Making Progress!

We had some interesting conversations about shapes last week.  I was still working on getting my math interviews done so I needed everyone to be independently busy while also learning.  You might think that by the time someone is 7 or 8 years old they know what they need to know about shapes and using blocks, but it’s just not so.  I think wooden blocks aren’t as popular as they once were, so kids don’t necessarily have them to use at home (where they have spent a lot of time in the last 2 year) and I also think it’s because when kids are playing for fun, they don’t have metacognitive conversations with themselves about what they are learning – they just have fun. After they had all rotated through the different types of blocks, I started asking questions and they didn’t have much to say.  But after I asked questions, let them play again and then asked the questions again, there was a lot to be said – two chart paper pages full in fact! 

One child pointed out that we can build castles and other stuff by stacking.  At first everyone thought that spheres and pyramids can’t stack, but after some consideration they realized that pyramids can be on the top of a stack, just not the bottom and spheres can go on top of things, but they need other things to keep them in place, like a cube to lean on. Some students noticed tat some shapes were not represented in the box. They then figured out they could make the missing shapes: two squares make a rectangle, two triangles make a rhombus, etc.

We also talked about the difference between 2D and 3D shapes. We need do some more work here. This week we’ll be talking in casual conversation about how 3D shapes are made of 2D shapes. We’re also going to try to get back on track with the curriculum map I made for myself. I need to get some patterning done so we’ll continue to use the shapes and now start to use them as pattern blocks, along with the colour tiles and lots of other manipulatives from my classroom. We need some community building too, so we are going to make our own bracelets using pony beads and elastic string. I have a collection of beads that’s been hanging around far too long so I want to use them up. AND I need to get going on all the Number Talks that will help us review basic addition/subtraction strategies for numbers up to 20. I completely skipped the fun unplugged coding activities I wanted to do in September, so I will be doing those during our gym time.  I’m excited about trying this out in the big space which we were not allowed to use last year. 

Whew!  I’m tired thinking about it. But also energized. My math interviews are complete and sitting on my desk waiting to be brought home, so I’ll sort through them this week (instead of today like I originally planned!) and find the trends and strengths/needs in number sense. I’m so glad they are done for many reasons, not the least of which is that I can be part of the explorations this week and can MAYBE start taking some anecdotal notes so I can make some informed decisions about what to write on progress reports. 

Week 1: Done

This week we did many of the same activities I used last September for the first week of school. Namely we measured things that are a meter apart. Once again I was hoping that all I had to do to keep everyone a meter apart is show them how big a meter is. Don’t you love my optimism? Once again, we finished the week still needing practice.

As I sit here today working on my plans for the coming week I’m reflecting on how quickly everyone did fall back into some of the Number Talk routines that are common in my school. I typically have a class mostly inherited from one teacher, but this year it is a mixed group. I’m at a dual-track French/English school and I have more transfer students from French Immersion than I’ve ever had at once. I wasn’t sure how many of them may have used a “thumbs up” for Number Talks, or how many may have discontinued this during online school in the spring.

Last week we did a lot of counting for our Number Talks. I know I originally got this activity from Graham Fletchy, but I cannot find it! Basically I had a plastic cup (noisy) and I dropped small stones into it while making sure they could not see the objects falling. The class had to count as I dropped and then tell how many were in the cup based on what they heard. It’s a great activity that helped us talk about listening closely while also establishing our Number Talk routine. I’m definitely doing the “popping balloons” activity (from Graham Fletchy) this week, and few others I’ll report on next week. I didn’t expect to need to spend time on counting (grade 2 and 3!) but we need it anyway. Many students went right to rote counting and reciting and I want to make sure everyone remembers (and is able) to match a number to a “plunk” in the cup, or to an object they touch or see. I suspect we just need to get back into the groove of school, but one can never tell in September!

This week I will also be plopping everyone online for a few minutes. I want to make sure everyone can sign in and knows where to find our class page. I hope we don’t ever end up back online again, but I need to make sure everyone is ready…just in case!

For our regular lessons, we’ll do some more measuring. Looking at our class numbers I’m predicting some reorganization AND I want to stick with a gentle start to the year. Everyone in grade 2 seems to like measuring.

