Summer PD: Day 2 Mathematical Flexibility

Summer Literacy and Mathematics Professional Learning
June 5-9, 2017
Day 2 – Mathematical Flexibility
Jill Gough and Becky Holden

Today’s focus and essential learning:

I can demonstrate mathematical flexibility to show what I know in more than one way.

(but , what if I can’t?)

Learning target and pathway:

Mathematics is a subject that allows for precise thinking, but when that precise thinking is combined with creativity, flexibility, and multiplicity of ideas, the mathematics comes alive for people (Boaler, 58 pag.)

…we know that what separates high achievers from low achievers is not that high achievers know more math, it is that they interact with numbers flexibly and low achievers don’t.  (Boaler, n. pag.)

UED: 8:45 – 11:15  / EED: 1:15 – 2:45

Resources:

#ShowYourWork, make sense and persevere, flexibility with @IllustrateMath

How might we learn to show our work so that a reader understanding without having to ask questions? As we work with our young learners, we want them to grow as mathematicians and as communicators.

We ask students to show their work so that a reader understands without having to ask them questions. What details should we add so that our thinking is visible to others?

To show (and to assess) comprehension, we are looking for mathematical flexibility.

I taught 6th grade math today while Kristi and her team attended ASCD.  She asked me to work with our students on showing their work.  Here’s the plan:

Learning goals:

• I can use ratio and rate reasoning to solve real-world and mathematical problems.
• I can show my work so that a reader can understanding without having to ask questions.

Activities:

Learning progressions:

Level 4:
I can demonstrate mathematical flexibility with ratio and rate reasoning to show what I know more than one way using tables, equations, double number lines, etc..

Level 3:
I can use ratio and rate reasoning to solve real-world and mathematical problems.

Level 2:
I can make tables of equivalent ratios relating quantities with whole-number measurements, and I can use tables to compare ratios.

Level 1:
I can use guess and check to solve real-world and mathematical problems.

Anticipated solutions:

Sample student work:

estimate and reason while dancing, singing, and playing

How might we promote peer-to-peer discourse that is on task and purposeful? What if challenge our students to estimate and reason while dancing, singing, and playing?

Andrew Stadel, this week’s #MtHolyokeMath #MTBoS Effective Practices for Advancing the Teaching and Learning of Mathematics facilitator, asked us to use visuals to engage our learners.  In his session, we used Day 127 How long is “Can’t Buy Me Love”?, Day 129 How long is “We will rock you”?, and Day 130 How long is “I feel good”? from Estimation180.

Here are my visual notes from class:

Our homework was to estimate  How long is “I feel good”? and to try visuals with students.

I asked Thomas Benefield, 5th Grade teacher and FSLT co-chair for 10 minutes of class to try Day 127 How long is “Can’t Buy Me Love”? with 5th grade students.

How might we make sense and persevere when making estimates? What is our strategy and can we explain our reasoning to others?

Students were asked for a reasonable low estimate, a reasonable high estimate, and then an estimate for how long the song is based on the visual. My favorite 5th grade response:

Well, you asked for a low estimate and a high estimate, so I rounded down to the nearest 5 seconds and doubled it for my low estimate. I rounded up to the nearest 10 seconds and doubled it for my high estimate.  For my estimate-estimate, I doubled the time I see and added a second since it looks like almost half.

#Awesome

It was so much fun that they let me stay for How long is “We will rock you”?, and How long is “I feel good”?, and they asked for Bohemian Rhapsody. Wow!

Andrew said that you know you have them when they start making requests.

As you can see, it was a big hit. They were dancing in their seats. This quick snapshot of joy says it is worth it for our students.

What if challenge our students to estimate and reason while dancing, singing, and playing? What joy can we add to our learning experiences?