All in with IM: A day in the life- Grade 8 Unit 7, Lessons 9-11

“Is there anywhere close we could see this in action?”

“Is there maybe a video that could help us imagine how this looks with kids?”

“How do these lessons work on a block schedule?”

“The lessons seem so scripted. I need to be able to adjust and make a lesson my own, and I am not sure that works with this curriculum.”

I just observed a wonderful lesson on a 113 minute block that answered so many of these questions beautifully. The teacher, Ms. D, agreed to let me share it with you.

Previous day:

Lesson 7 with a quick peek at 8.

During announcements:

Students read and annotate lesson 9 summary.
The teacher leads discussion: “What did you chose to circle or make note of?” etc.
She focuses students on middle line:

“The advantage of using powers of 10 to write large numbers is that they help us see right away how large a number is by looking at the exponent.”

and the final paragraph, circling: easier and avoid errors.

This, Ms D said, is the why of what we are learning today.

Opening Discussion:

To open the day they discussed together Lesson 9 Practice Problems 1 and 2. Problem 1 was a chance to check in on vocabulary for large and small numbers. During problem 2 she focused on all the different ways students could come up with to express each number as a multiple of a power of ten, and had lots of discussion until they felt comfortable moving back and forth.

Pro move– when students misspoke, she wrote exactly what she heard, and invited classmates to agree or disagree. This brought out simple things like the difference between “8 to the 7th” and “8 x 10 to the 7th”

As they finished each part a – e, the teacher circled the answer that was written in scientific notation without defining what that meant and said they would talk about definition later. On part f, she asked students to decide which was scientific notation. They were able to see the pattern and the need, since otherwise there are so many right ways. (MP8 in action)

Part 2:

Then she moved to 10.1. After a first round circulating and checking students work, she brought up a common misunderstanding she was seeing, and discussed the importance of having the tick marks evenly spaced. She showed that labeling with powers of 10 created tick marks where the first two were 10 apart (from 0 to 10), and the next two were 90 apart (from 10 to 100), etc. She asked, “How many tick marks are there?” “What if the last number was 20? (cover 10^7 with a post-it that said 20). A student was able to suggest dividing by 10 since there were 10 tick marks, and they successfully labeled the number line counting by 2s. Then they went back to the number line ending with 10^7, and applied the same process of dividing by 10. Ms D wrote out the division problem, and asked students to apply exponent rules to simplify. They found that they needed to count by 10^6. At this point she translated, “That’s 1 million, right? Can you count by one million up to 10 million?” Students all began counting out loud. She wrote 1,000,000 and 2,000,000 over the first two tick marks. “How could we write those as multiples of a power of 10?” They did those two together and then she asked them to complete numbering that line using multiples of a power of 10.

From here they moved to 10.3 (10.2 appears in the Desmos activity they did later). Ms. D asked student to work silently to express each number as a multiple of a power of 10. After a few minutes working with her circulating, she asked them to convert each of their answers to be written with same power of 10, to make them easier to compare. “Share your answers with your partner. Did you both chose same power of 10?” and finally, “Let’s all change to 10^8, to match number line we will use next.”
She showed the zoom in digital app and asked how they could label the zoom-in line. A student quickly suggested using decimals, and Ms. D encouraged them to complete that labeling with their partner.

Zooming out the rest of the way using the applet gives and chance for them to check their work ( see below). From here students added the points to the line (#3) and the class discussed #4-5.

Desmos Application:

From here they moved to this Desmos activity (If you haven’t played this yourself yet, follow the link and check it out!). Students worked individually all the way through, sometimes going back and revising their thinking as they saw what classmates had entered ( in slide 3 for instance). Occasionally a quiet collaborative conversation broke out.
Students who had looked less engaged during class discussion were super engaged and talking math 100% during this activity. For students who finished early, she had them listen with ear buds to Mr. Aaron’s lesson 11 video. On the last slide of the Desmos activity, which was her cool-down for the day, all but 2 students correctly answered the final question by themselves.

If your counting, that was 3 lessons with 94% mastery in one block.

All In with IM – Grade 8 Unit 6 Associations in Data

True confessions:

I thumbed through Unit 6 when the books were first delivered and saw it included scatter plots and two way frequency tables. No problem. I’ve taught those things before. And scatter plots means line of best fit, so we’ll be reviewing equations of line and slope shortly before testing. Perfect.

And I put the book away.

