The solution to each of the following problems is 20. Focus on finding the most helpful three or four algebraic steps to take someone reading your work from the problem as stated to the solution.
The solution to each of the following problems is 18. Focus on finding the most helpful algebraic steps to take a reader from the problem as stated to the solution.
The solution to each of the following twenty problems is 12. Focus on finding the most helpful algebraic step to take a reader from the problem as stated to the solution, and be sure you can explain why that step leads to a solution.
Many math students are given strict instructions by their teachers to do all their work in pencil. I disagree.
The advantage of doing work in pencil is that:
- it is easier to erase, so students are less likely to be paralyzed by “I am not sure this is correct, so I don’t dare write it down”
The disadvantages of working in pencil are that: Continue reading Math: Pen vs Pencil
1) Reflect and Summarize
at the end of each class, at the end of each week, at the end of each month. Review your notes and/or think back over the material that has been covered, then decide which skills or ideas you think are most important. Summarize the material you are learning as concisely as you can, because summarizing helps you learn. Identify any skills or ideas that you are not confident about. Write your reflections and summarizations as part of your notes, with reminders about what needs more work.
Some may have had trouble using my GeoGebra applets in their browsers. I have moved all of them to GeoGebraTube, which will hopefully fix the problem. You may search for them by typing “MathMaine” into the GeoGebraTube search box.
Links to all updated interactive graph applets are below. Comments and suggestions are always welcome!
GeoGebraBook: Exploring Linear Functions, which contains:
Check out this GeoGebraBook of nine applets that will help you explore Unit Circle Symmetries. It contains three applets per type of symmetry on the unit circle, one focusing only on the unit circle, and the other two linking unit circle properties to patterns in the graphs of the sine and cosine functions.
When two angle expressions, such as and , exhibit symmetry on the unit circle, an understanding of unit circle symmetries and reference angles often allow function arguments to be simplified. Mastery of symmetries and reference angles will also be very handy when expanding inverse trigonometric function results to describe all possible answers to a problem.
Suggestions for improvements to these applets, or additional applets, are always welcome via comments on this post.