math, Number Sense & Numeration

I can’t sum up this week in a title

Classes reorganized this past week.  I had a new class list on Monday, and about 1/2 of  my class is new since the first day of school. The dynamic shifted.  Though it wasn’t exactly like starting over, it was enough like starting over that I didn’t feel like I could move forward as quickly as I wanted to.  I decided, therefore, to do activities that would sort of take us back in time to the first week while also moving us forward.

These are three of my first 2 weeks goals that I needed to accomplish in just this past week – the 3rd week:  really work on how to use the manipulatives without driving our teacher bonkers, work on what to do during Number Talk/Number Sting time, and practice working respectfully with a partner.  The friends who stayed with me had already practiced this for 2 weeks so I couldn’t simply start over.  And they didn’t need me to anyway. The friends who moved in had already practiced some of this with their “first 2 weeks” teacher, but we needed to do it the Room 16 way.  I realize that makes it sound like I have some control issues, but I assure you I do not.  Really.  I don’t. Please believe me!

So…here’s what we did.

Guess my Number:  This is an activity from the Effective Guide to Instruction in Mathematics.  I displayed a hundred chart on the projector (This one, from Mathies.)  I had a number on a post-it note in my hand.  They had 20 guesses or questions to figure out my number.  At first, they were guessing one number at a time, but then one of them asked (I think it was accidentally, but I’m not sure) if it was one of the 10’s.  I turned over an entire column and a new strategy was born!  To make it a bit more fun, I was keeping score.  If they could get my number in 20 guesses or less they got a point and if not, I got a point.  By the second day we realized I had no chance of getting a point so we reduced the number of questions to 10, and they improved their strategy at the same time.  By week’s end the score was 6 to 2.  But their questioning strategy had improved so much that I’m not sure I’ll ever get another point. They are starting off every time with “Is it higher than 50?”  They can turn over half the board this way!  It’s a great first question.  Next, they start asking, “Is it in the 30’s?” or 20’s or 80’s or whatever they need to get a whole row turned over at once.  We had to talk about the word “teens” and “single digits”.  And we talked about being a gracious loser.  Or rather, I modelled being a gracious loser.  And they practiced not rubbing it in when they won.  Sort of.  And we practiced not shouting out but raising our thumb to indicate, “I want a turn.” We also talked about tally marks. I kept score with tally marks, which I discussed on the 3rd day, and a student used tally marks to keep track of how many questions had been asked.

Find it on the 100 chart: I gave them hundred charts, in groups of two.  I gave them containers full of counters.  I called out clues, from “Find it on the 100 chart”  by Marcie Cook which I have owned for approximately 100 years.  I called out clues, they had to cover the number I clued and in the end the manipulatives would have built a picture.  They had to cooperate with their partner and share turns.  They had to clean everything up, even off the floor, when we finished, and put it all away.

Counting Necklaces:  You’d think they’d be getting tired of this by now.  But they are not.  Not even close.  I’ve written about it before here, so I’m just going to say that we ended our math class with this all week and by the end of the week nobody was getting too upset about not getting a necklace because they realized there would be more turns on another day. Once again we had many opportunities to talk about what patterns we were seeing, and what happens to the pattern if someone leaves the circle to use the washroom or if someone moves to another spot.

Usually by this time on a Saturday morning I have a goal for the following week. In fact, I always start writing my lesson plans by writing my math plans for the week.  I’m not ready today.  We accomplished some good goals for the week, but we needed more repetition to get there.  That means I am not where I wanted to be on my curriculum map.  I’m generally okay with that, but I also think there might be a way to still get there by next Friday as planned.  I’m following the TIPS spiralled math document and even though I know I need to be flexible with the timing, I also want to try to trust the timing.  We’ll come back to all of our content again. I don’t need to teach to mastery the first time for every skill.  I think I’ll move forward with our 100/200 chart puzzles.  I think we’ll move forward with the estimation and counting jars/bags.  I think it’s a 4 day week with no other interruptions so we should be able to do that.  Maybe I am more ready to write my plan than I thought.

 

Data Management, math, Number Talks

Sorting and organizing

I am using the spiralling document found on EduGains to work through my math program this year. The first week is meant to be devoted to sorting and organizing skills from the Data Management strand of our math curriculum. I decided to get started on Monday even though we were, ironically, waiting for information about re-organizing classes because of our enrolment numbers.  Because I will be coming back to sorting and organizing many times, I didn’t worry about doing this without a few students who will be joining our class on Monday.

