math

## On our way…

This week we accomplished a lot in our math class.  I mean, not much of it had to do with curriculum and I am sure none of it will end up on progress reports (I’ve received two reminders that those aren’t going away!) but it was a great week anyway.

The highlight of my week came on Monday. I have three students who were with me last year has grade 2s and they are repeating with me again this year as grade 3s. On Monday I had occasion to describe a picture as “one one-fourth” of something. One of them said, “Hey. Wait.” then he muttered “one one-fourth” a few times and said, “I had no idea that’s what one-fourth means. It means one out of four of something. One-fourth…get it? One out of four. I never knew that before.” I taught a lot of fractions last year. I thought I did a pretty good job. But for some reason this understanding clicked for him in that moment. I was immediately reminded of something Christine Tondevold says:  Number sense can’t be taught, it’s caught!  In other words, as she explains in this blog post, kids need experiences with numbers in order to understand them. I know that this “discovery” comes after a lot of teaching, but he didn’t really get it until that exact experience.

The other thing I am feeling good about is the formative assessment I accomplished. I don’t think I wrote a single thing down, but I know a lot about my mathematicians already. I had everyone working in their math notebook and noticed how they print numbers and organize their thinking. I had everyone counting objects – some they could touch while counting and some that were on the board so they were encouraged to use other strategies.  We did a three-act math task every day I was able to start to establish our routine for Number Talks. Finally, we spent three days working on a math card game (a game like memory, but a match is two numbers that add up to 10.)

This is what I know we need to work on:

*Grouping objects to count them (sort of a surprise)

*Mathematical thinking (not a surprise)

*Organizing and communicating our math thinking (not a surprise)

*Working independently

That last one is going to be my biggest challenge. For a few years in a row, I have had a lot of kids in one grade and only a few in the other. This year I have nearly equal amounts. It’s a lot easier to have four kids working on an independent math task while I teach the other grade than it is asking 10 kids to be independent while I work with the other 10. I am determined not to make worksheets the independent activity every day, but I know that I will need to do that now and then. I do have 6 iPads and 2 laptops I can make into a workstation. It’s starting to sound like I am going to be doing Guided Math! I suppose that was bound to happen eventually.

On the agenda for this week:

*Learn another card game that can be used as an independent activity

*Start some math work disguised as science work (measuring puddles as they evaporate throughout the day)

*Strengthen our Number Talk routines

*Photocopy math interviews so I can start them the week after

math

## Back in the groove: Part 2

Well, that was a long gap! I stopped blogging last year because I had to cut some things off my “to do” list. I was taking two courses, I was teaching full time and parenting full time, and I was surviving a pandemic. Math blogging got the ax because I was working on a math writing project and I found I was tired of writing about math and didn’t want to reflect on it quite as closely as blogging forces me to do.

So here I am five sleeps away from another first day of school. I’m really glad I at least blogged about September 2020 because that’s helping me get started on planning September 2021. I already have the measuring activities in my day plans for next week. I don’t know if I will go from there to coding and dancing or to some of the patterning things I like to do with manipulatives. I am definitely doing some estimation jars. I need to meet my people before I can make set plans though.

Last year 15 of 19 students were in grade 3. That’s roughly 25%. This year 8 of 19 are in grade 2. That’s roughly 40%. It’s a game changer! I’ve had splits like this before and it’s very hard right now to predict how I am going to manage this. Stay tuned.

I’m not taking any courses this year. I am, however, working on a thesis. I’m predicting that blogging my math reflections will fit nicely with that. Math is not the focus of the thesis, but I am working a project about creativity in the classroom and math will definitely be part of it. In fact, I am now going to end this post so I am read about creativity as a mathematical process.

## Calendar

I’d normally have the first week all organized by now.  I’ve been going through my notes (mental and written down) as I try to plan out what my first week of school will be like.  There are quite a few of my old tricks that won’t work this year because of “you know, social distancing” as my son likes to say.  And, truth be told, I could still get a big assignment change so I am not putting too much effort into getting excited about exact plans. But there are certain things that can happen no matter what my assignment turns out to be and no matter who will be in my class.