Math on the Move

This was our math class this week:

Last Spring at the OAME conference, I bought a book called “Math on the Move” by Malke Rosenfeld.  My friend, who was at the conference with me, attended a workshop about the book.  We talked about it a few times.  She tried it out with her grade 2 class last year, and I read it over the summer. Then in December we had a day when we could sit down and do some planning together.

The premise of the book is that there is a lot of math students can learn while moving around.  This past week we learned about patterns in math while dancing. The squares on the floor, made with painter’s tape, give everyone a designated space to work in.  They also give everyone signals for where the feet should be at a given time.  I added the blue tape line because our previous work with directional words and spatial sense activities let me know that left and right are still tricky for quite a few of my people and I thought “blue side” would be less tricky. I still used the words left and right, and gradually stopped saying “blue line” over time. We worked with 4-count repetitive patterns all week. We got over some self-conscious feelings about dancing where others can see us.  We resisted the urge to pick the painter’s tape off the floor even though it was getting pretty scuffed up by Friday.  I like the way this activity integrates spatial sense, patterning, dancing, and self-regulation!  It was super hard for some children to follow dance steps instead of dancing free-style.  It was a lot of fun, and this can be quite dysregulating for some children. I had specifically planned to do this during the week we returned from Winter Break because I knew they would need to ease back into the routine of school.  I think this helped many of them.  I’m confident, based on the rest of our days, that sitting down and focusing on some table activities would have proven to be a challenge!

We have been using “Banana, Banana, Meatball” on Go Noodle for a few months during our DPA.  I used this to launch us into a study of patterns and dance in music.  The class, mostly, can do the moves.  It’s just hard to keep to the right pace.  However, everyone could follow the patterns, talk about the patterns, and create their own patterns.  We also watched some other music videos and danced to the music.  Turns out all dancers follow the same moves we were using.  There are patterns everywhere!

We didn’t get as far as I wanted in one week. I had hoped to have everyone using some boxes to record their moves so others could follow the pictures (this is all explained in the book.)  We will get there eventually, but it didn’t happen when I thought it would.  I’m not in a rush though.

To support our pattern learning, we were also using some “Eyes on Math” images for Number Talks this week.  Marian Small wrote this book several years ago.  I use it every year and I love the way the images get students thinking about noticing the math in the world around them.  This week we looked at a picture of a parking lot.  Cars were leaving a person was counting how many cars were left.  We had to figuring out how many cars were left as each left (shrinking pattern.)  On another day we  wondered how many eggs would be left if mom takes them away 2 at a time.  We talked about several different ways to figure out how many bicycle wheels were in a picture (growing patterns.)  We worked on a few money problems too!

While we were doing the Number Talks, we also talked about how to solve a problem.  In other words, the problem is up there on the board, or on the paper, and you need to read it and figure out what to do in order to find a solution.  How do you do that?  This is one of the times when I did some direct, explicit instruction.  I know how to solve a problem. I know how to break it down into steps.  They don’t.  I told them. I made a chart, we practiced, now some of them know what to do and more of them are going to know what to do after we do some explicit practice next week.  When I start the next Context for Learning unit they should be better equipped to work independent of me.

Next week our math focus will turn to telling time.  The turn of the year is a good time for that.  But we will come back to our dancing a few times.  We’ll talk about more Eyes on Math images and practice solving steps. And we are going to do an art project that uses patterns.  I’m excited to see what happens when we get started on this.

Subtract

I know it’s only Tuesday, but I’m in a “celebrate the little things” frame of mind.  It’s helping me cope, which is pretty important for teachers under stress.  And other humans of course.

This week, only 2 days old, I am teaching area and perimeter.  But I like to continue with Number Talks even when we’ve moved away from the computation portion of our work. Yesterday I started with one from Sherry Parish’s “Number Talks: Whole Number Computation” book. I chose one from the grade 2 section:  20-19, 20-14, 20-12.  We talked about how we could use all of our strategies from the math wall, but that counting up seems to work better than counting down.  We used the math racks for this activity, and I celebrated my own ability to say “subtract” every time instead of reading the problem as 20 TAKE AWAY 14.

