Tag Archives: #NspiredatT3

Making Time for Tasks

I co-presented a power session at the T3 International Conference Sunday morning, and I’ve posted the stories that I shared of Running around a Track I and Running around a Track II. I have also posted Running around a Track III during which I processed the feedback we received during and after the sessions.

Several participants asked about the time that rich tasks take, and so I thought it might be helpful to think about making time for tasks in this separate post. I enjoy teaching on a block schedule. I know I don’t feel as rushed as I would otherwise. But a friend asked me how often we do these types of tasks in our classes.

How often do you do this type of rich task?

There are some tasks through which the math content can be initially and naturally be learned. I think of Placing a Fire Hydrant (and last year’s notes here) and Locating a Warehouse (with last year’s notes here). There are some that are more culminating tasks for a unit, especially the modeling tasks. A typical unit for us lasts about 8 days. (See some of the Unit Student Reflections posts to know more about how we organize content: Special Right Triangles, Dilations.) We do the culminating performance type tasks 1-2 of those days towards the end of the unit. On the other days, we are learning the content using practices such as look for and make use of structure and look for and express regularity in repeated reasoning, but not always through tasks.

For example, when our learning goal is

G-C.A.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

I find that exploring the relationships using technology first, verifying conjectures using formative assessment questions (more skill-based practice), and then moving towards why works best for my students. If you know of a good task for learning G-C.A.2, I would love to know. But for now, at least, we end this unit with a few culminating tasks instead of beginning the unit with them. The culminating tasks are Circles in TrianglesInscribing and Circumscribing Right TrianglesTemple Geometry. I will note that while we didn’t actually do the tasks until the end of the unit, I did show students one of the diagrams from the beginning so that they could keep in mind throughout the unit where we were heading.

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So now that you know that I don’t give a rich task every day, let’s think about what steps we might take to reduce the class time for the tasks. [These questions and comments will make more sense if you have looked at how the lessons for Running around a Track I and Running around a Track II played out with my students.] One of the participants in our Sunday session wondered what would have happened if I had given the students a teaser of what was to come the day before this lesson. What if I had shown them the picture and asked what they wondered then? Or sent a link to a Google form for them to submit their question outside of class?


Or what if I actually showed them the tasks and questions (blacking out information in I that would give away II or vice versa) just so students could begin the process of thinking about the structure of the track before they did any calculations in class? I think these are great ideas – having students spend the “alone” time for processing the questions being asked could definitely make the time spent on the task take less class time.

Another question that tied into the idea of planning lessons with rich tasks was whether we use a textbook. I think of the textbook as a source of information and practice problems for students. We don’t have our units arranged like our textbook, but I do reference page numbers for each lesson on the student syllabus so that they will know where to look for extra help and practice. (Our textbook isn’t CCSS at this point, and I’m not convinced that the new ones have geometry written in the spirit of CCSS. When I’m reviewing a new textbook, I first look at the Table of Contents. When transformations is still the topic of chapter 8, I find myself skeptical.)

Someone else asked about how rich tasks complement some of the skills practice that students need. We don’t get to every practice problem that we include on our student handouts, but I have finally had the time to work through them, and so I post the worked handouts online for students to check problems they do outside of class for additional practice. We also give online practice assignments with two chances to students through Canvas so that they can get immediate feedback on what they know and don’t know. We are trying to teach our students how to use formative assessment.

[I’ve been reading Transformative Assessment and Transformative Assessment in Action, both by James Popham. According to Popham, the first level of formative assessment is when it is used by the teacher to make instructional adjustments as needed to further student learning. The second level of formative assessment is when it is used by the student to make learning adjustments as needed to further learning. The third level of formative assessment is when it is used by the class as a whole to help all students meet the learning goals of the lesson, and the fourth level of formative assessment is a transformation of the school – all teachers are learning about formative assessment in school wide PD and practicing it in their classrooms.]

My students and I have explicitly discussed in class that if you take the online practice assignment and miss every problem, you should make a learning adjustment before trying again.

So if I don’t use a textbook, how do I plan my lessons?

The top three sites that I use are Illustrative Mathematics, the Mathematics Assessment Project, and the Math Nspired lessons at TI’s site. I also follow a lot of bloggers. It helps that I’ve taught geometry for 20 years, and it helps that I’ve been making an effort for students to learn by doing for at least 17 of those years. (I owe a huge apology to all of the students I had the first 3 years.)

