Author: MaryAnn Moore
It's beginning to feel a lot like summer! Anyone else grateful for the rain we've been having here in Utah? I am! And not just because we need the water but because it helped keep my students from going wild this last week or two of school. I'm looking forward to summer, but I'm also that crazy kind of teacher who starts getting excited for the beginning of the next year before summer even hits. Here are a couple things I'm looking forward to using next year:
Make it Parallel
In the past, when I have taught parallel lines and transversals, I have always started by showing students two parallel lines and a transversal cutting them - and then from there we move to the converse to show that if all of the angle pair relationships are true, then the lines must be parallel. In this post, Jon Orr flips that idea on its head by asking students to create a third line that is parallel to one of the other two lines. Absolutely brilliant! I can't wait to try this with my students next year.
Dane Ehlert is doing some fantastic things with standards based grading, feedback, and grouping students according to their areas of need. Someday I am going to learn how to create and edit concept review videos for my students. Until then, I am so glad that people like Dane are willing to share theirs. Dane created a set of review videos for his students called Silent Solutions. Here's how he describes them:
"I created several silent solution videos as the first step toward responding to student progress (the idea came from Kyle Pearce and Cathy Yenca). The videos are short, silent and meant to be a quick how-to for students to learn from. I really like these because they’re straight to the point, and students can easily play them over and over without spending a ton of time."
Here's an example of one of these videos:
Check out this post by Dane Ehlert to learn about about how he and his students use these videos as well as other ways he responds to student progress.
Author: MaryAnn Moore
You know what I love about living in the great state of Utah? We are all about taking something good and making it better. Case in point - the proposed revisions to the Utah Secondary Mathematics standards. According to the Utah State Board of Education, "the secondary math core standards have been revised based on five areas approved by the Utah State Board of Education:
The drafts of these revisions were released to the public on May 8 for a 90-day public review. You can find the drafts here. I took some time earlier this week to review the revisions to the 8th grade standards and I'm generally very please with the clarifications. The revisions seemed very logical to me. I also submitted a suggestion for another clarification that I would to see in the revisions to the 8th grade core. If you haven't yet taken the time to look at the revisions, please do so now! This is your chance to submit feedback about the core standards!
Author: MaryAnn Moore
My students tested on Monday-Wednesday of this week. For me, the worst part of testing is the lack of teaching. All day long I'm in the same room with my students, but can't teach them, talk with them, or laugh with them. It had a seriously negative impact on my happiness levels. Thank goodness for Thursday! As always, I didn't cover the entire 8th grade core before the test. The next item on my teaching agenda was Scientific Notation. I didn't want to dive into it too deeply on Thursday, though, since several students would be missing my class to finish testing. Enter my very favorite introduction to scientific notation and powers of ten: Cosmic Zoom.
Cosmic Zoom is an iMAX movie narrated by Morgan Freeman. It's about 30 minutes long, but I never watch the whole thing with my students. About seven minutes into the movie, they start zooming out by powers of ten to the furthest limits of the known universe. Then they zoom in on a single-celled paramecium and continue to zoom in to quarks - the smallest known building blocks of matter. I usually stop the video at this point.
Of course with Morgan Freeman narrating, he could be reading the phone book and I could just press play and watch my students slip into a peaceful trance. However, I like to milk this video for all it's worth so I created some warm-up viewing guides to go along with it.
I love watching and listening to my students react to this video! What is most interesting to me is that I usually get the strongest reactions from some of my lowest performing students. They seem astounded to realize how very small they are in comparison to the rest of the universe. And they ask some of the very best questions during the movie! They wanted to know how light can exist in space. They wanted to know how long it would take to travel to the edge of the solar system. One girl asked how long a light-year was and I realized from the way she stated the question that she was considering light-years to be a unit of time. We talked about how we could create a unit of measure called a Lexie-Year by setting Lexie out on the road and asking her to keep moving for an entire year and then using that distance as our new unit. This seemed to be a very acceptable answer. As we've worked with Estimation 180 warm-ups this year, my students have gotten much more flexible in their thinking about units of measure. In fact one of my classes has started using one of their classmate's heads as a unit of measure. "I think that'd be about 2.5 Lucas-heads." So it wasn't too big of a stretch to jump from thinking about Lexie-years to light years both as a unit of length.
After watching the video, I asked my students if we were zooming out at the same speed at the end of the cosmic zoom as we were at the beginning. Almost all students agreed that the speed increased as we zoomed out, but there was some confusion about what happened as we zoomed in on the paramecium. Eventually they agreed that if zooming out meant increased speed, then zooming in must mean decreased speed.
