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?

 

Data Management

Which is your favourite?

Halloween is a great time to gather some data and manage it. There’s so much candy to sort!

In my ongoing effort to do things like surveys and graphs in a regular basis instead of as a separate unit, I planned to ask everyone about candy today. I already knew that everyone could come up with a “What is your favourite _____?” Or “Which _____ do you like best?” question. I decided to change the question. Instead, I told the class that I think all candy falls into 5 categories: chocolate, gummies, hard candy (lollipops and Jolly Ranchers), gum and liquorice. Nobody fought me on this. I’m just realizing now we could have had quite the debate about this. Where, for example, would Laffy Taffy and Starburst fit? And what about Reese’s Pieces? But nobody thought of those until just now!

Because I was asking which candy they liked, they could answer more than once. Only voting once is always tricky for kids with a question like this because they like so many things. And, I explained, I actually don’t like liquorice but am willing to accept that some people might.

Here are our results, tallied and then graphed:

We counted the chocolate tallies. As I tallied the gummy votes, someone pointed out that gummy and chocolate were the same. We talked about how we could tell without counting, which was actually a revelation to several students. However, they noticed it on their own for hard candy and gum. I’m glad we could talk about this one-to-one correspondence because it will come up again when we start talking about multiplication.

Since we have 22 students, and only one was away, we had to figure out who didn’t like some of the candies. We talked about how many people were not voting for each candy categories. Finally, we talked about how just because I don’t like liquorice doesn’t mean I shouldn’t buy it for them. (Nice of me, right?)

I’m going to add this to our math walk tomorrow. I want it up to remind everyone about organized data, and how it’s so much easier to follow along with than the other kind (haphazard tallied scattered abroad.). By the end of the month I want everyone to be able to come up with a good question and gather data. We’ll mostly be doing this during social studies as we begin our study of world communities.

Data Management, math, Number Sense & Numeration, Patterning & Algebra

Which Way Do I Go?

The beginning of the year is hard for me in math. There are so many things that need to be done!  This is especially true for those of us who are teaching split grade classes.  Some things are the same: number sense, for example.  I can figure out where everyone is and take them to where they need to be.  But my grade 2s are supposed to learn about some things that the grade 3s are supposed to already know (which sometimes they do and sometimes they don’t) and the grade 3s are supposed to do things that the grade 2s are not (which sometimes they are ready for and sometimes they are not!)  And I know I can still do the things, and it won’t hurt anyone to learn about something a year early, but it all takes time. And even though it’s only the 29th of October, I feel like time is slipping away and I need to GET ON IT!

So this week, I was feeling like it was time to move on from adding the tens and the ones.  I gathered the balances so we could talk about balancing equations.  I started planning in my mind where we’d go next.  But by Friday, I realized that I might be moving on a bit to fast.

Remember when I wrote about how we were having trouble communicating our math thinking? Well, that hasn’t gone away yet.  Now that we are adding, and even subtracting those double-digit numbers, I thought, wouldn’t it make sense to stop there and do some problem solving?  Wouldn’t it make sense, I asked myself, to take this thing we are pretty good at doing and use it to practice the communication piece?

So this is what we are doing.

  1. Trip over the balances that are shoved out of sight behind my desk. It was a pain to get them into the room so I’m just going to live with them for a while.
  2. Monday’s problem:  (Two versions because I am differentiating!)There are 14 red apples, 15 green apples, and 8 yellow apples.  Can each child in the class have one apple? 

     There are 4 red apples, 5 green apples, and 8 yellow apples.  Can each child in the class have one apple?

     

  3. Tuesday’s Problem: I bought some Halloween candy this weekend!  I have 15 suckers, 23 Smarties, and 30 Kit Kat.  Do I have enough for every child in our class to have 3 pieces of candy?   

    I bought some Halloween candy this weekend!  I have 10 suckers, 12 Smarties, and 4 Kit Kat.  Do I have enough for every child in our class to have 1 piece of candy? (The Smarties are stressing me right now because I mean 23 of those little boxes of Smarties, but there are 10 actual Smarties in each.  There’s a unitizing thing in there.  I think I’ll just have to verbally clarify with the class before moving on.  I’d just take out the Smarties all together, but I’m sort of feeling committed to them now because it’s going to give us something good to talk about.)