But it does take time. I am lucky to work with a great team of geometry teachers who are willing to help and try tasks and use formative assessment with their students. We taught our CCSS Geometry course last year for the first time, and our administrator worked it out so we could have 4 teachers and 30 students in our first block class together. We worked through the lessons together with the students and each other, and then the other 3 teachers had a planning block after that class so that they could correct everything we had done wrong the first time before they taught it in their own classrooms the rest of the day. This year, we have a team of Algebra 2 teachers doing the same thing, and next year, our Algebra 1 teachers will teach one class together. I didn’t know what my administrator would say when I proposed this idea to him, but I’ve learned it doesn’t hurt to ask. It was a total scheduling pain, and some of our other classes were more crowded, but that was worth the sacrifice for what we learned teaching the first class together.

I’ve just told you what works for us in our efforts to include more rich tasks, but it’s only one perspective. What works for you? What additional sites do you use to find rich tasks? Do you start with them more often than end with them? We’d love to learn more from you as the journey continues … easing the hurry syndrome, one task at a time.


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Running around a Track III

I co-presented a power session at the T3 International Conference Sunday morning, and I’ve posted the stories that I shared of Running around a Track I and Running around a Track II from the Illustrative Mathematics tasks Running around a Track I and Running around a Track II. In this post, I want to process the feedback that we received from the participants during and after the session. (There is not really an IM task called Running around a Track III, although there could be one from some of the suggestions participants gave for extensions!) Several participants asked about the time that it takes to do rich tasks in class. I’m going to address that conversation in my next blog post, Making Time for Tasks.

The tasks have students make sense of the lanes on an Olympic Track.

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One participant didn’t understand why I changed tasks with the two classes. I neglected to explain that during the session. I was really just doing an experiment to see how the tasks were different and how students approached them depending on the given information. Was one easier for students than the other? Did I need to scaffold the tasks for my students differently than they were written? Were students more successful with one task than with the other?

On Saturday, I went to a session by @bamentj from Darwin, Australia and learned about TodaysMeet. I wondered about using it as a backchannel during the session. A lot of participants were using Twitter throughout the conference, but we wanted a place where participants could interact with each other more than usual in a large session – and not get lost in the conference hashtag (or use two hashtags to make a subset of tweets for our session) being used by the other power sessions as well. Even though this meant that others at the conference wouldn’t find out as much as they might have otherwise about our session, we still wanted to try it. We made a room called CCSSPower. The link will only be live through March 15, 2014.

Several times we asked participants to use the protocol “I like, I wish, I wonder …” to provide feedback. So it turned out that we didn’t use TodaysMeet as effectively as we could have. In fact, one of the first posts I read was from Joe: I wonder what the purpose of today’s is. I did not see the use other than to post comments/questions that never were answered.

My reply, after the session (in 3 posts): Hi, Joe. Thank you for your comment. If we were to use TodaysMeet again, we would have a second projector to observe and use the comments. I like that the back channel can give participants a chance to communicate, whether or not the instructors are able to address the comments. But I will definitely use it differently if I use it again in a session.

I’ve also thought since my post, that since we had co-presenters, whether or not we had the second projector, one of us could have been monitoring a second computer with the backchannel while the other spoke. We learn from our mistakes, right?

As I have read through the other comments so that I could address some of the questions in this blog post that we didn’t get to address in the session, I will say that while we could have used the backchannel more effectively, it wasn’t a disaster. Those who were on the backchannel were having their own conversation. Several of the questions did come out in our whole group discussion, and some questions were answered by others in the backchannel without the presenters having to get involved.

One participant liked the pre-assessment ACT question being the same as the post-assessment.

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I am glad that one of the teachers on our geometry team had the idea to include the question in the lesson. I would not have thought of that myself. I looked back at Running around the Track I this week and noticed that one commenter suggested that the content in parts a and b of the task was on a grade 7 level. That might be true, but especially in this first year of CCSS implementation, the data I received from sending the ACT question without choices at the beginning of class (around 50% correct for both classes) indicated that our students had not thought through the mathematical content in the task before.

Several ideas for extensions came out during the session. What about having students also calculate area of the track for the ACT question? What about having student calculate the amount of paint needed for the lanes? Could you have students measure a local track with a trundle or wheel?

It occurred to me that it would be nice to take students to the track for the lesson. And then it also occurred to me that it would add at least 30 minutes to the time of the lesson for a visit to the track. I will note that one student in particular was engaged by this lesson more than any other this year. I asked him recently what his career pathway was, and he answered in all serious that is was to be a professional football player. He was an expert in class during this lesson.

