10 Dec

2013-12-10 20.33.43

A book, I’m pretty sure, compiled by teachers. And perhaps I’ve been teaching too long when some things don’t make me laugh as much as they make me cringe… like this…

PhotoGrid_1386735679846

This next one made me laugh though. =) Instead of a banana car, I’ve gotten monsters, rainbow lands, and narwhals. Same plea though.

2013-12-10 20.55.45

Amusing

20 Aug

The new school year has begun!!

While Common Core Geometry is consuming my time, a quick share:

In creating a floor plan for their “dream home,” not a single student included a laundry room. 

I found that amusing.

Length, Area, and Volume

17 May

Them-PosterDid you know… that if you DOUBLE up the size of a chair by doubling up its dimensions in every direction, you will need FOUR times as much paint to paint that chair and that it will weight EIGHT times as much?

Did you know… that if a gorilla was to really proportionally increase to be the size of King Kong, that his guts would just explode and gush out of him from the sheer weight of itself? (The same concept prevents an elephant from ever getting a c-section!)

Did you know… that if an ant was really the size of the ants in “Them!”, not only would they not be able to stand up on their legs, they would also suffocate immediately?

Did you know… that if you proportionally double up in size, you’ll only be able to jump the same height as you did when you were normal size? Likewise, if you got 100 times smaller, you will also be able to jump the same height as you did when you were normal size! (So how long should it have taken for the kids in “Honey, I Shrank the Kids” to get home?) 

tumblr_m78krxad8d1qiceiuo1_500Interesting, right?  All these facts  take into consideration that very first “Did you know…,” that changing a linear dimension changes the area and volume differently. Intuitively we all have some understanding of this. I mean, imagine making an itty-bitty model of a wee little ant out of Play-Doh. How easily will the ant stand on its tiny legs? Now can you imagine building a 2-foot model of the same ant? You’re going to have some difficulty making it stand on the same proportional legs.

So I found it all the more interesting when I went online to search for great lessons on this concept and found NONE. I had never been able to teach this topic to very much detail due to our crazy pacing plans and, frankly, due to my hazy knowledge of the science behind it. However, this year, I had a couple of advantages that allowed me to actually try to plan a lesson- time, of course, and an awesome student teacher who is ridiculously skilled in the sciences!

Anyways, Day 1, I started with a lesson on the basic concept* and followed it up with a follow-up to an exit ticket from the area chapter. It was pretty interesting to see how many students didn’t make the connection to the worksheet that was previously given. I’d say it was about 50/50. Half who figured it out and half who simply multiplied the 52 square foot tiles by 12 inches per foot… (I posted this student’s work because she had asked me if she could simply multiply by 12 or if she had to convert all the numbers on the page first and re-work it. Like a good teacher should, I said, “Exactly! Test it!”)

tiles

The next day was the fun day though. I had almost an entire block period to now talk about the implications of same concept in reality.


 

Again, looking online, I found almost nothing fun, nothing very deep, and nothing very useful to me, except these notes… which I devoured. And from these, we came up with this lesson

__________________________________________________________________________________________

FACT: If you double up the dimensions in every direction, then the area multiplies by ____four____________ and the volume multiplies by ______eight________.

QUESTION: If you have a chandelier barely hanging from a rope and you doubled up the size, including the rope that it hangs on, will the chandelier still hang or will the rope snap?

Why or why not? (Make your argument here. You will not be graded based upon whether your answer is right or wrong, but on how well you make your case.)

 By this point, most students understand that although the dimensions are doubled, the weight of the chandelier has now become 8 times heavier. However, italicizing the part about the rope has them also consider the fact that the rope has also gotten 8 times heavier proportionally. A very true fact. I have them in groups and ask them to talk about it and then write out their argument, emphasizing that they will NOT be graded on correctness. 

I then take a vote. The vote for all 3 of my classes was close to 50/50. I say awesome, and before I give away anything else, I have one person from each camp make their case. I then take out a piece of rope to begin my “Consider…” lecture:

Consider… a really heavy object hanging from this piece of rope. I want to make it stronger and so I double up the length, like so, because I know that this will increase the VOLUME by twice as much. Will that make the rope stronger? [Class agrees, no way!] So then, how do I make the rope stronger?? … exactly! I need to double up the rope by making it thicker. So what does that mean? What does the strength of the rope depend on? The volume? (no) The thickness (yes!). And how do we measure thickness?? … the cross-sectional AREA!

So will the rope snap of the chandelier snap or not?! Discuss…

So yes, the rope definitely snaps. The cross-sectional AREA only increased four-fold (which is what the strength of the rope depends on) while the weight increased eight-fold. In this case, two chords of the thicker rope will hold the larger chandelier.

