Mean, Median, Mode, and Range

I can't even begin to describe the work we put our brains through last week when we approached 'mean as a balance point' vs 'mean as fair share.'  Luckily, my kids are amazing and we challenged ourselves and ultimately came out on top, if I must say so myself.

Although most of my kiddos remembered median, mode, and range, I wanted to make sure they had notes in case they forget.  Also, it was important to me to make sure that they had notes comparing and contrasting mean as described above--as a balance point and as fair share.

I thought a semi-cootie catcher would do the trick with a little extra love on the 'mean' flap.  :-)

I was very mindful in how each word was written except for 'mean', which I knew would need two separate images for balance point and fair share, so I left the outside word 'normal-looking.'  You can see a green line (barely) under the word 'mode.'  The kids picked up on the idea that the mode is the response or data point that occurs the most often, sort of the way the word 'mode' appears here, as if it were on a line plot (come on, work with me here!).  Range has the arrows to demonstrate that it shows how spread out a data set is.  The picture didn't copy all that well for median, but I watermarked a median in the middle of two neighborhood streets and spread the word 'median' out (in the middle of the word, of course) to make that reference.

You can (kind of) see from the picture above that the mean flap has a flap within the flap.  Here is what is going on there...

Here, I was trying to show mean as a balance point within the phrase with the use of a balance scale.  Notice it is balanced :-)

And the other side to this flap within a flap...

Here I was trying to show that with mean as fair share, you are finding the average by divvying up the data points into even groups, hence, the 4 squares with one letter per box.

When you open the flap within a flap all the way open, this is what we created...

We based our outside flaps on the steps we completed throughout the week as we found mean as a balance point and mean as fair share and we used the example in the middle to show how mean as a balance point can be used to find an estimate when the data cannot be 'perfectly balanced' and then you can find mean as fair share to determine a more specific mean.

For consistency, on the inside flaps of mode, median, and range, we used the same data.

I knew this foldable was going to be pretty cumbersome with all of the gluing and the mind-boggling revisiting of mean as a balance point vs mean as fair share, so I kept the kids writing to a limit in the general descriptions for mean, median, mode, and range.  We just did a little underlining and highlighting.

Pythagoras, O Pythagoras!

I think I mentioned earlier that one of the concepts I miss teaching now that I've switched from 8th grade to 6th grade is The Pythagorean Theorem.

I decided to covered this with the students headed to Algebra next year prior to teaching surface area and volume of cones and rectangular pyramids so that I can incorporate some multi-step problems where they have to find the slant height or the height prior to finding the other measurements.

Here is what I gave each kiddo:



They need both because one is taped down to the composition book and the other is cut and used to prove the theorem.

In order to prove the theorem, we labeled the dimensions of the triangle and the squares and color coded each square.



From there, we cut out one of the pictures along the perimeter and we cut the other picture so that the largest square was still attached to the triangle, but the other two squares were separated. Then, we glued the squares with the triangle intact into our math 'textbook' attaching the triangle only to the paper. From there I showed the kids how one of the remaining smaller squares fit into the larger square and by trial and problem solving, we discovered how the remaining square could be cut to cover the remaining area of the largest square, thus proving the Pythagorean Theorem. I was sure to explain that this is ONE of many proofs, but I really like how the notes became the proof in this case!

i have been put to shame!

here i am thinking i am helping the better good and creating foldables and then my PLC partner BLOWS ME OUT OF THE WATER! She created an AMAZING foldable to show the relationships between and among parallelograms.

the best part:

i kept getting to say 'cootie catcher' when i was giving instructions because you fold part of the foldable in like a cootie catcher (fortune teller for those of you still scratching your head trying to figure out what on earth i'm talking about)

need to get her permission to post a picture...ashamed i'm not create enough to come up with anything this cool, but what can i say, she's a genius!

one of my students today said, "you guys should sell all of these foldables you create." how sweet was that : )

foldables storage

i will post more on this later, but so far the solution to the potential nightmare with foldables (where and how to store) has been a composition book. I like composition books just about as much as binder clips. it must be a teacher thing. i hoard composition books like crazy. my favorite thing to do with them is to put a book cover on them so that i can store pens and post-it notes in there.

i'm diverging.

moral of the story...i think the composition book will be the foldables BFF. i'm trying it out in tutoring to get confirmation that it is the way to go next year for my classes.

list for spring break

this is more for me than anyone else, i guess, but if you have any ideas, let me know!

• quadrilaterals--relationships, similarities, differences
• SA and V of pyramids and cones
• integer operations
• congruence

best way to store foldables

I am pretty sure this is the reason I took a vacation from foldables in the first place...I had no idea what the best way to have the kids store them.

We are making out okay currently by copying a sheet with a header on it and having the kids glue the foldable to it. From there, they add the page to their 3 ring binder with the rest of their math stuff.

I MIGHT (notice the emphasis on 'might') have come up with a solution for random, vulnerable foldables for the future. I am trying it out with the students I am tutoring before and after school. Rather than adding the foldables to a sheet of paper, we are gluing/taping them into a composition book, hence creating a customized, unique math textbook that can be used as a reference for this year and beyond. I wish I had thought of it earlier, but now I have the time to try it out with tutoring and hopefully identify any glitches prior to implementing the idea with close to 100 kids.

Any thoughts are welcome.

Area of a Trapezoid

First and foremost, let me apologize for the extremely poor quality of these photos.

Covered this with my students moving up to Algebra next year. We don't cover the area of a trapezoid in 6th grade.

As usual, I wanted them to understand the 'why' behind the formula.

We simply took a sheet of paper and hamburger folded it, ripped it, and shared with our neighbor (each student only needs 1/2 a sheet of paper). from there we folded it in half again, hamburger style. Then, we cut some off of the left and right sides to create a trapezoid from the rectangle.

To show that the formula of a trapezoid is 1/2 the height multiplied by the two base lengths added together, we folded the top layer of the trapezoid so that the front showed 1/2 the height. We glued it such that the portion of the trapezoid we cut off matched up with the 'flap' created from the fold.

{unfolded}

{folded up}