Another suggestion was to use a video. I agree. If you find the right clip, please share it with me! I started by looking for a clip, but those that I found were longer than I wanted to use, and longer than I had time to search for the perfect segment to watch.

A few more comments from the back channel:

  • With regards to everyone missing the question about whether the lane lines were similar: If everyone got the quick poll wrong, I wonder how they would respond if you told them the answer is “no”, could they rethink their reasoning.
  • I wonder how you selected the student to present his “wrong” answer?
  • Perseverance is a best practice that we have to facilitate in our classrooms.
  • FYI while we were doing the 400 meter question…US women won the 4×400 meter gold at worlds in Poland.

What do you in your classroom when everyone gets a wrong answer?

If you decide to have someone explain their work anyway to correct incorrect thinking, how do you select students to present their work? Do you use a random student generator (we have one where we check roll in our PowerTeacher grade book)? Or “equity sticks” (usually tongue depressors with student names – some teachers replace and some teachers don’t replace when you call on students)? Or keep a clipboard with notes about whom you’ve chosen for whole class discussions? I’ve been trying the latter this year. It’s not perfect, but it is a start to at least paying attention to how often I call on students.

And so the journey continues … collaborating with educators from all over the world to improve our classroom practices. Thank you for the opportunity to learn from you, and thank you to Ellen from Illustrative Mathematics for sharing such great resources with us during the session and giving us a preview of what is coming soon to their website.


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Running around a Track I

I have been at the T3 International Conference in Las Vegas this week. This morning, I had the opportunity to present a Power Session on CCSS: Bringing content and practice standards together. My next few posts will be a few of the stories from this session.

I gave a class of students Running around a Track I recently.

I started by showing them a picture of the start of the 2012 Olympic Women’s 400 M race. What’s your question? (I took a picture while watching the video.)


The students had good questions to get us started in our exploration.

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who won        1

What is the circumfrence of each lane?       1

how far is th last runnr to the circle     1

Why are the not in a line       1

how far away is the first runner from the last runner?          1

which track is longest 1

what are we trying to find      1

what is the ratio from lane 1 to lane 9          1

What’s the circumference of the track?        1

I know everything?   1

why are they not in a line?    1

who gonna win?        1

how far is the outer lane from the inner lane            1

does contestant number 9 have an advantage over contestant number 1        1

What is the ratio of the inner-most lane to the outer-most lane?  1

how much shorter distance does the inner lane runner have to run than the outer runner?         1

how long is the circumference of each circle            1

What are we looking for?     1

Are they all going the same distance.         1

Who won?     1

What is the measure of the intercepted arc?          1

is this the winter olympics     1

Next, I sent out a Quick Poll of a question from an ACT practice test that students should be able answer as a result of the lesson.

Dylan Wiliam talks in his book Embedded Formative Assessment about teachers needing time for collaboration. Our administrators take this seriously, and so our geometry team has the same planning block. One of the other geometry teachers had the idea to include the ACT question in with this lesson.

Who already knows how to solve this? Who knows how to solve it quickly, since the ACT is timed? I removed the choices, just to see how students answered without them. We didn’t talk about the results. I told them we would revisit the question at the end of the lesson. Just over half of the students had it correct initially: 14/26.

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We talked about a few of the student questions from the picture of the Olympic race. And then I passed out the student handout for Running around a Track I. I let the students work in groups to answer the questions, and I sent Quick Polls every once in a while to be sure that they were working productively. I sent a QP for question a) and noticed that 20/26 students had it correct. I was able to use the Navigator to determine who had missed it & provide help for them at their desk while the rest of the class worked ahead.

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I didn’t send a poll for question b). Instead I provided students the correct answer so that they could determine on their own whether they needed assistance or were ready to move on to part c).

Most students got a bit stuck on part c. I knew this because I sent a poll to find out student responses. No one had it correct.

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We used this as an opportunity to figure out incorrect thinking. One student came up to share his work, and the others critiqued his argument, figuring out where their own thinking had gone wrong, and correcting their work.

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To close the lesson, I sent the Quick Poll from the start of class:


75% of the students answered it correctly with no choices (up from 50% at the start of the lesson), and 96% answered it correctly with choices.


I think it is interesting to ask students which practices they used when working on a task.


And which was the most used practice:


At this point in the session, we asked the participants to process this part of the story using the protocol “I like …” “I wish …” “I wonder …” for the discussion. What worked? What would you have done differently had these been your students? What would you do differently if you were going to use this task with a group of students in the future? What if you were going to give students Running around a Track II? How would you intend for the lesson to play out?


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