Then today, we started with 20-19 (because one thing I have definitely learned from Cathy Fosnot and her Number String work is that starting with a helper problem is very important – this is not part of the Number Talks book work.)  Everyone remembered or quickly figured out that the answer is 1.  Then I wrote 30-19.  They weren’t so sure at first.  It took us a while to get to 11.  Some kids wanted to count all the way down (their go-to strategy).  Some wanted a math rack so I pointed out it doesn’t have 30 beads so what would they do, they didn’t have a plan. Some made random guesses AS ONE DOES!  We started to talk about our potential answers.  I purposely called on a student that I knew had the right answer AND that I knew could explain the thinking to share.  This child did a great job of noting that the helper problem was helpful.  If we think about how 30 is just 10 more than 20, but we still subtracted 19 then the answer should be 11, or 10 more than 1. I pulled out the math racks. I showed them 30-19 using a 20 rack and a 10 rack.  This way I could show how I added 10 more in but didn’t remove any more than I had the first time, leaving 10 more remaining after I “took away” or “removed” the 19 beads on the rack. After we did 40-19, someone noticed a pattern.  This is honestly the thing that makes me happiest sometimes.  Some groups of kids will notice patterns right away and then stop puzzling over the math because they have found the short cut.  But this class always takes a bit longer to see the pattern.  It’s fine with me, because we have a lot of good conversations along the way.  But I’m also glad when the pattern becomes part of our conversation too.  Even after this child thoroughly explained the pattern, some were skeptical.

Along the way I was drawing the number lines.  I decided to draw a new one each time because I wanted them to clearly see how each time the 19 didn’t change, but our starting and ending point did.  I also wanted to highlight the iterated units.

We talked about each of our strategies:  does it make sense to count up?  to count down?  to try and “take away” something?  to think of an addition problem that would help?

Two weeks ago I blogged about a moment when everyone was working independently.  It has rarely happened since. But it is happening, throughout our day.  Slowly but surely we are edging forward, and today’s math was a reminder to me that we are indeed doing good work. Not every day is easy.  In fact, today wasn’t that easy.  But this was my shining moment.

We’ll continue on with this tomorrow, but I will use some other number besides 19.  I am also going to write out today’s work on a chart paper because I think it will help us going forward and, therefore, deserves a spot on the math wall.

Number Strings/Number Talks

Math was fine this week. We started doing more place value work while working on “The T-Shirt Factory” Context for Learning unit by Cathy Fosnot. It’s always an interesting one, but I actually didn’t do it with my class last year.  We weren’t ready for it until much later than this and when we were ready for it…I forget what we did instead.

This week was Halloween. That means an interrupted day on Thursday because of the Halloween Parade.  I anticipated a day of difficulty on Friday as well, and while we’re at it, let’s just admit that Wednesday wasn’t going to be easy either.  See how hard it is to stay on schedule?  That’s why we didn’t exactly stay on schedule with the unit.  However, I didn’t skip math any of those days – even the snow day on Friday!

I did a fun mapping activity with a Halloween theme one day when I was pulled out for a meeting, and we did a lot of work with the base ten blocks.  But every single day I made sure that we were doing a Number Talk.

During a Fosnot unit, there will be a lot of Number Strings.  But when I am not teaching a specific skill and want to review things that I hope everyone already knows or that I know they need to practice, I go back to Number Talks.  This week we used some from the Grade 2 section of the book “Number Talks” by Sherry Parish.  We started with single digit numbers and I found out on day one that most everyone understands commutative property.  I repeated a talk that would reinforce this with double digit numbers on the second day.  On Wednesday, Thursday and Friday we talked about the “doubles plus 1/doubles minus 1” strategy.  These strategies are now displayed on our math wall so we can refer to them often.

This week, I am doing Number Strings to support the learning in the unit.  Because I can barely remember what day it is on most days I have to write my numbers on a Post-it note.  These will sit on my lap top all week or I will lose them.  I find it also has me thinking many times during the day about what we are doing in math, which is good for my brain.

Some of these are from the unit and some are from my head.  I know my learners well enough at this point that I’m sure we will need to do practice the skills that are in these strings multiple times.  They’ll be practicing them while doing the work in the unit as well.

I’m going to finish off my planning today by making my anecdotal record sheet for this unit.  (Just double checked and I already made one a few years ago! WOOHOO!

Estimating and Number Lines

This week we were focused on two things:  estimating stuff and counting to see if our estimate was close.  I’m feeling really good about it!

There were some fun activities we did that I think really helped.

