Graphing a Story

Video Productions for modeling mathematics in a graph.

We got the idea from this website.

Check out what our students created!!!!

They were busy working all week long.
Some chose the video option...

Some chose to work more directly with the content.

Making Sense of Exponents

Exponents are the little number "sitting on the shoulder" of the base number.

They basically tell how many times that base number needs to be multiplied by itself.

This week 8th graders explored various operations with exponents.

~ What happens when you multiply exponents?

~ What is the short cut when you divide exponents?

~ What do you do when you have to find powers of powers?

~ What does an exponent of zero mean?

~ Yikes!  You can have negative exponents???

They first found patterns and wrote hypotheses for what they thought the rule (we called it a shortcut) was.

Then the next day, we acted the problems out so we could actually make sense of what was going on!

a(to the 5th power) divided by a(to the 3rd power)

a(cubed)squared

By just playing around with the numbers, students came up with their own questions.  

Wondering outloud in math definitely moves our thinking!

~ When working with negative exponents, will the top numbers ALWAYS be a 1?

~ What happens when there is a negative exponent in the denominator of the fraction?

~ Does the rule still work if I use a negative exponent?

Students were using several math habits as they tried to decipher through the exponents.

1) Patterns

2) Finding structure

3) Wondering

4) Perseverance...there were four properties we had to get through!

More Spheres, Cones, and Cylinders

Besides finding the volumes of the Kansas sphere, cone, and cylinder,
A student traveled all the way to DisneyWorld and found another set containing a large sphere, cone, and cylinder.
Check it out!

What is the radius of this "cylinder"?

How was the volume found for Epcot?  What would the math look like?

How was the problem worked backwards to find the radius?
What information would you need to look up to be able to find the radius?
Find the volume of Mickey's Hat.

Figuring It Out

This last week, students spent their time in class attempting to answer the following questions.  It was exciting to see their minds at work!

1.  What is the linear dimensions of this gigantic ball of twine found in Cawker City?  

2.  How long would it take to fill up the hand dug well in Greensburg from a regular water hose?  

What would the equation look like?

3.  What would a graph look like if we were able to fill the TeePee in Lawrence to the top at a steady rate? 

Student examples...

Check out the following video for the 16 Habits...

1)  Did the student(s) show persistance in solving the problem?  How can you tell?

2)  Did the student strive for accuracy and precision?  What evidence shows this?

3)  How did the student communicate clearly?  

Thinking About our Learning

Here are some good questions to ask yourself

As we work through our volume unit.

Where are you in learning the formulas for volume?

Increasing Awareness

As part of our Awareness unit,
Students in math class analyzed the True Color data for organized groups here at RVMS.

Chart 2 App Sq Roots

Chart 1 App Sq Roots

Mixed Review for 8th Grade Quiz

Parents and students have been asking for some help on the real number system.
So here are some practice problems to help prepare for tomorrow's quiz.

Repeating Decimals to Fractions...Can It Be Done?

Yes it can!
Not only can it be done,
But our RVMS 8th graders found a shortcut to make the job easier.

Tonight, ask your 8th grader what the fraction would be for:
0.88888.... or
0.37373737.... or
0.123456123456.

We did have one question stump us.
What is the fraction for 0.999....?
When you do the math, it equals 1!
Hmmmm????

How do YOU see Real Numbers?

Check out some of the students projects on how visualize the real number system!

What creativity!!

Mrs. McCabe can RAP about Real Numbers

Check out my rap that I created!

Stay tuned to see student creations...
They are AWESOME!!!

Algebrainians At Work

Algebra is in full swing!  

Today we learned about the Real Number System and Absolute Values.

To help us remember the real number categories...
Mrs. McCabe sang us a song.

There was a real lady who swallowed a NAT

I don't know why she swallowed a NAT

Perhaps she'll fall flat.

There was a real lady who swallowed a WHOLE

That wiggled and jiggled and tickled her soul.

She swallowed the WHOLE to catch the NAT

I don't know why she swallowed a NAT

Perhaps she'll fall flat.

There was a real lady who swallowed an INTEGER

Oh what a stir, to swallow an INTEGER.

She swallowed the INTEGER to catch the WHOLE

That wiggled and jiggled and tickled her soul.

She swallowed the WHOLE to catch the NAT

I don't know why she swallowed the NAT

Perhaps she'll fall flat.

