## 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.

## 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.

## 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.

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.

## Summer Math: Maps

There’s some mapping skills in the Geometry and Spatial Sense section of our curriculum, so that’s the connection I’m writing about today. One of the Grade 1 big ideas is: “describe the relative locations of objects using positional language.”  For Grade 2 students, one of the specific expectations is: “describe the relative locations (e.g., beside, two steps to the right of ) and the movements of objects on a map (e.g.,“The path shows that he walked around the desk, down the aisle, and over to the window.”)

The girls at our church go on a camping trip every summer for a few days.  The girls have to be between the ages of 11 and 18 to go, but of course there are adult leaders.  I’m been about a million times and I love it!  We go to a place on Highway 144, north of Sudbury.  It’s in the town of Levack, and just past Onaping Falls. This year I only needed to go for one night, so I had my two children with me.  It was such a beautiful day that I decided we’d leave a bit earlier than necessary and stop at the Onaping Falls Lookout.  A.Y. Jackson painted a painting called “Spring on the Onaping River” here.

Thinking I remembered the way, we set off on a trail.  We got to here, but it was a dead end.

Back to the map we went!

Turns out we had followed the trail to the Handicap Lookout Area (it was wheelchair accessible.)  We used the triangle to orient ourselves, then re-parked the car in the “picnic and parking area” closer to the trail-head.  I wish I had a picture of the rocks we had to climb to get down into the river valley!  It was a lot of work and I didn’t have time to take photos on account of trying not to fall and break my neck – or allow my children to do the same.  At the bottom we enjoyed some time by the river.

After looking at the map, both children wanted to walk all the way to the lookout bridge, which we could easily see in the distance.  However, after this short hike, we all agreed that the bridge would need to wait for another time.  I think the trail would have been much easier after our descent, but I was already thinking about going back up the hill.

Car trips…or van trips…are a great time to practice lots of practical math skills.  For a while we played a “game” of finding numbers higher or lower than 50 on the road. The speed limit was 90Kp/h, we had to go 400 m to the next turn, there were 17 km until we got to Sudbury, etc. We then challenged ourselves to figure out how far away from 50 each number would be.  We mainly did this with the single- and double-digit numbers.  I feel like this is all part of gaining spatial sense.  By the end of the trip they were saying, “500 meters isn’t that far, right?” or “250 KM!  That will take forever!”

We’re headed off on another road trip today – this time going south. Both of my children are weirdly obsessed with taking surveys.  I’m going to challenge them to come up with some data they can gather while we are driving.

Finally, how beautiful is this:

As the end of Winter Break approaches, it’s time for me to sit down and do some planning for the coming weeks.  Reports cards are due at the end of the month and I need to get all of my assessments up to date and my comments organized.  The report card should reflect what the child is capable of at that time, not what they were doing 2 or 3 months ago. I last formally reported on everyone in November. I know there has been growth for everyone, some big and some small.

For math assessment, I am going to re-do the interview I used in September.  I know that for some children I can start in a different place because they have shown mastery in areas I previously assessed.  I will have to go beyond where I left off with them because they have shown growth toward the end of year goals. I also need to add in some geometry and data management questions so I can report accurately on that as well.  I have a lot of anecdotal notes to draw from, but I want to be really sure of what they can do now.

As I have been reflecting on this, I am struck once again with how hard it is to divide math into 5 strands.  I suppose it is easy in the Primary grades to do that with Geometry, Data Managment/Probability and Measurement.  But even at this point they are all starting to blend together. Everything we learn in Number Sense is related to everything we learn in Patterning and Algebra.  I can hardly decide how to mark everyone sometimes because I’m not always sure if the things they need to build understanding about exist in one strand of the curriculum document or another.  I have to consult it every time because in my mind it’s all mashed together into “math”. Everything we do in Number Sense is related to what we do in Measurement too, but it’s a little easier to seperate out the skills that will be reported on.  Same for Geometry and Data Management/Probablity.

