math

Monday night and I just realized I never posted a reflection for last week! It was sort of normal, not very exciting week. I’m headed into a week of guided math in which I’ll be working with small groups to do sone learning about money (not very exciting) and everyone will be at other centres solidifying their math facts by playing math games.

It’ll be fine.

But last week I did notice how often our calendar is being accessed by kids. I saw a blog post this summer (I’ll try to find the link!) and decided I would display the whole calendar on our wall this year. I put up the 10 school months and then started the year, intending to find time to make it fancy.

I’ve also been creating PicCollages of class photos to create a visual timeline. I need to get October printed! (Ugh!) it’s fun to look back at those memories too.

I haven’t done a class calendar in years. I thought it took too much time and space. But this very casual calendar, with no forced routine for its use, has been such a great addition to our class!

Counting

I never used to worry too much about teaching students to count. I mean, the year I taught kindergarten we did a lot of counting, but in grade 2…or 3…or 4? Nope.

In the last few years I’ve become aware of how important counting is, and the layers of skills that are involved.

After interviewing my people, I discovered most can start at 30 and get to 100 without difficulty. Some had trouble not starting at 1 – and they also had trouble assembling a 100 chart. This is not, I think, a coincidence.

Some students were very organized with their counting…

And some students were not organized with their counting.

After we congressed these photos, I sent everyone off the do more counting. I asked them to count out 17, or 24, or 52, or 65 of the math tool they wanted to work with. Everyone tried an organization strategy of some sort! Even when they sorted into rows or groups of 5, many were counting by tens.

I loved this one because this child said, “10, 11, 12, 13, 14, 15, 16, 17!” It was great to see her counting on!

I think when we look at these images and congress them today, I need to make sure I talk about how the organizing helped. One of the things I know I need to do better is point out these things that seem so obvious to me.  Some students will have already realized the advantage of using groups, but some will not have.  I need to help them with that.

I used to always start the year with addition. This made more sense I guess when I was teaching grade 3/4 classes. But starting with counting and making sure everyone has a strong foundation of number sense to build on has truly made my addition and subtraction units go more quickly. Everyone seems more prepared for the addition and subtraction work once I know they are solid with counting skills.

math

Summer: done

Where to start the math year is always a big question for me.  I want to start out on a positive note, with lots of accessible, confidence building activities.  I want to do a little bit of assessment – not necessarily of my new students’ math abilities but rather of their attitude toward math.  I want to set up a few routines that are going to carry us through at least the first few months of school.

This coming week will be spent mostly building Number Talk/Number Sting expectations. I want everyone to have a chance to show they have figured out the answer.  I want everyone to know that it’s all about the process, not just shouting out the answer first.  And they definitely need to know that they are not going to the washroom every day during the first 10 minutes of math class! (Nice try, you guys, but I’m on to you!)

I plan to spend the first week of school watching my new friends count.  There is so much to be learned about their math skills by watching them figure out how many they have of something. I have sorted most of my classroom library, but left the levelled readers in a few big piles so the class will have an accessible, authentic task to help me with. I do plan to tell them that I need to know if we have enough – the recommendation is for a Primary classroom to have 300-600 books in the classroom library that the majority of students can read independently by the end of the year.  I think I have that, but we’re going to find out for sure this week!

Finally, my overall goal for this week is for everyone to feel like they contributed to our math conversations, and will continue to be able to do that.  Confidence in one’s math ability is an over-all goal for me, mainly because I didn’t have any until I was out of University and low these many years later I still find myself questioning myself all the time. ALL. THE. TIME. (But a lot less than I used to.)

My dot number talks are ready to go in Smart Notebook.  My math

have all been disinfected.  My group learning area is all set up. My daughter is sorting through her shoes trying to decide which will be the indoor shoes (did I mention she is going to be in my class this year?)

I think I’m ready!  Just one more (sleepless) sleep to go.

Candy Math

If one buys a bag of Sour Patch Kids, will there be an equal distribution of the good colours and the gross colours?  Because if I could buy a bag of just red and avoid the gastly green, and blue, I’d be happy about that!  The children in my class disagreed and hoped that there would be an abundance of blue.  But we all agreed that it should be equal.  Time to test it out!