__________________________________________________________________________________________

FACT: The height that a body can jump vertically is directly proportional to the ratio of muscle mass to the total mass of the body.

jump height

, where C is a constant (enough).

QUESTION: If a human being who can jump 1.5 feet is doubled up in size (pretending like it’s actually possible), how high will the new larger human be able to jump? Explain.

 This was the section that my student teacher had helped me out the most in. He came back w/ an equation that we boiled down and simplified to the one above (apologies to any physicist who might get offended by this). I helped to explain what this equation meant and how it made sense. I made sure they all knew that working out actually made your muscles heavier, which makes total sense in this equation. I had them discuss and then take a vote. 

Their logic behind this one was so adorable. Most of them completely ignored the equation and went straight to guesses. “If twice as tall, muscles get bigger so they’re stronger… they can jump higher.” But the winner of all arguments…

He jumps shorter! Like Mario! When Mario grows, he can’t jump as high! 

The group cracked up and then voted, yes, he jumps less than 1.5 feet… like Mario. 

Final answer? This person will jump the same height of 1.5 feet. His/her muscle weight will definitely increase eight-fold, but so will the person’s total weight, canceling each other out. 

QUESTION: Now reverse the idea. If the same human being is shrunk to half the size, how high can the new small human jump?

Likewise, the smaller human can jump 1.5 feet.

(So how long would it have taken the kids in “Honey, I Shrunk the Kids” to go home?!)

It would’ve taken the same amount of jumps as when they were full size! This was an awesome discovery after reading that one professor’s notes.

__________________________________________________________________________________________

FACT: Ants don’t have lungs. Air is received through “blind tubes” that cover the surface of the ants’ bodies where air enters through.

QUESTION: If an ant was to be blown up as big as the ants in the movie, “Them!”
(pretending the physical structure is possible), what can you conclude about the
air intake of the giant ant?

 We didn’t have time in class to go over these, but these should be easier after all that we’ve learned. I should’ve given it to them for homework… 

 FACT: With larger animals came the development of blood circulation and lungs as a more efficient way of oxygen distribution. Lungs increase the surface area available for oxygen absorption by the blood.

QUESTION: If a human was blown up twice as big (again pretending like the physical structure is possible), how do the lungs have to increase along with the body in order to support the oxygen level needed to survive?

__________________________________________________________________________________________

Anyways, if there are any other lessons/facts out there that you think are good for this concept, let me know! I didn’t have this much fun lecturing in awhile!

*Some of the problems from that worksheet were either directly taken or modified from the NCTM Illuminations site.

And the winner of the Flashcards is…

12 May

www.QUIZLET.com!

After attempting my own templates at creating flashcards on Word and Excel, a student showed me this site and I cried, “HOORAH!!!!”

FINALLY! A website that gets it! At least for flashcard needs.

Screen Shot 2013-05-12 at 9.08.21 PMPROS:

  • It’s FREEEEEEE!!! At least until you need to upload your own images. Otherwise, it’s $15/ year. I happily paid it so that I can freely use screen captures and whatnot for geometry figures and algebra graphs.
  • They have an APP for it!!! Tap to flip, swipe for next card. Awesome.
  • Super easy and clean spaces for you to put in your words.
  • They have multiple languages you can type in, including MATH. =)
  • Your students can look you up and freely print your sets, or even create their own sets!
  • And my favorite?! They have 5 different print options!!! –>

CONS:

  • You can’t input images on both sides. Therefore, my cards are not all flipped in the same direction. I print, cut, and rearrange which way they should face, if and when it matters.

You can see the sets I have already created by searching my full name, jinnahwang (or by clicking here). I like to create class sets for them to practice with and have my own set to do my verbal vocab with. I’ve had students often ask me if they can get a copy and its always been clunky in printing out a PDF and then posting it on my website. I LOVE the print and fold flashcards as well so I can quickly print them on regular paper for students who are not-so-web-savvy and they can create them at home.

Love it!

Toblerone Challenge –> Can Top Challenge

28 Apr

Here was another fun one.

The Word file here: Toblerone Challenge

Screen Shot 2013-04-28 at 11.20.36 PM

A few logistics:

  • They got to work either alone or in partners. Winner gets ONE Toblerone bar, so if partnering up, they must share.
  • 20 minutes was all that they had. After the Play-doh activity the previous day, they understood that the winner would be the BEST net for this Toblerone box in those 20 minutes. No extension of time.
  • Only one sheet of cardstock was actually passed out to the groups. All other materials were available to them for pickup, if they needed- rulers, scissors, compasses, protractors. They had to build everything until they needed the gluing, pretending like I was the one who will be gluing (there was no glue involved).
  • Collect all nets immediately and put them aside to determine winner when they are doing classwork.
  • At the end of class, when announcing the winner, I took apart the real Toblerone box under the doc cam to see how the actual engineers did it. I then wrapped the chocolate bar w/ the winning net and awarded the winners their chocolate.
  • Hw was to find the lateral area, base area, and total surface area of the box.