Here is one example of this from the Grade 2 curriculum document (2005):

• identify and describe, through investigation, growing patterns and shrinking patterns generated by the repeated addition or subtraction of 1’s, 2’s, 5’s, 10’s, and 25’s on a number line and on a hundreds chart (e.g., the numbers 90, 80, 70, 60, 50, 40, 30, 20, 10 are
• count forward by 1’s, 2’s, 5’s, 10’s, and 25’s to 200, using number lines and hundreds charts, starting from multiples of 1, 2, 5, and 10 (e.g., count by 5’s from 15; count by 25’s from 125);
• count backwards by 1’s from 50 and any number less than 50, and count backwards by 10’s from 100 and any number less than 100, using number lines and hundreds charts (Sample problem: Count backwards from 87 on a hundreds carpet, and describe any patterns you see.);

Two of those are from the Number Sense strand and one is from P/A.  But I teach them simultaneously. And if a child is having trouble with skip counting is it because s/he isn’t understanding the patterns associated with the skip counting, or is having trouble memorizing the order, and if they seem to not be having any trouble is there some rote counting, or is the child processing the numbers and thinking about the patterns?  It’s tricky to assess sometimes. And sometimes it isn’t. For instance, if a child can say, “2, 4, 6, 8, 10” but then stops and can’t figure out what comes next, I know the first 5 terms are acutally just counted by rote. Or if a child can count by 2’s even further, but then isn’t able to do this when there are actual things to be counted, I know there has been some memorizing. And if a child gets to ten, then pauses to work it out in his head, comes up with 12, then slowly with 14, and so on, I know there is some understanding.  It’s tricky to boil all of that down to a letter grade.

Someday when I open my own school and can make my own rules, I am not going to assign letter grades to Primary kids ever. The report cards at my school will be all about the comments.  And I will definitely not divide math up to strands!  But for now, I’ll sit down and go through my assessment and the curriculum documents, then I’ll sit down with everyone in the next 2 weeks or so and ask them the questions I’m wondering about.  And then I’ll sit down and give them all a grade that reflects what they can do.  Easy, right?

## Real Geoboards vs. Virtual Geoboards

This past week we’ve been doing some geometry work in class.  The grade 2 curriculum expectations for geometry are fairly simple:  name, sort and make 2D and 3D shapes.  In general, children arrive in grade 2 already knowing most of these.  The more common the shapes are in the natural environment, the more likely this is true.  Octagon and hexagon usually give everyone a hard time with their tricky names, but by the end of grade 2 few children can’t recall these names.  In grade 3, we have to do a few more things. The vocabulary is increased (quadrilateral, angles) but again other than folding and unfolding nets of 3D solids, it’s nothing too complex.  Of course, I say that from this point of view – some kids do find it a bit tricky.  In all, however, it’s about 1 week’s worth of expectations.  I like to teach them early on because there are a lot of problem solving opportunities that can involve geometry and once we have the vocabulary learned the problem solving comes more easily.

This week I had rubber bands on hand.  That’s not actually something that happens all the time.  Since we had them, I pulled out the old geoboards.  Lack of rubber bands is actually one of the main reasons I don’t always pull them out.  The virtual geoboards, available here, here and here, are so much more reliable.  And nobody can shoot a virtual geoband across the room at somebody.

In the activity shown below, our Friday lesson, students were asked to make some shapes according to a rule.  Then their classmates had to figure out the rule.  Was the rule: shapes that have 3 sides?  Shapes with 4 corners?  Shapes I enjoy making because they create cool patterns? Here are some of our results:

A few years ago I remember reading an article about how important it is for students to have a real experience with a manipulative before they move to the virtual version.  I tried to find that this morning and couldn’t.  My brain doesn’t remember the source!  So I put it out to my virtual PLN (Professional Learning Network) on Twitter, and found a lot of teachers agreeing with my thinking. Reflecting on our week today, I was so glad that I had used the real geoboards.  There was some really interesting stuff that happened.

First, students were making shapes of different sizes over and over in different ways.  On the apps, they tend to get busy playing with other tools – like changing the colour of their geobands, or colouring the shapes in with a variety of colours.  They get focused on the wrong things and come up with rules like:  Shapes that are orange.  And I’m sorry, but orange is not a geometric attribute.