I put a bag of Sour Patch kids on every table, and told the students they could pick their own groups.  This doesn’t happen often for us, but I wanted to see if they would distribute themselves evenly. One group of 3 got a whole bag to themselves because nobody else wanted to work with them. That left one big group of 6 to share a bag.  I think the kids in that group will think twice before they settle on a group next time (cause you know there will be a next time!)

I was very interested in the strategies students would use.  I had predicted that there would be some organizing into groups by colour, and I was right for all but one table.  It took them a few minutes of debate before they all agreed to do this.  At first, each was starting his/her own groups, stealing from the others to try and create one pile for each colour, except they were all trying to create the pile right in front of themselves.  They had 4 red piles, 4 blue, etc. Finally they realized, with a tiny bit of prompting, that one pile for each colour would suffice.

Since September, we have been talking about how organizing into groups of 5 makes counting a lot easier.  But…still…lots of kids were counting by 1’s.  *sigh*

Over time, however, they switched to grouping, usually by 2’s, but at least it was grouping.  One group, the group I would least expect to struggle with this, organized each colour by a different number.  Then they couldn’t figure out how to make that into a graph.  We had a very interesting conversation about this, so I’m counting it as a win.

The graphing was fun to watch too.  We’d talked about how we don’t always have to count by ones on a graph, but we clearly have some growth to do in this  understanding.  Though I’d given them a task that required more than the number of rows I had given them on the graph template, they still thought they could just fudge it.

Let me interpret this for you:  this group had 21 Red, 17 Green, 15 Orange, 13 yellow, 22 Blue, and 1 split (I have no idea why, but one child was obsessed with the possibility that 2 colours might have melted together and therefore 1 SP kid fell in to 2 categories AT THE SAME TIME! This did not actually happen, but this student really wanted me to believe it was not only a possibility, but an inevitability!)    I have just one picture of this to share, but it happened all over the place.  I eventually pulled them together and reminded them about choosing a scale.  The grade 3’s got it after that, but the grade 2’s not so much.  It’s not one of their expectations anyway, so I’m not worrying about it. They could read the graphs the grade 3’s created, so we’re good!

This week, assuming the one day I have to do some actual teaching actually doesn’t get interrupted by the unexpected, we are going to find out if we get more caramel popcorn or more cheese popcorn in a bag of Chicago Mix.  We are going to compare the store brand to the Orville Redenbacher brand and see if one is more even than the other.  We are also going to compare the Humpty Dumpty brand “party mix” and the Doritos brand “party mix” to see if I am truly being ripped of, as I suspect, and getting more than half a bag of pretzels.  I firmly believe there should be a “No Pretzels!” option here, just like there is a “No peanuts!” option for a can of mixed nuts.  Am I alone in this?

I used to do food math all the time.  Froot Loops, Smarties, M & Ms – they all make great math manipulative.  But for several years I have had students with food allergies and bring any sort of food into class was so stressful for me that I avoided it at all costs.  This year I have very little of that to contend with, so I’ve been going for it.

Oh…almost forgot!  One group got two half Sour Patch Kids.  They weren’t sure what to do about it.  We had a great conversation about the 2 halves making a whole.  They were reluctant to believe me, which just shows that I didn’t do quite enough with fractions this year.  I’ll have to rectify that next year.

Slice of (Math) Life

Way back in September, I had read about this neat activity from Marilyn Burns called “The Door Project“and had decided to use it to start my school year.  On day one I always like to take the students for a walk around the building.  If anyone is new, or even if they are just coming to my end of the school for the first time, I want to make sure they have a chance to orient themselves, find the washroom and drinking fountain – that sort of thing. On the first day of school, I combined that with some math.  It was our first provocation, if you will.

