Too many resources

I was recently asked:

How do teachers make sense of this stuff that gets designed by other people and use it for their own purposes?

I usually take a quick look at the resource and think about if and where it may fit. I may make a note to myself to consider including it when I reach the appropriate part of my school year, and put together a unit plan, then I’ll return to it and consider its appropriateness with my students to achieve a specific learning goal.

There is an abundance of resources available online of varying qualities. I usually do not jump into and investigate a new thing just because somebody pinned it or shared it on Twitter, but I am always afraid I may be missing out on something awesome. I’ve learned that if it is awesome, I’ll continue hearing about it over time and be able to benefit from learning about its implementation in other classes

I am most likely to use a resource either because I learned to know and trust the source, understand the approach and can adapt it to my style and the needs of my students (Desmos activities Shell CentreIllustrative mathematics) or, because I read blog posts from other teachers discussing how the resource fits in their lesson the strengths and weaknesses of the lesson, what they plan to do next.

As an example: For many years, I heard about a barbie zipline lesson, but I never seriously considered incorporating it into my geometry class until I read a few descriptions of how it worked in other classes. Then I could adapt it to meet my learning goals.

My process when planning a unit:

After developing a list of learning targets for the school year and developing a high level pacing plan, I think about how students make sense of the content, and what content they already know that I can relate it to or build upon. I then sequence the learning targets for the unit. Next, I find, adapt or develop a synthesis project for the end of the unit that incorporates as much of the learning targets as possible from the unit and hopefully also draws in learning targets from previous units & grades too. Rolling cups or spiky door, for example.

After that, I look for hooks. I try to create conditions where students ask me to help them improve at the learning targets I have planned. I try to create a need to learn the thing. After that, I find, adapt, or develop application lessons where they can apply the learning targets as a culminating activity after developing basic understanding of a target – 3 acts and Mathalicious lessons fit well here.

I then lay it all out in a calendar incorporating days for direct instruction, notes, basic practice, and standards based assessments where they are appropriate. I usually build in a few unplanned days in order to allow for some flexibility throughout the unit to make space to dive into teachable moments that may arise.

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It is all in the set up: The Waiting Game

It needs to feel authentic

They need to get captured in the intensity of the moment. They need to feel that they are a part of the development of the situation. As much as possible, I need them to ask the questions, not the other way around.

The Waiting Game by Mathalicious

I choose this lesson on Valentine’s day as a preview to our probability unit. The premise of the lesson is to determine how many people a person should seriously date before committing to a partner for the rest of their lives.

The lesson plan as written begins with a very involved handout that lists all of the possible orderings of dating 4 different people: 1234, 1243, 1342, etc… Students are supposed to consider how frequently the end up with their number 1 partner if they choose to commit to their first love compared to if the break up with the first, but then commit to their second person that is a better match than the first, or the third, or wait for mate number 4.

I checked the reflect tab of the Mathalicious lesson to see if there was any thoughts from other teachers:

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I thought:

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How I adapted the lesson

I did not use the complicated student handout. They need to own this.

I opened the lesson by talking about love. I asked students if they thought they should marry the first person they fell in love with. I showed them some published advice column letters. They debated the advice they would give in each scenario. We talked about the episode of Friends where Rachel and Ross are on a break.

Students had intense opinions.

Quiet students who rarely speak up in math class gave thoughtful reflections.

We invested a good 20 minutes on the buy-in. It got to the point that students were asking; “Is this what we are doing today?” “How is this math?”

Then I asked: “Let’s assume there are 4 people you may fall in love with. If you marry the first person you date, what are the chances that this person is your best match, #1?”

Students replied: 25%

I directed students in small groups to the nearest dry erase board.

What are all of the possible orders that you could date the 4 people? Can you list them?

It started off a complete mess, but eventually groups learned that they needed to organize their thinking.

I followed the rest of this lesson as described in the teacher guide, but using dry erase board and discussion in lieu of a worksheet.