There was a real lady who swallowed a RAT (rational)

Imagine that!  To swallow a RAT.

She swallowed the RAT to catch the INTEGER

Oh what a stir, to swallow an INTEGER.

She swallowed the INTEGER to catch the WHOLE

That wiggled and jiggled and tickled her soul.

She swallowed the WHOLE to catch the NAT

I don't know why she swallowed the NAT

Perhaps she'll fall flat.

There was a real lady who swallowed an IRR (irrational)

Oh my dear!  It isn't clear...

She fell on her rear!

Why All the Fish in Math???

Students always comment, "Why all the fish, Mrs. McCabe?"
"How do fish and math have anything in common?"

I'm sure I could come up with a math problem (or two...or three!) including fish,
But this FISH! lesson is more important.
We focus on four FISH! to help us understand the math expectations in Mrs. McCabe's classroom.
And the best part?
These four FISH! ideas are a great reminder for life in general.


If the video doesn't play, you can click here to watch it.

We watched how Pike's Place Fish Market became successful,
And then we took their four ideas and brainstormed how it would look like in math class.

1.  Choose Your Attitude (Focus on Attitude):  Be happy!  Come in a good mood.  Make Every Day A Good Day!  Don't Get Mad, Get Glad!  Look on the Bright Side of Things.  Don't Be a Bummer.
2.  Play (Interject Fun):  Get Involved!  Movement.  Play with Numbers.  Math Games.  Have Energy!
3.  Make Their Day (Serve Others):  Help Others.  Don't Be Negative.  Compliments.  Be Encouraging.  Smile.  Be There.
4.  Be There (Here and Now):  Show Up Ready to Learn.  Keep Together.  Focus on Math.  Communicate about Math.  Engage with Students.

Go Math!

It's Friday.
We started math class today in a huddle.
Go Math!

Math Equate...It's Really Math Scrabble

Can't believe it's been almost a week since our first day of school!

So much has happened since we spent that first day with our new students 

Playing a scrabble-like math game.

Playing with Numbers & Learning Math Practices

Students on Friday and Monday worked on solving the Locker Problem,

But in the process, learned some valuable math skills to use throughout the year.

1.  Persevere when solving problems.  Most of the time our first strategy won't work.  We need to try it again or implement a totally new idea.  Working with others and not giving up helps us to meet our goal of finding the solution.

2.  Use the correct math tools when solving problems.  Math tools come in all shapes and sizes.  The most popular math tools are a simple pencil and paper.  Other math tools can include two-colored counters (shown above), graph paper, rulers...whatever is needed to help the solving process.

3.  Find patterns and shortcuts.  Math is full of patterns and if a pattern can be found a shortcut might not be too far off.  Patterns help us to make sense of our solution and to help us solve even more complex problems!

4.  Be precise.  When sharing our work, using the correct vocabulary adds precision to our explanation.  "Squaring the number" is more precise than "multiplying the number by itself".

Expectations

Perseverance

Perseverance.
What is perseverance?
According to Webster it's the continued effort to do or achieve something despite difficulties, failures,  or opposition.

It took perseverance the other night when trying to puppy proof our backyard.
See, we brought home an 8-week-old basset hound the week before school started.

Fillmore is your typical puppy.
He loves to chase his tail,
and run...subsequently stepping on his long ears and thus sent into a spiraling tumble,
playing with our boys and neighbor kids,
and since he's a basset, he loves to sleep!

At this age, though, I don't think Fillmore truly believes he's a basset.
Bassets are low to the ground and actually quite clumsy.
Basically, not the most graceful.
However...
One evening, we found him flung over the top of the dog run as he had somehow managed to climb on top his LARGE crate and somehow flop his body then over the two foot section of fencing still above him.
He also is not afraid of heights apparently
As we've seen him scamper up the ramp to the fort and enjoy the sights of neighborhood from 5 feet off the ground instead of his normal 10 inches.

This is where perseverance comes into the story.
From both his perspective and ours.
With going back to school, I knew we needed to make the backyard safe for him.  I couldn't have him hurling himself off the fort!  With my husband, the handyman out of town, I was going to have to solve this by myself!  Looking around the backyard, I decided to employ all the patio chairs and carefully and strategically placed them along and around the ramp.  Problem solved!
Later I saw Mr. Invincible scampering and scrambling his way up and over all those chairs.  Oh no!  This would never do!