And because I can't help myself, I had my students turn their viewing guides over and we created a graph of the speed on the back. Interesting conversations about how to label the axes! What are the variables? Which label goes on the x-axis? Why? Once we got them labeled, I asked all of the students to trace in the air the shape the graph would make. Almost unanimous:
And of course, one has to make zooming sound effects when tracing this graph in the air. :) There was also some disagreement about where to place the y-intercept. At the beginning, my students placed it at zero, but then weren't sure what to do for the negative powers of ten. How can you have negative speed? Eventually they agreed to move the y-intercept up a little bit on the y-axis.
Inventing Scientific Notation
The next day, when I had the majority of my students back in class, we dived into the nuts and bolts of scientific notation, using this lesson by Dan Meyer. To make it easier to present, I created my own set of google slides based on the slides in Dan Meyer's post. Feel free to use the google slides, but lease read Dan Meyer's blog post, or they won't make sense at all. (Let me tell you, it's a pretty fun thing to see the looks on your students' faces when you tell them to get out their math notebooks and write down the word New Hampshire.)
My favorite adaptation to this lesson came from a question that student asked, "Why does it have to be 5.12 x 10^7? Why couldn't we write it as 51.2 x 10^6?" I explained that both were mathematically accurate but that using one digit to the left of the decimal is just an agreed upon norm - sort of like how driving on the right side of the road is an agreed upon norm. There wouldn't be anything wrong with driving on the left side - and some countries do - but if everyone decided to drive wherever they wanted, mass chaos would ensue. In fact, in later classes, I specifically asked students to give me alternate but mathematically correct ways to write 5.12x10^7 just so we could talk about this issue. Hence the slide about which side of the street is the correct one to drive on.
Author: MaryAnn Moore
Previous volumes: Volume 1, Volume 2
Do you ever struggled to get students to converse productively about mathematics? It sort of reminds me of when I learned about parallel play in my human development classes in high school. Wikipedia defines parallel play as "play in which children play adjacent to each other, but do not try to influence one another's behavior. Children usually play alone during parallel play but are interested in what other children are doing. This usually occurs after the first birthday. It usually involves two or more children in the same room who are interested in the same toy, each seeing the toy as their own. The children do not play together, but alongside each other simply because they are in the same room. Parallel play is usually first observed in children aged 2–3. An observer will notice that the children occasionally see what the others are doing and then modify their play accordingly."
This kind of interaction is often what I see when I put my students into groups. They're sitting next to each other, working on the same problem, and interested in what the other person might be writing down. But they don't know how to actually interact with each other to discuss their mathematical reasoning. When I want my students to engage in less 'parallel play' type of group work and more 'exploratory talk', I design a Talking Points activity for them.
Talking points is a structure created Lynn Dawes and recently adapted and made popular by @cheesemonkeysf, a California math teacher. This introductory post by @cheesemonkeysf is a very helpful. Here is a picture of a talking points that my students did in class recently.
I created this after my students took a quiz in which they needed to place some rational and irrational numbers on a number line. Almost 90% of my students incorrectly placed the irrational numbers on the number line by placing them directly above the closest rational number. I used the exact same number line from the quiz and hand-wrote in the numbers where the 90% of my students had placed them on the quiz. I then divided my students into groups of 3 or 4 and had them take turns telling whether they agree or disagree or are unsure whether each number was correctly placed, using the Talking Points structure described by @cheesemonkeysf. What was wonderful about this activity was that it provided a structure that caused them to engage in some mathematical debate while still providing a safe environment. And boy did they ever debate! There may have even been some raised voices when it came to determining the correct location for pi plus one. The next day I gave my students a different version of this number line quiz and over 95% of the students placed all of the numbers correctly.
Talking Points does not always have to be about mathematics. In fact, especially at the beginning of the year, I like to have my students use Talking Points to talk about what good group work looks and sounds like. Last year, @cheesemonkeysf led a Morning Session about Talking Points at the TMC14 Conference. You can find a wealth of other information Talking Points, including many examples of Talking Points for various topics and grade levels, on this page of the TMC14 wiki.
Author: MaryAnn Moore
This week on Friday Favorites (my apologies for the belated Saturday-ness of this post): Exploring the Math Twitter Blogosphere, Logic Puzzle Love, and Put(t)ing Rational Numbers in Order
Exploring the Math Twitter Blogosphere
Have you been following along with the challenges posted by our good friends over at exploremtbos.wordpress.com? It's never too late to get started. Find out what it's all about in this overview and then get started with Week 1: Blogs, Week 2: Twitter, and Week 3: Organize. (Still to come- Week 4: Resources.)
Logic Puzzle Love
This week Sarah Hagan from Math Equals Love wrote about a kind of logic puzzle I'd never heard of before: Shikaku. This area-based puzzle has a lot of potential ties to math curriculum, including area, perimeter, prime and composite numbers, and factoring. Sarah references an NCTM article about using logic puzzles in class and describes how she taught this to her class by showing them a 'solved' puzzle and having them figure out the rules. Sounds like a lot of fun!
Put(t)ing Rational Numbers in Order