  4. Wednesday: Give in to the evil of Hallowe’en and graph some candy.  (I try to do random survey’s and graphing instead of a data management unit.  I’m going call it spiralling, like all the cool #iteachmath teachers.)  Then they’ll work on these alone, not with their Learning Partners:Make a list of 10 ways you can add two numbers and get the answer 37 every time. 

    Make a list of 5 ways you can add two numbers and get 10 every time. 

  5.  Thursday and Friday: Depends on how the other days are going.  I really want to make sure that I am not rushing through.  I want to take the time to congress the solutions properly, and to talk about what makes a good visual representation of the groups thinking.  We are starting up with November Learning Partners (a few days early because we were all just DONE with the October groupings!) I have a fun nrichmaths activity that we will do if things are going well.  And I have some 100 chart puzzles we can do, which will help reinforce the work we’ve been doing about noticing patterns in the 10’s and ones that help us take leaps of 10 and 1.  We are on to Measuring for the Art show next, and this is an important understanding for that unit.
  6. Then it’s Monday again, and we can balance some equations.  Probably.  Most likely. “It is highly likely that the class will work on balancing equations next week.” to put it in data management and probability  language.  And then we should move on to some geometry because that is something I have a hard time integrating on it’s own at this particular grade level.

Even though I am feeling compelled to get moving, what I really want to do is make sure everyone understands what we are doing now.  These adding and subtracting and patterning and data management skills are so important and there’s no sense in moving on until everyone is ready, not just me.

 

Data Management, math

Birthday Graph

Can you imagine not remembering when your birthday is?  The struggle is real for many 7 and 8 year olds I know.  Combine that with the fact that I have set a goal of visiting and resisting graphing often this year  (my goal now is once a month) and you’ve got a good first week of school activity.

Today we went outside for math, and we created a graph of our birthdays using a jump rope and some paper.  Here is some of our work, with student names cleverly disguised of course.

We used the rope to form the x and y axis. It allowed us to do some revision so everything would fit.

I did have to look up the birthdays of a few friends.  But tomorrow we are going transfer this giant graph to a small corner of a bulletin board and then I’ll never have to look them up again!  (ha)

The thing that amazed me most was that as soon as the graph started to take shape, I started to hear students comment on  what they were seeing.  “July is the most popular month to be born in our class.” and “I was born in the same month as Mrs. Corbett!” It was a lot of fun, gave me some insight into how much they know about graphing, an also showed me some learning skills we need to look at.

Data Management, math, Math Workshop, Number Sense & Numeration

Candy Math

If one buys a bag of Sour Patch Kids, will there be an equal distribution of the good colours and the gross colours?  Because if I could buy a bag of just red and avoid the gastly green, and blue, I’d be happy about that!  The children in my class disagreed and hoped that there would be an abundance of blue.  But we all agreed that it should be equal.  Time to test it out!

I put a bag of Sour Patch kids on every table, and told the students they could pick their own groups.  This doesn’t happen often for us, but I wanted to see if they would distribute themselves evenly. One group of 3 got a whole bag to themselves because nobody else wanted to work with them. That left one big group of 6 to share a bag.  I think the kids in that group will think twice before they settle on a group next time (cause you know there will be a next time!)

I was very interested in the strategies students would use.  I had predicted that there would be some organizing into groups by colour, and I was right for all but one table.  It took them a few minutes of debate before they all agreed to do this.  At first, each was starting his/her own groups, stealing from the others to try and create one pile for each colour, except they were all trying to create the pile right in front of themselves.  They had 4 red piles, 4 blue, etc. Finally they realized, with a tiny bit of prompting, that one pile for each colour would suffice.

Since September, we have been talking about how organizing into groups of 5 makes counting a lot easier.  But…still…lots of kids were counting by 1’s.  *sigh*

Over time, however, they switched to grouping, usually by 2’s, but at least it was grouping.  One group, the group I would least expect to struggle with this, organized each colour by a different number.  Then they couldn’t figure out how to make that into a graph.  We had a very interesting conversation about this, so I’m counting it as a win.