Students calculated the likelihood of committing to their best match if they committed to the first person that was better than their first match. There was some debate and confusion, but eventually students convinced each other that in this case there was a 7/24 chance that you would end up with your best match.

They concluded that the highest probability of ending up with their best match (#1) was if they did not commit to their first love. It was a great Valentines day!

We acknowledged the weaknesses of the initial assumptions and students wrote a reflection on how these assumptions impact our results and weather or not they agree with our conclusions.

 

I Cannot Think When Cheetos are Present

I wanted to make a quick post to remind my future self how the Mathalicious lesson Cheese that Goes Crunch went this school year & how I should adapt it for the future.

The purpose of this activity is to have students develop a method to relate cheesiness to the non-cheesy portion of a crunchy vs puffy Cheeto in order to develop a measurement of which is cheesier & by how much. It is a realistic application comparing surface area to volume.

I have 3 sections of geometry, so I attempted this lesson 3 times, each a little differently – and I’d do this lesson again next year, but with more changes.

In my first class I made a fatal error – I distributed cups to the students and then ran around the room with a giant bag of Cheetos pouring them into each cup. This turned the class into a party. Students sat with Cheetos while not working on anything. BIG MISTAKE. When I tried to engage the class in the lesson there was little buy in or understanding of the goal of this activity and I ended up dragging my class through each component of the activity. While it was completed in the end, it was not understood by students.

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For my next two classes, I set up cups with crunchy & puffy Cheetos in advance and set them out of sight. I introduced the activity and had good discussion and student ideas of which type of Cheeto was more cheesy and why. I didn’t provide them with Cheetos until they had a plan for determining which one was more cheesy and they concluded that the cheese was around the exterior, so the needed to compare surface area to volume.

I also found it pretty amusing how many students felt the need to organize their Cheetos:

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Overall the activity was a great way to have students apply volume and surface area to a context. Next year I will make this task run more like a 3 act and less like a guided worksheet. I don’t want to tell the students what to think and when. It’s too helpful to tell them to approximate each Cheeto as cylinder and guide them to find the surface area and then the volume, and then find a ratio. Students don’t have the same degree of curiosity and satisfaction compared to them deciding what they need to do themselves.

This lesson took one 45 minute class period, but If I make these adaptations for next year It will most like take two: One period for the initial student question development and calculations and a second for student presentations and possibly time for them to improve or reflect on their work. OR maybe a gallery walk and whole class discussion.

I’ll adapt it like this next year:

Act 1 will beg the question of which type Cheeto has more cheese flavor. I will work through a notice/wonder and develop a main question.

Act 2 will be students determining what information they needed and equating a serving of crunchy Cheetos to puffy Cheetos. Then finding the volume and surface area of an average Cheeto and developing and justifying a method to measure cheesiness.

Act 3 will include student presentations of their analysis effectively sequenced as described in the 5 Practices book and maybe a reveal of how much more cheese powder per volume there are in crunchy vs puffy Cheetos (although this may not be necessary).

This task is a great idea and is worth doing with students. I think I struggled with its implementation because I did not develop enough student buy in and understanding of the question from the start – which I continue to be reminded is a critical component to successful student problem solving.

Day 155 & 156: The Triplets of Cellville

I chose this Mathalicious lesson because we have not used circles enough in my geometry classes. We stared the school year with constructions, but haven’t used them much this semester and I wanted them to recall and extend prior learning. I also wanted students to gain more experience modeling real world scenario’s with mathematics & I thought this task would be engaging do to it’s relevance to students lives.  I started off showing the introductory video clip which is a news story of a woman explaining how photos taken with a cell phone include GPS data and how your cell phone records your location. I was surprised that ALL of my geometry students were furious at this video. They thought this lady was dumb for being surprised because “…everybody knows that you can turn on and off the location settings on your phone!” one student argued that if this woman in this video was her mother, she would be furious at her for being so clueless. It was great because it got very intense, and I had no idea how savvy students are with their cell phones. After this discussion died down students inevitably asked: “Wait, what are we doing today? Are we learning how to stalk people with their phones?” and “Mrs B, you are so weird.” Also “This is going to be awesome!” They were hooked.

