review tool for A-level maths developed by the NRICH project at the University of Cambridge. It is advertised to work in Chrome, Safari, and on mobile devices. There are questions on wide range of topics in a typical American high school curriculum, though the range of question types within a topic is very limited. In some topics (logarithms, for example) there are a few different types of questions, but in most there is a single question type where just the specifics (numbers, functions, etc.) vary. You can ask for random questions from the wide range of syllabus topics or can choose your own specific topics to build up a set of questions. You work the problems on paper (or in your head) and then push the check answer button to compare your answer with the given one. If you want several questions on the same topic, you can add the topic multiple times to your question list or can click the new button from within a particular question.

I did experience a couple of minor bugs. Sometimes, the first time you look at a question you see the code rather than the mathematical notation. Clicking (or tapping) the question changes the code to notation. The description says that the color of the question changes once you indicate whether you got the question right or wrong. I didn't experience that either on the iPad or in Chrome.

Simplifying Expressions with Integer Exponents

This applet from Larry Green provides practice in simplifying expressions with integer exponents.

Napier's Gift

I was inspired by the first chapter of Eli Maor's e:The Story of a Number to create this GeoGebra applet designed to help the user discover how to simplify the process of finding a quotient by subtracting exponents. The idea is both to introduce students to logarithms (though they are never mentioned explicitly) and to help students understand why they were so heralded when they were introduced. The applet is also posted on GeoGebraTube.

Equation of a quadratic

This sleek GeoGebra applet by Michael Borcherds provides practice in determining the equations of quadratic functions from their graphs. Some of the generated parabolas are easier to write equations for in factored form while others are easier to do in (h, k) form. All have leading coefficients of 1. After each function you type in, the function you have given is graphed for comparison with the original and you're told how many you've gotten right and the total amount of time it has taken you.

Factoring Trinomials

Factor trinomials while looking at the graph of the quadratic. Some of the examples are not factorable. It is also possible to turn off the graph. There are options to time yourself or to print a worksheet of randomly generated factoring practice problems.

• Problems where a = 1
• Problems where a is not necessarily 1

Find the equation of a line

In this applet a line is randomly generated and the user enters what she thinks the equation is. Her equation is then graphed for comparison with the original. There is a scoring mechanism incorporated as well.

This is my first applet created with JSXGraph , which looks quite promising (though it does require learning Javascript.)

Particularly helpful to me in developing this were Dr. Carol Fisher's Reference on JSXGraph Commands and the convert-to-math script  in use at interactive mathematics. (The latter enables the user to enter the equation using standard calculator notation.) I also found the javascript tutorial at w3schools.com a very useful introduction to javascript.

The application uses MathJax to produce nice mathematical notation.

Solving Absolute Value Equations and Inequalities

When teaching the algebraic solution of absolute value equations and inequalities, have students try problems generated here (on one of Dr. Carol J.V. Fisher's many great interactive math pages). I bet some students will start figuring out function transformations on their own as a result!

A First Course in Algebra

Dr. Carol J. V. Fisher has created a thorough online Algebra 1 course complete with interactive exercises for every topic. You can also choose to have a worksheet of practice problems and answers generated. I haven't explored the site that thoroughly yet, but there's a link to a beautifully formatted pdf text for each topic and the interactive web exercises are of good quality. I love that there's an option on the trinomial factoring problems to show the graph of the associated quadratic function!


There are also lots of interactive exercises for Geometry and Algebra 2.

Practice writing linear equations

This applet that I developed using Geogebra generates a line, asks the user to provide an equation and then indicates whether the submitted equation is correct.

Finding Equations of Lines in Photos

This is a set of applets I made using Geogebra. In each applet you fit linear equations, in slope-intercept form and point-slope form, to linear elements of photographs. The applets are all the same except that each uses a different photograph. I also developed a worksheet to go along with the applets, and it is included at the bottom of each applet.

David Young's Interactive Mathematics Resources

David Young has developed a high quality collection of interactive resources, primarily, but not solely, for algebra and pre-algebra. My favorites are the Graphing Linear Equations modules, which teach and then provide guided practice in graphing by plotting points, graphing using intercepts, and graphing using the slope-intercept method. A student worksheet to go along with these modules is provided as well. There's also lots worth exploring here beyond the applets. For example, there is a nice PowerPoint template for Jeopardy-style review and a video which shows you how to create your own applet using the free and versatile Geogebra.

HippoCampus

This site provides high quality interactive, multimedia "textbooks" (for want of a better word) for algebra, calculus, statistics, and several non-mathematical subject areas.

Interactive Algebra Practice

This site offers an easy to use interface for practicing a fairly wide variety of math topics. I especially like the "graphing" and "formulas" in the algebra section. In these problems, if you choose a difficulty level of 5 or higher you can choose linear graphs, quadratic graphs or a mix. When you have finished the set number of problems, you have the opportunity to redo the problems you got wrong.

Visualizing Multiplication of Binomials

This applet from WisWeb provides interactive help with visualizing binomial multiplication.