Integer Stories

My Pre-Algebra students were given the task of creating integer word problems from a picture they had drawn.  The idea was to make the problems interesting and include information to solve the problem.  We discussed that to make a good integer problem, we needed to know "where did you start", "how far did you go", and "where are you now".  This was a great activity and gave the students a chance to show some of their creative side too!  I have to admit I got this activity from the NCTM May 2010 issue of Mathematics teaching in the Middle School.

I think next year, I may have the students take actual photographs and write word problems from a real life picture.

Imaginary Numbers

We've been talking in class about Real Numbers.  The Real Number System includes rational numbers, irrational numbers, whole numbers, and integers.  Of course, the students say, "well, what other kinds of numbers are there?"  I've explained there are other types of numbers called Imaginary Numbers and they don't quite get it.  I've done a little research for them and here are a few links, along with a video I suggest anyone interested can look at to understand Imaginary Numbers.
www.en.wikipedia.org/wiki/Imaginary_number
www.mathisfun.com/numbers/imaginary-numbers.html

Now, don't worry if you don't get it!  You'll have a chance to learn more about them when you get in high school.

Wow, that's a lot!

How many football fields does it take to make a mile, including the endzones... 14 2/3 fields!  Many students did not catch that I said to include the endzones so their answer was a little bit higher.  I also got some answers like 14.7 or 14.67 fields.  If we are talking about a football field what form of the number is best to answer in?  Can we think of the football field in parts or does it have to be as a whole when talking about this particular problem?  Why?

As an extension and for more extra credit, answer the above questions in paragraph form.  Your paragraph is due by Friday, September 23.

How much is a mile?

On Sunday, I was out walking with my two daughters at our neighborhood high school.  We were having a fun time and exercising hard, or at least two of us were!  My oldest daughter, Emily, is quite the athlete and loves to run, but my younger daughter, Lauren..not so much.  As I finished up my laps and sat down with Lauren, Emily kept running/walking laps.  Because Lauren needs to get in shape for soccer, I told her "let's race down the football field!".  As we finished racing and met up with Emily, we started discussing how far she had run doing laps around the field.  Emily then asked, "well how many football fields does it take to equal a mile?"

Here's a real life question you might actually want to know the answer to and you might have to do a little math to figure it out!  For EXTRA CREDIT, determine how many football fields it takes to equal a mile.  Include both endzones in your computating.  You must show your work on paper and then using WORDS, explain your reasoning and how you came up the with solution.  This is due by Friday, September 16. 

We'll let you know the answer after Friday!  And in case you were wondering, I only wish this was the picture of my neighborhood with the beach in the background! :)

The Math in a Garden

This week I tried a new experiment.  The experiment was to show the students a picture, have them ask questions about it, and develop a word problem from the picture.  Of course, the first thing the students said about this picture was, "this is an overgrown garden with lots of weeds."  Yes, it is, but it DID produce a lot of great vegetables this summer!

Once we got past how the garden looked, the students commented that the garden was L-shaped and that it was built up with two boards.  We talked about the process of building the garden and we came to wonder how many bags of soil it would take to fill this garden and how much it would cost.  The students quickly realized we needed to know the volume of the garden so we calculated that.  Then I had pulled up two different bags of soil from the Home Depot website.  Because I had measured the garden in feet, we saw that the bag labeled 40 lbs was not going to be helpful for us at this moment.  Therefore, we took the 1.5 cubic foot bag and calculated that we would need 70 bags of soil and that it would cost a lot of money!

After solving the problem, we then wrote out what we did and presto, we had a word problem!  The point I made to them...life IS one big word problem!  This was a wonderful, engaging activity and I hope to do more like this throughout the year.  If you have any pictures, that provoke a math question, send them my way.  I would love to look at them and develop a math problem from it!

Calculator Time!

This week we pulled out the calculators in Algebra.  I am both excited and nervous to be using our new TI-Nspire calculators!  These are very different than the older versions of graphing calculators, but they proved to actually be a little friendlier to use.  We practiced inputting points into a spreadsheet, creating new document pages, graphing our data, and experimenting with different functions on the calculator.  The students like that the calculator has a touchpad function and found that they could "grab" points and shift their picture around.  Here are a few pictures from our day's work.

You can see that the students were very focused and while they may have looked a little frustrated, the activity went fairly well and most students felt good about what they accomplished.  Our final product was a picture of a fleur-de-lis.