A Touch of Number Sense

About 4 years ago, I purchased a Groupon for 10 yoga lessons.  Being a former gymnast, I quickly noticed a connection between yoga and gymnastics.  Both disciplines combine strength, balance and grace in a flow reminiscent of a beam or floor routine.  When my Groupon ended, I joined the studio and power yoga has been my workout of choice ever sense.

Screen Shot 2015-09-06 at 10.49.25 AM

Shayna from, The Yoga Room, demonstrating boat pose. She designs her classes to work every muscle in your body – and I’m stronger for making it through her classes.

Core strength is the key to a yoga practice involving arm balances, standing balances and tricky transitions, which is why instructors integrate a “touch of core” into each class. Hands down, “a touch of core” is the most painful part of class and boat pose is my biggest nemesis, but the benefit of a stronger practice is worth a short period of discomfort.

Recently, I had surgery to fix a ventral hernia located in my core region.  My doctor repeatedly warned me to let my body heal before going back to yoga.  I listened.

At the time of this post, I was cleared for yoga and have attended 5 classes.  I spent these classes modifying the routine and recovering from losing my balance.  I have no issues with falling when working on a new pose or tricky transition. Falling helps me learn.  But I was losing my balance on poses that were once automatic.  Personally, this was blow to my ego. Professionally, the continued falling lead me to an “aha” moment.

C0re strength is to yoga as number sense is to math!!

************************************************************************************

Classroom Connection

Capture

Slide 1

Prior to my “aha” moment, I was working with 7th & 8th graders (LCAP groups) on a Desmos activity builder task: Number Sense w/ Multiplying Fractions.

Capture1

Slide 2

I noticed that students easily answered the first slide correctly, but a significant number were not able to answer the second slide correctly.  At first, the 2nd question paralyzed them.

Students moved the red dot to either the 15 or the 45 mark.  After getting a few shrugs when asked how they arrived at 15 for the answer, I decided to teach an impromptu mini lesson.

At the end of the period, I asked the teacher if I could open his classes with a number sense activity for the next 2 days.  He agreed.  Although my openers weren’t Number Talks, as promoted by Sherry Parrish, the experience caused me to value Number Talks at a deeper level.

To strengthen our students’ math practice, teachers should explicitly discuss number sense or in yoga terms, provide “a touch of number sense” regularly.

************************************************************************************

Number Talks

  • Screen Shot 2015-09-08 at 9.34.47 PMThe first time I heard the phrase, Number Talks, was in 2012 during a Math Solutions training.
  • The second, during a summer training in 2013.
  • Last year, I attended Sherry Parrish’s Number Talks workshop geared more for the elementary level.
  • I attended Chris Harris’ Number Talks workshop at Twitter Math Camp 2015
  • For the 2015 – 2016 school year, my district is sending the Math coaches/TOAs to Ruth Parker’s workshop:  Number Talks for the Secondary Level.

Prior to Sherry’s workshop, I asked a few 6th teachers if I could practice the Number Talk protocol.  A true number talk should last roughly 5 – 7 minutes.  Mine lasted longer.  Why?

  1. Students were not in the habit of practicing number sense in the way I presented it.
  2. I should have started with an easier problem.  I started with (16)(25).  The number 1 strategy used was the traditional algorithm.  Since pencil and paper aren’t allowed during a number talk, I saw many students calculating the problem in the air or on the desk with their finger.
  3. To get students talking more, I treated the activity as a lesson.

As the activity turned into a lesson, students began having “aha” moments.  In my eyes – mission accomplished.  After practicing in 3 classes, I didn’t revisit Number Talks for the rest of the 2014 – 2015 school year.

********************************************************************************

10 months later….

Although I didn’t continue practicing the Number Talk protocol after the initial 3 attempts, I did spend lots of time in classrooms working with kids. Across the board, I noticed a weakness in general number sense which I presume caused students to hold back from participating in group discussions. I’m convinced that incorporating a 5 – 7 minute number talk regularly will increase number sense and therefore increase both participation in and quality of mathematical conversations.

Abiding By the Number Talk Protocol – Kind of…

Recently, when a colleague asked me to run a number talk in her 6th grade class, I promised to stick to the time boundaries.  She specifically wanted me to incorporate a number talk involving a double number line.  I had never seen anyone run a number talk involving a double number line before.  So…. my mind went to work.

