Literal Equations: Tweets from #mtbos

 Literal equations is one of the topics in Algebra that I struggle finding different activities for. Literal equations is one of those topics that is very procedural and not very conceptual. I put together a list of different activities from #mtbos on Twitter. Look through each of these and see which ones you might like. 



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Teaching Scientific Notation Using Omni

A normal resting heart rate is between 60 and 100 heartbeats per minute. Use the following calculator to help answer the following questions.

Scientific Notation Calculator
    

                                                                                            Number                            Scientific Notation
a. How many heartbeats happen in a day?                    _____________                __________________

b. How many heartbeats happen in a week?                 _____________                __________________

c. How many heartbeats happen in a month?                _____________                __________________

d. How many heartbeats happen in a year?                    ____________                ___________________

e. How many heartbeats happen in a lifetime?            _____________                ___________________

What are some questions you might have?

__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________. 

Let's draw a number line... how could we put all the data points on a number line?


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What do you notice about the scientific notation row? What do you wonder





What number might you think 2.05x10⁵ might be?




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Chef's Table

I love good food. I love trying new places. I love the idea of curating an experience, especially with my wife. One place she took me on my last birthday was V. Mertz, probably one of the best restaurants I have ever been to right here in Omaha, that includes going to the James Beard Award Winning Zahav. But, one of my big life goals is to go to Alinea in Chicago. I was trying to get my brother-in-law to understand why going there would be so awesome, but words weren't cutting it. So we watched the 55 minute long Grant Achatz episode on Chef's Table.

Rewatching this episode during this time where education isn't really education and not knowing what education will look like for next year, this one quote stuck with me when Achatz was starting his new restaurant Alinea he said:
"We gathered the staff and I say everybody needs to believe the fact that we are about to open the best restaurant in the country. And anything else will be a failure."
Now I think that almost every part of this episode can be dissected and adapted to education, but when we start again in August, September, October, or whenever we start, what are we coming back to? Worksheets? Taking notes? Sitting in rows? Furthering equity gaps?

What if instead of going back to the same old school in the traditional sense, we came back to school thinking how would the best school in the country open? What would the first lesson be? What would the first unit be? How can we transform the learning of our students?

Listening to Zaretta Hammond's webinar Moving Beyond the Packet: Creating More Culturally Responsive Distance Learning Experiences she went into detail about making connections, using background knowledge, and actual doing. How can we rebuild school, because next year isn't like starting a new year. We have a chance to build a new system?.

Will we think that this chance is the one chance to be the best and anything else will be a failure?


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The End of the Decade

I vaguely remember they Y2k scare (I was 11). I don’t really remember how the 2010 new year was, but as 2020 comes closer and the end of this decade approaches it has put me in a reflective mood over the past 10 years. For me educationally, I feel like my philosophy of education has changed, especially outside of the teaching math realm. Below are some things I used to think were important or how I thought about education.
  • I used to think that engagement was key and building elaborate learning experiences would help my students make gains and remember the material for the long term. 
  • I used to think that the latest and greatest would help bridge that gap from coming to math class to enjoying math class.
  • I used to think that being a teacher was only going to be a part of my life.
  • I used to think that I could carry the weight of the class on my shoulders.
  • I used to think that content was king.

From the end of college, to subbing for a full year, to my first teaching job, to my second, to my third. My first teaching job left some scars that I am still getting over. I feel like I left a home at my second job to become a better teacher. I got my Masters a few years ago and there have been countless people and PLN members that have been influential these past 10 years. There have been countless teachers that have opened their doors for me to come in and look. To mention a couple of people, first off Marty Fetch who is an instructor at Doane University that focused on building classroom culture. I’d like to thank countless people in #mtbos and #cleartheair specifically Marian Dingle and Val Brown, whose guidance and leadership in these spaces makes it evident of the work that needs to occur in our classrooms.  I am thankful for all the experiences this decade and all of the teachers and students I have had.
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Golden Sower and What Needs to Change

I've been participating in #cleartheair on Twitter for a little more than a year now. It has led to me to know some amazing educators doing amazing things in their classrooms, but more importantly it has showed me what I need to do to be a better educator for every single one of my students. One thing they led me to was the National Antiracist Book Festival, it featured great books that I have read and one of my challenges this summer was to read all of the ones featured, I know that will not happen now. But, one thing I learned from reading some of these texts was to use my privilege to let others, especially people of color, have a voice in the conversation.

This leads me to one of the things I like to do is read YA, even though I am a math teacher and I haven't read in a while, but I am a part of the golden sower reading committee one of the things we do as a group is narrow down all the choices of books librarians, students, parents, and us submit to 10 titles. Students then read these 10 titles and vote for them and one of them wins. The author is normally invited to the state to speak, sign books, but one of the big things is advertisement in the state for all of the libraries for the 10 selected. Normally each library has a collection of golden sowers and the winners.

Here are the 2019-2020 nominees for golden sower.

One thing I want to bring to light is the number of diverse books we are choosing for this list. You can see the 10 nominated going back a decade an a half here. At most we have 2 diverse books per year. Here is a breakdown of Nebraska Public Schools as a whole. Does 2 books suffice?