When we got back to class, I asked, “Did you notice how many different types of doors we have in our school?”  We took a look around the class, and started thinking of ways to sort the doors in our school. Some have windows, some don’t. Some are metal, and some are wood.  Some go to the outside, and some into closets.  I gave everyone paper, asked them to think of 2 or 3 categories to compare, and away we went.  (I’ve condensed it here – we actually spent a whole class period on this!)

It was a disaster. I just looked back to link you to my post, and found I didn’t write about it at all!  That’s how bad it was.  As I recall, we were having a lot of trouble managing our data.  The categories were all mixed up, the tallies were not organized, and nobody could do anything with the information we collected. I had intended to graph our data, but, alas, it was not meant to be.

Today we tried again.

I reminded everyone about this activity, and some sort of remembered it.  We quickly reviewed our door types.  I gave everyone a choice of paper – plain, lined, or graph.  They grabbed clipboards and pencils, and lined up like pros!

We made it all the way around the school, gathering all of our data, in very little time.  Nobody had to shut their door when we stopped to count!  When we got back to class, everyone was able to count their tally marks by 5’s and find their totals in record time!

I reminded them how far we had come.  I reminded them that in September this activity had been really hard, but now it was barely a challenge.  Everyone collected the information independently, found their totals, and is now ready (and able!) to graph it tomorrow.  Now I am sorry I didn’t keep our first disastrous attempt so they could see how far they’ve come! (Who am I kidding…I probably do have it and will find it on the last day of school when I am finishing my clean up!)

What a difference a year makes!

Math Is Everywhere!

The other day we arrived at school about 5 minutes later than usual.  It isn’t much, but it means we have arrived after the first bus has dropped off some children.  My 5 year old walked up to the boot line and started counting.  “1, 2, 3, 4, 5, 6, 7 and I am 8!  I am the 8th one here today Mommy!”  He was unitizing the pairs of boots and knew that 2 boots is equal to 1 child.  I was also impressed that he knew about “8th”.  He, for a long time, only seemed to understand 1st and last.  I suppose some of that comes from being the second of two children, one of whom is keen to point out when she has beat her brother at everything. He understands first because he’s been last a lot.  But eighth?  That was interesting.

This week I started participating in an online writing challenge I’ve been participating in for 11 years!  The participants are mostly writing teachers, definitely people focused on literacy.  I’ve been surprised how many, in just the first 2 days, have posted about their gratitude for not having to teach math because they 1) don’t feel competent at math, and/or 2) don’t like math.   I honestly don’t know how anyone could possibly spend any time in an elementary school environment and avoid doing math!  The boots are just one example of the math that I see all around us daily.

My school’s electives have just wrapped up, and every single week I found myself integrating quick math lessons into our cooking.  I know you’re thinking about measurement, but there were a million opportunities to count things. Did we have enough cookies for everyone to make an ice cream sandwich?  Were there any cookies to take home?  How many brownies would each person get?  Did we have enough bowls for everyone to have a serving of apple crisp, including the office staff?  If we counted up the number of children in the group, took into account the number of kids who said they hated pineapple-upside-down cake, and divided all the pineapple up, would there be enough pineapple to eat plain?  These were important questions that had to be answered.

Of course we do a lot of intentional math, but incidentally there is math around every corner, in every classroom, and definitely in every line of items or children!  Maybe the trick is to get the grown-ups to stop treating it like a room to be avoided.

#WODB

I wrote back in August about a great book I wanted to use during the first two weeks of school.  It’s called “Which One Doesn’t Belong” and is written by Christopher Danielson.  (You can read about that here.)

Today was an inclement weather day, meaning the busses were all cancelled.  It was our second in a row, and we have actually had a lot this winter now that I am thinking about it.  I needed to spend about an hour doing an activity with a bunch of kids (grades 1, 2 and 3), over half of whom are not in my class on a regular day. Actually, probably 3/4 of them aren’t in my regular class. I decided to pull this book back off the shelf.

I explained the concept and read the first few pages.  I made sure that every child knew that on every page there would be 4 things, and they could think of at least one reason why three of those things would go to together, but one wouldn’t belong. I explained that there is not one right answer for each page, but what matters is justifying your own thinking so others can at least see what you mean, if not actually change their own mind.  It’s great math!  And it is also so interesting to see how children think.  I have been through this book a few times now, and I am always amazed at how they come up with answers and justifications that I haven’t noticed.

