Noticing and Wondering Across the Grades

I have been reading a lot lately about having kids “notice and wonder” to start off a math task.  This seemed to be a nice extension from the Number Talks that I have been doing lately, so I was looking for an opportunity to visit some classes to try it out.  Then, last week, a friend of mine posted this picture to her Facebook page…

Egg Array
An egg array – beautiful!

… and I knew I had to use it!  There are sooo many awesome things to notice and wonder about in this picture!

 

So, I “invited” myself into some classrooms at my school.  I was especially curious about how kids at different grades would respond similarly/differently to this photo.  I visited a Grade 1/2, a Grade 2/3 and a Grade 3 class with the same activity.  First, I showed the whole class the picture and gave them a few minutes to observe and think about what they noticed and wondered.  Then, I collected all their ideas onto the whiteboards at the front.  I was so impressed!  I love how curious kids are at this age, and I love the variety of things that they noticed and wondered about:

P1000152
Grade 1/2 noticings and wonderings – lots of math “noticing” already
Branigan
Grade 2/3 noticing and wondering
Dunn-notice
Grade 3 noticing (I JUST realized that I put a “wonder” in the “notice” list – oops!)
Dunn
Grade 3 wonderings

I love how many things the Grade 3’s wondered about before they wondered how many eggs there were! I think my favourite “noticing” is “it looks like they just came out of a chicken!” And I love how much real-world knowledge is being talked about here – in addition to the math.  I thought it was so interesting to hear the variety of background knowledge that the kids had about chickens, farms, eggs, and where their food comes from.  They were all very enthralled by that tiny egg in the middle (which, by the way, had no yolk according to my “farmer” friend).

Next, we did some “math” with the picture.  I gave all the kids a black and white copy of the picture in a sheet protector and a dry erase marker to use.  I challenged them to figure out how many eggs were in the picture WITHOUT counting one-by-one.

Here are some samples from the 1/2 class…

Grade 12-3
Grade 1/2 sample – I have never taught these grades, so wasn’t sure how easily kids would be able to count by grouping.  I was expecting to see a lot of this, but only had a few that ended up counting one-by-one.
Grade 12-4
Grade 1/2 – A slightly more sophisticated version of one-by-one counting.
Grade 12-1
Grade 1/2 – interesting! This student started counting by 2’s but got to 22 and couldn’t continue, so she switched to counting by 1’s to finish off.

 

Grade 12-2
Grade 1/2 – counting by 3’s, but a little mix-up at the end.  This reminds me of a hundreds-chart layout for counting by 3’s (row-by-row).
Grade 12-5
Grade 1/2 – this was the most sophisticated version from the 1/2 class.  It looks like he counted 1 by 1 but when I asked him about his picture, he explained that he did 9 groups of 4.  I like how he arranged it as a grid.

And a few from the 2/3 class…

Grade 23-1
Grade 2/3: Counting by 3’s
Grade 23-5
Grade 2/3: Counting by 4’s

 

Grade 23-3
Grade 2/3: Counting by 4’s a different way
Grade 23-4
Grade 2/3: Counting by 6’s
Grade 23-2
Grade 2/3: Hmmm… interesting.  I’m just guessing here, but maybe the student decided that counting by 2’s would take too long?  In any case, this is probably the most unique grouping I saw!

With the Grade 2/3’s we ended up discussing that 36 is a really interesting number because there are a lot of ways that you can group the eggs and still get to 36.  We talked about the word factor and how we could use it to describe the way we grouped the eggs (ie. my picture shows 9 groups of 4 – 9 and 4 are factors of 36).

And the Grade 3’s:

Grade 3-3
Grade 3: Counting by 3’s – an interesting way of grouping
Grade 3-1
Grade 3: This student actually grouped them a few different ways.  He counted by 2’s and then by 3’s and then had a great idea: “I bet I can put them in dozens!” Kind of a cool connection to real-life knowledge about how we buy eggs.

So… after all that… what did I notice and wonder?

I noticed that the kids were all really engaged in this activity.
I noticed that all the students (even the lowest Grade 1/2’s) were able to meaningfully engage with this activity.
I noticed that many kids wanted to try different ways of grouping and were getting ideas to try from their neighbours.
I noticed that all the students were keen to explain their thinking.

AND… I noticed… that not ONE student in any of the classes grouped the eggs in a “traditional” array pattern.  There were some kids who counted by 4’s, but none made columns of 4.  And nobody thought to make rows of 9 or to turn the page and make columns of 9.  This is a big ??? for me, because I would think it would be natural to group things in rows and columns, and this is where we want kids to access multiplication.  So, this leaves me wondering… do the students naturally group things the way that they did because of experience using hundreds charts?  What kinds of activities can we do to help them see things in arrays?  Should I be “encouraging” kids to see an image like this as an array, or will that representation naturally develop over time?

