Posts Tagged ‘Lessons’

Graffiti Graph-iti Wall. That was an amendment made by kids.

Students had filled in their own unit circles (measuring the angles with protractors etc.), created charts to help them easily identify the sine, cosine, and tangent of all the angles, and worked out several unit circle problems.

Next came graphing.

We began our journey with this “guided notes”/discovery activity.

I won’t lie – the intent was students would move seamlessly from their unit circle into this x/y table and plug in and graph away. They would work individually or with a partner discovering and having a grand ol’ time.

Uh no.  With my two lower level classes I did need to provide more scaffolding. I started off with a simple x/y table of a line and reminded them how we chose the values for x and so on. Then I placed this table on my smart board and explained I had chosen my x  values as certain angles around the unit circle and we used the unit circle to find the y values. I also drew a “regular” x/y plane with 1,2,3 but then explained those are not my x values so it doesn’t make sense… and so on.

The students did a fantastic job after the appropriate scaffolding and continued the project for the rest of class and then for homework. The next day we practiced graphing with the Graph-iti Wall. All around the room I had placed different charts like the one below.

Students began at one station and were timed for 5 minutes. Everyone had a marker and everyone had to write. Everyone had to write, even though they were writing the same thing. They did as much as they could until the timer rang (or the music stopped, I couldn’t get my music working though!) and then faced the center of the room. The next task was to head to the next station and check the work completed before them. They had to actually check off  each answer and again everyone was checking off then they could move on from where the last group left off. They rotated around to about 4 stations and then were sent back to their original to see what happened.

There was a lot of writing – in fact you could barely make out the first group. Hence the graffiti idea. It’s an awesome activity for anything  multi-step and I look forward to doing it again!

Students got the amplitude and vertical stretch/shrink DOWN after this activity – which made teaching period (horizontal stretch/shrink) easier without the confusion of the “inner” number and “outer” number.

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I sent out my “rigorous revised lesson plan” before the break and I got a lot of positive feedback from the principals. As I reflect further and discussed rigor more with fellow teachers I realized I needed to go back to Bloom and all of his higher order thinking. I decided to rewrite this lesson plan using the row game model that I found by Kate Nowak (I think she invented it..?!) because it allows for individual practice, self/peer-checking, and a bunch of extra problems should the student finish earlier.

I also edited my do-now and exit ticket to exhibit that higher order thinking as well and put in more questions for the do-now tickets (as modeled by my observations of other staff in the building).

In the end, I was very happy with the revised lesson and so was the department head at the school. I think it still showcased creativity (row game), collaborative learning (working together, helping your classmate), and rigor (higher order thinking, scaffolding between activities).

As I know so many of you are completely fascinated by my job hunting: I am now being flown back out to Chicago by a different school within the same network on Monday – I will be doing a demo lesson for 11th grade pre-calculus on matching basic trig functions to their graphs. I now know I need to use some of the same principles of rigor in this lesson plan and I’ve already begun scouring the blogs and twitter for some good resouces and ideas.  So expect to be flooded with my many questions on twitter as usual (you guys are the best!).

Do- Now:

Row Game:

Row Game (KEY):

Exit Ticket:

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My students rock. We just finished a 3-4 day unit on Surface Area that ended with a quiz that only 3 students out of 70 did not pass – amazing progress!!!!

I started out the volume unit by handing-out a warm-up worksheet that asked students to count the number of cubes that made up each figure. There was an example at the top of the page that also showed students that it was cubic centimeters so answer with the units cm^3. I got fantastic questions immediately:

Are we counting the faces or are we counting the cubes?

Score 1 for a successful surface area unit yet again. I explained we are counting the CUBES, I saw many students erasing their previous answers. They finished the problems in about 3 minutes once they realized it was simply counting up boxes. We went around the room answering the questions making sure to include the correct units (hey, it’s cm^3 because they’re little cubes!).

Next I directed their attention to my desk, and asked them to turn their warm-up paper over and SILENTLY write down their prediction on which container held more and give a reason why. I stated again the need to not shout out because they don’t want to share their answers with their neighbors. I held up each Tupperware for them and its corresponding name (neighboring  high schools).

My demonstration table

I asked students to raise their hands for each Tupperware, we started with St. Joes. In the first class nobody raised their hand (interestingly, in the honors class about a third believed it was the biggest which shows they are different kinds of thinkers, but I digress). Instead of just moving on I asked if somebody would raise their hand and explain why they did NOT pick St. Joes. The volunteer’s responses included words like deep and short. I reenforced the word Height and when they explained that it was in fact wide I used the word Base. I continued to use those words over and over until the students started to include them in their own descriptions.

As expected, we became split on Masterman and P E&T and it was time to figure out how we were going to measure this! I held up my marshmallows and explained these were my kind-of-cubic centimeters like in the warm-up activity and we were going to count how many cubes filled it up. I asked why this wasn’t perfect and students explained that they were cylinders, wouldn’t fill up the perfectly, could we have half layers?, smushy, etc. And we agreed upon no smushing and a good estimate. I also asked if I could just dump a bunch in and they emphatically responded NO! I must build a layer on the bottom and build carefully.