Last year, I added a new calendar routine to my class and I really liked how it all unfolded.  I had the whole year on the board at once, and I loved how the students used it to count “how many days until” things would happen.  I’m not usually one for celebrating birthdays in class, so I wasn’t expecting them to do their favourite thing:  add their special day to the calendar.  We added the holidays together as the approached and talked about how some holidays are always on the same day (Feb 14 = Valentine’s Day) but others float around according to the cycles of the moon (Passover). This is a grade 2 social studies expectation and I liked how that became part of an ongoing conversation in our room.

This year I have decided to do it a bit differently.  Instead of printing a complete calendar, I found some blank calendar pages here.   I am going to fill out September (maybe only the first 2 weeks?) and then get kids to help fill out the rest.  I made a poster to post beside the calendar:

I want the students to fill in the dates on their own because there are so many patterns to the counting on calendars.  If they are filling out the dates themselves I think it will help them see the patterns. During the first week, maybe in the second week, we are going to work on this together.  I still haven’t sorted out all the details though because, “you know, social distancing!” is going to effect this for sure. Maybe the students can have their own mini version to work on at their desks.  (I keep reminding myself that some kids are going to really love working alone at their desks!)

I’m going to keep this at the front of the room because we referred to it so often!  I want it up close.  I know things will be different now because we can’t have any carpet time, but we didn’t really use it for that anyway. It was just an ongoing topic of conversation all year. Kids like to know when things will happen. This helped with that. I’ve been reading a bit of executive function skills and some of these are the ability to organize, to be able to plan things, and of course manage time. I know that I personally need a calendar or day book for this, and I really do much better if I have written it down.  My phone calendar is great for reminders, but I still need to physically use a pen and paper to write it down before a scheduled activity is in my brain. I need to know when something is due and then I need to write out a plan for how to do that slowly over the course of a week or more.  I need specific small deadlines (because one of my executive functioning strengths is that I am goal oriented) to keep my on track. The wall calendar seemed to provide support in all of these areas for the kids in my class last year, and I suspect it will help this year as well.

So…20 minutes of each day of the first week…sorted!

## First 2 Weeks: Frog Jumping

I have made a commitment to myself to work through the Edugains document that spirals the math curriculum this year. I’ve put a fair bit of time into creating a long range plan that follows the document. But one thing I’m worried about is that it will effect my flexibility. Will I be able to follow our interests on a tangent? Will I be able to speed up or slow down as we want to? I suspect I’ll be able to, but I’m still wondering about it.

The activity we’ve been working on this week is an example. I’d intended to spend one day on it, but tomorrow will be day 3 and I am sure I’ll have to/want to come back to it. We’ve had such a good time and have used so many math skills at once, not to mention some science and literacy skills. I want to keep doing that! I also want to reap the benefits of spiralling our learning.

I bought a bunch of plastic frogs from Amazon. I wanted us to measure whose could jump furthest.

Day 1:

They came up with fun ways to get the frogs to go farther. They had them jumping from chair to chair, and across a gap between tables.

They even got interested in how high the frogs could jump!

Getting the frogs to jump took some fine motor skills I hadn’t anticipated, which is the main reason this 1 day activity needed a second day…or so I thought!

Day 2:

Day 3:

Finally the contest! I thought, based on previous results, that a ruler would be long enough for everyone to measure the distance their frog jumped. Then I sat beside a friend who had a metre stick and made my frog jump 74 cm. We spent Friday discovering lots of could make the frogs jump farther than we thought. Having the contest going helped them focus on that one thing instead of continually experimenting. One group even showed us a great way to record the measurements:

We were interrupted as I was beginning to get to the group who was using this strategy, so I can’t explain what the S’s are for. We’ll take this up on Monday! my nicely organized measuring tool bucket looked like this as we rushed out the door for dismissal:

I learned a lot from this activity! I know that everyone knows about rulers and tape measures. I know that not everyone sees them as the best way to measure distance. I know some kids recognize the need to record their thinking so they can share later. I know who has some great strategies for working with partners and who sees math as a solitary venture. At least this math anyway.

