Posted in Algebra, Math blogs

Math Teachers at Play at Math Mama

Math Teacher at Play (MTAP) #51 is now live in Math Mama Writes …. Really great collection of 51 posts from teachers, lecturers, professors, bloggers, … in the following categories: Arithmetic, Patterns and Logic, Visual Math, Algebra-Geometry-Trigonometry, Puzzles and Games, Notations and Logic, and Breaking News, and may favorite, Teaching Mathematics.  I even got two posts in the carnival. Thanks Sue.

The next MTAP carnival will be hosted in Let’s Play Math. Submit your post first week of July using the MTAP submission form.

Posted in Algebra, Math Lessons

Ten problem solving and geometric construction tasks

I’ve written a number of posts the last couple of months which I published in other sites. They are problem solving tasks mostly in geometry using GeoGebra and a few on function, trigonometry and calculus. May I share 10 of them here. The first six are teaching resources which I posted in AgIMat, a site about science and math teaching resources. The last four problems are in Math Problems for K-12 to help students in their revision.  Both sites are new ones. I hope you subscribe and promote them in your social networks. Thank you.

  1. Problem solving on congruent segments
  2. Square and triangle problem
  3. Triangle Congruence by ASA
  4. Angle bisector – two definitions
  5. Constructing the perpendicular bisector
  6. Exponential function and its inverse
  7. How to sketch the graph of the derivative of a function
  8. Ratio and probability problem
  9. Trigonometric equations and their graphs
  10. Proving trigonometric identities #1

 

Posted in Algebra, Number Sense

Line multiplication and the FOIL method

Line  multiplication is a nice activity for teaching multiplication especially for more than one-digit numbers. The method is shown in the figure. The horizontal line represents the number 13 where the top line represents the tens digit and the lines below it represents the ones digit. The lines are grouped according to their place value. The same is true for the number 22. To find the final answer, count the number of intersections and add them diagonally. Dr. James Tanton produced a video about line multiplication. Click the link to view.

 

James Tanton related this procedure to rectangle multiplication. For example, the problem 13 x 22 in rectangle multiplication is

#multiplicationIf this is done in class I would suggest that before you show the rectangle multiplication as explanation to the process of line multiplication it would be great to connect it first to counting problem. Instead of counting the points at each cluster by one by one, you can ask the class to find for a more efficient way of counting the points of intersections. It will not take long for students to think of multiplying the array of points in each cluster. Given time I’m sure students could even ‘invent’ the rectangle multiplication themselves. Inventing and generalizing procedures are very important math habits of mind.

Line multiplication or counting intersections of sets of parallel lines is generalizable. You can ask your students to show the product of (a+b)(c+d) using this technique. The answer is shown in the figure below. Note that like rectangle multiplication this can be extended to more than two terms in each factor also. This is much better than the FOIL method which is restricted to binomials. I’m not a fan of FOIL method especially if it is taught and not discovered by the students themselves. Through this line multiplication activity I think they can discover that shortcut.

#multiplication

Posted in Algebra

Guest post: Online Resources to Supplement Math Lessons

Teachers struggling to improve their students’ math experiences can look online for a plethora of fun and interactive games and programs. All of the online math curriculum help outlined in the following list is free to access and simple enough that a basic computer could run them with no problem. The games are all browser-based, and most will need a version of Adobe Flash Player or equivalent. The first three sites are primarily interactive online games. The last two sites provide printable resources for teachers and students.

1. CSI: Mathematics

This site is the perfect blend of online games and printable supplements. It is organized by grade level and them by subject. Each subject includes a free and printable color resource PDF that gives tips, tricks, and explanations for each subject. There is also an applicable book list included. The PDF would be perfect for in-class reminders and to send home to parents. The site then links to online activity resources for each subject.

2. Sheppard’s Software

This simple and effective site arranges interactive math games by subject. It covers early math through simple algebra. Importantly, it directs students toward games on important concepts like time, measuring, money, and place value.

3. Math Playground

This simple website organizes games by popularity and subject. Students will be attracted to the game through an introductory picture. The games are interesting, although the site is somewhat less organized than the others.

4. Cool Math Games

This is an incredible online resource, and it is first on our list because you just may not have to go any further to find something great for your students. The site is completely free and includes both activities and virtual lessons to supplement teaching. It is visually pleasing and simple enough that elementary-age students could navigate it with some simple directions. It does have an almost overwhelming amount of material.

The best option would be to have a direction and purpose for the class going-in rather than just letting them explore. The website has lessons ranging from basic numeration to pre-calculus work. The one disadvantage to using lessons from this site is the restrictions on printing and downloading. All of the work must be viewed and manipulated through the website. For a class lesson, hook your computer up to the projector.

5. Math.com

This is a site full of resources and games. It is last on the list because it would be the hardest for students to self-navigate. However, it provides an excellent mix of materials including items for homework help and activities for tutors and volunteers.

When it comes to making math interactive and entertaining there is no reason to not try to incorporate as many games as possible.  While technology becomes more and more popular in the classroom, teachers should embrace all forms of online resources in order to supplement their own lessons.

Author: Brandy Olsen