Monday, February 2, 2015

Number Talks Book Study -- Chapters 5

Hello from snowy Illinois!  Today we continue our Number Talks book study sponsored by The Elementary Math Maniac. We move on to a discussion of chapters 5.  Originally, I had planned to discuss chapter 6 as well, but I will be lumping chapter 6 with chapter 7 in next Sunday's post. Both chapters focus on designing purposeful number talks in the 3-5 classroom.

To read past chapter posts, visit the Number Talks Book Study Archive!  

It feels a bit funny saying this is an excellent chapter because they're ALL wonderful.  But, this chapter brought back memories of teaching third and fifth grade for many years and provided for a huge amount of self-reflection and assessment of days gone by.  At the same time it serves as affirmation for my current practices and fuel for the future.

I have spent the majority of my years teaching 3-5 grade students, moving to second grade four years ago. I have to say I loved my days at 3-5, and parting ways was not due to a growing dislike for the age, burnout, our a need for change due to becoming stagnant.  My decision to move grade levels was actually due to what I noticed about my fifth grade students year after year--a lack of conceptual knowledge in mathematics that was accompanied by a series of memorized steps to get an answer.  Did I move to second grade because I was tired of taking them "back to the basics"? No! Was I frustrated by what was done before they got to me? Honestly, yes.  Did I play the blame game? At times. Is this where it stopped? No.  I have been blessed to be surrounded by outstanding educators during the 20+ years I have been at this, and I can't say a focus on procedures without the depth of understanding was intentional by my students' previous teachers, but I do believe it came with a lack of understanding/knowledge--and, yes, I was in the same boat many years ago myself.  What is most important? Self-reflection and a commitment to continuous growth. Chapter 5 has something for everyone, whether you teach 3-5 or not!

Chapter 5: How Do I Develop Specific Addition and Subtraction Strategies in the 3-5 Classroom?

Chapter 5 begins by outlining five number talk goals for 3-5:

Number Sense: Number talks help to develop number sense by---asking students to assess the reasonableness of a solution, having students make estimates BEFORE choosing a strategy to solve an equation, and requiring students to justify their solutions. These behaviors place emphasis on understanding, not on the memorization of steps/procedures. Parrish's discussion of the importance of students' abilities to estimate is almost identical to that shared for K-2.  Just recently, I have experienced the power of having students make estimations before selecting a strategy.  I began using number talks with my students about a month ago, but most recently I began our number talks with some estimation.

With my second graders, I asked students to answer 2-3 questions and justify their thinking.  For example, Is 50 a reasonable solution? Could the sum be 100? and we moved to more general questions such as, About how much is each addend? What is a good estimate of the sum?

How has this helped?  The number of incorrect solutions has reduced considerably with 1-3 solutions being shared, and students who had not previously shared began to share (their thinking being recorded for all to see "up on the board").  Asking students to estimate before finding a solution creates the mindset for reasonableness.  Below you can see a number talk without (left) and with estimation BEFORE (right).

Place Value: I think this quote says it all, "The true test of whether students understand place value is if they can apply their understanding to computation." Place value should be a focus for understanding and application at ALL levels.

Fluency: As shared in a previous K-2 post, Parrish states, "Fluency is knowing how a number can be composed and decomposed and using that information to be flexible and efficient with problem solving." When students have fluency with composing and decomposing "small" numbers they begin to understand that this can also be done with greater numbers.  This is foundational for understanding that making landmark/"friendly" numbers makes mental computation easier. Such fluency is essential at all levels and is strengthened with the use of number talks.

Properties: Parrish stresses how number talks foster students' use of their own strategies and their thinking can be directly linked to mathematical properties.  This in turn creates opportunities for students to apply properties while understanding their meaning.  Can you see the use of any properties in the strategies recorded in the following number talk?

Connecting Mathematical Ideas: Whenever possible, help students to understand that mathematical concepts are related. Some examples Parrish shares,  How can addition be used to solve subtraction problems?  How are arrays in multiplication related to division?

Chapter 5 goes on to overview the use of an open number line and part-whole box.

Open Number Line: If you are not familiar with open number lines, I highly recommend this introduction by Jeff Frykholm--Learning to Think Mathematically with the Number Line. It comes from his book of the same name.  Click here to learn more and view a sample lesson.  The open number line is a strategy many of my students use to model their thinking.

Also, Dreambox is a wonderful resource for using the open number line on an interactive whiteboard/computer--Teaching Number Sense Using the Open Number Line.

Part-Whole Box:  This visual helps students understand the relationship between parts and a whole.  Part-whole boxes are ideal for use when solving word problems with the unknown in different positions (start unknown, change unknown, and result unknown).

Download a simple part-whole box here!

Parrish continues by stressing the importance of using real-life contexts, discussing efficiency, and anticipating student thinking (as presented for K-2 in chapter 3). 

Finally, three common addition strategies, and five common subtraction strategies, are shared.  These illustrations are great for helping teachers anticipate the strategies their students will use and how to record them.

We would love to hear your thoughts about chapter 5, so feel free to leave a comment!

AND, keep those questions coming! Sherry Parrish, the author of Number Talks, will be doing a Q&A after the completion of our book study!  We will take questions through this coming Sunday--so don't hesitate to ask! You may send questions to Thanks go out to Sherry!

Lastly, stop back this Sunday for Chapter 6 & 7!

Have a fabulous week--

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