After, I challenged them to create their own using LEGO, two colour counters, attribute blocks, colour tiles, and poker chips (I got them cheap – over 1000 in lots of different sizes and colours at Value Village.  Best investment ever!)  Here are a few:

I took photos and we projected them on the whiteboard so we could share our thinking.  They LOVED it.   This one with the dominos really intrigued me.  I immediately saw kids doing some counting, but nobody used the counting in their answers.  I decided to take that one a bit further.  I wrote the totals on the board beneath each domino.

Several thought the 13 does not belong because they are all in descending order, but it is out of place.  Some thought the 12’s do not belong because they each have a twin and none of the others do.  Finally, several thought 9 does not belong because it is a single digit number (they actually said because it is less than 10 and the others are over, so I pointed out the single/double digit difference.)

It was a fun activity, and I think all of the students learned something!

They heard me. They really did!

Last week, I was ending the week feeling like I may have spent a few days talking to the walls. (You can read about it here.)   This weekend, I feel much better.

We spent the week working on building an understanding of number lines. After making a measuring strips, in groups of 5’s and 10’s, and measuring some things, we needed to start thinking about how a person could skip around on that number line and use it for adding.  When I taped a 100 strip to the board and started asking kids to tell me the number of a certain cube on that number line, it was like a miracle had occurred.  Because nobody could reach the number line to touch each square, and because we’d talked a lot in our math congresses about how we could use the 5 and 10 structure of the paper number line to skip count, they started actually using the number line tool and the skip counting strategy to find the answers I was seeking.  THEY ACTUALLY DID!

Oh, and no big deal, but they were finally counting on from a known number instead of starting back at zero every time.  Seriously.  I’m not even exaggerating to make myself look/feel better.

Here’s the lesson for me:

1. Trust Cathy Fosnot.
2. Sometimes moving forward helps some kids who appeared to not be ready to move on.  I thought I would do a quick number string, sort out who needed some more help with skip counting and counting on, and then make up some Math Workshop groups.  But, low and behold, some of the kids who haven’t been counting on started counting on!  And many who had been fully committed to counting by ones were using the 5s and 10s.

So there you have it:  Valentine’s Day, Winter Electives, and a field trip, all in the same week, and we still moved around on the Landscape of Learning!

math

Not Done Yet

Yes, I am in fact still teaching math.  We only have 4 more school days, and 2 of those are booked solid.  This might be my last real math class of the year, but there’s still hope for Thursday!

One day last week, I saw this on Twitter:

I really wish I had not just saved the photo and could tell you where I found it.  But honestly, it was probably around 10:00 at night and I’m surprised I even remember I copied the picture.  I appear not to have retweeted it because I have really searched and can’t find the original source.  If you know who it is, please tell me!

Today I had a long math class (a full 90 minutes, which happens once a week. We don’t always use the whole time, but I am always glad for the extra!) so I pulled this picture up on the Apple TV.

We talked about what we saw.  Then I asked, “How can this child say that 3 hexagons is equal to 11 other shapes?”  I was met with blank stares, which is exactly as I had hoped it would be.  I sent them back to their tables with pattern blocks to see if they could figure out what this random stranger was talking about, and if s/he was actually right.

They played around for a few minutes, and then one child showed me this:

I asked him to explain.  “Well, I saw that 2 of the red were the same as the yellow, so I just tried out the others and it worked.”  Good old “Guess & Check”.  As soon as he explained, other people at his table gave it a try.  In the meantime, on the other side of the room, another child had discovered the same thing.  When I talked to him, he added, “And now (X) is copying me!”  The child next to him had made the same representation.  “It might seem like copying, but I think X was just learning from you.  And look what (X) is doing now.”  I asked her to explain, “Well, I wondered if we could make more hexagons with other shapes, not just the red, triangles and the blues.”  That inspired the other children in her group to start exploring more options.  Could anything be done with the square, for example.