Immediately after they turned in their net and before any kind of clean-up, there was a 5-minute bonus challenge.

Screen Shot 2013-04-28 at 11.36.11 PM

I had the actual can in my hands w/ the actual label on it. The label was only taped down on one side so I could show how it wraps around the can and opens up to be a rectangle. I pretty much laid it all out save handing the can to them. I think I still only had about 2 groups per class understand how to find the perfect circle to go on top of the can. Most of them just eyeballed it. Ha!

Winners of that challenge got a mystery can that I had pulled the label off of last year for last year’s lesson. At least the expiration date was on there to prove it wasn’t expired yet! They just wouldn’t know what it contained until they actually opened it. Heh.

Play-Doh Solids

28 Apr

(The lessons from this chapter are not coming out in the proper order, but hopefully they can still be useful independently…)

20130409_161828What better way to gauge how well your students understand solids than by PLAY-DOH! This was tons of fun.

Each team got one tub of Play-Doh, some fishing string (to cut), and a plastic knife. The Play-Doh had to rotate hands every challenge. The challenges were on Powerpoint, one challenge per slide.

First slide, person #1: in 3 minutes, build your best… tetrahedron. GO!

At the end of the 3 minutes, everyone has to throw their hands in the air and wave ‘em around like you just don’t care!… or just hold them there. I collect all the CORRECT tetrahedrons and then judge the BEST ones for 1st, 2nd, and 3rd.

The challenges/slides go something like this:

  • build your best tetrahedron
  • octahedron
  • dodecahedron
  • model of what the following net will build:
    tetrahedron-net
  • Regular pentagonal prism
  • Polyhedron whose cross-section is a triangle
  • model of what the following net will build:
    net_of_pyramid

You can add or subtract what you like to the slides and to the time allotted for building.

To consider for next year: Add a drawing section and have them next DRAW THE NETS to a given solid.

Raffle Tickets to Teach Perseverence

8 Apr

Again, back to this area chapter. Once the basics of finding area is taught, it’s a great chapter to get them to start thinking of different ways to solve a problem. But how do we get our little trained monkeys to do so?! Especially when they are so used to teachers teaching them exactly how to do a problem and then having them mimic our process? I don’t know about you, but I can’t stand hearing “but you didn’t teach us how to do this!” when there’s really nothing new to have taught!

Here’s one solution: Raffle tickets!

I used this for group work on one very difficult problem that required multiple steps. For example, for this chapter, ONE problem that looked similar to the following examples. (This came after finding the area of a regular polygon given the apothem and a side length.)

  1. Find the area of a regular octagon with side length 6 cm.
  2. Find the area of a regular octagon with radius 20 in

  3. Screen Shot 2013-04-08 at 9.26.35 PM

  4. Screen Shot 2013-04-08 at 9.28.48 PM

Every group had these hints written under their one problem:

Hints:

  • Did you try drawing a picture?
  • What do you need in order to answer the main question?
  • Can you draw any other parts that might be useful?
  • Did you try it multiple ways? (Try to re-draw, rotate the picture, split the picture, etc.)
  • Did you try using our extremely useful RIGHT triangles?
  • Did you double check your work? (Make sure you did not make any assumptions, that your answer makes sense, used units, maybe even try it a different method, etc.)
  • REMEMBER: You already have all the information you need in order to solve this problem!

Raffle Rules:

  1. Every team receives 5 raffle tickets to start.
  2. Up to 3 bonus raffle tickets will be awarded for the correct answer with proper and clear work.
  3. One bonus ticket can be earned for working well together.
  4. Each question that the teacher answers or hint that the teacher gives will cost 1 raffle ticket.
  5. Answer check is free only when the problem is finished. If correct, receive award. If incorrect, it will be made clear that there is a mistake. Each group can either try to find their own mistake without losing any tickets, OR teacher can point out where the mistake is at a cost of one  raffle ticket.

20 minutes were put up on the timer to solve just one of these problems on their own as a group of 3 or 4. In my classroom, each group also had their own large white board to work on.

And wow! did they work their butts off! It gave every student an incentive to fight through the problem. I had a couple of groups refuse any hints and tried to find the mistake themselves. I had a few groups not get the extra 3 tickets because they did not finish on time, but they still kept the first 5 so they still had a chance at the prizes at the end. It was awesome. At the end, they all wrote their group number on the back of their raffle tickets and we pulled one ticket from a shoe box and the whole group won a prize. Can’t wait to try this again soon.

My worksheets used here.

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