One thing I want to point to you to, if  haven't heard about this story is Dr. Ferial Pearson, "Deceit Wrapped in Kindness." There was an article published in the Omaha World Herald, but it was pay-walled. Read it. Take your time to fully digest it. I will wait.

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I grew up in Blair, I went to college in Crete, I live in Bennington, taught in Schuyler, taught in Omaha.  I've been all of this state and I have never once felt uncomfortable being anywhere and I know that is my white privilege. That I can walk anywhere being a white cis-gendered male and know I will be safe.  I am not going to judge, but I do have some questions. How are we as a state educating our youth? What books are they reading? Are they reading about people who don't look like them?

This just isn't a Mullen problem, it's a Nebraska problem. I believe there is a direct correlation to the books we choose as a part of the Golden Sower and biases and stereotypes that we perpetuate in our state. I have been less vocal in the past about the books chosen for the Golden Sower. That comes to an end today. It is my duty to put books who look like all of my students in front of them as a part of The Golden Sowers reading committee.

Next year's Golden Sowers are already chosen for 2020-2021 they are not set in stone, but overwhelmingly chosen. My personal goal is to have the 2021-2022 Golden Sower selections to be the most diverse since the beginning of Golden Sower YA in 1993.

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Exponential Problem

It has been a couple of weeks since I taught exponents and logarithms. We do all the normal things we do with them in Algebra 2. We changed from one to the other, we graphed, we looked at their properties, we did half-life and doubling problems. When my students took the test I was happy to see good scores this late in the school year when motivation can run low.

Today I found a great problem on a site called FiveThirtyEight it has a weekly puzzle people can submit to and it was relevant because Avengers EndGame had just come out. The problem looks like this:

I was going to use this as a bell ringer. I thought it would take them about 2-3 minutes to do. I gave them no further instruction than answer the question. They could use their notes from the last chapter, anything that could help them. After 5 minutes, some students had started to give up. Some students were having rich-mathematical conversations with each other. Talking about halving, did the number of Thanoses also halve, does the original Thanos die when he snaps his fingers. This bell ringer that was supposed to be taking 5 minutes at the maximum is now going on 10 minutes. I felt like there were some misconceptions that students about this problem and that more time would help solidify exponential equations.
I let students struggle for the next 25 minutes, working with partners or in groups, using their notes. Some of the students and groups persevered through the problem, other groups were harder to get moving through the question. Here are some examples of the work my students did.
 



I taught this class three times, after the first time I went to some of the teachers that teach the same thing and asked them if this was beyond their thinking, after a while they decided that the students should be able to answer the problems from what we went over in class, but they added that the student’s wouldn’t be able to get an answer. After two days of sitting on this I went back to them, I wanted to know why they thought the students couldn’t answer the problem and what we could do next year to remedy this.
Here were some of the teachers responses to why the students weren’t able to answer the problem:
  • One teacher said we did exponentials and logarithms too long ago for students to remember. Also students only remember or do what we teach them.
  • Another teacher said students don’t know how an exponential equation works.
  • Another teacher said students can’t persevere or formulate questions.
Here were some of the teachers responses to what can we do differently for next year so we can solve this problem:
  • One teacher said we need to be more connected across Algebra 2, we should start with a question and answer it over the course of the unit or chapter, it needs to be an expectation that students can problem solve, students need to get use to out of the box problems from the start of the year.
  • Another teacher said we need more modeling and that students need more practice at it because the capability is there.
  • Another teacher said we should start off the chapter and year with questions like these, we need to change the way vocabulary is taught especially when it comes to a problem like this, we need to teach students how to use a simpler problem to solve.

I agreed with all of the responses that we should be doing next year. When you value problem solving over speed and simplicity you help your students become better mathematicians. This was a good problem for my students to work on for a day, this will help me become a better teacher for them in the future.
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Creating a Polynomial Function

One thing that I have been looking forward to trying in Advanced Algebra is more tasks. One of my goals for this year is doing more mathematical talking and orchestrating better discussions in the classroom. One task I created recently that still needs work is this creating a polynomial function from zeros task. Previously students have only factored and solved polynomials with P's and Q's. I was thinking they could work their way backwards from the previous days material.





Here is a link to a better looking version.

I gave them the task to work on for 15 minutes and I went around the classroom getting students started and answering questions.  If I had more time I would have done a better job of calling students up and presenting their work, but I was running short on time. I was hoping their thinking would help them think backwards especially with day before lesson.

Some places they might have gotten stuck at that I had posed responses for:

  • Students will have a hard time getting started (it feels like a high entry task)
    • I will ask them to go through an example problem we have done before, such as x^2-4x+3
  • Multiplying the "i's" together, it has been about a full quarter since they have seen imaginary numbers multiplied together.
    • I will ask them what i squared is? What do they remember about imaginary numbers?
  • Distributing correctly.
    • Ask them how they would distribute (x+2)(x+2)?
If you are really digging this lesson, you can view 28 minutes of the lesson here. 

I still feel like the entry to the task is too high, I would love comments on how this could be a better lesson.
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