math, Mathematical Processes, Measurement, Problem Solving

Synchronicity

Bigger, Better, Best by Stuart J. Murphy

We’ve been working on multiplication and we’ve been having a good time doing it. It has taken about two weeks longer than anticipated, but I’m going to mostly blame snow days for that.

About a week ago I walked into the library and the book above was on display. It’s been in our library for a long time, judging by the state of it, but it’s a new to me title. I love this Math Start titles, and was so happy to discover that this book was going to help us move on to finding area.

In the book, the children are arguing over who has the bigger bedroom. They solve their fight using math. To measure their bedroom windows, their mom suggests using sheets of paper, and to measure the whole room they use sheets of newspaper. One child’s window takes two rows of paper with six in each row. The other child’s window is four rows of paper with three in each row. That lead to a fun discussion.

Then I set them up. We have several different kinds of tables in our classroom and I asked them to help me figure out which kind of table has the bigger top. We brainstormed a list of tools, and “sheets of paper” was added as a measuring tool. They also wanted sticky notes, but I only have tiny sticky notes so we decided to pass on trying those.

Next, everyone got to work.

Everyone used their favourite tools to measure, but only one team used the sheets of paper. On the second day, we used the photos I took to have a “mid problem” math congress. I focused on the snap cubes and the sheets of paper, so on the second day when we took up the measuring again, more groups used those two tools.

One group was really finding the area, as opposed to other groups that got sidetracked with finding the length and width. It’s okay and we’ll work it out, but I really wanted to focus on the concept of area so we talked about this one a lot. We have several rectangular tables like this. As you can see, it takes two rows of paper with six sheets in each to cover the top. We did get them lined up pretty exactly, even though this picture doesn’t show that well. But we had a problem…

…it was really hard to lay out the paper on the trapezoid shaped tables. They arranged and rearranged but couldn’t quite get it. They then started to try measuring the leftover bits with other tools and we were finally saved by the bell and they had all night to figure out what to do.

The next day, this group was at it again. They tried several different layouts but couldn’t figure out what to do about the gaps. I stepped in to help. I put down a piece of paper so half was on the table and half was off. Then I took a pair of scissors and cut it. “There,” I said. “So we know it is ten pieces, plus at least two halves, so we’ve used eleven pieces so far.” This was met with silence, then they got to work. They needed a bit of help with some of the wee corners, but in all, we finally figured that it took thirteen pieces of paper to cover the top, and we would need a bit more so clearly this brown table has the larger surface area.

Unbeknownst to me, one of our kindergarten teaching teams has been hoping to get a different table into their class. On the second day of this investigation, my colleague posted a request asking if anyone had a smaller table they would be willing to trade. I showed this to the class and told them that I asked if by “smaller” she meant shorter or smaller area on top. She meant shorter, but also needed the table to fit in a certain spot, so the surface area needs to be just right too. They then set out to measure the height of all our tables, especially the one with the smallest surface area, so we could see if it would be a good trade. Not wanting to disturb the kindergarten class, I took just two of my students to measure her table so we could compare.

Are you dying to know the results?? Well, I think we’ll need to trade her for one of our adjustable tables. Her table and our adjustable tables have the same surface area, and the table we have that has a smaller surface area is the same height! I’m going to try to have the children present their results to the kindergarten teaching team one day this week so they can decide. It will be a good chance for my students to practice communicating.

There were so many good things that happened: we got to talk about using the snap cubes in groups of 5 so they are easier to count; we had reminders about centimeters and meters; we did some mathematical modelling; we had conversations about why the centimeter cubes need to be in a straight line (see how it curves in one of those pictures?); we had lots of opportunity to practice communicating our thinking and solutions.

This week we will spend more time talking about area specifically. We will also be talking about why it takes fewer snap cubes than pieces of paper to cover a table, and why it takes so many centimeter cubes compared to snap cubes.

math, Mathematical Processes, Social Emotional Learning

98…99…100!

We started keeping track of our own acts of kindness about 2 weeks ago. We needed to know of what it really means to be kind, and conscious of when we were actually doing it.

To help us out, I printed a sheet of 100 hearts. Our goal was achieved in only 6 school days!

Of course I found a way to add some math. There are ten hearts in each row. Initially I coloured in 5 hearts with one marker and the other 5 in another colour. We were counting by 5s and it was all going well until someone decided to put us on the fast track and do some covert colouring of hearts.

For the second attempt I switched to bingo daubers and counting by 10s. At first only one child was counting the hearts…both up and down. “We have 12, so 88 to go!” They’d say. Then more kids jumped in and every time I’d colour in a few (they always had many acts of kindness to report after recess) more and more kids would help with the running total, as well as the number remaining. They’ve been less than enthusiastic about lots of the math we’ve done, so I was excited that they got excited about this.

Of course we had to keep going. Today I added more hearts to our new chart. The filled chart was behind it. “How many do we have now?” I asked. They all agreed we had seven. “I disagree I said. They started to try to convince me I was wrong. It was good to see they are learning some math reasoning skills, but I was right. I pulled out our filled chart and put them side by side. “I think we have 107,” I said.