I don’t want to describe the entire lesson in too much detail because I want you to support Mathalicious and their quality activities, but students constructed circles on a map to determine possible locations of a person in relation to a few cell towers. The lesson also discussed coverage vs locate-ability and students had to use estimation & area formulas in order to draw conclusions and also to determine and justify where they would add a cell tower in a city if they were in charge of making the decision. The only thing I would change for next school year is that I would modify the lesson to use our town and cell tower locations locally to make this more relevant and less hypothetical. Students were engaged and it was a good way to use student interest and incorporate modeling at the end of a school year when motivation is typically pretty low.

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Day 85: Viewmongus Awesomesauce

Today was so fun! We did a warm up reviewing Pythagorean theorem, then as a class, we worked through finding the dimensions of the 55″ television at the beginning of act 2.

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Students then worked in small groups to answer and discuss whether an 80″ TV is really more then double the area of a 55″ TV.  There was struggle, success, frustration, persistence, debate. Standards of mathematical practice abound!  Ahh, it was beautiful.

I had a few students who found a more efficient methods for finding the area of each TV:

The student below found the proportional increase from a 55″ to an 80″ and just multiplied the side lengths by the same ratio:

20140115-134412.jpgThis student calculated the area of each “square” in a 16 x 9 TV, then multiplied it by 144, saving him the effort of finding the length of each side and then the area:

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I love how students develop such smart methods when left to their own devices. Its sad to think of all of the times I’ve stifled that creativity by showing them just one method to solve a problem, instead of equipping students with tools and a good understanding of a problem and allowing them to use the tools as they see fit.

Day 84: starting Viewmongus

This was rough. I noticed that when I get frustrated, I push students harder & talk more, meaning that they learn less & I get exhausted & more frustrated. They did well with act 1, but then it fell apart. I need to shut up and give them time to think and trust that they will get there. Why is it so obvious as I post this, but it wasn’t an hour ago?

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Day 69: Starting Transformations unit: Face off by Mathalicious

Warning: this post makes a lot more sense if you are looking at the Mathalicious lesson, Face Off.

I worked through this activity prior to the start of class and thought that the geogebra files may impede students understanding of what they are measuring & why. I also knew we would not get to this until day 2 of the lesson, so I wanted to see how day 1 unfolded. Students seemed to really respond to faces. It got serious when we started looking at Beyonce’s face. I had no idea she was so polarizing!

Students had some great strategies for drawing the right side of each image in act 1. One student traced the left side using patty paper, flipped the patty paper to the right side and scratched it with her fingernail, which transferred the image to the right side. She then went over it in pencil and it was flawless! It was hard to not be helpful, but I consider it promising that students keep expressing frustration that I am not giving them enough direction or telling them what to do., but then they proceed to do a great job.

Many students flipped past the second part of act 1 and started jumping ahead while their peers were finishing their drawings. I had to tell them that today we are only looking at act 1, and I am giving them plenty of time because I expect them to do quality work. I made up a story to make it more personal: Demitiri made the drawing on the left and Kayla made the one on the right. I think Kayla’s looks better, but not perfect so I’m going to give her a B, and Demitri should get an F because that just looks bad to me. Arguments ensued. Measurements and rulers came out, it was a good discussion on how to fairly measure imperfections in symmetry.

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Next we used geogebra, because measuring was getting tedious, and completed the celebrity analysis. My only complaint with the geogebra file is that the titles on the right side points were movable, so some students moved the titles instead of the points, resulting in inaccurate measurements and lots of cursing & frustration on their part. Some of my classes got to the Obama part, but not all of them.

This lesson went well, but I did not feel like it ended with any real conclusion. The students were engaged, and they developed mathematical systems of measurement, which I think is much more important than being able to repeat a process. I will definitely do this again

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