Number Talks

Last year I was introduced to a book called Number Talks: Helping Children Build Mental Math and Computational Strategies written by Sherry Parrish.  It is a little pricey, but well worth the investment.  It is a wonderful resource for grades K-5 because it provides chapters on how to create meaningful number talk and gives lots of samples that you can use.
So, if you've never heard of number talks- what is it? In a nutshell, it is a time to develop mental math strategies and a time to practice communicating and listening in math.  It's designed to be short, but powerful.
Here are some guidelines the book provides for Number Talks.
1.  Pick a location in the classroom where you are close together so it is easier for you to observe and interaction.
2.  Give plenty of wait time for all students to be able to attempt the problem.
3.  Accept, respect and consider all answers.
4.  Encourage students communication throughout the math talk.

In Kindergarten,  I used the SmartBoard to do my number talks.  I focused primarily on Dot Cards and different representations of numbers.  At the beginning of my math talks, I focused on subitzing and they were more Tell Me Fast kind of things where students looked at dots on a ten frame or random dots and figured out how many there were.  Here's a blog post about it from last year and a freebie.  Later on in the year, I focused on how students added to get their answers.  I would give them a dot configuration and students would see combinations of numbers and add to get an answer.  For example, if I showed this:

Students might see the top 5 and the bottom 2 and say "I see 5 on the top and 2 on the bottom.  That's 7."  or a student might see the 3s on the side and say "I see 3 on one side, 3 on the other and 1 in the middle- that's 7."  I would write down the number sentence that they did just to connect it to an equation.  Students LOVED this- it was one of their favorite parts of the day!  Sometimes I used dice, sometime I used dominoes, sometimes I used 10 frames and sometimes I used rekenreks.   You can get my dot configurations that you see above by clicking on the link.

The great thing about the book is that they give you samples of what to do!  That's such a time saver for me!

So, moving to 3rd grade I still want to use number talks in the classroom as a piece of my math instruction.  I went to the book for help!  It gives you sample sequences for addition and subtraction and multiplication and division.  I began with addition.  I made cards that look like this.

The author broke the addition into different categories:

• Making 10
• Friendly Numbers
• Doubles and Near Doubles
• Place Value
• Adding up in Chunks

I made header cards for each of these.  I plan to print, laminate and cut out the cards and store them in those index card holders that Target has right now in back to school supplies.  We will begin easy with the making 10 cards, I think, until I get a feel for what they know.  Then we'll move wherever they need to go depending on their needs.

We will do Number Talks in our meeting area and I will write the number sentences, one at a time, on my white board/easel.  Then I will give students time to process.  The book suggests a signal that students do that shows they have an answer- like a thumbs-up in front of their chest or something like that.  Then I will ask students to explain how they got their answer and I will record their thinking on the white board.  We will talk about their strategies as a class and ask questions/discuss as needed.

I don't think students will have done this a lot in previous classrooms so it will be difficult at first to get them to share their thinking.  But once they begin number talks, it is such a powerful way for students to talk, discuss and ask questions about math.  It hits upon the mathematical practices standard MP1: Make sense of problems and persevere in solving them. MP7: Look for and make sense of structure and a whole bunch of Speaking and Listening standards.

If you'd like to try Number Talks, you can get these addition cards here. 

Karla

Number Sense Routines Chapter 1

I am linking up with Little Minds at Work for a book study on Number Sense Routines by Jessica Shumway.

I was so excited I did this post about it before Tara gave us questions to talk about... so, skip to the bottom if you only want to see my answers or read the whole thing.

Let me tell you how excited I am for this book study!  I read this book for the first time back in January and started implementing some of the ideas right away in my classroom.  I am kind of a math geek and my teammate teases me all the time because I will happily get into these deep mathematical conversations about students’ thinking and my philosophy of teaching math if someone doesn’t stop me.  We often have PLC meetings that focus on math and many times I am apologizing for  monopolizing conversations or getting on my math “soapbox”, so I will apologize ahead of time if these posts ramble a bit or it’s hard to find the point I am trying to make.

What I loved about Chapter 1

I absolutely loved Box 1.1 What’s the Math and the Early Number Sense Learning Trajectory.  I loved the clear descriptions of subitizing, magnitude, counting, one-to-one correspondence, cardinality, hierarchical inclusion, etc…  As a teacher of little ones, I think we know these things and we see the progression in the students.   But up until a few years ago, I had never heard the word subitizing.

