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Lesson Study: The Math and the Lesson Plan

February 3, 2017 / by Kristin Gray

Getting Better Together

This entry is the second post in the series Getting Better Together: A Lesson Study

In my first Lesson Study post, I discussed choosing a mathematical goal and task. In ending the post, I invited you to take some individual think time to work out the four questions posed. This was your time to think about how you would plan the lesson for your class, what sequence you would use, and what questions you would ask. You were also tasked with choosing a warmup to engage your class and a formative assessment strategy. Now it's time to think about the math and the lesson plan.

After solving each part of the task individually, we discussed how we thought students would think about each problem, in particular, which parts of the task were most connected to what they were currently doing in class, and which parts might be a stretch. Only having an hour for math class, we knew we wouldn't be able to get through all four of the questions if we included a warmup, discussion, and journal prompt, so we narrowed it down to three. Since we were unsure how the students would attack part b) of the task and, quite frankly, struggled with how we would explain it based on students’ experiences, we kept parts a), c), and d), and put b) aside for those who finished early.

During our planning, the teachers asked a great question about ratio tables. Since a few of us had used them in solving parts a) and c), we could also see students using something that resembled a ratio table in their work. The teachers were curious when students were formally introduced to them. This is the part about planning that I think is so valuable, but often lost, in the everyday rush of teaching. It's not very often that we have the opportunity to sit and really think about the ideas the lessons are building upon, and equally as important, where particular standards are heading.

We paused our thinking about the task for a moment so I could briefly give a glimpse into the progression of standards leading up to ratios in sixth grade. If we had more time, I would have loved to have everyone look into Student Achievement Partners’ Coherence Map and dive into each standard surrounding the task; however, in this situation, it just had to be my CliffsNotes version of it!

The good news is I have time now. Here's the progression of student learning that I find so incredibly interesting about the math in this task and where this standard is heading in future grade levels:

Common Core Standards Math: 3.OA.A.3

Common Core Standards Math: 4.OA.A.2

Common Core Standards Math: 5.NF.B.5

Common Core Standards Math: 6.RP.A.1

Ok, back to the task planning!

Since the third grade team all have their math block at the same time, we decided to do the lesson on three consecutive days so I could be in each room. Then we would have a chance to reflect on the lesson and make changes as we went.

Here is the general structure we planned for the first class:


Warmup (10 minutes)

  • Ask “What is multiplication?”
  • Record student responses on the SMARTBoard.

Task (20 minutes)

  • Launch the task by reading the directions to students and focusing their attention on answering whether the problem could be solved using multiplication.
  • Give five minutes of individual work time.
  • Give 15 minutes of small group time to share their responses and try to come to a consensus on each question.

Discussion (20 minutes)

  • Poll the groups to determine if they thought they could use multiplication for each of the three questions.
  • Share responses for each problem, beginning with the most agreed upon to the least agreed upon answer.
  • Questions to ask during the discussion:
    • -- What about this problem made you think it was multiplication?
    • -- What equation could you use to represent your thinking?
    • -- Did anyone think about the problem in the same way?
    • -- Did anyone think about the problem in a different way?

Journal Prompt (10 minutes)

What is it about a problem that makes you think it's multiplication?


After thinking about the math of the lesson and the structure of this lesson plan, I'd love your thoughts and/or questions on a few things:

  • The math in this task in relation to the progression of standards
  • The planning template we used
  • The lesson plan we developed for the first class

In my next post, I'll reflect on how the lesson played out and the adaptations we made in the other classrooms based on the first one!

Topics: Professional Learning, Coaching, Math

Kristin Gray

Written by Kristin Gray

Kristin Gray, a National Board Certified, 21-year veteran teacher of grades 5-8, is currently the Director of K-5 Curriculum and Professional Learning at Illustrative Mathematics (IM). She has served as a writer for the IM 6-8 math curriculum and as a Teaching Channel Laureate. Kristin has developed and facilitated mathematics professional learning at district, state, and national levels and presents annually at the NCSM and NCTM conferences. To reflect on her experiences, she blogs and connects with educators on Twitter, @MathMinds. Kristin has a B.S. in Elementary Education with a concentration in mathematics from the University of Delaware, a M.Ed. in applied technology in education from Wilmington University, and is the 2014 Presidential Awardee for Excellence in Mathematics and Science Teaching.

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