Second, I noticed that some children were struggling to stretch the bands across the pegs.  Some of the rubber bands are smaller than others, so this became a problem solving challenge.  I feel like they were motivated by the task to work through the challenge and find a new rubber band or change the perimeter of their shape.  This simply doesn’t present as a challenge to be worked through in the virtual environment. I had forgotten about this part!  Developing learning skills needs to be embedded in every part of our day, and I’m glad they got this chance to work on some problem solving skills.

Finally, there were some social things that we could work on.  Sharing is always an issue for 6 and 7-year-olds. They had to cooperate and collaborate to share the rubber bands on their table, and to decide who would get which geoboard.  I tried to make sure that every board at least matched the other boards in a group, but I didn’t always make that happen.  Again, students had to talk through this because everyone wants the one that is different, and therefore special.

Now that we have spent some time with the geoboards,  they can become one of the activities students can do during a Math Workshop session.   I can put them on a table with some task cards, or the students can request them to help solve a problem.  When we move on to perimeter and area (after we spend some time working with number lines for the next 3 weeks!) I can incorporate questions about shapes and feel confident that everyone knows the shape, and can work with the shape.  And I can add some

## Mapping

I sat down with the social studies curriculum the other day, double checking to make sure I hadn’t forgotten anything.  As I looked at all of the expectations, I realized I hadn’t done that much with mapping this year.  We did a bit, but not much.  Then I looked over the geometry things I knew I had left and realized that I really hadn’t done enough mapping.  So last week, we worked on mapping!

After talking about maps and their need to make things really clear and help people find things, I gave everyone a piece of graph paper.  They all drew a map of our school yard.  They did a pretty good job!

Then when we went on a walk for science, I asked everyone to pick up a small rock.  Back at the class, we painted them different colours.  The next day, I asked everyone to think of a place where they could hide their rock, then mark that spot with an X.   We were going outside to hide our rocks in that spot, then trade maps and see if someone could find our rock. Everyone was very excited to head outside and get started.

I hadn’t, of course, anticipated that the kindergarten would be outside at this exact time. It’s ridiculous because they go outside at the same time every day, but I was so excited about my own thing that I forgot about their thing.  Soon, as you may have guessed, there were 10 or so kindergarten completely over the moon because they’d found a gorgeous rock unexpectedly in the yard.

New plan:  The next day, I drew a map.  We were talking about symmetry, and I had shown a picture of school on Google Earth.  It’s a completely symmetrical building!  My map was an ariel view of the space just outside the fence.  We’ve walked there a million times.  During recess I ran back to a less than secret spot, and hid a bag of candy.

When the bell rang, I met everyone outside.  I had them join their May Learning Partner and share a copy of my map while they searched for the treasure.  Everyone wandered around for a about 10 minutes before someone said, “This doesn’t make sense.  The X is behind the school, not in the play yard.  It doesn’t make sense!”

“Why not?” I asked.  He just kept repeating “It doesn’t make sense.”  Finally I prompted, “Well, are you trying to say we need to leave the play yard and go behind the school?”

He gave me a blank look and then said, “Yeah.  I think we do.”  He then went about trying to see if anyone agreed with him and soon we were headed to the back yard.

“Pick a landmark,” I told them. “Someplace where you want me to stand.” They picked a spot; I reminded them that if they found the treasure they were to keep it a secret and come sit beside me.  Two people actually did that before another person was overcome with excitement and gave the hiding place away with a loud, “Here it is!!”  But they were all in the general vicinity when he did that, so I’m calling this a success.

For the past few weeks I have been experimenting with using the outdoors as the classroom.  We go out to do work we could be doing indoors, but I am also trying to do things that teach about the outdoors, and use the outdoors as a resource, not just a work space.  I feel like this activity would have been less successful inside because we would have all been a bit more stressed about the noise we generated.  (Ok, mostly that would be me.) I also feel like it would have been less successful if we hadn’t been outdoors so much lately, taking the time to notice the yard and the trees, and exploring the landmarks (natural and human made) around us. I feel like putting the math and mapping skills into this context helped everyone see meaning in the activity.  (Another example of how Cathy Fosnot is right about everything!)