I feel like I want to do more measuring. I also want to move forward with patterning because we clearly need that. According to The Plan, we are going to start with sorting and classifying objects.

But the whole point of spiralling is that I figure out how to measure AND pattern next week. I’m also documenting this work electronically so I don’t have to start fresh again next year! I’m also noticing, but probably won’t bother collecting data (maybe I should?), how often I mention “other” math. We weren’t talking about fractions but I found that discussion about 1/2 came up frequently. We weren’t talking about probability but we did talk about “average”. And we weren’t talking about data management, but we certainly did manage our data.

So there you have it! First 2 weeks: done!

## First 2 Weeks: Bulletin Board Borders

One of the things I love about the first 2 weeks of school and the last two weeks of school is the freedom I feel to do fun and interesting things without feeling pressure to stick to curriculum or assess and document what happens all the time. I can focus on relationship building and connecting with my students.

One of the activities I had planned for this week is something that many of the kindergarten classes in my school have done. It doesn’t represent a whole lot of creativity on my part, but I’m so glad we’ve done it!  We have been creating our own borders for the classroom bulletin boards!

A few more than half of my students are looping from grade 2 into grade 3 with me.  I love this!  Last year we completed a Context for Learning math unit called “Measuring for the Art Show.”  In that unit we use cash register tape to measure things and create number lines. For this activity, I gave each group a roll of the paper and asked them to use it to create their borders. I assigned each group one bulletin board to work with.  I asked them to measure properly, and decorate the paper with patterns.  Those are all of the instructions I gave.

Three of the four groups actually measured.  One group has decided to keep cutting pieces of paper, different lengths, and then piece them together like a puzzle.  I was happy today when a child in that group told me exactly where to put one piece of paper.  It fit exactly in a gap, and the child said she measured before she cut the paper to make sure it would fit.  So this is a bit of a “guess and check” strategy, but I feel like it’s evolving into measuring.  They still have a few big pieces to do, and I think they will use this strategy going forward to create bigger pieces.

Of the three groups that measured, two realized that they could measure the bottom, easy to reach edge and then cut two of that length.  They didn’t have to reach up to measure the top because the top and bottom are the same.  They also realized that the left and right are the same. The third group needed some prompting for this.  I think if they could have reached the top they would have simply measured 4 times.  Of the three groups that measured, only one used a tool (measuring tape) to measure instead of simply using the paper.

It has been very interesting to note that there has been very little actual patterning occurring.  Some of the groups have drawn on the paper.  We’ll have to work on that a bit. I want to make sure they understand the difference between patterns and designs.

There has been a lot of cooperative work happening.  There has been some arguing.  C’est la vie! That’s how a community of children often gets started in their work together.

I have already decided I will do this activity several more times throughout the year.  I want to see how it evolves.  I am going to keep the groups the same each time.  I can’t wait to see how their thinking and group-work skills grow.

One of the big jobs that needed to be done was writing up some lesson plans. Some teachers are very relaxed about this in the first two weeks, but I like to hit the ground running! I like to establish the work routines early, and I don’t want to waste any of our time. I won’t dive into any serious units right away, but there are some other important things that can’t wait.

I don’t usually plan two weeks in advance. I have units planned out, or picked out, but I like to let the kids establish the pace. During the first two weeks, however, I do have a pretty good idea of how long things are going to take.

The structure of my math instructional block will go like this: read aloud, lesson, activity, congress, counting routine. I have 60 minutes, so my plan is for everything to last about 10 minutes, with the activity lasting 20.

I have two goals during the first 2 weeks.  First, I want to set up the routines for doing our math.  I want everyone to know that we don’t shout out answers, we disagree politely, we try and try again, we don’t throw math manipulatives (at each other, or otherwise).  My second goal is to make sure I can start my math interviews.  I need to spend a few minutes with each child and ask them some questions one-on-one.  This is going to take longer than 2 weeks.  My grade 3s, the ones who are with me for a second year, have already completed this in June (hmmmm….didn’t come across those in my unpacking!) so I can start with the grade 3 interview, a bit later. I know them as mathematicians already, so I know where to start their instruction.  My priority will be to get to know the grade 2s and anyone new to me.

