Monthly Archives: March 2015

How to Seem Smarter Than You Are…A Math Trick That Will Impress Your Friends

We’ve all been jealous of the math whiz who can compute everything in their head and has buzzed in the answer before we can even read the question.  But what if you could be that person?  How would you like to wow the college class (or co-op group) on that first day with your incredible mental abilities?

What follows is a mental math trick that will allow you to square numbers in a matter of seconds.  Read through the steps…practice a few times…and then call over a parent and get ready to wow them!

Step 1: Ask your friend (parent, grandparent, etc.) to pick a number for you to square.

ex. 84

Step 2: Find the number d that is the difference between the number they picked and the nearest multiple of 10.

In this case it would be 4 because 84-80=4.

Step 3: In your head multiply (x+d) and (x-d) where x is the number they picked.  It isn’t as hard as you think because one of those numbers will be a multiply of 10.

(84+4)*(84-4)=(88)*(80)

In my head I do 8*88 and then add a zero on at the end.  I get 704 so add the zero and you have 7040.

Step 4: Take your result and add d squared.

7040+16=7056

It takes a little practice, but it is so impressive once you have the hang of it 🙂

Bonus: For those of you who are true math enthusiasts…can you figure out why this works?

How to Choose a Math Curriculum

It’s that time of year…home school curriculum fair season!  Growing up we traveled with our mom around the U.S. to countless fairs, it became a family tradition.  Some people celebrate Mother’s day and have annual picnics on Memorial Day.  We rented U-hauls, crammed into the back seat together, and spent our time selling language art curriculum.  Believe it or not it was pretty fun.

If you’re headed to a curriculum fair this spring (hopefully using it as a much needed mom’s night out as well) you might be searching for a math program.  After 12 years of home education and 8 years as a high school math teacher I have seen some great and some awful approaches to explaining math.  And the textbook makes such a difference!  So here are three things to keep in mind as you’re perusing the table.

1. Student engagement.   Bring your student with them and guage their reaction. Or try to include them in some way even if it means having them “look inside” a book you’re thinking about buying on Amazon.  My mom used to include me in all the textbook purchasing decisions and this meant I had to take responsibility later in the school year.  I couldn’t real complain about my dumb and uninteresting math book if I had picked it out.  Now this doesn’t mean your child has the final say, but it let them read at least one lesson and see if they like it.

2.  Skill acquisition.  There are so many glitzy and engaging programs out there and that is great.  But the top priority…especially for struggling math students…should be the clear and organized presentation of skills.  Are the lesson readable?  Are the examples easy to follow?  Do the practice problems gradually increase in difficulty?  Are there enough practice problems?  These are the essential questions to ask.

3. Additional resources.  Make sure there is a good test bank or better yet quizzes after groups of sections.  Is there a home school edition that allows you to purchase everything you need without buying 5 different books?  In an ideal situation you’d have clear lessons, practice problems, additional problems if you need them, quizzes, tests, and even some ideas for projects.  And let’s not forget the all important solutions manual (not just an answer key!).

If you’ve checked off those three things off than narrow it down from there based on which program looks the most appealing to you 🙂

Kids Teaching Kids: The New Khan Academy

We all love the short, simple video lessons of Khan Academy…but what if there was a way to make them even more interesting?  A 6th grade class in California did just that by making the videos themselves.

Students love using the technology and acting as the director and producer of their own video lesson.  And as a math teacher I love the higher-order thinking skills they are developing as they decide on the simplest way to explain the problem.

So how can you incorporate this into your online class, local co-op, or home school program?

If you have an iPad you can use an app like Show Me to easily record.  Otherwise you need some type of screencasting software.

Try it out and make your own little math video.  It’s fun!

X Ruined My Life

 

The sentiment expressed in the title of this post is a direct quote from a high school math student…and many of us can relate.  Math is simple, predictable, and fun as long as it revolves around numbers.  And then all of a sudden in middle school this mysterious “X” appears and everything goes crazy.

So where did x come from?  Most of us were doing just fine with it only appearing in about 0.15% of English words and then all of a sudden it is THE letter in our math textbooks.

What is x?  And why do we use it?  Why didn’t we just use “a” or something more common? This fascinating clip from NPR reveals it all.  It is a fascinating story well worth 4 minutes of your time, it reminded me again of why majoring in math and minoring in Arabic wasn’t as strange as it might seem 🙂

Chopped

I’ve recently become a fan of the show Chopped.  The combination of crazy ingredients and a time crunch make for a thrilling 45 minutes.

 

But recently I stumbled across this blog post which describes a math version of the show that would be great in any co-op.  I also might do an online version for my students.  A quick summary of the activity is that students get certain  mathematical “ingredients” (paper clips, rubber bands, blocks, and a cup) and they have to use these to make a video that explains different functions.

The whole idea of students making mini-videos to explain math is a recent educational phenomenon.  Students love using the technology to make the videos and it forces them to really think about the mathematical concepts and vocabulary if they are explaining it to other students.  But I’ll post more on that in a future post.  For now, grab some mathematical ingredients and get chopping.

 

 

Snowflake Fractals

We’re snowed in again here in Philadelphia…again.  As 8 inches pile up outside of my door I couldn’t help think of this snowflake:

colorfulnestedKochsnowflakes

It is called the Koch Snowflake and it is an example of a fractal.  Fractals are a really beautiful field of mathematics where geometry and exponential functions overlap.

The Koch Snowflake is created by repeating a pattern over and over again.  Here are the first six steps:

kochsnowflakesteps1thru6

You can create your own Koch Snowflake by following these instructions here.  Or you can watch this video to learn more about them.


Koch snowflake fractal: A shape that has an infinite perimeter but finite area

Photo credit

Rumor Has It

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When I was on Semester at Sea in 2005 my friends and I noticed an interesting phenomenon.  With 800 or so people all stuck on one ship and no access to internet, rumors spread like wildfire.  One of my friends decided to start the craziest rumor we could think of and see how long it took to get back to us.  Within 4 days someone came up to our lunch table and told us the rumor that we had started!

This week in Algebra 1 we’re talking about exponential growth.  We talked about how rumors spread as one example of this.

Suppose you are on a cruise ship with 500 other people.  One person spreads a rumor to two people.  The next day those two people each tell 2 more people and so on.  How long will it take for at least half the people on the ship to hear the rumor?

The problem is actually a little trickier than you think the first time you hear it.  There is an equation for how many new people here the rumor each day:

1*2^t

But that doesn’t tell you how many total people have now heard the rumor.  We used a table to help.  Tables are always the best!!  They simplify the most complicated problem.

Day 0 1 2 3 4 5
New People 1 2 4
Total People 1 3 7

Can you complete the table and answer the problem?