Technically I have now accomplished what I wanted to accomplish.  But there are only a few weeks left until the summer break and that is when the really good stuff happens if you ask me.  I am quite sure that I could do this activity a few more times.  My map drawing skills will greatly improve!  I also think I can get some members of the class to draw the maps for other members to follow.  I have 6 grade 3s and the drawing is more for them anyway.  They will love drawing a map to help their classmates get to the ingredients for an ice cream party on the last day!

## I’m making a plan!

This is the point in the Winter Break when I have started to think about sitting down to do some lesson plans. Instead, I just spent 30 minutes on social media reading garbage, and am now writing.  My lesson plans will wait until Sunday night, right?

I have started to work on report cards this week though.  This always gets me in a reflective mode.  Mainly I am asking this:  Have I covered something from at least 4 strands of the math curriculum in a way that will allow me to write a good report card?  I still have 4 weeks to go, so if the answer to this is “no” then I have time to make up for that.  I know we have done plenty of Number Sense and Numeration, and lots of Patterning and Algebra.  I think we have done enough Geometry, if I spend another day or 5 (or 6) on that, and I am going to comment on Measurement this term too, but will need to spend a few days doing some of those activities.  We did a lot of measurement in science, but I haven’t asked them do anything lately.  I want to make sure I have done something recently that I can comment on.

That leaves Data Management.  We have done quite a few things that are part of Data Management, but I don’t feel like I have done enough to comment on this strand yet. One of the things I have been working on this year is integrating math into other parts of our day.  We did lots of measurement in science, for example.  I wanted to do more data management in science as well, but we got side tracked.  I have not taught a single measurement lesson during math though, so I feel good about that.

Number Sense and Numeration, as well as Patterning and Algebra, are the areas I have always felt I needed to spend a lot of time on during math.  As a result, I have often rushed through Measurement and Data Management/Probability.  It’s not that I don’t think these are important.  It’s just that I was prioritizing one over the other.  By thinking about how to teach these outside of my regular 60 minute math block, I think I am seeing connections that will help my students build connections and we can all use math in more meaningful contexts.  For science, we were growing plants on the window ledge. For 3 weeks, every couple of days we pulled out the rulers, measured the height of our plants, and recorded that in our journals.  That’s meaningful.  I also recorded the results of a mould growing experiment on a chart as part of our science learning.  But we haven’t taken the next step and graphed any of this, and that is why I’m feeling like I am not ready to report on this yet. I could get there by the first of February if I really wanted to, but I have other plans for this so I’m not going to rush it.

In the coming term, we are going to be learning about Movement, and Strong & Stable Structures.  February and March are really interesting months to track weather in Ontario.  These are things that will give us a context in which to use some data management and probability related math.  I’m not worried about making sure we get enough practice with these concepts.

To get ready to finish first term reports, I guess my math month long plan will look something like this:

Week 1:  Measure things, like temperature & time (January is an interesting time for this, I think.  We’ve talked about time on a clock a fair bit, but need to talk about this human way of measuring the passing of our lives.) (This will also lead us into a social studies connection since we will be learning about Canadian Communities 1780-1850 in Social Studies during the second term.)

Week 2:  Use pattern blocks to measure length, width, area, etc. Talk about why we get different answers when we use different pattern blocks to measure the same thing. (geometry connection…this will give me a chance to check in with a few kids who were having trouble naming attributes of some 2D shapes and see if they’ve met that goal.)

Week 3:  We’ll do this part during our science time: Build 3D shapes using stuff (cardboard, spaghetti & marshmallows, etc.) and start talking about strong, stable structures (science connection for 2nd term)  In math we will start our next Context For Learning math unit (“Measuring for the Art Show”).

Week 4:  By this time I need to be finished with all of my math recording, and should be able to write everyone’s math report card comment.  Should.  🙂  I really want to sit down with each child and ask them some of the questions from our first math assessment in September, but realistically I’m setting an “end of February” deadline for that.  If the Polar Vortex (is that what were are calling it this year?) continues to churn over North America, we’re likely to have some bus cancellation days. This will help me meet that goal since I’ll only have a few students each of those days, but will also hinder me in meeting that goal because I tend to have the same few students each of those days.