I am switching to an electronic day book this year.  I have made my own using OneNote.  I have been committed to paper, but my binder is such a mess early on, and I get tired of dragging it home every weekend. I also find I have more times when I am using  electronic resources, so I want to simply link those in my plans instead of having them several places. I have decided I will do the e-daybook for at least September and October and I can always print a paper book if I need one. The only thing I haven’t quite figured out is my Number Talk/Number Stings.  I like to write them on Post-it notes (one per day) and stick those in the day book.  I think right now that I am going to still do this, but then stick the Post-it note somewhere else…not sure where.  If I can keep my desk clean I can put them there.  We’ll see!  LOL

Here is my plan: (Sorry I couldn’t figure out how to make it look nicer!)

## Math Interviews as Assessment

On Friday I was working on finishing math interviews with my students.  I am ¼ of the way through the class already! (growth mindset)

Me:  What is 4+3?

Grade 2 student, without hesitation: 7

Me:  How’d you do that so quickly?

Student:  Because last year my teacher had us work on things like that on this app on the iPad. We had to do those kind of problems every day.  It was so annoying (insert eye roll) day after day! But now I’m really quick at it.

Me:  That’s great! What is 8 + 14?

Student (blank stare):  Um, yeah. We aren’t on that level yet.  I think that’s like level 17 and I was only level 16, so I don’t have that memorized yet.

Me:  Well, do you have any way of figuring it out?   (I’m trying not to look at the 20 “special stones” that were just counted out, or the Rekenrek sitting to the right, or the whiteboard and marker to the left.)

Student: Ummmmmm……no.

Me:  What if you were using some of these tools? Or your fingers?

Student:  Ummmmm…….no.

Apparently they valued memorizing the basics at his previous school.  You can draw your own conclusions about how I feel about that. But this isn’t about judging another’s teaching based on the word of one 7 year old.  The real question for me is this:  What am I going to do about it for this child?

The start of the year is always a tricky time for me.  No matter what “last year’s teacher” has shared with me about a child, I feel I never really know them until I complete a reading Running Record, a writing conference, and a math interview.  This conversation above is exactly why I think a math interview is important. Thanks to this and a few other questions, I now know that this child is subitizing numbers less than 6, can skip count, count on and count back when counting objects but not when presented with just the numbers, can draw a number line that shows where 7, 10, 20, 30 50 and 48 would be, but that these will not be drawn in iterated units, and can count from 30 to 100 but has a long pause when moving between decades (48, 49……….50!)  I also know that though this child has some basic facts memorized, there isn’t a whole bunch of understanding behind that fact, so little understanding in fact that the child had no idea what to do when the answer wasn’t already known.

Years ago, I had a math textbook to use that provided a “pretest” and a ”post test”.  They were of very little use. Sure they gave me a score I could use for a mark, but that was often all they gave me.  The interview, however, tells me so much more about where to start, where to go and how fast to try and get there. A follow up interview after a few months tells me if I am moving at the right pace, if someone needs to be pushed faster or slower, and if I need to circle back to a place I thought we’d already covered sufficiently.

The major questions that always comes up is this: What do the other 20 children do while I spend 10 or so minutes with a child one on one.  During a Running Record, they all read and look at books. During a writing conference, the others are all writing. But we can’t just have a bunch of 7 and 8 year olds “do math” independently in September.  Here is what I have them do:

