Investigations with Number Talks

Our last *sniff, sniff* book club meeting was held this week.  We are so appreciative of the teachers who signed up to participate with us.  We are so grateful for the rich and thoughtful conversations and collaborative trouble-shooting that went along with our study of Making Number Talks Matter.  We really believe that professional learning is so much better with colleagues and that setting aside time for professional learning is great for our students, but also helps us (as teachers) stay excited about our work on a day-to-day basis.

This week, we looked at Chapter 9 – Investigations.

We started our meeting with our usual check-in about how Number Talks have been going in the classroom.  It sounds like most people have established a good routine with Number Talks.  Some folks are taking a short break and shifting focus but planning to come back to Number Talks in the New Year.   We did some trouble-shooting discussion about how to deal with students who offer silly answers or make up strange answers that don’t relate to the question posed.  We talked about using phrases that help the student connect their answer with the question (can you explain to me where in the question you got the numbers that you are using in your strategy?).  We also talked about moving on from a student who is having trouble explaining his/her thinking clearly with a statement like: I’m having a hard time understanding your explanation and I would like us both to think about it some more – can I check in with you about your strategy after the number talk is over?

Next, we talked about our BIG IDEAS for the day:

investigations-big-ideas

And outlined how to do an investigation:

investigation-procedure

We then delved into exploring the multiplication strategy of halving and doubling using the general procedure for an investigation.  We started with the question 8 x 26 to try to elicit the strategy of doubling and halving.  Once we looked at all the suggested strategies, we focused in on doubling and halving and talked about the big question of “Does it always work?”  The group split up into partnerships to explore this question – we provided graph paper, colour tiles, rulers, paper and scissors and then circulated to try to see how the investigation went.

It was interesting to note that it is really difficult to be a skeptic in Math – the strategy might make sense to us, but actually thinking about what it takes to PROVE that it works requires much more depth to our thinking.  Many groups got started by discussing WHEN it would be good to use this strategy (ie. what circumstances/numbers make it an efficient strategy).  Some groups explored odd vs. even numbers, some explored big and small numbers, some tried to delve into fractions to see if it worked there.  Some groups worked with the colour tiles to make arrays and others used the graph paper to show the strategy visually.

Then, we wrapped up with a discussion – different groups shared their approaches and it was interesting to note how varied the ideas were.  We looked briefly at the questions offered in the book to guide small group work for this investigation:

  • Will it only work with even numbers?
  • What would happen if, instead of halving, you took a third of one factor?
  • Can you represent this strategy visually/geometrically?
  • What generalizations can you make?
  • Would this work for division?

We had hoped to have time to also have teachers choose another investigation: either the same difference strategy for subtraction or the halving-halving strategy for division, but we ran out of time.  I think participating in an investigation was really valuable.  I enjoyed seeing how much mathematical thinking (curricular competencies) is involved in this type of activity.  Of note – mathematical investigations take time, and it is worth setting aside some time to do activities like this in class.

Once again, a HUGE thank-you to our teachers who participated!  We will be running some more after school PD for intermediate math teachers in the New Year – likely a Mathematical Mindsets book study at some point – so keep an eye on your email in January for information on how to join in.

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Number Clothesline Test Run

We (our district’s 2 Intermediate Math Liaisons) are doing a “Getting Started with Number Talks” workshop on our ProD day this upcoming Monday.  This is the last Number Talks workshop we will offer this year, and we have decided to open it to K-10 teachers.  We have been getting quite a few requests for Number Talks in primary and secondary grades, so we thought we would stretch ourselves.

For part of our workshop, we are going to showcase the Number Clothesline as a nice complement for Number Talks.  In the past, we have done this activity with fractions, decimals, and percentage cards (see this post), but we wanted to try to differentiate a bit for our primary and secondary attendees.  I have been intrigued by the idea of using a double clothesline for algebra concepts and so for our secondary extension, we are going to try this activity from Andrew Stadel’s Estimation 180 website.

I was trying to imagine what a beginning clothesline might look like for our early primary students, and so I made up some cards with numbers, dots, ten frames and fingers (after reading this fabulous article by Jo Boaler).  I thought I would do a test run this weekend with my own kiddos (Kindergarten and Grade 2).

We set up the double number line in the living room and this is how it went down…

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We started with the numbers all mixed up and I asked them to help me fix it…
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A standoff…   (My oldest son (blue shirt) doesn’t have dirt all over his face… we forgot it was moustache day at school today to celebrate the end of Mo-vember, so he took it upon himself to draw one on.)
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Using the 5 card to measure out how much space needs to be left for the missing 3 and 4 cards.
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Watching big brother make enough space for the missing cards.
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My little guy was pretty pumped about the hand cards.  Took him a bit to figure out where “neuf” would go on the bottom if there was no “neuf” up top (french immersion is working!).
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A 15!!!!
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Big guy using the 10 card to help him figure out how far over the 15 should go.  Little guy was pretty stumped by the “zero” hand for a while – he couldn’t really tell what number it was supposed to be – kept guessing it was a four.
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A 20!! Not enough room – we’ll put it way over here!
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Another “neuf!”  We already have one!  They decided to start doubling them up.

