math, Problem Solving, Spatial Sense

Stay apart

I started my school year with three students. We had a staggered entry and my two grades straddled the split between who started Wednesday and who started Thursday.

I was thinking a lot about physical distancing. Kids don’t really know how long a metre is – they really truly don’t! A metre, a mile, a moose – these units of measure are things they are still trying to figure out. In addition, they are busy figuring out where they exist in space. They aren’t all really sure where they end and someone else begins.

I decided to start off by asking them how big a meter is. I wanted them to have a frame of reference and a benchmark for how far apart they should be from one another.

We watched a video about the importance of staying 1 metre apart from each other. I said to the three, “Do you know what a meter is?” They did not. Makes sense since they are in grade 2. I asked, “Can you find some things that are as long as this meter stick? Some things that are 1 meter long?”

We then spent an hour measuring stuff in the room and in the hall and then we had to go outside for another thirty minutes of measuring because my three friends were obsessed with holding the metre stick up to things and asking, “Does this count?” Sort of like when we were driving across Ontario in August and my own children were obsessed with asking, “How much longer?”

Some really cool things happened during this time. We found out that you can stand at certain spots beside our tables and be a metre apart, but if you stand at other parts you are not a metre apart. We discovered that three floor tiles are equal to 1 metre. This was true for the white tiles in our classroom, the white tiles in the hallway, and the blue and yellow tiles in the hallway. We discovered that 2 1/2 bricks on the hall wall are 1 meter long. And the ladder on the play structure is less than a meter. So is the storm drain.

I spent a lot of time asking them if they were a meter apart and they had to use these benchmarks to figure it out.

The rest of the class joined us the next day and I couldn’t take 20 kids out to measure stuff in the hall so we used the photos from the day before. They had to basically memorize the two benchmarks we focused on and they were sort of good at it. They were very good during the lesson! They were less good at doing this in the wild. They even had trouble with the “Superhero arms” measure of distance. They are kids after all.

So I’m plotting my next step now. In the new curriculum both grades need to do some work with centimetres and meters. (E2.2) For now I am going to be content with helping them develop a feel for how long a metre is. We have moved into doing some work with figuring out how to use manipulatives, especially now when sharing has become complicated.

Executive Skills, math, Patterning & Algebra, Problem Solving

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:

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You can have a copy

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!

math, Number Sense & Numeration, Problem Solving

Baking

Are you still baking bread? At the beginning of the world-wide shutdown, everyone was baking bread and cookies and their own pizza. We are still doing this – we were doing this before. We’ve slowed down a bit because it’s been too hot to turn the oven on. But yesterday I made some bread and today my daughter is baking cookies.

She wants to do this all by herself. I have a recipe that’s meant to be easy for children to follow, and she has a lot of kitchen experience for a 9-year-old. She’s only needed help so far with the “1 slash 2 cup” of butter. We’ve talked about 1/2 dozens of times but it still eludes her. I showed her how to use the markings on the butter to figure out 1/2 of a cup. She then needed help with 1/2 cup of honey. Partway through pouring she realized she had the “1 slash 4” cup and thought it was going to be too much because she only needs “1 slash 2”. We’ve talked about this a bunch too, but in the moment she was confused again.  I coach her through it.  “1/4 is 1/2 of a 1/2.  So if you have 1/4, you have 1/2 of what you need.  So what do we need to do?”  She figures it out, I pour her another 1/4 cup of honey, and she’s back to working on her own.

I’ve been thinking a lot about baking and the learning that goes along with it. Little of it actually shows up in our curriculum. There’s problem solving, some collaboration (her brother doesn’t like chocolate so this is always part of our conversation when making cookies), communication, following instructions and, of course, measurement and fractions. At home this type of learning is very important to me. I want my children to head off to university with the ability to cook more than Kraft dinner, grilled cheese and scrambled eggs. The curriculum connections are a bonus. At school I cook or bake with my class maybe twice in a school year (less if there are students with allergies or special dietary needs in the class.)  I learned to cook at my grandma’s house, at my parent’s house, in Home Economics classes, and in neighbourhood 4H clubs.

If I was in charge of the curriculum, I’m not sure what I would eliminate in order to make space for cooking in the elementary grades.  I’m not sure there is anything we should exchange for cooking time. Secondary students still have the option of doing catering courses so they can learn to cook. Mostly I feel like learning to cook is part of how we pass our family and cultural traditions and values down to our own children.  I know some parents don’t teach their children to cook, but maybe that needs to be up to them.  Maybe this is one thing the schools have let go of for good reason. If I cook with my class it’s because we have a connection to something we’ve read about, or it’s a snow day and we need to fill the time with a worthwhile but fun activity.  I don’t feel compelled to teach them life skills like cooking or sewing.

 

 

math, Math Workshop, Mathematical Processes, Problem Solving

NOMA Summer “Book” Club #1

Today we at the Northern Ontario Math Association (NOMA) had our first summer book club meeting.  Instead of reading a book together, we are finding resources on the Internet we can read for free – things we can get without having to wait for delivery!

Today we discussed a webinar found on TheLearningExchange called “Teaching Math Through a Social Justice Lens”.  I highly recommend this learning series. It is basically a problem-based math teaching approach. Students are using real-world numbers to think about real-world problems with a social justice focus.  In this exact case, the students were mostly focused on an inquiry that had them wondering about their shoes – where in the world do they come from, who makes them, how much are those people paid to make them, etc.

Preparing for this has had me thinking about some social justice issues I could cover in my primary class.  We study water in science, so it would be interesting to do something with water bottles – collect data on the number of bottles used in our school, how much we save by using refillable bottles, what is the environmental impact on not only using them but having them delivered to your local store, what is the financial impact on buying disposable water bottles…etc.   I definitely need to think more about possible topics, but I also want to make sure I am paying attention to what my students are interested in.