We all gathered on the carpet and I put up a few examples of the student’s work.  “Now,” I told them, “I’d like to see if you can come up with balanced equations of your own.  Maybe you’ll come up with something that doesn’t even use hexagons!” and away they went. Here are some of the things they came up with:

I have to say I was pretty happy with the results!  There was a lot of deductive reasoning going on as students built one shape and then reasoned that they could build other similar shapes.  It was interesting and I am sorry I don’t have more pictures to share!  My favourite was a long row of rhombus’ on one side of the balance, and a long row of triangles on the other, all neatly stacked in a row that equalled the length of the rhombus row.

This is my other favourite:

She built her own balance!  At first I thought she had too many blocks for no reason and was very close to questioning her when I realized it was a model of the balance.

I figured out, a few weeks too late, that we need more practice with shape names. But I was happy with the spatial reasoning I saw!

So, #SorryNotSorry kids!  You may have thought you were finished with the year, but, alas, you were not!  And stay tuned to find out what we are doing on Thursday!

math

Counting

I’ve learned a lot about counting this year.  It’s more than just reciting the numbers – I’ve known that for a while. It’s really important for kids to be able to touch a thing and say the correct number as they recite the numbers. I knew that too. But I’ve started to understand more about how children count and how their counting skills develop over time.

My son is in ELK year 1.  He started JK 20 days after turning 4.  His ELK experience has been different from my daughter, who was 4 years 8 months old when she began.  It’s been different for a lot of reasons, but I think this age thing is an important one to note.

Spencer started JK being able to count to 10.  What I mean is, he could say the numbers in order from 1-10 without errors most of the time.  When it came to actually figuring out  how many of thing he had, he often made mistakes in his one-to-one correspondence.  He’d have 5 things, but count past 10 and then declare he had 18!  Eighteen, for a very long time, was his equivalent for “infinity”, the biggest number he could imagine.

Over time, I started to notice that he could say the numbers to 13 without mistakes, and that his one-to-one correspondence had improved.  He could have 7 to 8 things, and correctly identify that as his amount.

A few months ago he was counting the muffins at breakfast.  He counted them a few times, touching each as he went.  If he made a mistake before he got to 5, he’d start over.  I realized he was subitizing and that is how he knew he needed to start over. When he’d correctly counted to 8 twice, he was satisfied that we had 8 muffins left. He was right. I loved that he was double checking his answer, and that he knew when he’d reached the correct total.   He can now do that with 10 things consistently.

The end of ELK year 1 is just around the bend.  Where is he now?  He can now recite the numbers to 14 without mistakes. Past 14, he says the correct numbers but often gets the order mixed up.  The really interesting thing that happens though is when he gets past 20.  Suddenly he is able to recite all the numbers to 29 without mistakes. I think it is because 5 and 25 sound more alike than fifteen.  I think he is using some of these as landmarks to keep himself on track.  He loses it at fifteen because fourteen should be followed by five-teen and it isn’t.  That’s just my theory based on what I know about his language development and the patterns in his mistakes.

We have been playing games with dice, and I know he can subitize 1-6.  At least he can using the typical patterns of the dots on a regular set of dice. I am going to pull out some dot cards over the Summer and see how he does when the dots are in different arrangements.

Spencer has been able to look at a printed numeral and say it’s name for a long time. Now I am curious about how well he can connect that skill to the dot arrangements. Can he match them up? We’re going to do some investigating about that too.

The final thing I am going to look at is whether or not he can place some of these numbers in order when they are all jumbled up.  Can he do this with the numerals, and can he do this with dot arrangements, putting them in order least to greatest?

Finally, I should note that currently 18 is not the largest number he can imagine.  Now, the biggest number is “humungous”. Ten minutes is the longest amount of time he can imagine though. If I say we are leaving in 20 minutes, he’ll negotiate for a 10 minute departure time.   I should start looking at the way he is developing an understanding of magnitude.

Or I could, you know, just leave my kid alone and not analyze all of his work. 😉