Overall, a pretty successful test run.  A few thoughts…

  • They both enjoyed the activity, especially the different types of pictures.
  • They were both disappointed that there were no numbers between 10 and 20 for the bottom number line.  I can’t really do that with fingers, but maybe I will make ten frame cards up to 20 and look for domino pictures (at least up to 15’s… do dominos go up to double 20’s?).
  • As usual, I am impressed with how kids solve problems when they are left to themselves to figure out what makes sense.  They didn’t need me to help them with anything – they figured out how to make the right spaces, what to do about missing numbers, what to do about double numbers etc. all on their own.  Another good reminder that sometimes the most powerful teaching is to set the stage carefully, ask good questions and then stand back and let the kids do the thinking!!

If you would like to have these cards for your class, you can download them below.  I will update this file if I manage to make some more ten frame or domino cards, but for now they only have numbers 1-10 in the dots, hands and ten frames.

Downloadable Primary Clothesline Cards

 

Number Talks Meet Fractions

We had our fourth meeting of our “Making Number Talks Matter” book club last night.  Our focus for this meeting was on Fractions.  We spoke a little bit about decimals and percents, but we spent most of our time looking at how we can support our students in developing conceptual understandings of fractions.

This blog post is meant to serve as a recap for those who were there, a fill-in for those who couldn’t make it, and a record for anyone else who is interested!

We started off our meeting with our usual conversation about how things are going in classrooms with number talks.  Some participants shared their ideas for how they are keeping track of student thinking.  One teacher has tested out incorporating our student self-assessment and another has been using her document camera instead of the whiteboard to record student thinking – she then has a record of strategies being used with student names attached to help inform her Number Talks planning.  It is so inspiring to hear about how excited students are about participating in Number Talks.  I hope you will all continue to carve out time in your class for them!

We then looked at a “Fractions on the Number Line” activity as a group.  We used a double number line for this activity.  We placed the benchmarks of 0, 1/2 and 1 on the top number line and then each participant had a number to place on the line.  First, we had teachers talk in groups to order the numbers at their table and then one-by-one the tables came up to put their numbers on the bottom number line, re-arranging as necessary to make it make sense.

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The benchmarks (once again a photo re-enactment)
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The Double Number Line (imagine the cards are hanging on the wall on two pieces of yarn)

From this activity, we moved on to talking about the BIG IDEAS for fractional thinking in the new Grade 4-7 curriculum.  We used this quote from the book as our jumping-off point:

…for success in high school, there is no avoiding fractions.

We talked about: what do our students struggle with in terms of fractional thinking? And: what do we want our students to understand about fractions?

Some thoughts that came up:

  • We want our students to understand that the size of the piece changes depending on the size of the whole.  It is possible to have a quarter that is bigger than a half if the two wholes are different.
  • We want our students to understand that fractional pieces have to be the same size but not necessarily the same shape.
  • We want our students to understand that fractions are numbers that exist on the number line.
  • We want to help our students make connections between their existing understanding of number and their understanding of fractions.

We then looked at the BIG IDEAS from the curriculum from Grades 3 – 9: where are our students coming from in primary, and where do we want them to go in secondary?  Now that all the fraction operations have been moved to Grade 8, we have the opportunity to solidify a conceptual understanding of fractions in elementary school so that students are prepared for fraction operations and linking of fractions to algebra in Grades 8 and 9.

From here, the teachers did another activity that connects a visual representation of a fraction to its place on the number line.  (Activity adapted from this blog –  printable download of the activity cards are available).  Teachers coloured in a section of the given square and determined what fractional part they coloured.  They then placed their fraction on the number line again.

fraction-clothesline

As a wrap-up, we briefly reviewed the other three types of Number Talks for fractions that are described in the book: More or less (give a fraction and have students defend whether it is more or less than a half); Closer to 0, Closer to 1/2 or Closer to 1 (give a fraction and have students decide which benchmark it is closer to), and Which is Greater (give two fractions and have students defend which one is greater).

Last but not least, we had a mini “make and take” – teachers took home yarn for a double number line and a package with coloured fraction, decimal and percent cards.  I will update this post with a link to the printable package as soon as I add some improper fractions and mixed numbers to it!  I will also have these packages at our final meeting for people who were unable to join us this week.

