All in with IM – Grade 8 Unit 7 Exponent and Scientific Notation Practice

Here’s a quick resource for exponent and scientific notation practice that aligns nicely with Illustrative Math / Open Up Resources Grade 8 Unit 7.

I first saw the “One Incorrect” activity model on Greta B’s blog Count It All Joy. I believe her original inspiration is from the work of Don Stewart  here.

Since Unit 7 includes so much “Which of the following are the same as . . . ?”, this practice structure seemed like a perfect fit. Use whichever pages fit your needs. Note the open middle style appear on this unit assessment. Chose the level of openness you are comfortable with.

Some details on construction: Each sheet has a picture over the top of the actual editable equations/text. So if you would like to edit problems, or make a different page for each group and have students rotate and find the “one incorrect” on their classmate’s creations, you can easily duplicate a slide and edit it.

Tips for those feeling pressed for time as they approach unit 7:

Lesson 1-3 can be condensed. Use the pre-assessment to decide how much. 2 days? 1 day?

Lesson 4 and 5 are worth slowing down on a bit. The tables are amazing in lesson 5. Take time to fully understand all that first table does for you and reference back to it through the lesson.

Lesson 6 and 7 extend exponent rules to other bases. If you have an anchor poster for your work from lessons 1-5, update it here. See the note below from the Activity Synthesis for lesson 6, activity 2:

I would do this by using post-its to replace the 10’s with 2’s, then 5’s, and eventually rewriting with x’s. These are the lessons where lots of exponent rule practice is built in.

Lesson 8 and Lesson 9: Great lessons, but if time is an issue and you are able to revise a test question, this is a spot where the time desperate can cut. Note that test question number 6 part c is covered in lesson 8.

If you are minimizing lesson 9, be sure to include a moment for big and small number vocabulary, maybe including an anchor chart for reference.

Lesson 10: Spend the time here. There are some amazing resources to explore with this lesson.

For Activity 10.2, check out the applet in the on-line materials for placing numbers on the number line. This is something to consider having students interact with in pairs.

Also in Lesson 10, Activity 3 has a must-use applet to visualize the expanding number line.

Lesson 11 goes through the same thinking, only with very small numbers. Desmos has a activity, The Solar System, Test Tubes, and Scientific Notation, that combines lesson 10 and 11, as well as some fun Scientific Notation practice.

In the Activity attached at the top, there are also 4 pages practicing the second half of the unit.

A Day of Desmos – Parabola Slalom

On the Thursday before Thanksgiving break I had the opportunity to try out the Desmos activity builder Parabola Slalom in Scott Davidson’s Math 2 class. This is how that happened:

Tuesday: Spent the day at a Desmos training and played Parabola Slalom for the first time. So much fun and potential for learning! If only I could do this with students. . .

Wednesday morning: I reached out to the teachers in my district who I knew were teaching quadratics. “Can I come do a lesson on Thursday or Friday with your kids?”

Wednesday afternoon: I heard from Scott Davidson, the Math 2 lead at a high school in my district. “Sure, but time is a little tight. Thursday Block we are reviewing and Friday students are taking a midterm on all things quadratic.”
From there the whirl-wind began. 15 hours until I’d be teaching a lesson with students I had never met. And some of that time needed to be spent on eating and sleeping.
The next step is where you’ll begin if you are a teacher using a Desmos activity with your class. I went to the activity builder and played it again. You can try it here. On Tuesday at the training I had the opportunity to talk with other teachers about which slides would be good to stop and talk at, but now I had specific students at a specific spot in their learning, and I needed to rethink where the valuable conversations would be for this group. After playing it again, I printed the attached Teacher Guide. (see button in top right corner)

Teacher guides are a great place to start with any Desmos activity. They allow you to think through what you want to get out of the activity, the teaching moves you will make, which things you can skip and which things all students will engage with. This checklist is at the beginning of each teacher guide:

I had already done step one. Check! That felt good. On to step 2 – learning targets. Desmos activities are very flexible, and you might chose to use them at a wide variety of spots in a learning progression. I’d love to try Parabola Slalom as an introduction to vertex form sometime and let students explore what the happens as you change different numbers. If I did that, my goals and planning would be very different. For this day I settled on these as my goals:

Next, according to my checklist, it was time to think about how I wanted to lead discussion with these kids I did not know. When would I bring the class together using “Teacher Pacing” and “Pause Class”? What would I discuss on those screens? I felt a lot of pressure to make sure the lesson prepared the students for the next day’s exam, because Scott was trusting me with this time. I wanted to make sure I picked up the students that were really struggling and gave them one more opportunity to make sense of this equations of parabolas thing. I decided that screen 3 was the first place where equation of parabola came up, so I would stop and question to see where kids were at. For students that were confused, I planned to make a connection to the y=mx+b as an equation of a line.I decided to look for these examples to discuss:

1. I wanted to look for a sample of student work that used an upside down graph and asked what in the equation made that happen.
2. I wanted to find a student that had made a parabola with vertex other than (0,0) and discuss what about that equation caused the shift.
3. I also knew I wanted them to realize that the square was important, so decided to watch for someone who entered an equation without the square and then pause to discuss the resulting graph.

After this discussion, I would pace them to work on slides 3 to 5. The Tip for Teachers provided by Desmos gave me some suggestions to help lead conversation on slide 5.

Having looked at their previous work, I anticipated that most students would give an answer in vertex form. I decided I would focus on those answers here with the whole group, and help struggling students focus on what vertex form looked like. I decided I would NOT give away yet what effect changing the a, h, and k would have, even though technically this should have been review. Instead I would encourage them to play with the form, trying in different numbers and seeing if they could figure out what changing each of them did to the graph.
I decided slide 6 and 9 were other places I wanted to have discussions. Slide 6 would give me a chance to talk about the usefulness of factored form. I considered taking time to explain why x-intercepts are easy to solve for from this form, depending on student response. This was a secondary goal for me and I didn’t want to overwhelm with too much information. Slide 9 would give me a chance to consolidate the learning, and I would chose to push kids all to 9 at some point to catch the struggling students up and clear misconceptions. In the discussion about slide 9 I would listen to what they had discovered about a, h, and k in vertex form, and make sure all students were hitting the learning targets. To support their arguments about why each answer was incorrect I might open a desmos calculator page, graph the given points, and put in the equations. With their groups, I would ask them to propose an equation that would work. From there I would open slides 3 – 11 let them work at their own pace, giving extra time to students who had misunderstanding I had uncovered.
The teacher guide encouraged me to plan something for students who finished quickly, but I felt like slide 10 and 11 would cover that. I only had an hour and the note at the beginning said the activity could take more than one regular class period. I decided I would have students log in so they could go back to the activity at home.
Last steps – I printed a copy of my teacher guide with notes for the teachers that would be coming in and out to observe. That way they could quickly see where we were in the lesson and what had happened so far. Excited to work with actual students tomorrow, I set my alarm and dropped into bed.
Thursday morning at 7:15 I arrived at Scott’s classroom. I connected my computer to the projector, logged in, and made a class code for the activity. I jotted the code down on my teacher guide and copied it to the whiteboard. I paused the activity so early students couldn’t begin before I was ready. Then I helped Scott set out laptops and soon students begin to come in.
The activity was even more fun than I imagined. Being with kids was such a rush, and watching the ah-ha moments gave me all the warm fuzzies. Man, I love teaching.
A few things that came up during the activity/lesson:

• Making the connection between ended up being a big thing for a few students. There was more good discussion to be had there about how an equation in two variables defines/creates as set of points that are arranged in a certain shape. Something to come back to.