Math Topics

Linear Transformations with Graphics

I made this video when I was thinking about ways to teach the basics of linear transformations and matrices by illustrating their connections to computer graphics.  I wanted to show the actual matrix calculations that lead to the graphics, as well as a slider to show the graphics dynamically.  Since I made the video, GeoGebra added a spreadsheet, and it’s actually much easier and more versatile to do the same thing in GeoGebra (I’ll post that link soon).  However, it was a fun challenge to figure out how to push Excel to do graphics in this dynamic way.  To date, this is my most popular video on youtube.   Spreadsheet used in the video.

Clock Buddies — A Round Robin Tournament Activity

This is a great first day of class activity, which works well with math phobic students (I use it in a math for elementary teachers class). Students make a list 1:00, 2:00, etc. on a piece of paper — however many times I assign — and then they have to make an appointment with a different student in each slot. Students move around the room making appointments and learning each other’s names. If there are an odd number of students, I passively participate, accepting appointments whenever students come and ask me.

At some point a student or a few students will announce that they are done, and I tell them they aren’t done until everyone’s schedule is filled in. It’s an interesting question to figure out a good number of appointments to give them so that they will get stuck, but not overwhelmed; I usually go for a few more than half the number of students (12 for a class of 20). Read more >>

Multiplication Table

Making a multiplication table is an excellent beginning Excel Activity.  This video shows an efficient way to do it using absolute references, but there are many other approaches.   I use an open-ended handout for this activity in class.   This video is a good introduction to absolute references.   Spreadsheet used in the video.

The Biggest Product

I start this activity by handing out buckets of tiles (any small objects will do) and asking students to take 10. They can sort their ten tiles into any number of piles, and their “prize” is the product of the sizes of their piles — so if they sort them into piles of size 5 and 5; their prize is 5 x 5, and if they sort into piles of sizes 1, 2, 3, and 4, their prize is 1 x 2 x 3 x 4. The goal, of course, is to get the highest possible prize, and then to generalize for other numbers of tiles. Read more >>

Base Two Quiz (Random Order)

This one’s harder.

Pool Table Math with Excel (includes a Video)

This is a classic problem solving activity that I first saw many years ago in Mathematics: A Human Endeavor.   The NCTM has a nice applet to test cases one at a time.  

Since I like playing with Excel and trying to extend what it can do, I wrote a spreadsheet to represent the problem.  The end result is much better than expected — this representation uses a slider to show many cases in a short period of time, and with it I noticed patterns that I never had before (e.g. if you start at (1,0) on a rectangle whose sides have GCD=2, you get a loop that goes through all squares). Read more >>

Counting in Base Two

Practice with this Sporcle quiz — three minutes to count from one to twenty-five in base two.  Let me know what you think.  This is my first Sporcle Quiz ever.

Primes Less than 100

Sporcle game here.   Name all the primes less than 100 in 3 minutes.

The Handshake Problem

The handshake problem is an old chestnut — if everyone in the room shook hands with everyone else, how many handshakes would there be? Then generalize. What I have to add to teaching the problem is a handout (doc version, pdf version) with different (fictional, but based on reality) students’ strategies for solving the problem. This handout is good for homework after students have worked on the problems themselves and listened to their classmates’ strategies. Read more >>

Pascal’s Triangle

I was pretty excited when I figured out how to use conditional formatting in Excel to make a Sierpinski triangle.  I used very tiny cells, and then used conditional formatting to color in the cells corresponding to odd numbers in Pascal’s triangle.  The video also introduces Pascal’s triangle and explores some number patterns.  Spreadsheet used in the video (Excel 2003).

To do the conditional formatting in later versions of Excel, go to the Styles Group on the Home Tab.  Choose Conditional Formatting, and then choose New Rule.  Choose the last option, “Use a formula to determine which cells to format.”  Then enter the formula as in the video.

Newer Articles »