Here are a few useful links that we talked about in our meeting:

‘fessing up – Number Talks gone awry

One of my professional goals this fall as a Math Liaison in my district is to spread the message of Number Talks far and wide in intermediate classrooms in my district.  Between the readings I have done (Making Number Talks Matter and Number Talks, blog posts, articles), the Pro-D workshops I have led (Number Talks book club, Number Talks and the Curricular Competencies, Intro to Number Talks), and the various Gr. 4-7 classrooms I have visited, I am starting to feel like a bit of an “expert” on the subject… and yet, Number Talks are still complicated and challenging.  I think that’s one of the things I like most about the Number Talks routine – it is simple enough to be accessible, but challenging enough to keep both students and teachers engaged.  So, today I thought I would share a blog post about a “failed” number talk that I have been pondering and what I learned from the experience.

The setup:

I was visiting a Grade 4 class – This was my third visit to this classroom this year, and I have done Number Talks with them on each visit.  We have done some dot talks and some addition number talks, and on this visit, we were going to be working on subtraction. Students in this particular class (and at this school in general) are very capable but tend to just do the traditional algorithm in their heads – this happens much more frequently here than at other schools that I visit (my theory is that it is related to high levels of parental involvement).

The Problems:

Rather than just one number talk, I brought a number string with me… My plan:

img_1745

I really thought that these (especially the first one) were going to be easy, but when we got going on the first question, I ended up with 4 different answers.  I have led a lot of number talks with multiple answers, and 99% of the time (100% of the time before this particular visit), the errors work themselves out nicely during the discussion of the problem.

So, for this particular problem, I got the following 4 answers:

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Take a minute and see if you can figure out where the errors come from.

I wish I had thought to take a photo of the board after we were finished (need to get better at documenting things for the blog!).  First, I had a few students who defended the correct answer of 6 with some good strategies – adding on, counting back, making 44 into 45 etc.  If I had taken a picture, you could note my nice use of number lines and whatever else I did to record student thinking…

But what I really want to discuss is the student who wanted to defend the answer of 14.

She said something like:

“I did the 5 minus the 4 to get 1 and the 4 minus the 0 to get 4.  The answer is 14.”

This is not really earth-shattering… probably the most common mistake made in subtraction by Grade 4 students.  Here is the interesting thing: this student had just listened to 3 or 4 of her peers defend (very clearly) their answer of 6 with very good strategies (and I’m quite sure she was listening).  This is the first time I have had a student sincerely defend a mistake after multiple other students have made their case for the right answer – she had no recognition that her answer might not be correct.  In hindsight, I can think of quite a few good ways to respond, but in the moment, I was caught off-guard.  I wish I could tell you that I referred her back to the original problem to see if her answer made sense… or that I asked a classmate to respond to her thinking… or that I asked her to explain why what she did made sense to her.  But… I just told her that you couldn’t flip the numbers around and subtract from bottom to top.  Sigh. Fail.

Even in the moment, I knew that my response was woefully inadequate… I could tell from the look on her face that I had done nothing to convince her.  I think she believed me that her answer was wrong, but she had gained no understanding to move her thinking forward.  Other students had not learned anything useful from our exchange.  And, possibly (hopefully not!), the experience has discouraged her from taking another risk to share her thinking.

Moving Forward

So, what have I taken away from this experience?  I went back to Making Number Talks Matter and reminded myself of some guiding principles…

  • Through our questions we seek to understand students’ thinking: It is not my role to be the judge of student answers, or even to correct mistakes.  It is my role to try to understand why students are thinking the way they are.  I need to focus my responses on questioning with the genuine desire to understand student thinking.
  • One of our most important goals is to help students develop social and mathematical agencyThis exchange would have been a great opportunity to encourage students to respond to each other.  By “explaining” the right answer, I removed the opportunity for students to be the thinkers and brought the responsibility for “correct mathematical knowledge” back to the teacher.  My new #1 goal for number talks: stop talking so much and LISTEN.
  • Confusion and struggle are natural, necessary, and even desirable parts of learning mathematics: In hindsight, it is really interesting how uncomfortable I felt dealing with this mistake… as teachers, it is very hard to let go of our instincts to help our students through their struggles.  I am totally on board with the IDEA of stepping back and letting my students wrestle with mistakes, but in the moment, it is still a challenge to stop the “traditional teacher” who hides out in the back of my brain.

I am thankful that teaching is such an interesting job – regardless of how much experience we have, there is always more to learn.

I am going to better prepare for my number talks… I have been lazy about anticipating student responses. For our last workshop, we prepared a “cheat sheet” of phrases and sentence stems, and I have printed a copy to refer to.

I am giving myself some grace… making mistakes is the best way to learn, even for teachers!

And I found this lovely quote from Ruth Parker to help me remember why I am so excited about doing Number Talks in the first place:

I’ve come to believe that my job is not to teach my students to see what I see.  My job is to teach them to see.