In our first year we ended up moving unit 6 to last, because unit 8 seemed more important to get in before testing. So it turned out we barely touched any of unit 6 the first year, and definitely did not take time to get the big picture of the unit.

So here I am in year 2, finally digging into Unit 6. And I can say there was a lot I didn’t get first time around. Let’s begin with the title: Associations in Data. This title fits the two ideas I formally thought of as separate into one overarching concept, and that understanding frames everything you are doing in the unit. (I wish this was a little more explicitly discussed in the unit overview – maybe next edition??).

In grade 6 students work with displaying and analyzing numerical data around a single attribute. They recognize that data can be described in terms of it’s central tendency and it’s spread, and use line plots, box plots, and histograms to display the data and make visible these important features. Early in the unit, students are asked to recall these terms as ways to display single variable data sets.

What is different in 8th grade is the addition of a second set of data that may or may not be associated in a predicable way with the first set. When the data is numerical, we can use a scatter plot to see if there is a predictable pattern or association between set 1 and set 2. If the data is categorical, we can use the two way frequency table and relative frequency to determine whether there is an association we can use to make predictions.

Numerical Data and Associations

Using numerical data on a scatter plot we can ask does the daily high temperature have any connection to the number of snow cones sold on that day? We might say:

  • As temperature increases, the number of snow cones sold increases.

We might describe the association using more precise mathematical vocabulary:

  • There is a positive linear association between temperature and number of snow cones sold.

Or we might describe the association using the equation of a line of best fit:

  • The relationship between temperature, T, and cones sold, c, can be modeled using the equation T = 2c -70.

Or potentially just in terms of the slope of the line of best fit:

  • Two additional cones are sold for each 1 degree increase in temperature.

In all cases we are implying that there is an association between that two sets that allows us, knowing something about 1 set, to make a prediction about the other set.

(So far, nothing dramatically different from what I expected, except perhaps the opportunity to describe the relations ship in terms of just the slope of the line of best fit.)

Below are some additional practice and review problems we made to focus on this part of the unit. Questions circled in red emphasized using the slope (and units) to describe the association. Our first time working through the unit test we were worried that students might struggle with that. After working through the unit I see this idea comes up a fair amount, but I do like the chance to re-emphasize the meaning of slope of a line in terms of units.

Graphs That Don’t Begin At (0,0)

Sometimes it is just not convenient for a graph to begin at (0,0). A graph where the x axis is labeled with the year is a perfect example.

Image result for average home price vs year

Watch for situations in the unit where this comes up. The first is in the lesson 2 summary, then twice in lesson 3 and 5 times in lesson 4. This same graph and context from lesson 2’s summary comes up in the lesson 3 and lesson 4 summaries. The fact the graph is familiar when you summarize 3 and 4 lets students focus on the mathematics from that day. Don’t skip the Lesson 2 graph – be sure to deal with the “not (0,0)” issue when it first arises.

Below part of our review problem 6 is shown, where we took some time to focus on the fact that not all graphs begin at (0,0). (see green circle). There is a spot on the test where the line of best fit exits the left side of the graph above the x axis, but the y intercept is actually negative. We added this problem to create a discussion about y-intercepts that don’t show on the piece of graph that is given.

Categorical Data and Associations

Lessons 9 and 10 focus on categorical data. My teaching in the past has focused primarily on displaying this data using bar graphs and two way frequency tables, but in this curriculum, the question is consistent throughout the unit: Is there an association between the two sets of data? In categorical data, this can be interpreted: If we know a subjects answer to question A, can we predict their answer to question B? How reliable is that prediction?

Lesson 9 begins with a chance for students to notice such and association. Students who do not play sports are more likely to watch a fair amount of TV.

9.2 introduces students to 3 ways that data might be displayed: two way frequency tables, bar graphs, and segmented bar graphs. There is a short card sort included in 9.2 to let student practice matching data sets that are displayed differently. In activity 9.3, students learn to find relative frequencies from data in a two way frequency table. they are asked to make conclusion about whether an association exists based on these relative frequencies.

The next day, they will actually create segmented bar graphs with these relative frequencies and most students will find the visual helpful in determining the association. If the percents are very close to the same in each segmented bar, there is no association to help make a prediction about one thing given the other.

Here are a few practice and review problems we made for this section of the unit:

The questions circled in blue really ask the same thing in two different ways, and are meant to create a discussion around what it means for their to be an association between the data. Several of the other questions offer chances to continue this conversation.

Links to questions pictured in this post: review as pdf

review word version

extra practice

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.