Top 5 Percent

I may be jinxing myself but I feel pretty good about my approach to teaching percent this year. Here are 5 things that made me happy…

5. I usually give my students a “Benchmark Fractions/Decimals/Percents Quiz” that I think came from planning with one of my math learning specialist co-teachers years ago. Sometimes I have presented this as a mad minute quiz, seeing how many they can do off the bat. Instead, I just handed it out, one side blank, one side with correct answers and without making a big fuss said, “These are ones you should know better than you know your dog.” (Always greeted with “but I don’t have a dog!”). I asked students to check off the ones where they already felt comfortable and share out which ones they were going to have to work on committing to memory. It was a good conversation. Aforementioned dog is also often tasked with quizzing students. A few classes later when I asked kids to convert 0.66666…. to a fraction, we had already talked so much about % that lots of them just said 66.6/100. The kid who said 2/3 got a dramatic faint and my undying devotion.

4. I find that a frequent misconception with the whole “decimal to percent” thing is when the percent you’re representing actually isn’t an integer percent. During the lesson where we worked on converting between percent and decimal, I spent the most time on these special cases, less than 1%, over 100%, or ugly fractions where they would have to round. We emphasized the % symbol helping us to know if it was the decimal or percent representation.

3. M&M math. Open a bag. Does the % of each color match what the company’s mix is? Always fun. Planned in our unit last year from @PIspeak via@jreulbach. The focus on this was just writing percents from weird fractions. Refined a little bit this year and it was great. Need to circle back and talk about why their final answers may not have added to 100%. I loved when my students related it back to a population capture/recapture experiment we did.

2. When learning the equation P = % • W, I worked on getting my students to take a textbook question, determine which numbers referred to part, percent, or whole, and then trusted them to solve the equation no matter the missing part. Trusting them to solve the equation, rather than trying to get them to understand a different procedure for finding part, finding percent, or finding whole, was great. Also loved using PearDeck for this lesson and asking multiple choice questions where I gave them a problem like “34 is 25% of what number?” and asked them

Which is the part?

A. 34

B. 25

C. ?

1. My fave: I did a weird version of a Counting Circle at the end of one day. I think it was after M&M math. At the end of the class, I put a bunch of different percents on the board in red, starting with some ones we had talked about — 50%, 25%, 10%, 1%. In blue, I wrote the number that represented our whole. We did our regular circle routine, but this time we were finding the % that we landed on. I mixed it up with some more challenging percents and some more challenging wholes.

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This activity created a memory that I could refer back to when showing students the percent equation. We called this our building block method. Once we moved on to doing the computation using the percent equation and multiplying by hand or with a calculator, it really helped my students with deciding if their answers were reasonable.

Coding in 6th Grade Math

This year, with the help of resources from Dawn DuPriest, I’ve been integrating coding tasks into math class. I thought I would write a summary of my experience so far.

Some background on my setup:

  • We have a 1-1 technology program and this year we switched from MacBooks to iPads for our 6th graders. As a consequence of switching to iPads, the coding teachers landed on using Snap! for our 6th graders.
  • My students take coding as part of their language rotation, so at any given time, a quarter of my kids are in that class, and throughout the year there are increasingly fewer kids who haven’t yet taken coding as a class.
  • My coding knowledge is limited to having taught myself HTML when I was in middle school, playing with block-based code tutorials, and seeing what my students can come up with.

 

What we’ve done so far in class:

  • Coding Task 1: As per Dawn’s recommendations, I made the first task a geometric drawing task. I had them use the app HopScotch at first, which was really fun and engaging. They loved all of the characters, emojis, etc. they could use. This is the perfect low floor/high ceiling task for students. The student who struggled the most was still able to make the most basic square or triangle. The student who maybe came in with a lot of experience could be pushed to think about angles of rotation for anything all the way up to a octagon, making their code more efficient, or just making it pop with funny effects.
  • Coding Task 2: I used Dawn’s Variable Challenge which used word problems to introduce them to how to make variables. It worked great! I connected it to order of operations, but next year I think it would be more effective if we did this after a lesson on evaluating expressions.
  • Coding Task 3: I got into a rut and we hadn’t coded in a while, so without worrying too much about connecting it to curriculum, I revised Dawn’s intro to conditionals and assigned it to students. This time I didn’t give them much choice, showing them them an example of how to use the “If” and “<,>” blocks and then they all had to use the blocks to code the same word problem. It wasn’t the best — kids could basically just ask their neighbor for how to make it work. However, if I’ve learned anything in this, it’s to not wait until it’s perfect. Just do it. And now I can count on kids knowing how to use that block and we can connect to it again when we study inequalities.
  • Coding task 4: My favorite! We have been studying two-step equations and I desperately want students who are so strong that they don’t depend on memorizing rules and are rockstars at solving equations. So I came up with a task that would make them better at solving in general. Here was the sample code:
    codingtask4I asked them to read over the code and tell me what it accomplished and what the most important line of the code was. When writing equations from word problems, we had previously talked about writing equations and the difference between writing an equation that “told the story of x” and an equation that was already solved for x. We were able to connect this code to that conversation. They loved it when I described this task as building a cheat code for someone’s homework. They chose one of the following equations to write their own code.
    codingtask42
    By teaching this to the third section of students, I realized it was more helpful to front-load it with some one-step equations like ax=b, x/a=b, x-a=b, and x+a=b. It also helped to show them examples with values for a,b, and c and ask them how they would normally approach them and then generalize it by replacing with a,b,c. They had to write their “set x to” line of code on paper and have it checked before starting their code.