I started with some “Guess My Rule” slides I made on PowerPoint. I had enough to do 3-4 each day this week.  As we discussed them, everyone tried to “guess my rule” and we discovered that there could be 5 or 6 different guesses and all could be correct.  What mattered here was the ability to justify one’s “guess” about my rule. This is a really important skill that everyone needs early on!

Next, out came our math tools.  Everyone worked on sorting the tool of their choice.  I haven’t started with a “guess my rule” game before and I was pleasantly surprised to find that my students did not focus on sorting by colour.  This is often a problem.  I have to spend a lot of time getting them to think about other attributes.  I feel like the “guess my rule” activity set them up for success because they were already trying to be very clever and “trick” their friends.  Nobody is tricked by colour, so we (most of us) tried to think more deeply about our tools.  Those who needed prompting quickly moved on past colours. The work we did last week on how to use the math tools properly also paid off!

Some of the tools I chose for them to use included the necklaces, coloured glass marbles from the dollar store, attribute blocks, and base ten blocks.

The necklaces were sorted by colour, but also by bead type.

Attribute blocks were sorted by colour, shape and thickness.

These glass beads are the best money I’ve ever spent at the dollar store.  They are very versatile: bingo chips, counters, sorting tool, and some kids just love playing with them for no reason at all!  They can only be sorted by colour…or so I thought!  Turns out they are not all exactly the same size.  The  new ones I bought this summer, 10 years newer than most of the others, are slightly larger and a slightly different shade of blue and green.  I’ve lost a whole bag worth of red over time.  They are very popular!

We did this sorting activity for 2 days because we had some other interruptions that shortened our math class.  On the third day, I asked them to use any material in the room to create their own “Guess My Rule” page.  Here are a few.  Can you guess the rule?  Once again, there were many possibilities guessed, so I know students were looking at many attributes of the materials they chose.

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Bright colours vs. dark colours

 

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None of us got this one! “I will not buy containers without matching lids!”
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Some guesses: flexible and not flexible, longer than a metre & shorter than a metre, colourful & wooden, inches and centimetres & only centimetres.

This activity was a lot of fun.  We had a field trip on Thursday, so we were doing math in the real world instead of in the classroom.  On Friday, the students had all been re-sorted into the class they will have for the rest of the year.  I elected not to do the math I had planned because I want to do it with my “new” class (about 1/3 are new to me since the first day.) So here I am, going into the 4th week of school and already “behind” where I thought I’d be.  Typical!  But I am not worried because I will come back to those activities later when sorting comes up again.

Next week:  Counting! This is where I would typically start.  I’m glad I started somewhere else because I have seen everyone as mathematicians aside from their ability to count. I need to start my math interviews as well, so some of the centres I had created for organizing will work as activities  to keep people productively engaged while I am doing individual assessments.

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.

 

math, Math Workshop

Ready (or not!)

School starts tomorrow. My classroom is ready. My house and family are ready. I’m ready. Mostly.

One of the big jobs that needed to be done was writing up some lesson plans. Some teachers are very relaxed about this in the first two weeks, but I like to hit the ground running! I like to establish the work routines early, and I don’t want to waste any of our time. I won’t dive into any serious units right away, but there are some other important things that can’t wait.

I don’t usually plan two weeks in advance. I have units planned out, or picked out, but I like to let the kids establish the pace. During the first two weeks, however, I do have a pretty good idea of how long things are going to take.

The structure of my math instructional block will go like this: read aloud, lesson, activity, congress, counting routine. I have 60 minutes, so my plan is for everything to last about 10 minutes, with the activity lasting 20.

I have two goals during the first 2 weeks.  First, I want to set up the routines for doing our math.  I want everyone to know that we don’t shout out answers, we disagree politely, we try and try again, we don’t throw math manipulatives (at each other, or otherwise).  My second goal is to make sure I can start my math interviews.  I need to spend a few minutes with each child and ask them some questions one-on-one.  This is going to take longer than 2 weeks.  My grade 3s, the ones who are with me for a second year, have already completed this in June (hmmmm….didn’t come across those in my unpacking!) so I can start with the grade 3 interview, a bit later. I know them as mathematicians already, so I know where to start their instruction.  My priority will be to get to know the grade 2s and anyone new to me.

