Reworking Sugar Packets

Seeing the look on student faces as the video plays makes the problem. Seriously! What is that guy doing? (This is a Dan Meyer 3Act Problem – please see link for original problem and video.)

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I ran two versions of the problem in class. Due to a testing schedule and late arrival of many students, my first class’ time was whittled down to 30 minutes. We’re getting into a rates & proportions unit and a goal was to connect back to work done in sixth grade to continue getting a feel for where my students are meeting me in the class. So, the problem unfolded generally as given in the 3 Act flow. There was high engagement at first but then the problem was solved immediately. Woops – good thing that the class was a short one! However my next math class of the day was a full length class (80 minutes) so reworking was needed. Here is the new flow and it provided for a better lesson where students were more engaged and actively discussing mathematics for an extended time.

The hook – got ’em.

Immediately after playing the video, student tables were given a red and an orange card tent and asked to come up with an estimate that was “too high” and one that was “too low”. We stretched a clothesline across the room and members of each group came up to begin placing their tents on the line. The clothesline is a great tool for these problems as students work together to sort their estimates along the line. Students then gave a quick explanation for their team’s estimate. The best was the estimate of 50 packets of sugar due to someone’s little brother who once put lots of sugar into a drink and a “stickiness” scale was developed…

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So far, the problem is unfolding as the 3 Act is laid out. The next step is the shift. Instead of providing the given nutrition level, I grabbed multiple nutrition labels from the Coke site. The intent here was to have students work with more data. Does Coke keep the same proportion of sugar in each size beverage?

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Multiple labels were printed and placed about in the room. For the smaller sizes, the serving size changed but for 1L and up, the serving size was based upon 12 oz (360 mL). This led to great small discussions as many students did not understand how to read a nutrition label and what a serving size meant.

Compared to the first pass of the problem, students were now up and out of their seats collecting data from the different nutrition labels. Their target had shifted as students now needed to determine whether or not all Cokes are created equally. Yay – we now had a need for determining the unit rate. (Interesting side note – the 7.5 oz bottle does seem to have a higher sugar content if you are looking for a sweeter Coke.)

For me, the shift in the problem opened up the class to a higher level of activity and discussion. I appreciate the window this gives me to have more conversations with students. Working through the nutrition labels resulted in a good stretch for some students. My weakness in wrapping up and really pulling out key understanding through class discourse showed itself again and I’m back to reading the book below. Processes that others have for wrapping up a 3Act task to pull out the learning for students would be much appreciated.

5 Practices for Orchestrating Productive Mathematics Discussions

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Opening with Estimation180 on a clothesline

I’m a big fan of Andrew Stadel. If you haven’t checked out his awesome contributions to teaching math, please head on over to his blog, Divisible by 3. For years, I used resources from Estimation180 to get my students estimating and talking math. Last year, I decided to institute a more regular warm-up and cycled Estimation180 into my weekly rotation. Then, Mr. Stadel began stringing clotheslines all over the place as dynamic number lines. For no good reason, I did not string one up in my classroom last year – no clotheslines in China? (yea right) – but came back to the start of this year with a clothesline in my bag.

Talks surrounding Estimation180 have often been rich as students explain their reasoning. I’m a fan of the “too low” and “too high” bounds. I want my students to be able to set these limits. I want them to get the feeling of a range and that they do not have to zero in on a specific number. So, airtime in discussions leans towards setting these bounds, discussing the reasoning involved, and working as a class to develop (or recognize the levels of) confidence in our estimations.

To start this year, I decided to use a clothesline as a way to make the math talk a bit more dynamic.

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Here is the flow from my first go – any suggestions / tweaks greatly appreciated!

  1. Start with the image – students Notice / Wonder to get their minds into the math class. We then bounce a few ideas around as to what we could possibly be getting ready to estimate.
  2. Individual – students work on a “too high” and a “too low” estimate. A focus is on paying attention to the thoughts and processes involved in setting the bounds.
  3. Table talk – after each student has made some individual progress, get them talking.
  4. Group talk – this is where the clothesline comes in
    1. Too Low – orange cards used to place values on the clothesline. Several students came up and shared.
    2. Too High – red cards used and again several students placed a value and shared reasoning.
    3. Table groups then had a few moments to agree upon one “just right” estimate. We just finished a lot of processing so they take it one step farther and decide upon a value that answers the estimate question.
    4. A group member comes up to place the group’s value on the clothesline. Yellow card tents used this time. No discussion at this point unless it is making observations about the values.
    5. Check out the actual value and move on…

That was the process yesterday. What did I like about using the clothesline?

  • In the past, we had the conversations regarding low and high values but the lack of organization was clear. Students would write a value on the board and talk and it was challenging to visualize the range. Now, we begin to see the distribution of values.
  • Developing more number sense – When final values were placed by a class, the value 185 cm was used on multiple occasions. However, these values were not stacked to represent the quantity but lined up to represent each group’s idea. A nice conversation ensued about value.
  • Developing a sense of placement and spacing – As values are placed on the clothesline, we can begin talking about keeping a general sense of equal spacing. 10 cm on one end of the number line should represent the same value distribution as on another place on the clothesline.
  • Visual Representation – Wow! My lack of organization from last year’s conversations was quite apparent. The clothesline immediately organized and the colors of the number tents allowed us to easily talk of the highs/lows. Maximum and minimum values were easy to discuss. Students can walk the range.
  • Shift to students – I felt that more of the focus and attention was placed on students as they walked the number line and explained their reasoning. It is helping me fade to the background!

To improve upon? Time. I am looking for ways to tighten the process up a bit. I like the different colors of number tents to place onto the clothesline and wonder how I can better distribute them to students. Possible idea – provide each table group with a tent of each color (representing too low, too high and actual estimate). The too low and too high values are written first and at the same time a member from each group comes up for “too low”. They have to work together for placement purposes and then give an explanation. Repeat for “too high”. Have a number talk regarding patterns seen and explanations. Final estimates are placed. Other ideas?