Discovering Negative Numbers

Today I had a three hour Math Boot Camp where I reviewed basics and exposed new to our school students to math topics that our current students have already been taught.  I do not expect them to grasp these topics in one day.  But, it is great exposure for them and I get to see where they are mathematically so I can more accurately plan for these students this fall.  Again, this is exposure, not a full blown lesson.

One of the main topics today was the discussion of negative numbers.  Kids have such a hard time with this because they are taught so many “rules”.  Man, I hate rules kids have to memorize for math.  Today several kids even told me some of the rules they had learned, but didn’t know what they meant and could not apply them.  I actually prefer this to kids that just apply these rules because I can wipe the slate clean and start fresh with them.

I started with the idea of a negative number, showed them patterns so they could discover the answer, and then moved to a number line.  I also frequently referred back to the “concept” of a negative number often and pull finances in at every opportunity.  I mean seriously, what kid doesn’t understand simple money spending?  (As in, I want this awesome xbox game that cost $50, but I only have $30.  My Mom buys it for me and now I owe her $20, thus -20).

To introduce them to the idea of negative numbers, I asked them to represent (on a whiteboard) numbers for the scenarios that I gave them.  You received $45, 15 degrees below zero, you owe 27 dollars and 62 cents (decimals too), the depth of the titanic and the height of skydivers.  I told them they have been using negative numbers for a long time and didn’t even know it.

Then I moved on to patterns. The patterns I used were very simple and kids even laughed when we went through them.  This stuff is TOO easy and they loved that.  They got to see negative numbers come out and they were excited that they discovered the pattern.

  • 4 – 1 =
  • 4 – 2 =
  • 4 – 3 =
  • 4 – 4 =
  • 4 – 5 =
  • 4 – 6 =

After this I modeled subtraction on the number line, always bringing in parallels to money.  Then, I moved on to more patterns.

  • 4 – 2 =
  • 4 – 1 =
  • 4 – 0 =
  • 4 – (-1) =
  • 4 – (-2) =
  • 4 – (-3)=

This was a brief introduction today.  I am going to add more discovery and the need for working with numbers like -4 – 5  =  for an in-class lesson.  I didn’t hit them with multiplication and division of negative numbers as I didn’t want to confuse them.

After all of our pattern work today, one kid even said, “My IQ just doubled today.”  Did I mention how much I LOVE 6th graders?

I hate saying, “Subtraction of a negative”.  Or “minus” a negative for 4 – (-3).  What does everyone else say?  And how are you all teaching negative numbers?  I would love more ideas and discussion.

MS Sunday Funday – First Day / First Week Activities

Hi!  Be sure to follow me on Twitter for more updates!  I am @jreulbach.  🙂

Welcome to a collaboration of posts by amazing middle school math teachers!

This week’s theme is First Day / First Week Activities.  Next week, the theme will be sharing how you have your students set up their math class notebooks.  This can be interactive notebooks or traditional notebooks.

To submit a blog, click on this link.

** Brand new blogger!

Math For Math Mondays – Adhesive Tape Measures

As a middle school math teacher, I have been having the students take their body measurements for the past two years.  They usually stand up against a post, use a whiteboard and sidewalk chalk to mark their height, and then measure themselves.  Every month when they measure each other, I have a LEAST one student who exclaims with much dismay, “Oh my GOSH!  I SHRUNK – BY TWO INCHES!!”  Of course they didn’t shrink, but trying to convince an “eager to grow” middle school student of this fact, especially after they were SO proud the month before of how much they had grown, is almost impossible.  And of course, they had charted their imaginary grown spurt the month before – in PEN no less.

There are several errors they make when measuring their height.  One, they don’t hold the whiteboard straight, ever.  Two, my tape measures are only 60″ long, so they have to hold their finger at 60″, measure the remaining distance, and add the two measures together.  Also, their accuracy will depend on whether or not they are standing up against a flat surface.  Many times students stand against the whiteboard and measure themselves, then let the tape measure loop around the eraser tray but don’t take off that extra couple of inches gained.

Luckily, I found these very cool Komelon flat shell measuring tapes with adhesive backs at Amazon.comThere are a couple of different brands out there, but these had the best reviews.  THEY ARE FABULOUS.  They are STEEL, so they can withstand middle school students and will resist pencil markings.  They were CRAZY sticky, so they will NOT come off.  They were 12 feet high so they went up my entire 8 foot wall!  And, they were only about $4 each.  I ordered five of them, and hung them on the walls today.  I cut off the first 4″ so that I could install them over the baseboards for greater accuracy.

Hopefully, I won’t have any (or at least not MANY) distressed, shrinking middle school students this year!  🙂


On a side note, I woke up to another amazing measurement solution on Pam’s Blog.  I had never thought of buying the vinyl ones and hanging them.  She is much craftier than I.  I love that we both picked the same week to blog about the same thing.  I’ll say it again, Twitter blogging math teachers are AMAZING!