The great thing about a book club is that other people think of things that I don’t. In our conversation there were a few important things that were brought up.  Some of the issues might be upsetting to families who feel the teacher is trying to push their own political agenda.  Some issues might be upsetting to students (we talked about all the amazing data related to Covid-19, for example, which our students might not be ready to analyze in the next year…or more!) And we have to make sure we are still teaching math and not just doing these projects that use the math. We want them to have a certain sense of exploration and problem solving, but we also need to make sure they know how to do all the necessary calculations for their particular developmental needs and grade level.

One of the big hurdles for me in my own thinking and teaching has been how to come up with projects that have my students doing math, literacy, science, social studies across the day instead of each happening in their own separate, compartmentalized time block. I have this figured out with literacy, but math…I’m still working on it. As I watched this webinar I feel like I have a new understanding of how to create inquiry problems that students could work on all day and still hit all the topics.  Now, I do think I wouldn’t jump right into this in September (though maybe with the right problem I could…) and I definitely think I will need to still have a time set aside on most days when we are focused on learning to do calculations.  But I’m thinking of some social justice and global citizenship issues that could really take over the class (in a good way!) for a solid week.

I’m also still trying to wrap my head around having students part-time in school and part-time at home but still working and I think this integrated approach would be a good way to have them working at home on things besides worksheets.

I’m still thinking through all of this!  But the book club was a good way for me to consolidate some of my thinking…and it gave me more to think about!

 

Relevant article:

Caswell, B., Stewart Rose, L., & Doura, D. (2011). Teaching Mathematics With a Social Justice Focus. Inquiry into Practice: Reaching Every Student Through Inclusive Curriculum, 81–88. https://wordpress.oise.utoronto.ca/robertson/files/2017/03/Teaching-Mathematics-with-a-Social-Justice-Focus.pdf

 

math, Problem Solving

Math at Home: Week 1

Every day we do math at our house. That’s not new. But this week we are going to be more serious about addressing some gaps. I get to be a one-on-one teacher for my children, which they need.  Well, really every kid needs it!

We started working on printing numbers correctly last week. One of my babies has some bad habits and the numbers are backward all. the. time.  Last summer we painted a chalkboard wall in the basement and it’s come in very handy many times.  It is now part of our makeshift classroom.

My son, who is in grade 2, is working on number lines.  He is very good at mental math, but doesn’t have a way to visually represent his thinking. I thought long and hard, but try as I might I can’t remember all the lessons from the Context for Learning units.  However, I do know that Antonio is 2 years younger than his sister and there are a lot of interesting math conversations that can come from this.  The sister is 10, and Antonio is 8, and Dad is 40 and Mom is 38 and I can’t remember right now how old the grandparents are.

Today we talked about how far apart Antonio and his sister are on a number line.  Then we talked about how that would look at different times in their lives.  How old was she when he was born?  How old was he when she was 6?  How old will she be when he is 10?

See the trouble making the jumps on the number line?  That’s a handwriting issue, but it’s effecting his math so we’re working on it!   Tomorrow we’ll continue working on this before we move onto finding the difference between the children and their parents.

We also did some counting.  Spencer needs practice skip counting so I have him counting his cereal and candy.  He doesn’t mind.  We do it only once per day, not over and over. When we worked on 3s today I modelled it for him first then he repeated what I had done.  We’ll see how it goes later.

My grade 3 daughter is ready to practice the 7 times tables.  We started by going over everything from 1×1 up.  We played Multiplication War last week.  This week we are going to do that some more.

Both kids are working on Dreambox for a few minutes every day.

Geometry, math, Mathematical Processes, Problem Solving

Geometry

Teaching geometry in grade 2 and 3 isn’t all that exciting.  I mean, we have to make sure everyone can identify their shapes, can name a few attributes of those shapes, can manipulate those shapes and make things. It’s not all that interesting when we first get started.  Well, I should say that it isn’t all that interesting to me.  The kids love it!  And they think it’s awesome and the pattern blocks feel nice and everyone feels really confident about themselves during math when we are talking about geometry.  That makes it a great topic to work on during December.  December is a crazy month with a lot of different things happening and emotions running around so it’s nice to have geometry to come back to.

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I promise next week I’ll have a lot more to reflect on.  We are moving on to 3D geometry and angles.

We spent some time using the Spheros this week as well.  My friend and I spent some time writing up an instructional unit that involves math and science expectations.  This past week we mostly spent time playing with them.  Luckily one of my students from last year, who is also in my class this year, remembered some important things like how to charge them. There are so many steps involved in using tech!  Even though they aren’t complicated steps they still take up a lot of time, and can cause a lot of trouble if any of them are not followed.  Which is the whole point of learning coding, I suppose.  Try something, fix up the problems, try it again, fix up the problems, repeat.

Like I said – nothing too exciting.  But everything we did this past week set us up for some bigger learning in the next week.  The weeks when we go back and remind ourselves what we already know are quite often as important as the weeks when we are learning new things.

Data Management, math, Measurement, Problem Solving

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:

Uncurling the paper was a big challenge!

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!

math, Measurement, Problem Solving

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.

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Why yes, I do need to straighten out “hooray” now that you mention it.

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I got the pretty yellow signs from @sarahlalondee (on Twitter).  Pretty, right?

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Nice pattern!  Pretty shoes!

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I got my word wall headers from Lindsay Hill on Teachers Pay Teachers. 

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Beautiful!  But not a pattern.

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Work in progress! This is the group that is making random sized pieces and fitting them in wherever.  I think we’re about to transition to some measuring with this group.

 

math, Number Sense & Numeration, Number Talks, Problem Solving

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.

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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:

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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!

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

 

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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.