“The more we as teachers know about these big ideas in students’ mathematical development, the better we are able to support students’ numerical literacy by planning appropriate routines for their mathematical development.”  I love this quote- I think too often, and maybe it’s just where I teach, teachers don’t spend the time in math that they do in literacy getting to know the student as a mathematician.  For example, I think at my school, if I asked a kinder teacher to tell me what a student is like as a reader, they would tell me lots of information.  They would tell me whether or not they can blend and segment, if they know all their letters and sounds, how many sight words they know, what their guided reading level is, etc…  But if I asked the same teacher to tell me what the student is like as a mathematician, I am not sure what I would get.  I think the answer wouldn’t be as in depth.  I am guilty of this too- I’m working on it, but nowhere near there yet.  We spend the time to get to know students as readers and we group them according to their needs during guided reading groups.  I think it’s equally important to do the same in mathematics especially with our little ones.  But I don’t think teachers are given as much professional development in the realm of math- anything extra we know, we’ve learned ourselves through books like this.  And, I think the nature of our math programs that districts adopt is not conducive to this kind of in-depth understanding of students’ mathematical thinking.   That’s why we have to read books like this during the summer!

Students with strong number sense:

Have a sense of what numbers mean- they have a visual model and concrete understanding of quantity

Have an ability to look at the world in terms of quantity and numbers and can understand relative magnitude of an amount

Have an ability to make comparisons among quantities using landmark numbers like 10, 50 and 100

Have flexibility, automaticity, and fluidity with numbers and can apply this knowledge to solve problems and reason through number relationships

Have an ability to perform mental math

Have flexibility with problems

Have automatic use of math information.  They readily use what they know to solve problems

Have an ability to determine reasonableness of an answer

Have an ability to decide on a strategy based on the numbers in a problem.

This list is pretty extensive and nothing that we can truly say the students mastered in kindergarten, but we can definitely give them a good start on their path toward strong number sense.

Teaching for Number Sense: A process leading to understanding

Lately, I am hearing a lot of bashing of the Common Core from “informed” parents who are worried about their child’s educational future under the Common Core Standards.  I can see some of their concerns, but they are overlooking some really good pieces to the Common Core.  Love it or hate it, I feel like, particularly in math, it has our students starting off on the right path.  I feel like if you take the Kindergarten standards, especially the Counting and Cardinality and Operations and Algebraic thinking standards along with the Mathematical Practices standards, it really has our students building a strong number sense.  I feel that if it is done with fidelity and teachers go to great lengths to move beyond their adopted math series and really teach the standards, I think that our students will leave second grade with a strong number sense that will help them in the rest of their mathematical education.

As Chapter 1 concludes I really like this quote:  “In order to get to that point (numerically literate students) a student needs multiple opportunities to bump into number sense ideas, use number sense, and discuss number sense ideas and strategies with peers.”

Here are the answers to the questions Tara asked over at Little Minds at Work.

1.  What is your current comfort level with teaching number sense?
 I feel like last year I really grew a lot in terms of my comfort and knowledge about number sense.  Overall, I have a better idea of where students are coming from and a better sense of where I want to take them with regards to number sense.   But I am nowhere near an expert and I know I have so much to learn, but I feel more comfortable with the topic than I have in past years.
2.  What have you already started in your classroom to build number sense?
I did a lot with subitizing and unitizing this year.  Early in the year, I created slide shows in Power Point- dot cards, ten frames, tally marks etc... and I would do some of those cards each day with my kinders.  They were "Tell me Fast" cards where students would need to quickly tell me how many were there.  They also had to explain their strategy for finding how many.  When students came up with a new strategy for knowing how many, we added that to our anchor chart.  Some examples around mid-year were things like, "Presley's Find Ten and Count the Rest" or "Cora's Group What You Know and Count On".  We also implemented the "Count Around the Circle" routine that is talked about later on in the book, but I will save discussion for later.
3.  What have you considered adding to your classroom that will give students that much needed "multiple exposure" component?
 The Tell Me Fast Cards will definitely have a place in my classroom.  I will continue the Count Around the Circle routines and my daily math journals.  I also like Number of the Day and saw that at the end of the year, my kinders really gained a lot of valuable insights into numbers when we did this as part of our math time.  There's so many great number sense activities and I can't wait to read everyone's ideas.

Can’t wait to talk about Chapter 2!