So… who else wants to ‘fess up?  What surprises have you been faced with during a Number Talk?

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:

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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:

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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 Lines + Fractions

As a grade 4/5 teacher for the last 4 years, I generally find that my students enjoy working with fractions.  They like working with fraction manipulatives and approach visual representations for fractions with relative ease.  Naming and identifying fractions is rarely a problem.  But then we get to comparing and ordering fractions… and it all falls apart.

With my tutoring students (Grades 9-11), fractions are generally a disaster.  They are chugging along fine with whatever they are working on and then… a FRACTION!!!  Reducing fractions and finding common denominators is sometimes OK, but if a fraction is tossed into the middle of an algebraic expression, they don’t know what to do.  There seems to be no recognition that fractions are, in fact, numbers.

I have been doing a lot of thinking this year about how and why fractions seem to be a place of struggle for so many students as they advance through math.

Many of my students treat fractions as a completely new set of numbers, with no connection to whole numbers.  They are obviously not getting the big idea that all numbers are connected and have their own place on the number line.  Part of me wonders if this is because we (I?) over-use certain representations for fractions (pizzas and chocolate bars) and under-use others (number lines).  So, this year, I have really been trying to help students connect what they already know about numbers with the new information that they are learning about fractions.

One activity that I have used a few times this year – very successfully – is a fraction clothesline activity.  This week, I was invited to visit a Grade 4/5 class to introduce decimals by linking them to what the students already knew about fractions (they have been working on fractions for a couple of weeks).  I thought this was a perfect opportunity for me to combine two great things and I set the fraction clothesline up like a number talk (yes, I am obsessed with Number Talks).

I set up the clothesline at the front and we looked at the three benchmark cards I brought: 0, 1/2 and 1.  We hung the 0 and the 1 on the number line and then… NO ONE could tell me where 1/2 went.  Yikes.  This is the part of number talks that still makes me anxious… the WAITING… letting kids think… and HOPING… that SOMEONE… will come up with something to move the conversation forward.  My patience paid off… eventually someone suggested – “well, if it’s one-half, couldn’t we just put it in the middle?”  And, whew… yes.  Yes, we can.  We were rolling again.

Fraction Benchmarks

So, once we had the benchmarks on the line, I handed out a fraction card to each student.  Because we were looking at connecting decimals and fractions, I gave each student a “tenth” – nothing tricky.  Just 1/10 – 9/10.  I asked the students to think for a moment and give me a thumbs up when they were pretty sure they knew where their fraction was supposed to go.  And I waited.  After a while, a few kids (probably about 1/2) had their thumbs up.  So I invited those students who had an idea to come and place their fractions, and others could just watch to see if it helped them figure out where theirs should go.  And… this is what I got:

Fraction Number Line
This photo is actually a re-enactment… I need to get better at taking photos as I go.

Yikes.  Again.  But mistakes are SUCH a valuable opportunity to pinpoint misconceptions. The first student started by defending the location of 9/10.  He explained that because 9/10 was almost one whole, he put it close to the 1.  Whew.  Good start.

Then, the student who placed 1/10 wanted to explain.  She said she placed her fraction there because 10 is bigger than 2, so 1/10 must be bigger than 1/2.  Cool – good explanation, and a good misconception to tackle.  But, this is where I am still working on my “thinking-on-the-spot” skills, and trying to find the balance between “teaching” and letting the students help each other and wrestle with their own thinking.  I ended up drawing some pictures on the whiteboard behind the number line – I went back to the classic “pizza” shape.  I asked the students to help me draw 1/2 behind the 1/2 benchmark card and then 1/10 behind the 1/10 card.  Gasps all over the classroom.  I asked the student if she was still happy with where her card was and – NO, she was not!  She came and moved it to its correct location.  I asked if any other students wanted to move theirs and several more came up to make adjustments (accurately).  I asked the students to explain why they chose to move their cards and they were able to relate the spot on the number line with what the picture would look like.

I then encouraged the students who had not yet placed their cards to come up and find a reasonable spot for them.  This worked well – most of them were able to be successful in the location and were able to explain why.  We also talked about the spacing between fractions on the number line and how it is hard on a clothesline to be exact, but we know that fraction pieces all have to be the same size.

I was pretty happy with this number talk.  The students were pretty confident with ordering fractions with the same denominator, and I thought we got a good start at thinking about fractions with different denominators.  At the end, I gave a few students some “tricky” cards – 0/10, 11/10 and 12/10 and they were able to successfully place and explain these fractions as well.

This lesson really highlighted (again) for me the power of number talks and having opportunities for students to own and explain their thinking.  The real power of number talks is in giving students these types of opportunities on a DAILY basis.  This is what helps them to build up their number sense over time.

What other activities do you use to help students build a broad, connected understanding of fraction concepts?

 

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!