They had no choice but to agree with me.

I can’t wait to see where this goes tomorrow.

It also helped them become more aware of opportunities to help out. Someone dropped crayons one day and I made a big deal out of adding some hearts for the helper. I truly don’t know if they had ever considered helping a classmate out, especially for a chore like cleaning. I’m happy to report this type of thing has become more common for us.

Geometry, math, Mathematical Processes, Patterning & Algebra, Social Emotional Learning, Spatial Sense

Month 1: Done

It feels like school just started. And yet, September is nearly over. In fact, it ends this week. We are headed into our fourth week of school. At this point I would usually know if my class was going to be reorganized due to school enrolment, but it’s all still being organized. I’ve decided not to worry about it and carry on.

This year I am using a curriculum planning guide I created last year and updated over the summer to reflect the new curriculum. Of course, the Ministry has also released some suggested long-range plans of their own. (Found here.) I was really intentional about where I put things on my own calendar, and I liked the sequencing I was using last year. In addition, I like how it was spiralled and we came back to every concept at least once over the course of the year. When school closed in March, I had already covered everything at least once – even probability! I am inclined to stick with my own plan. However, I am also going to consult with the Ministry suggested timeline just to see how that team has set it all up.

Last week my class spent some time on patterns. We made patterns with manipulatives, and we made patterns with numbers on the 120 chart. It was fun! I was initially worried about using manipulatives, but have decided the hassle is worth it. I spent time every afternoon washing manipulatives in hot water and soap so we could use them again the next day. I bought some colanders at the dollar store to help with the draining and drying. It’s working out okay.

I feel like there were one hundred different things going on, but the fast pace and changes from one thing to another seemed to be what we needed so I went with it. We have been doing some dancing for our Daily Physical Activity (DPA) and several of the dances we used were patterned repeating dances. In coding this is called a loop, so that is what I have been calling them. This is our favourite:

By the end of the week we had met all the goals on our success criteria:

*making repeating, growing and shrinking patterns with math tools, numbers and our bodies.

*explaining our patterns to others. (a math process skill)

*being creative in math. (another math process skill)

*persevering through the hard parts. (This is one of the social emotional learning goals in the new math curriculum.)

So what’s next? According to the Ministry long range plan, the one organized by guiding questions) I should be doing some data management about the class. We should be gathering info about our height, our siblings, etc. and graphing it. They also have movement words this month. I’m still not feeling 100% certain about reorganization, so I think I’ll put that off for a week.

On my plan, I have some work with 2D and 3D shapes. We need to be describing them by their attributes at this point (we’ll work on them more in depth later.) I am going to stick with this, and add the movement expectations (E 1.4 relative location, and E1.5 directions for movement). These fit with the work we have been doing already. I also have the robots on loan from the resource centre, so I am going to want to use those. I have a fun lesson plan from the math project I’m involved in and I need to try it out. This is why I borrowed the robots actually. So this week we’re going to work on movement and we are going to work on following patterns on the 120 chart with the help of our robots. And I am now going to spend some time today figuring out how to make a giant 120 chart since my hundred carpet is now banished to the attic until the pandemic is over. I’m tempted to start number line work simply because a long number line is going be easier to create on the floor than a hundred chart.

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

 

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.

img_8770

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.

math, Mathematical Processes, Number Sense & Numeration

This week we did…something

It was a weird week for math. I spent some counting routine time counting backwards. They’re pretty good at it. I thought they could be independent as a small group while I worked with some people on something else. I was mistaken. We’ve still got some social collaboration and problem solving things to sort out. That’s the thing I’m reflecting on most as I move forward into next week. I know where I’m going lesson wise, but am still sorting through some of the mathematical process teaching I need to do.

Because of the work I’m doing to spiral in math this year I am feeling like I don’t have a lot of things to use for comments on progress reports. I’ve decided to focus my commenting on some of the mathematical process skills.

This week I’m realizing that so far I’m doing a lot of the selecting when it comes to the tools we use. I put a lot of work into making sure everyone knows how to use the tools properly. Now it’s time for me to talk about how the tools have specific purposes for which they are best suited. We can’t always choose the colour tiles because we like how they stack! It’s time to move along and choose based on what each tool helps us understand. I’m doing some guided math rotations this week, and want to come up with some opportunities for kids to articulate why they chose a certain tool.

That is going to lead us to some communication work. We’re doing okay with this when I am poking and prodding. Now it’s time for the students to think about being really clear with their communication. I’m going to jump in and set up a FlipGrid they can use to explain something they’ve done. They’ll have to think about how to make me understand their thinking when I watch the video at home (cause you know I’ll never find time or a quiet spot where I can view these at school!)

Finally…actually, I’m going to stop there. Don’t need to set too many goals at once, right? I’m also diving into “The T-shirt Factory” Context for Learning unit with my grade 3s and we’ll need to be focused on that math at the same time. Not totally sure what my grade 2s will do next week, but I’m sure I’ll get it sorted out.

It’s important to have a focus on teaching and doing math. But the seven processes are an important part of that we can’t neglect. In a problem solving based classroom students need to be able to do more than accurately find answers.