First, I had some small jars full of stuff.  We started the week by reading a book about estimation.  Then I held up one jar at a time and asked everyone to estimate how many were in the jar.  After the second one, I sent them to their tables to practice.  They had a great time estimating how many paper clips, beads, erasers or rocks were in each jar.  We did this on Tuesday and on Wednesday.  (We didn’t have school on Monday.)

We also played a game that I first learned this summer during a free week of online PD offered by Christine Tondevold.  There were new webinars every day, and one of them featured Graham Fletcher.  He dropped counters into a container but students couldn’t see what he was doing.  They had to rely on their hearing to count along and then identify how many were in the container.  We did this each day last week as a counting routine at the end of the lesson.  On Thursday, I started with this activity.  We had estimated enough times this week that I was ready to take it to the next level.  I pulled out one handful of counters. I asked the class to estimate how many I had.  They turned to a partner and discussed, then I constructed a number line as we went along to show where everyone’s estimate fit on the number line.  They were all convinced that I had no more than 12, so that was the last number on my line.  Then, I dropped them while they counted.  I had 17, so we had to stretch out the number line.  Next, I took 2 handfuls and asked them to estimate.  They did a quick turn and talk.  The first child I called on said, “Well how much is 17 and 17?  Cause if you can fit 17 in one hand then you probably have double that amount.” I was excited about this response!  The child is in grade 3, and I thought this was prefect reasoning. I annotated his explanation as he explained how he added 17+17 (sorry…had to erase that before I got a picture.)  We all agreed that it was pretty likely that I had 34 in my hand.  We started to count.  I had 37, which we all agreed is pretty close to 34, so 34 was a good estimate.

After we had counted them, one of my friends suggested that maybe I had 47.  Win some, lose some, right?  But I put that on the number line and we discussed our answer of 37 again and I think that friend understood that I had 37 and how far away from our estimate 47 is.

An interesting thing happened while we were counting.  Thirty-seven is a high number for some kids to hold in their head so they were using fingers and counting out loud to aide their working memory. I wanted to talk about this strategy so that those who hadn’t done it would know it’s a strategy they could use.  One friend said that he had actually only been able to count to 10 on his fingers at first so each time I got to ” a group of 10″ (“Like 10, 20, 30…like that!”) counters he held up 1 finger. He knew he had 3 fingers and that is 30 counters, then he just had the 7 to go with the 30.  I tried to draw that thinking too.  This strategy actually lead really nicely into our lesson.  We are working on the “Collecting and Organizing” Context for Learning unit next, and counting stuff is the beginning of that unit.  He introduced to us the idea that things can be put into groups of 10 to help with organizing and counting.

We did a bit more counting on Friday.  Everyone tried to make groups of ten, but many aren’t yet convinced that this will help.  We’ll dive deep into this unit whenever we go back to school (hopefully Monday!) and I feel confident they will have it by the end.

We finished on Friday with the “Flying Cars” Esti-Mystery from Steve Wyborney’s new Esti-Mystery set.  It was a huge success and the students were so excited that their estimate was so close to the real answer.  I was so excited that their ability to both reason and explain their reasoning had come so far in just one week.

Up next on the spiralling document I have been following is more counting (forward to 100 for grade 2 and 200 for grade 3).  This week we did some hundred chart puzzles.  I had some made with 101-200 charts for the grade 3s to work on.  They all did pretty well.  They can now become a centre when I need everyone to do independent activities while I run Guided Math groups.  This will become really important in about 2 weeks (depending on if/how long schools are closed for the strike) when I want my grade 3s and grade 2s working on some different units. We also need to be able to count backward (from 50 for grade 2 & 3, and from 500 by 100s for grade 3s) so that will be the focus of our counting routines next week.

And look….nobody went to the washroom during our Number Talk that day!  Interpret that as you will.

 

Sorting and organizing

I am using the spiralling document found on EduGains to work through my math program this year. The first week is meant to be devoted to sorting and organizing skills from the Data Management strand of our math curriculum. I decided to get started on Monday even though we were, ironically, waiting for information about re-organizing classes because of our enrolment numbers.  Because I will be coming back to sorting and organizing many times, I didn’t worry about doing this without a few students who will be joining our class on Monday.