Question: “What is the essence of a Number Talk?”

Answer:  A problem is presented and students explain how they arrived at their answer. The problem presented must have multiple paths to the solution.

Screen Shot 2015-09-06 at 11.03.34 AM

Number Talks are amazing because a rich discussion can stem from what’s viewed as a simple problem.  I drew the double number line on the board with 2 blue squares representing the missing numbers, 6 and 9.

Before I could explain the number talk protocol, many hands were waving in the air.

Me:  If you know which numbers go in the squares, form a fist with your hand and hold it close to your chest.  I’ll give you 20 seconds to determine your answer.

I called on 2 students, 1 to give the answer for the top part of the number line and 1 to give the answer for the bottom.  This is not typical protocol but I wanted to move beyond the answers and get to the core of the activity.

Me:  Now we’re going to enter into the best part of a Number Talk.  I’d like to hear your strategies for arriving at 6 and 9.  Before I call on anyone, I’m going to give you 1 minute to come up with more than 1 way of getting 6 and 9.  (I then showed them the hand signals)

Capture   Capture1    Capture2

I have 1 strategy.                  I have 2 strategies.                I have 3 strategies.

************************************************************************************

Student Responses

  • 2 x 1 = 2                  3 x 1 = 3
  • 2 x 2 = 4                 3 x 2 = 6
  • 2 x 3 = 6                 3 x 3 = 9
  • Screen Shot 2015-09-06 at 10.47.13 AM3 is a multiple of 3
  • 6 is a multiple of 2
  • 3 + 3 +3 = 9
  • 2 + 2 + 2 = 6
  • 4 + 2 = 6
  • 6 + 3 =9
  • 8 – 2 = 6
  • 12 – 3 = 9
  • 9/3 = 3                                  Not pictured:  1 1/2 x 4 = 6
  • 6/3 = 2                                                                 1 1/2 x 6 = 9

************************************************************************************

Misconceptions

If you look closely at the picture, you’ll notice that one student wanted to make a connection using exponents.  Actually, in 3 out of 5 classes, students wanted to use exponents as a strategy.

What do you do when you know a student is making a mistake?  Roll with it.

In this particular class, the student started to explain her reasoning:

  • Student: 2 to the 3rd power is 6.
  • Me: How many 2’s do you multiply when simplifying 2 to the 3rd power?
  • Student:  Oh!  I get it.
  • Me:  Nice, will you answer my question?
  • Student:  2 x 2 x 2
  • Me:   and that equals…
  • Student:  8

The interaction from a different class.

  • Me:  Roberto, what’s your strategy?
  • Roberto: I have one for the bottom part but I don’t think it works for the top line.
  • Me:  Start sharing and we’ll see what happens.
  • Roberto:  3 to the 2nd power is 9.  Pause… But 2 to the 2nd power isn’t 6.

This was an opportunity to emphasize that testing out new ideas and searching for new connections are valued actions in a math class.  My discussion with Roberto, prompted another student to ask a question about exponents, that eventually led to her share:

  •   1 1/2 x 4 = 6
  •   1 1/2 x 6 = 9

************************************************************************************

Incorporating More Discussion

1. Finishing another student’s strategy:

  • Haylee:  I added 2 + 2 + 2 to get 6
  • Me:  Haylee, thanks for sharing the first part of your strategy.  (To the class) Would someone like to apply Haylee’s strategy to get the 9?
  • Jacob:  To get the 9, you can add 3 + 3 + 3.

 2. Summarizing or repeating another student’s strategy:

  • Me:  Is there someone who could explain Haylee’s strategy?
  • Damian:  She kept adding 2’s until she got to 6

About jgvadnais

Math Coach. Desmos Fellow. Google Level 1 Certified. SoCal transplant. New Englander at heart. Lover of yoga, dogs, green smoothies and coffee.
This entry was posted in Math Education, Number Sense, Number Talk and tagged , , , , , . Bookmark the permalink.

4 Responses to A Touch of Number Sense

  1. Pingback: Kicking Off Genius Hour – A Guide | Communicating Mathematically

  2. gfletchy says:

    A touch of number sense….with a whole lot of understanding. Love this Jenn.
    More please!

    Liked by 1 person

  3. Pingback: Percents and Proportions and Desmos – Oh My! | Communicating Mathematically

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s