I am switching to an electronic day book this year.  I have made my own using OneNote.  I have been committed to paper, but my binder is such a mess early on, and I get tired of dragging it home every weekend. I also find I have more times when I am using  electronic resources, so I want to simply link those in my plans instead of having them several places. I have decided I will do the e-daybook for at least September and October and I can always print a paper book if I need one. The only thing I haven’t quite figured out is my Number Talk/Number Stings.  I like to write them on Post-it notes (one per day) and stick those in the day book.  I think right now that I am going to still do this, but then stick the Post-it note somewhere else…not sure where.  If I can keep my desk clean I can put them there.  We’ll see!  LOL

Here is my plan: (Sorry I couldn’t figure out how to make it look nicer!)

  Monday  Tuesday  Wednesday  Thursday  Friday 
Week 1:  

Sept 3-6 

Labour Day  Story:  Which One Doesn’t Belong 

 Lesson:  Routines for using math manipulatives – go over where to find the math tools, and how to use them in a respectful way. (Share, Don’t take – ask!, Take only what you need,  pass them politely, clean up) 

 

Activity:   

Put a bucket of manipulatives on each table and give kids time to play with them.  

 

Counting Routine:  

1-10 with necklaces 

 

Story: Niel’s Numberless World 

Lesson:  Review “How to use the math tools” And allow 15-20 minutes of play time with the tools. 

 

Activity:  

 

Counting Routine:  

 

1-10 with necklaces 

Story: Spaghetti and Meatballs for All 

 Lesson:   

Working with a partner – Anchor Chart -> “A Good Math Partner… 

Listens, waits, lets others have a turn, etc…kids make the poster.  

 

Activity:  

Super Source – Closest to the Finish Line.  Students need adding machine tape in random lengths.  They try to lay pattern blocks or other tools end to end to see who can get closest to the end. They will work with a partner to do this.   

 

Counting Routine: 

1-20 

 

 

 

Story: Everyone Can Learn Math 

 Lesson:   

Clear Communication with your partner – say “I think…” “I don’t understand…” “I want to…” “Please don’t help me…”   

Grade 1 – just scoop and sort…maybe with a different tool? 

Activity:  

Super Source:  Scoop and Sort – scoop out a handful of pattern blocks and sort them.  Grade 2, 3 – how will you record your data?  Work with a partner for this. 

 

 

Counting Routine: 

 

1-20 

 

Week 2: 

Sept 9-13 

Story: City by the Numbers 

 

Lesson:   

Number Talks Routines – 10 Frame Dot talks all week!  (On Smart Notebook…if I have grade 1s I need to make some 5 frame slides 

Start “I have an answer”…thumbs up routine 

 Activity:  

Classroom Calendar Bulletin Board.  Put the numbers 1-30 in order on a human number line/clothesline math. 

 

https://catchingreaders.com/2018/09/09/the-linear-calendar-wall/ 

 Counting Routine: 

 

Story: The Math Curse 

 Lesson:   

Number Talks – 

Thumbs up routine 

 Activity:  

Students will measure the calendar pages to create month labels.  They will write the name of the month on the label.  We will add these to our bulletin board. 

 

Counting Routine: 

 

 

 

Story: Estimation book 

 Lesson:   

Number Talks –  

Adding on to what someone said, or agreeing with another person 

 

Activity:  

Students will measure the other bulletin boards and create borders for them using adding machine tape.  

 

Counting Routine: 

 

 

 

Story: Amanda Beans Amazing Dream 

 Lesson:   Number Talks –  

Disagreeing with someone 

 

Activity:  

Students will decorate the borders they made on Wednesday 

 

Counting Routine: 

 

 

 

Story: I see a pattern 

 Lesson:   

Number Talks –  

Consolidate the routines 

 

 

Activity:  

If borders are done, then: Measure how far your frog can jump. 

 

Counting Routine: 

 

 

 

 

math, Math Workshop, Number Sense & Numeration

Counting

I never used to worry too much about teaching students to count. I mean, the year I taught kindergarten we did a lot of counting, but in grade 2…or 3…or 4? Nope.