I started with some “Guess My Rule” slides I made on PowerPoint. I had enough to do 3-4 each day this week.  As we discussed them, everyone tried to “guess my rule” and we discovered that there could be 5 or 6 different guesses and all could be correct.  What mattered here was the ability to justify one’s “guess” about my rule. This is a really important skill that everyone needs early on!

Next, out came our math tools.  Everyone worked on sorting the tool of their choice.  I haven’t started with a “guess my rule” game before and I was pleasantly surprised to find that my students did not focus on sorting by colour.  This is often a problem.  I have to spend a lot of time getting them to think about other attributes.  I feel like the “guess my rule” activity set them up for success because they were already trying to be very clever and “trick” their friends.  Nobody is tricked by colour, so we (most of us) tried to think more deeply about our tools.  Those who needed prompting quickly moved on past colours. The work we did last week on how to use the math tools properly also paid off!

Some of the tools I chose for them to use included the necklaces, coloured glass marbles from the dollar store, attribute blocks, and base ten blocks.

The necklaces were sorted by colour, but also by bead type.

Attribute blocks were sorted by colour, shape and thickness.

These glass beads are the best money I’ve ever spent at the dollar store.  They are very versatile: bingo chips, counters, sorting tool, and some kids just love playing with them for no reason at all!  They can only be sorted by colour…or so I thought!  Turns out they are not all exactly the same size.  The  new ones I bought this summer, 10 years newer than most of the others, are slightly larger and a slightly different shade of blue and green.  I’ve lost a whole bag worth of red over time.  They are very popular!

We did this sorting activity for 2 days because we had some other interruptions that shortened our math class.  On the third day, I asked them to use any material in the room to create their own “Guess My Rule” page.  Here are a few.  Can you guess the rule?  Once again, there were many possibilities guessed, so I know students were looking at many attributes of the materials they chose.

Bright colours vs. dark colours

 

None of us got this one! “I will not buy containers without matching lids!”

Some guesses: flexible and not flexible, longer than a metre & shorter than a metre, colourful & wooden, inches and centimetres & only centimetres.

This activity was a lot of fun.  We had a field trip on Thursday, so we were doing math in the real world instead of in the classroom.  On Friday, the students had all been re-sorted into the class they will have for the rest of the year.  I elected not to do the math I had planned because I want to do it with my “new” class (about 1/3 are new to me since the first day.) So here I am, going into the 4th week of school and already “behind” where I thought I’d be.  Typical!  But I am not worried because I will come back to those activities later when sorting comes up again.

Next week:  Counting! This is where I would typically start.  I’m glad I started somewhere else because I have seen everyone as mathematicians aside from their ability to count. I need to start my math interviews as well, so some of the centres I had created for organizing will work as activities  to keep people productively engaged while I am doing individual assessments.

This past week at OAME, I was pretty focused on spiralling the math curriculum and on finding more problem solving tasks to use with my class.  I find that a lot of the tasks are a bit beyond our reach, which is frustrating.

One of the things I was introduced to was Graham Fletchy’s 3 Act Math Tasks. I so appreciate when a person is willing to create a resource like this and then share it with the wide world!  While planning my week, I picked out a few in particular that I thought would engage my students, while also spiralling us back to some Big Ideas we haven’t worked with for a while.

Today we did this task, called Snack Machine.  We have had a lot of practice working with each other.  We have had a lot of practice thinking about a strategy to use to solve a problem.  But this task, and others on the site, really allow for a lot of divergent thinking.   There are multiple entry points, and multiple paths to a solution.  It’s great!

In the Snack Machine, a video shows a girl buying something from a vending machine.  We watched, then talked about it, then watched again, then talked again.

At this point, the children didn’t know what the problem would be.  They were simply looking at the video and mathematizing it. The discussion started off with someone suggesting that the girl in the video looked at her change and was disappointed.  That definitely had people thinking about why.  I got a kick (as my grandma would say) out of one of them suggesting that the machine scammed her.

After the second viewing, we had things to add.  We heard 4 coins fall, so which coins might they have been?  That lead to a long conversation, mainly because 4 toonies would make that sound, but would be an awful lot of money for a bag of chips, but 4 nickels wouldn’t really make sense either.  In act 2, there is a picture of the vending machine showing us that the chips actually cost 60 cents. Then another video shows the machine counting up the money.  We added that to our board:

Sorry about the cropping – I have written the initials of the person who contributed the idea and don’t want to publish them. Also, SO THAT’S WHERE MY ERASER AND RED MARKERS HAVE BEEN ALL DAY!