Time for strategy #2!  Wanting Fillmore to have the run of the backyard, I thought I could employ the dog run to simply block the ramp.  Alas, the length of the gate was too long and provided a hole for my ever curious pup to find.

Strategy #3 was my son's idea (it's always best to employ more brains than just one when solving problems).  He suggested we place the dog run so the entire ramp was inside.  Perfect idea!  We had to use some muscles to lift the ramp out from where the grass had grown into it, but in no time at all, we had the entire ramp inside the dog run.  Without missing a beat, Fillmore ran under the ramp, found a little space, squeezed through and heroically ran up the ramp right in front of our amazed eyes!

Time for strategy #4, which ended up involving power tools.  With the waning light, this strategy proved to be a longer process than we had sunlight.

Finally, we had to look at our priorities...keeping the little guy safe.  We had one option left for the next morning, simply put him in the dog run with the crate in the MIDDLE.

During this whole process,
Lots of brainstorming and creative thinking was taking place.
One of us would suggest an idea
And then we'd quickly critique it as to whether it would work.
Some we tried out.
Others we simply discounted.

So, how does math fit into all of this?
Finding solutions to math problems is exactly the same to finding solutions to those problems that hit us in everyday life.
The first strategy we try may not work out.
Neither may the second one.
It may take quite a few tries before we come across something that works.
However, it's perseverance that allows us to keep thinking of new, innovative ways until we finally find something that works.

Welcome to 8th Grade!

I'm ready!

Are you?

I'm excited!

Are you?

So many new things to learn this year!

We're going to be moving our thinking

As we connect math to the real world out there.

Math is all around us.

Math is our friend.  :)

We need you!
Without you, our learning will not be complete.

Our focus that drives us every day is the FISH Philosophy!  You may have heard about the Pike's Fish Market in Seattle, WA and how businesses are using these concepts to become huge successes!  If it can work in the business world, it will also work in our math classroom.

Here's what it is!

F...Focus on Attitude!  
Attitude is a little thing that makes a big difference.  Come to class everyday with a positive attitude!  You'll see what a difference it can make and how much more you can learn!

I...Interject Fun!
We are going to make learning math FUN!  What other alternative do we have?  Not having fun isn't even an option.

S...Serve Others!
We work with others every day and will continue to do so for the rest of our lives.  If we try to make another person's day by treating them respectfully and positively, they'll feel better and surprisingly, so will you!

H...Here and Now!
It is important to be in the moment...not off daydreaming or planning what to do afterschool or doing homework for another class.  You will be MISSING OUT on all the fun!

This year in math, you will learn all the skills to help you be successful in here and in every future math class you participate in...not to mention, skills for life in general!

1.  Perseverance
2.  Reasoning
3.  Constructing/Justifying
4.  Math Models
5.  Using appropriate tools
6.  Precision
7.  Finding patterns
8.  Finding structure

Can you feel the excitement yet?
Can't wait to see you all on Friday!

Mrs. McCabe

What Do I Need For Math Class?

That is a great question!

Thought you'd never ask.  :)

To be a successful student in math, you will need to come prepared every day.

This means that you will have all the necessary materials needed to do the job...in other words, to do math.

Here is a list of items that I require you to bring every day.  Be sure to always check that you have the items before coming to class.

You won't want to miss anything just because you forgot something!

1.  3-ring notebook with dividers.  This will be just for math.

We are going to build our own math book this year!  We have a math textbook, but we don't use it much!

2.  Notebook paper - This can be in either form...loose leaf or spiral.

3.  PENCILS, PENCILS, PENCILS, and a pen to two.

4.  Calculator.

We have some to use in class, but often times students prefer to have their own, right at their fingertips.

5.  A Good Attitude
Some days we will be learning some pretty cool, but brand new, math concepts.  I don't expect everyone to get it right away.  By keeping a positive attitude, you're allowing the learning process to proceed without putting up any walls to jump over later.  You might just surprise yourself...math can be really fun!  :)

A New Year!

Dear 8th Graders,

Happy New Year!  August always seems to ring in a new year for me more so than January 1st for some reason.  I just love the excitement that a new school brings with it.  New faces.  New learning.  New experiences.  What's not to love?!

Enjoy this last bit of summer and stay cool!
We'll see you in a few weeks!

Mrs. McCabe

Happy 4th!

Courtyard Transformation

Check out the most recent pics of the courtyard!