In the last few years I’ve become aware of how important counting is, and the layers of skills that are involved.

After interviewing my people, I discovered most can start at 30 and get to 100 without difficulty. Some had trouble not starting at 1 – and they also had trouble assembling a 100 chart. This is not, I think, a coincidence.

One of the classes figured out we need 12,000 laps around our track to equal Terry Fox’s journey across Canada.  We’re keeping track of our contributions with tally marks!

Some students were very organized with their counting…

And some students were not organized with their counting.

After we congressed these photos, I sent everyone off the do more counting. I asked them to count out 17, or 24, or 52, or 65 of the math tool they wanted to work with. Everyone tried an organization strategy of some sort! Even when they sorted into rows or groups of 5, many were counting by tens.

I loved this one because this child said, “10, 11, 12, 13, 14, 15, 16, 17!” It was great to see her counting on!

I think when we look at these images and congress them today, I need to make sure I talk about how the organizing helped. One of the things I know I need to do better is point out these things that seem so obvious to me.  Some students will have already realized the advantage of using groups, but some will not have.  I need to help them with that.

I used to always start the year with addition. This made more sense I guess when I was teaching grade 3/4 classes. But starting with counting and making sure everyone has a strong foundation of number sense to build on has truly made my addition and subtraction units go more quickly. Everyone seems more prepared for the addition and subtraction work once I know they are solid with counting skills.

math

More on Assessment

I’m nearly finished with my math interviews (minus the two who were absent today, of course!) One interview really sticks out because It wasn’t a good interview and I finished it off thinking, “WOW!  There are basically no skills here.”  Now, this isn’t the first time that has happened to me, and I know what to do about it. It’s just that this child had come to me with comments from last year’s teacher that lead me to expect some skills.  So…I went to her for some clarification.  She had saved the interview they did together last year in June.

So instead of a score from a test, or a report card mark and comment, I got to see exactly how he had answered the questions she had asked.  In our board, there is a set of interview questions that most people use, and she had used those.  I use different ones, but have been choosing 3 or 4 of my students as “marker” students, and I do this longer interview with them so I can have the same data as my colleagues for some discussions in the building.  I was so grateful that my colleague still had the exact interview sheet lying around, and wondered why I hadn’t thought to keep more of them.  Likely because I have decided not to be a hoarder in my classroom, which is an important goal, but at times like this I question my reliability as a goal setter.

This weekend, one of my school jobs is to go through my interviews and sort the data.  The board math people (I can’t ever remember all the job titles) have provided us with a tracking sheet.  I haven’t spent any time really looking at it, but I’ll probably give it a go so I can use it to participate in math conversations in our building. I also need to plot everyone on the Landscape of Learning.  Even though I feel pretty confident about my decision to start with the “Collecting and Organizing” Context for Learning unit, I have this niggling suspicion that I will maybe have to run two units at once because a few of my friends are in a very different place than the rest of us. That’s the beauty of the Landscape!  I will know who needs to start here, and who needs to start there. It’s a counting unit though, so I think it will be the only one for now.

I know that people love Teachers Pay Teachers units.  They are super easy to print and photocopy. And I know it’s much easier to mark 10-20 questions on a math test or quiz than it is to conduct individual interviews and then plot each individual on the Landscape.  But when I am considering taking some assessment shortcuts, I can’t stop thinking about a girl I taught a few years ago.

In grade 4, I gave everyone a quick multiplication sheet so they could do some practicing.  She got every single question right! But along with the quiz, she had also been working on a separate sheet of paper.  I knew she was drawing pictures to solve some problems.  But when I sat down to look at everyone’s work, I realized she had drawn a picture for every single question.  For 8×7 she drew a picture, which is fine because 8×7 can be tricky.  But for 2×2 she  also drew a picture. And for 1x 6 and for 3×3, and on and on. Her score said “Level 4”, her drawings said “Level 2…maybe actually 1”.   And back to my friend from this morning – I would have had to consider that child a “beginning” mathematician at best, but thanks to information that came out in interviews with his previous teacher, I know him to be much more.

In conclusion, I’m busy too, but I make time for this even though “all the other kids” get a bit loud playing their games, and they spent more time on Dreambox this week than they’ll spend in a single week for the rest of the year. It’s time well spent.