Data Management, Geometry, Measurement, Number Sense & Numeration, Patterning & Algebra

Another One About Reporting

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?

 

math, Measurement, Number Talks

Who is the tallest?

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

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

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

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

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

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

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

Guided Math, math, Measurement, Number Sense & Numeration, Number Strings

Use the 5’s and 10’s, PLEASE! I’m Begging You!

This week I started a new Context for Learning unit with my grade 2/3 class.  Prior to this unit, we have completed the “Collecting and Organizing” unit, which encourages the use of the 5 and 10 structure to organize and then count large groups of items.  We counted books in our classroom because that was a meaningful thing for my class.  The parent council had recently offered up money to buy more books, so I tied that all together. After that, we completed the “Double Decker Bus” unit, again using 5’s and 10’s and thinking about adding and subtracting.  Simultaneously, my grade 3’s – who were already doing well with the models and strategies taught in the bus unit – were working on “The T-Shirt Factory” unit.

Measuring for the Art show comes next on the recommended order list.  I should be starting “Grocery Stores, Stamps, and Measuring Strips” with the grade 3’s.  However, I really want to solidify this number line business, so I am not going to go forward with that unit for another week…maybe two. I am going to extend the numbers well past 100 in this unit so the grade 3’s are still challenged. Picking the numbers is my job this weekend.

So…here we are, measuring for a fictitious art show, and also thinking that we will run this year’s school art show.

I gave groups of children baskets of cubes in 2 colours and set them the task of using the blocks to measure the papers.

As you can see, there was some great measuring going on!  We even agreed on the measurements!

Despite all the work we have done with counting things in groups of 5’s and 10’s, some of my little friends really can’t stop counting by ones.  I asked myself, “WWCFD?” (What Would Cathy Fosnot Do?) I finally had a serious talk with them about it.  “WHY?????”  I screamed. But out-loud I said, “I know you guys can count by 5’s and 10’s, but you keep counting by 1’s even when we have a lot of things to count.  What’s up with that?”  They gave me the blank stare.  “Here’s what I think,”  I continued.  “I think you know how to count by 2’s, 5’s and 10’s, but you’re not sure you are getting the right answer so you always count by 1’s because you are sure that will give you the right answer. Am I right?”  There was a lot of vigorous nodding.  “What I want you to do is keep counting by 1’s.  But do it after you count by 5’s or 10’s. Do it to double check your work.  But challenge yourself to grow your brain and do it the harder way.  I know this is going to help you feel more confident!” So now we are doing that, except a lot of them quickly realized they were getting the right answers the first time, and it was a lot more efficient to skip count.

After 2 days of this, including a congress when we had the above conversation, I asked them to help me make a number line, organizing the cubes into groups of 5.  Believe it or not, there was magic!  As soon as I had a long string of cubes up on the board, out of everyone’s reach, 15 out of 18 immediately saw the value of using the 5s and 10s.  We worked on related Number Strings for 2 days, and then I asked them to make a number line like I had been making using their own cubes and a piece of adding machine tape.

The group pictured on the left kept counting  by 5s, but when they got to the mis-matched groups of 5, they realized that maybe I am a genius after-all and they should have listened when I said, “Make all 5 the same colour!”

So everyone make beautiful number lines, with mostly iterated units.  We put the cubes away and I didn’t get them back out. When I asked them, the following day, to figure out where numbers like 13, 23, and 33, should go, they did a great job of reasoning their way through the problem.  I can look at these and see some immediate needs I need to address on Monday or Tuesday.  But I feel like we are on our way!

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In a VoicEd.ca radio broadcast (You can listen here!) , Cathy Fosnot said she hoped that teachers who were listening would stay curious and keep wondering about the things their students are doing.   For me this is some of her most valuable advice.  Being curious about why my students are doing something, especially if it is something that makes no sense to me, has paid off so many times.

So…there you go, Cathy Fosnot.  You were right again.

math, Measurement

Slice of (Cooking) Life

I couldn’t help myself.  I mean, it IS cooking, and people can’t cook without doing math.  So even though I had signed up to lead a cooking elective group, and even though the 14 children who signed up to be in the group were expecting cooking, we were actually mathematizing as much as we were cooking.

There was all the standard math you are expecting, like measuring and running the timer.  But at one point in the lesson, after the first batch of cookies had come out of the oven, it came time to see if we were going to have enough.  Plans were being made to take some home, of course.  “Wait,”  I said. “If you want 2 cookies each to make your ice cream sandwich, we have to make sure we have enough for that before you start making plans to take some home.  So..do we have enough for that?”  And I walked away.  Everyone, grade 1-6, started counting each other and counting cookies. A few kids jumped up and ran over to the oven to see how many cookies were in the oven.  A few others were checking the bowls to see if we had enough dough for  more cookies.

“Well,” I asked again, “do we have enough cookies so that everyone can make an ice cream sandwich?”  They agreed we did, and several spoke over the top of each other because they were so excited to justify their answers.  These aren’t my regular students, so I have no idea what sort of work they usually do.  However, their explanations were great!  And I loved that some were counting by 1s and some by 2s and some counted all of the m by 1s or 2s but then said, “We have 14 here, and 13 in the oven, so we need 1 more cookie from the next batch before we have enough for each of us to make a sandwich.”

Next week we’re making pizza.  I don’t really intend to turn this into a math club, but we’re probably going to have lots of chances to talk about fractions. Hearing all of the awesome mathematizing was almost as great as my oatmeal cookie + homemade ice cream sandwich!  Almost.

slice-of-life_individual
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.

 

Geometry, math, Measurement, Number Sense & Numeration

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.