After this, I sent them off to figure out the coins she must have used.  Amazing things happened!  After everyone had a pretty good shot at solving the problem, I showed the final video.  In that video we see that the change was 2 dimes.  They used this to confirm that 80 cents had gone in, 20 cents had come out + 60 cents worth of chips, so it all made sense. No scam!

This friend needed help putting in the + sign, and also knowing where to put the $ sign.

 

This friend needed help knowing that she’d arrived at the answer. Annotating our thinking continues to be a skill we need to practice.

The money used was American money, and of course a little bag of chips would cost more than 60 cents in a Canadian vending machine. But I told them the two coins we saw were dimes, and that was good enough for them.

Yesterday we worked on Sliced Up, which had us estimating, thinking backward from oranges cut into wedges to whole oranges, and finally multiplying (5 whole oranges, 4 wedges from each orange so how many wedges in all?) For tomorrow, I am debating between It All Adds Up which is a nice money connection to Snack Machine, and The Whopper Jar   which is a nice follow up to the estimating we did in Sliced Up.  Whichever problem doesn’t make the cut tomorrow will our Monday task.  I’m learning toward the money problem because I have a bunch of activities we could do as Number Talks to stretch that learning all week.

It’s EQAO week at our school and I like having some fun, confidence building task for my students to work on.

Slice of Life: Multiply the Money

I wrote yesterday about a Number Talk I had worked on with my class.

Today I extended that activity by making an array using money.  I used the Mathies money tool to display an array made of nickels, then I asked, “What do you see?”

We built this display of our thinking a bit at a time, so I am sure it made more sense to us than it might to you!  Someone saw 45 cents.  Then someone else saw 15 cents (3x5cents) and then 3 groups of 15 = 45.  Some saw the array 3 x 3 = 9 nickels all together. I pointed out 3 x 15 and 9 x 5.  Thanks to our work with fact families, a few realized 45 “shared by” 3 people means they get 15 cents each.  Seriously!  They didn’t just point out that 3×15=45 so 45 divided by 3 = 15.  They actually explained what was happening! (Full disclosure: not all of them.)

After this conversation, I cleared the board and made an array using toonies. Now, you might have been expecting me to use dimes, but I thought the $2 coin was better considering that we haven’t talked about multiplying by 10 and my grade 2s would get a lot more out of the conversation if we were thinking about multiples of 2 rather than 10. I will probably give 10s a try tomorrow on their own.  After our success today it seems like a good way to get everyone to start thinking about multiples of 10. I’m looking forward to it!

 

Just about every Tuesday I blog for the Slice of Life challenge over at Two Writing Teachers. You can read more posts on that blog.

What you see isn’t what I see

For Number Talks this past week I made some arrays on Smart Notebook and projected them on the board. We spent time each day talking about what we noticed and thought. Early on the fact families emerged. I’m glad because we’ve just finished up some multiplication and division learning and I was glad to see this being put into practice.

On Friday I displayed the picture below:

As you can see there were multiple ways to see this picture. Immediately people saw the array of 4 rows with 3 bikes in each.

One child kept insisting it was 2 groups of 6. It took a minute for him to convince his peers, and I had to help by circling the 2 groups. I’m glad we took the time to let him explain! He was clearly showing some beginning “partial products” thinking and I wouldn’t have known this if I hadn’t probed for an explanation.

Finally someone started talking about the bike tires. I don’t have a photo of that annotation, but it was interesting to see how the students went in to figure out that 12 groups of 2 = 12+12 = 24. Of course they were able to complete the fact family. At this point very few were counting by one’s. I was quite happy about that for sure!

It took me very little time to use the tools in Smart Notebook to make these arrays. I’ve definitely used Mathies for this as well, but the pictures in Smart Notebook led to a deeper conversation. This week I need to find some cars with 4 wheels to expand on our conversation.

This work also builds on the “Eyes on Math” number talks and picture-based number talks we’ve been doing all year. Tomorrow we are going on an array hunt around the school with our iPads. That activity has been preempted a few times but I think it will end up being a better activity now that we’ve discussed the picture arrays a few times.