 

img_3170.jpg

The graphing was fun to watch too.  We’d talked about how we don’t always have to count by ones on a graph, but we clearly have some growth to do in this  understanding.  Though I’d given them a task that required more than the number of rows I had given them on the graph template, they still thought they could just fudge it.

img_3180.jpg

Let me interpret this for you:  this group had 21 Red, 17 Green, 15 Orange, 13 yellow, 22 Blue, and 1 split (I have no idea why, but one child was obsessed with the possibility that 2 colours might have melted together and therefore 1 SP kid fell in to 2 categories AT THE SAME TIME! This did not actually happen, but this student really wanted me to believe it was not only a possibility, but an inevitability!)    I have just one picture of this to share, but it happened all over the place.  I eventually pulled them together and reminded them about choosing a scale.  The grade 3’s got it after that, but the grade 2’s not so much.  It’s not one of their expectations anyway, so I’m not worrying about it. They could read the graphs the grade 3’s created, so we’re good!

This week, assuming the one day I have to do some actual teaching actually doesn’t get interrupted by the unexpected, we are going to find out if we get more caramel popcorn or more cheese popcorn in a bag of Chicago Mix.  We are going to compare the store brand to the Orville Redenbacher brand and see if one is more even than the other.  We are also going to compare the Humpty Dumpty brand “party mix” and the Doritos brand “party mix” to see if I am truly being ripped of, as I suspect, and getting more than half a bag of pretzels.  I firmly believe there should be a “No Pretzels!” option here, just like there is a “No peanuts!” option for a can of mixed nuts.  Am I alone in this?

I used to do food math all the time.  Froot Loops, Smarties, M & Ms – they all make great math manipulative.  But for several years I have had students with food allergies and bring any sort of food into class was so stressful for me that I avoided it at all costs.  This year I have very little of that to contend with, so I’ve been going for it.

Oh…almost forgot!  One group got two half Sour Patch Kids.  They weren’t sure what to do about it.  We had a great conversation about the 2 halves making a whole.  They were reluctant to believe me, which just shows that I didn’t do quite enough with fractions this year.  I’ll have to rectify that next year.

 

Data Management, math

Slice of (Math) Life

Way back in September, I had read about this neat activity from Marilyn Burns called “The Door Project“and had decided to use it to start my school year.  On day one I always like to take the students for a walk around the building.  If anyone is new, or even if they are just coming to my end of the school for the first time, I want to make sure they have a chance to orient themselves, find the washroom and drinking fountain – that sort of thing. On the first day of school, I combined that with some math.  It was our first provocation, if you will.

When we got back to class, I asked, “Did you notice how many different types of doors we have in our school?”  We took a look around the class, and started thinking of ways to sort the doors in our school. Some have windows, some don’t. Some are metal, and some are wood.  Some go to the outside, and some into closets.  I gave everyone paper, asked them to think of 2 or 3 categories to compare, and away we went.  (I’ve condensed it here – we actually spent a whole class period on this!)

It was a disaster. I just looked back to link you to my post, and found I didn’t write about it at all!  That’s how bad it was.  As I recall, we were having a lot of trouble managing our data.  The categories were all mixed up, the tallies were not organized, and nobody could do anything with the information we collected. I had intended to graph our data, but, alas, it was not meant to be.

Today we tried again.

I reminded everyone about this activity, and some sort of remembered it.  We quickly reviewed our door types.  I gave everyone a choice of paper – plain, lined, or graph.  They grabbed clipboards and pencils, and lined up like pros!

We made it all the way around the school, gathering all of our data, in very little time.  Nobody had to shut their door when we stopped to count!  When we got back to class, everyone was able to count their tally marks by 5’s and find their totals in record time!

I reminded them how far we had come.  I reminded them that in September this activity had been really hard, but now it was barely a challenge.  Everyone collected the information independently, found their totals, and is now ready (and able!) to graph it tomorrow.  Now I am sorry I didn’t keep our first disastrous attempt so they could see how far they’ve come! (Who am I kidding…I probably do have it and will find it on the last day of school when I am finishing my clean up!)

What a difference a year makes!

slice-of-life_individual
Just about every Tuesday I blog for the Slice of Life challenge over at Two Writing Teachers. You can read posts from others on that blog.