I had a student volunteer and a supervisor (both rooting on opposite teams) to come up and measure P E&T while I measured Masterman for the class (it was clear). I found there were 6 marshmallows on the bottom layer and I showed this to students and asked if I could find a shortcut. I decided to look at how many layers could I fit and noticed there were four (I stacked four marshmallows on the side and showed students). About half the class shouted, TWENTY-FOUR MARSHMALLOWS WILL FIT!

Score. How did you get that number? I multiplied. Why? Ummmm. Okay, let’s see if you’re all right! And then I proceeded to fill up the Tupperware and WOW, 24. And then I asked them use the terms base and height to explain their shortcut and they explained they multiplied base by height.

The next awesomeness happened when skinny ol’ P &ET ended up with 25 marshmallows and we were flabbergasted on how the two different shapes could hold such a similar amount! And then students started to realize that maybe ones fatter base made up for the shorter height. The conversation was mind-blowing and it occurred in all three class periods.

So when time to show them the volume formula for rectangular prisms and cubes it was super easy for them to see we just get the area of the base and multiply the height. They wrote down the formulas I put on the board and did the following two pieces of classwork, exit ticket, AND completed their homework. Mind you, we did all this in a short day – which means 38 minutes. WOW.

They continued to show me they understand the concept of volume when we moved onto more figures including cones and pyramids which we compared to cylinders and prisms and saw how their volume was related (I put figures inside of other figures and asked questions like which holds more to reenforce similarity/differences) and thus the formulas would be related. It’s been a very successful and exciting 2 weeks of learning for us!

Unfortunately – I only have 10 days left of student teaching. Which means I am going to do some AWESOME things for the next 10 days to get the most out of the last few days – up next, Pythagorean Theorem (looking for projects!)

Sources: All worksheets (except Molly-made exit ticket) taken from: http://www.superteacherworksheets.com/volume.html

My Links: Classwork:http://www.scribd.com/fullscreen/73201749?access_key=key-1f62a6i45ii2q5u5p4zf. http://www.scribd.com/fullscreen/73201750?access_key=key-2kgmvw3emrxadclicsrr


Exit Ticket: http://www.scribd.com/fullscreen/73201835?access_key=key-rishm72tbtyzsvm7aqf

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It seems like forever ago but I wanted to finally blog about the success of the Discovering Pi/Discovering Circumference formula project I did with my students.

I used this as a warm-up to squash any questions students may have had about vocabulary etc.

That took about 5-10 minutes for us to answer as a class and reinforce the correct answers and why. I also made a point to let students know that they should pay attention or take notes because they would need to know all these things to successfully complete the project. I also explained that this project would count as a quiz grade and an opportunity to boost their averages. These were all (bribes?) incentives for students to engage with the project and do their best.

I handed out the worksheet and read the directions out loud. I also read the rubric out loud for students with a strong emphasis on the FOCUS ON TASK points.  I passed out supplies or in some classes I let students help me pass out supplies. We don’t have enough scissors or glue so students had to share those but each student got 2 different sized pre-cut circles and two different colored pieces of yarn.

I would probably not use yarn if I were to do this again, it stretches and makes a lot more opportunity for measurement error. I used yarn for a prettier poster option but in hindsight something without stretch would be better.

I also put a giant grid on the white board for students to put their name and their two decimal answers up on the board when they completed their calculations and before they could get construction paper. In the last 10 minutes of class we looked at the results on the board and at least one student in each class recognized we were awfully close to pi.

I then wrote C/D = pi and then solved for C = pi*D, and then we discussed radius and diameter and substituted and got C = 2*pi*r. A lot of students were shouting out “pi-r-squared” but when we got the end they were able to see that the circumference formula is not “pi-r-squared,” and why. They did identifying radius, diameter, and find the circumference procedures for homework and do-now’s the next day.


Students got so creative and were so engaged and here are some of the results:

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Since the principal special requested math-art to decorate the 9th floor hallway I finally get to do a project with my students. Unfortunately, I’m pressed for time and I have to do a one day in-class project with posters up by Friday. But fear not students, I think I have an idea.

I found this online and it’s pretty much what my co-op described he wanted to do. In 48 minutes I think we can move this 2 day 7th grade lesson to an 11th grade discovery activity. Furthermore I know these students do not know what pi really means – hell it took me a whole week to teach that it was irrational (but they ALL got that one right on the previous quiz, yay!).

The one thing I preferred about the original activity was that students measured 6 different objects on their own. My students really struggle with measurement in general (i.e. they don’t quite know 12 inches in a foot etc.) so I don’t want to take away from the purpose of the project by creating too many obstacles but I also don’t want to lose the fun in it.

The students will measure 2 pre-cut different sized circles and fill out the worksheet accordingly.  I was thinking to put a big grid on the board where all the students would record their final column. Once we discover that “Hey – that’s pi!” – we’ll see which student measured closest to pi which can lead us to discuss measurement error and so forth.

Thoughts? Revision suggestions? This is not happening until Wednesday so I look forward to your comments.

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I really liked the way I introduced square roots and it was completely stolen from Dan Greene (and all of his awesome Algebra 1 lessons can be seen here).