So much to think about!!  I love activities that make me wonder about my teaching and student learning.  I will definitely be doing more noticing/wondering with kids…

If you are interested in doing activities like this one with your students, there are many more images like these available on the Number Talk Images website and I have submitted the picture from this activity there as well.

 

 

Number Talks

This year has been my first year as an Intermediate Math Liaison with my district, and it has been a learning curve.  I LOVE teaching math and talking about teaching math, and I have tried to take advantage of any and all opportunities to learn more about best practices in teaching.

One topic that has come up over and over again in different places this year is “Number Talks.”  They were on the conference agenda at the NWMC in October, but I didn’t have a chance to attend a session.  Just before winter break, the District Learning Commons sent out an ad for some new materials – Number Talks by Sherry Parrish and Making Number Talks Matter by Cathy Humphreys and Ruth Parker.  I immediately tried to sign them out, but apparently everyone else in my district did too and I ended up on a wait list.  I finally tracked down copies of both just before the Christmas holidays and there they sat on my shelf.

In January, the other Intermediate Math Liaison and I decided to do a presentation for our district’s annual Zone Conference on Number Talks in the intermediate grades – since they seemed important and we were both intrigued.  So then I really got motivated to crack open those books and see what Number Talks were all about!

And I was hooked.  I dove into Making Number Talks Matter first and – WOW!  What an eye-opening book.  It seems that everything I have pondered about Math is highlighted in here – why kids don’t have number sense and what we can do as teachers to help to develop it.  And they make it seem so easy – it was time for me to explore!

So… what is a Number Talk?  It’s a short (10-15 minute) activity in which students use mental math skills to solve a computation problem.  The teacher’s job is to choose an appropriate problem (or problems), carefully record student thinking and facilitate the conversation.  Students are to solve the problem mentally using strategies that make sense to them and then communicate their thinking clearly.

I started my exploration in my Grade 4/5 class with dot talks as suggested by Humphreys and Parker.  I teach in an inner city school and I am always curious about how suggestions from a book will translate into my particular teaching environment – I am forever making adaptations to things.  But I was pleasantly surprised.  My kids LOVED the activity and every.single.child participated (a first for sure).  They loved looking at the dots and explaining their thinking.  I loved that it was a non-threatening activity and encouraged so many different ideas.

These are the dot talks we did (taken from Making Number Talks Matter by Cathy Humphreys and Ruth Parker).  The students were instructed to figure out how many dots were in each picture, without counting one-by-one.

dot card 1.jpg

Dot card 2.JPG

 

My kids came up with some ways to figure out the number of “dots” that I hadn’t thought of, and it was challenging but fun to listen carefully and try to make sure I was recording their thinking accurately without putting words in their mouths.

Next up, I threw in some numbers.  I was prepared for this to be less successful, given that numbers are a bit “scarier” than dots, but it also went well.  I used this sequence from Number Talks designed to encourage students to use the take-and-give strategy for addition.

19+2
19+5
19+8
19+12

I was so impressed by the strategies that my kids came up with on their own. By the fourth question, we had several strategies in play – some were using take-and-give, some were grouping by place value; some were using the previous answer and adding on. One student talked about “lining the numbers up in her head” (ie. the traditional algorithm), which gave me a chance to think about how I wanted to respond to this as a strategy.  I just named her strategy as the pencil-and-paper way that we often add and put it on the board with the other ideas.  I even had a “wrong” answer – one student mixed up the signs and was multiplying 19×2 for the first question, so I had an opportunity to talk about why making mistakes is important and how we can learn from mistakes as well as “right” answers.  Admittedly, this sequence of questions is pretty easy for Grade 4’s, but I really wanted them to feel like they were successful right from the start.

So – after just a few lessons, I am hooked.  I love the potential that this strategy has to develop number sense in kids.  I love that it is relatively simple, easy to plan, accessible for all learners, takes up very little instructional time and encourages thinking and communication.

And, as for the presentation that sparked all of this – it went well – hopefully we “hooked” a few more teachers on the idea of number talks.  As part of our presentation, we made a planning page (adapted from Making Number Talks Matter) that you can download from Google Drive here.

As a note on the two books – Making Number Talks Matter is written for Grades 4-10 and Number Talks is designed for K-5.  As a 4/5 teacher I think I would use both regularly in my planning.  As an intermediate teacher, I really appreciate the focus on fraction and decimal understandings in Making Number Talks Matter.

Thanks for reading!  Go try out a number talk!