Measurement

Time…

This week we had to pivot to online learning. There are a few topics I have figured out that are really good for online learning. One of those topics is telling time. The curriculum expectations for time are:

Grade 2 is in yellow and grade 3 is in blue.

I think this is a good topic for at-home learning because there are some very active things we can do instead of staring at the computer all day. It’s also easy to find meaningful worksheets that those who are not meeting with us online can finish at home with their parents.

Telling time, however, is a topic that I often wonder about. Is it really useful to today’s children? When I asked them to tell me the time, every kid could do it. They looked at their computer screen and that was that. The digital clock is right there.

The grade 2 expectations make a lot of sense to me. Kids do need to develop a sense of the time it takes to do something. I had them talk about some things that might take an hour, or a minute, or a second, or longer to complete. We timed ourselves to see how long it would take to touch the front door, the back door. We talked about relative time when I asked them to touch a bedroom pillow. That wasn’t long for some who are working in their bedrooms but it was longer for those working at the kitchen table.

The grade 2 expectations are a little more challenging. Digital clocks are no problem at all, although some aren’t quite sure how to say the time when they see it. 9:00 is “nine o’clock” but some want to call it “nine zero zero”. It’s easy to clarify that for them. 9:15 could be nine fifteen, or quarter after nine, or fifteen after nine. Again, it doesn’t take long to get everyone to start saying this the right way, and we will have many practical opportunities to practice at home and at school. The analog clock is quite a bit more challenging, but after a few days all those who are working online with me are doing okay.

It does have me wondering if being able to read an analog clock is a skill that will become obsolete in the not-to distant future. I wear a watch, but it is digital and it’s really there tracking my movement through the day. If I need to know the time I always have my phone with me. Will there every come a time when analog clocks disappear?

Coding, math, Measurement

It’s sinking in

I had intended to spend the whole week measuring. But guess what? They’re really pretty good at it! It’s the second time this year we’ve visited measuring and I’m pleased to see the spiralling is paying off. I had an activity planned that involved us measuring which of my many mini cars could go furthest after one push, but decided that is better suited to a science investigation we’ll do later. I

t was pre-Halloween week and I wasn’t sure we could handle that much excitement.

Instead we worked on an unplugged coding activity. (Find it here) It went so well! I’m feeling hopeful that we have rounded a corner. I finished gathering all the math assessment data so I feel better able to meet the range of needs (because I know what the needs are!) This week we’re tackling addition. I’ve done a few addition number talks but this will be our first real jump into the fire. Then in two weeks we’ll circle back to coding.

math, Measurement, Number Talks, Social Emotional Learning

Week 1: Done

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

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

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

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

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

math, Measurement

Detour to Measuring

This week we took a slight detour on to some measuring.  We spent the week talking about making sure the measuring tool goes from end to end when measuring length.  We talked about the difference between length and width.  We talked about why we need to use standardized measurement tools.  (Most of my class are in grade 3, and that is the year students move from non-standard to standard measurements.)

One of the activities we did comes from the Effective Guide to Instruction (Page 99 of this document).  Last week I wrote about how I wanted my students to make more intentional decisions about which tools they choose for their math.  The day before we measured the paper snakes, we had measured our shoes. As always, the two most popular tools were the connecting cubes and the “special stones”.  Before starting with the snakes, we had a talk about why they like these, and which one is actually better for measuring.  I was excited at the end when most of them were talking about using the connecting cubes because you can take them apart and put them back together in different shapes.  One student told us they can be used to go around the perimeter of things.  Several of them talked about how the special stones, the colour tiles and the pattern blocks slip and move around, but the connecting cubes stay put which makes them easier.

On to the activity:

 

Two children also tried to use rulers and measuring tape.  Discussing their experience was a great way to wrap up the lesson because even though these are specifically measuring tools they weren’t the best tools for this job.

We had a really good conversation about which method was actually going to give us the real length of the snakes.  Everyone agreed by the end that we have to measure every part of the snake’s length, and many of them wanted them put the cubes into connected towers.  I was sorry that none of them thought to do groups of 5 to help make the counting more efficient.  That’s something we clearly need to work more on. We recorded everything on a chart and that’s where we started on Friday.  We talked about why everyone had different answers, and why it was important to have the same answers which we get when we agree on the units.  I told them about the king’s foot and how this wasn’t even that standard, and that even though a lot of grown-ups still talk about inches for certain measurements, we are going to focus on the metric system and I think they’ll agree that it’s a lot more efficient.  I had them wander around finding things that were the same size as a 1cm cube.  Then we used the rulers and the measuring tapes to find things that are 10 cm.

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“Jack” refers to the word Jack on our poem of the week which is called “Jack-O-Lantern”.  The hand washing sign is a rectangle, so we had a good conversation about length and width and how rectangles have a different length than width.  And I have no idea why there is a mandarin orange on the board marker tray.  #PrimaryLife

I think it’s so important for them to have these many points of reference.  It helps them to estimate measurements.  They all now know that their fingernail is about 1cm and they will always have that fingernail to help them measure.  We even talked about how for me it’s only my pinkie finger because I have grown over time.

Next week it’s on to addition and subtraction.  But we’ll be coming back to measuring on a regular basis. This is actually the second week we’ve spent measuring this year, so now I feel confident that everyone has a pretty good idea of how to do it, and we can focus on practicing.  We are also going to do a fair bit of our measuring during art and science, especially when we move on to capacity and weight.

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.

 

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.