The course I’m teaching (11th grade PSSA prep) is basically a “review” that helps kids pass the state test. How I’ve decided to teach the course is a “problem solving/critical thinking” course and I’m allowed to do this because most people associate any problem with words with critical thinking *not true*. The cool thing is since I’ve deemed this as a critical thinking course and the students are required to actually take Algebra 2 concurrently I’ve requested to simply teach concepts and reenforce understanding rather than memorization/procedures. So far I’ve gotten the green light from my co-op.

So, right – square roots. Most students should know this by 11th grade but the truth is these students didn’t. They had heard of a square root, they’d seen the symbol and some even could list the perfect squares (not from understanding but by adding consecutive odd numbers) but they didn’t know what it was, why, or where it came from. Enter Student Teacher Molly.

I taught this lesson over 2 days and introduced square roots by relating finding area of a square with given side lengths and looking for the inverse/opposite, what if I give you the area of a square – how would you find the side lengths?

I started with the side lengths of 3, which gave us an area of 9. Then after doing side lengths of 3-5 I put up a square and said the area was 9, so what must my side lengths be? Since we had just done this they knew it must be 3. We did this a few times and I introduced the new notation saying that the side length for the square with area 9 is the sqrt(9) = 3, and I wrote that along the side of the square. We did area of 25 together and wrote it as sqrt(25)=5 on the side length. Then they did the 3 squares on their sheets alone. I easily saw the misconceptions of side length being sqrt(5) and so I was able to walk around and address that discussing area etc.

(**My only issue here was the introduction of the square root symbol which felt a little forced like, hey this is a quick little shortcut symbol we use to denote this idea and this is what it means, I would’ve liked to do some history or something else on the symbol in hindsight**)

Then we filled in the proper way to say square root of A and what it was, “the length of a square whose area is A” (most of the students actually did that on their own). Then we talked about perfect squares and how they get their names and we made our lists. We began to talk about estimation and what to do when it’s not a perfect square; the first day we just left the side lengths in square root notation (before we got ‘2 answers sqrt(9)=3, but now we just get sqrt(10)) but the second day we started to estimate what they would be between.

The next day we talked about estimation which was actually a breeze. I started by actually drawing the squares next to each other so they could see porportionally what perfect square was bigger and smaller. After we did it with the phsyical squares, I just used our new notation and placed the question on the board, filling in the small square root above the one in question and the bigger one below (like a smush sandwich) and voila, you can find the whole numbers it lies between.

And the students really got it. When we went back to the PSSA book that asked questions about square side lengths and area the students were able to answer them easily (or maybe easier is being more honest) than if I were to have to introduced the square root more abstractly with all symbols and no squares. Thanks @dgreenedcp!

Here is the worksheet taking almost exactly from Dan Greene with some changes based on stretching the lesson and a few other things.

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I don’t know what I would do without you guys. As I explained a couple posts ago my goal is engagement, engagement, engagement. I am teaching a lot of dangerously boring procedures in these test prep classes with students with short attention spans and not a lot of respect for authority and mathematics. Basically a recipe for a student teacher meltdown.

I searched and searched and searched and finally SUCCESS. I stumbled upon this set of postings (with worksheets) by  Mr. K and then I hit the jackpot by finding an amazing introduction by @ddmeyer here. He introduces the idea of scientific notation by asking students to write down names of states which ultimately leads to a discussion of common abbreviations of states. He also gives students a bunch of insanely long numbers and has them kind of invent scientific notation on their own. That’s amazing but I only had 38 minutes of awesome to provide to kids who barely want to listen to me (and no tech to display said long numbers) so I had to modify slightly. Luckily this woman Amanda commented on dy/dan’s post and offered the suggestion of using text messages abbreviations and VOILA I knew I had a winner.

I placed this on the white board.

Students got really excited, “I can write whatever I want?” Yes, absolutely, as long as it’s appropriate knock your socks off. So as I went around and checked homework students wrote their new text message, abbreviating whatever words they wanted. I gave the following lead off example, “I know you all probably say ‘hey’ instead of hello.” Then I asked them to raise their hand and tell me a word they changed. This was the result on the board (summary from all 3 periods):

Then I asked them if everyone would know what “wsp”  would mean (or whatever the odd man out was up there), most said maybe (it means what’s up) which transitioned beautifully into a conversation about abbreviations, usefulness, standardizing for understanding, etc. One student even said she added extra vowels for emphasis, her example, “I don’t knoooooooow.” This was awesome because that led right into abbreviating large words/text messages or making small words larger. Then I talked about how in mathematics we do the same thing – take the distance to the sun .. and so on.

It went great! The kids were talking and completely engaged. I kept emphasizing raising their hand in order to contribute to the board so it was reasonably controlled chaos. They even paid attention to the somewhat lame procedural lecture that followed when we discussed the previous nights pattern homework worksheet from the Math Stories blog. (*They could use a calculator until they found the pattern. It was assigned as a pattern hunting worksheet rather than a scientific notation one).

Love when plans go well, I know it’s rare so I’ll savor this moment.

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