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Posted in Algebra, Math blogs

Math Teachers at Play at Math Mama

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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

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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

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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 Humor

Two Plus Two Apples or Why Indians Flunk

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I found a piece of paper with this little poem inserted in my old notebook. It was written by Beverly Slapin. I realized I was born an Indian and will always be.
two apples

All right, class, let’s see who know what two plus two is. Yes, Doris?

I have a question. Two plus two what?

Two plus two anything.

I don’t understand.

OK, Doris, I’ll explain it to you. You have two apples and you get two more. How many do you have?

Where would I get two more?

From a tree.

Why would I pick two apples if I already have two?

Never mind, you have two apples and someone gives you two more.

Why would someone give me two more, if she could give them to someone who’s hungry?

Doris, it’s just an example.

An example of what?

Let’s try again—you have two apples and you find two more. Now, how many do you have?

Who lost them?

YOU HAVE TWO PLUS TWO APPLES!!!! HOW MANY DO YOU HAVE ALL TOGETHER????

Well, if I ate one, and gave away the other three, I’d have none left, but I could always get some more if I got hungry from that tree you were talking about before.

Doris, this is your last chance—you have two, uh, buffalo, and you get two more. Now how many do you have?

It depends. How many are cows and how many are bulls, and is any of the cows pregnant?

It’s hopeless! You Indians have absolutely no grasp of abstraction!

Huh?

-by Beverly Slapin