1. Dreambox.  If you do not have access to this, I am VERY sorry for your luck.  It’s great. It’s a bit expensive, but if your luck is good your board has purchased a license and your class can use it.  If not, try Prodigy.
2. Dice Games
1. Race to 100:  Here is one version I’m excited to try.  We actually play for counting chips.  Every child has one die.  Simultaneously they are rolling that die, then taking the same number of counting chips.  When one person gets to 100 (we were playing to 50 this week) the game ends.
2. Tenzies/Yahtzee
3. Card Games
1. War
4. Math Manipulatives
1. They love to use pattern blocks and there is a lot of spatial reasoning work than can happen even if the class seems to be “playing” with these blocks.
2. They like to “play” with 3D shape blocks for the same reason and it gives them the same learning experience.
5. Finally, if you haven’t read “What to Look For” by Alex Lawson, you should.  At the end of this fabulous book, there are a collection of games that can be played to help move students along in their mathematical understanding.  You can look at specific skills your students need, then choose a game that helps them work  on that specific skill.

I will admit that it gets a bit loud while we work on this. This might feel like a waste to some teachers.  I think it’s a great chance for us all to practice what we do while the teacher is busy with just one person. I also feel that the information I gather from each child saves me so much time down the road that it more than makes up for these first few days of playing at math. I am not guessing about a starting point – sometimes missing the mark by a mile and starting too far ahead or too far behind my students.  I can confidently set up my guided math instruction in a way that is truly differentiated for the class. Finally, who says math can’t or shouldn’t be fun?

*I’ve had a few requests for a copy of my assessment.  I hesitate to share it, but I’m not sure why.  I can’t think of a real reason not to, so I guess I will.  It’s going to be most useful to you if you are familiar with the Landscape of Learning, created by Cathy Fosnot.  I don’t ask every child every question.  If they are having a lot of trouble with the first 1 or 2 addition or subtraction problems, I don’t ask the others.  If they are having trouble with the number line, I don’t ask all those questions.  But I don’t stop asking after the first mistake, because sometimes the child will go back and revise their number line, and that’s useful information for me too!

Here it is.

## Who is the tallest?

Every June I wish I had measured everyone’s height in September so we can see how much everyone has physically grown. Every September I forget. But not this year!

On the third day of school, we started talking about measuring things. Grade 2 is the first year students use standard units of measurement instead of investigating things like “how many markers tall are you?” I know the grade 1 teacher was working on this in May and June, so measurement seems like a good place for us to start. It’s a quick thing we can work on after spending some time each day setting up Number Talk routines.

It was really interesting to note that the grade 3 students in the class aren’t necessarily the tallest, and the tallest grade 2 is not the oldest grade 2.

After measuring our height, we brainstormed other things we can measure and compare – who has the longest feet, the biggest hands, longest hair, and biggest eyebrows? We don’t have answers to these questions yet, but we will by mid-week.

Changes in season make interesting times to measure temperature too. I’ve got my thermometer ready to go, and we’ll be tracking the temperature each day as we move from “It’s so hot we shouldn’t be keeping schools open” to “Sorry I was late. I had to scrape ice off my windshield.”

Grade 3 students study plants in science, and this is a great opportunity to integrate math into science, or science into math if you prefer. We’ll be planting some plants for our windowsill soon, and measuring their growth.

Most exciting of all is that when the final days of this year arrive, we’ll have both the skills and the data to determine exactly how many centimetres taller everyone has grown.

## Birthday Graph

Can you imagine not remembering when your birthday is?  The struggle is real for many 7 and 8 year olds I know.  Combine that with the fact that I have set a goal of visiting and resisting graphing often this year  (my goal now is once a month) and you’ve got a good first week of school activity.

Today we went outside for math, and we created a graph of our birthdays using a jump rope and some paper.  Here is some of our work, with student names cleverly disguised of course.

I did have to look up the birthdays of a few friends.  But tomorrow we are going transfer this giant graph to a small corner of a bulletin board and then I’ll never have to look them up again!  (ha)

The thing that amazed me most was that as soon as the graph started to take shape, I started to hear students comment on  what they were seeing.  “July is the most popular month to be born in our class.” and “I was born in the same month as Mrs. Corbett!” It was a lot of fun, gave me some insight into how much they know about graphing, an also showed me some learning skills we need to look at.

## #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!