    I realized that this would be a great performance task later on to see if they could understand the abstraction. I also realized this would be really helpful to my 8th graders who struggle with solving an equation for a particular variable.

Lessons Learned:

  1. Don’t be afraid of what you don’t know. The kids will always have a better answer to their classmates’ questions than you would anyway.
  2. If you have a 1-1 program or can count on students having access to their work at home, don’t be afraid to ask them to finish as homework. It’s the best homework they will have and their parents will love seeing what they’re doing. It will help them develop persistence, curiosity and understand that coding is about trying and troubleshooting.
  3. Don’t wait for all parts to be perfect. Jump in.

    “Don’t be afraid that it won’t be perfect. The only thing to be afraid of really is that it won’t be.” – Company by George Furth and Stephen Sondheim.

First Few Days of Year 9

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Students working on “3-1derful Challenge”

I’m finally sitting down to write my first blog post of the new school year. For the first time this week, dinner and dishes are done at a reasonable hour and I actually have some time to putter around, though I should probably be editing lessons. I’ve graded some Pre-Assessments, though I have not yet started to think about what those results mean… avoiding thinking about the challenges of differentiating for sixth graders coming from a wide range of places, who all need to be challenged. I’m going to stop “should”-ing all over myself.

I had been feeling a little bit deflated, as I had to take on some extra responsibilities last minute, adding to my number of preps and presenting me with new and unexpected challenges. I’m not deflated because of the extra work, but because it means putting aside some of the things I wanted to work on to make my classes extraordinary. So I’m feeling a little mediocre right now, but that’s okay… The new challenge is good for me.

Next week, I shall focus on my #1TMCThing of integrating Explore Math (@samjshah) into my 8th Grade Integrated Math 1 class. I am very lucky to have two collaborators who will also eat it up, once I decide how best to present it to 8th graders.

 

Fractions as Division and Dividing Fractions

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At Twitter Math Camp, I attended a session by @bstockus about teaching fractions. There were great strategies presented for ensuring that you help your students understand fractions as a value on the number line, understanding when you are using fractions as an adjective rather than a noun.

As I mentioned in my Top 5 TMC Things,  the conversation at my table segued into teaching fractions AS division. And I was lucky to be directed to some resources that I am excited to explore in planning related units.

Later on Twitter, I brought up the fact that the first time someone showed me I could divide fractions by dividing the numerators and dividing the denominators (I believe they had talked about it while attending Park City Math Institute), it blew my mind. Later on twitter….

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I’ve tried to think through this a bit and draw some things out.

At first, I wrote down a problem with nicely divisible numbers. But then I was completely stuck.

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I was stuck, but also not realizing what a HORRIBLE choice it was to try and show this using division of a fraction by itself.

So I went on and tried something simpler… a whole number.

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But right now I can’t see the forest for the trees.

So I went back to the initial problem: dividing two fractions with nice divisibility happening, and made a better choice….

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But I think I’m getting nowhere with WHY this works, just demonstrating why the answer is correct visually. So I figured someone much smarter than me HAS to have thought about this and written about it extensively. Here’s what I found:

Mike’s Math Club
• Math Forum
• NCTM blog post by Tina Cardone, whose book, Nix The Tricks, covers this in section 3.5 and 3.6. Tina does an AWESOME job of it.

I still have many questions about if/how/why/when I should present this to my 6th graders. I often do show this to students who need differentiation on the extension end, not the remediation end, and then ask them to play around with it and see if it always works.

Do you have any other resources for explaining this? Do you think it’s worth showing to your students? Do you think it’s only useful once students are comfortable working with complex fractions? Have your students shown you something cool when playing with this? In other countries do they teach using the divide across method?

 

 

 

 

 

Top 5 TMC Things

This morning I woke up, home from #TMC16, where my wonderful colleague showed me the ropes. I drank my morning latte out of the very appropriate mug pictured.
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As I write this, I have TMC-induced ADD, with five million tabs of blogs and resources open. It even took me a long time to link to @PIspeak because the act of going to twitter is now like….
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I learned so much at TMC and it’s so easy to feel overwhelmed and distracted. It will take me a while to dive deep into the things I want to understand and adopt, but my goal for this blog is to be a short, quick, Top 5 digest.  Here goes nothing. Continue reading

Top 5: Tech Tools for Formative Assessment

How can we transform the good old Exit Ticket to make formative assessment more frequent, more useful, more organized? Working in a school with a 1-1 laptop program is an extreme luxury. I try not to let this opportunity slide by, using it for formative assessment as often as possible.

I have been so lucky to have colleagues and conferences introduce me to these great tools. I am hi-lighting the ones that are (mostly) free and easy to set up.
Continue reading