math, Math Workshop, Number Sense & Numeration, Number Strings

Subtraction

What does “-” mean in math? As in 5-2=

We had an excellent conversation about this during a Number String this week. I went off script after discovering that some of my friends didn’t know how (as in “no idea” how) to subtract 23 T-Shirts from their inventory in our math lesson.

This is what we decided:

The next day we talked more about “take away” using the math rack. Then we talked about how we can count back on a number line. Then we talked about how we can actually count up on a number line in order to find the space, or difference, between 2 numbers. One friend was very keen to keep explaining how adding and subtracting are opposites, and during one explanation solidified his own understanding of how he uses what he knows about adding to subtract.

I had my strings planned out for the week, but on Wednesday I realized we actually needed to do something different than planned. Literally everyone in grade 3 is doing well adding double digit numbers. They need more practice for sure, but the Strings were not moving us forward. At the same time a weaker skill (from way back in grade 1) popped up and I felt it was a good time to address it.

I’m thinking more and more and more about how math learning happens on a developmental continuum. Everyone travels along the continuum at a different pace. Hopefully nobody dawdles in one place for too long, and hopefully they remember what they’ve learned. I’m confident everyone has past experience with subtraction. However, for some reason, it didn’t stick. It’s for this very reason I had my grade 2’s dawdling in their own spot on the Landscape of Learning all week. They played games that had them practicing addition facts, and started creating their own flash cards to take home and practice. Next week they’ll be doing the same with subtraction facts.

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, Number Strings, Number Talks

Early Algebra

We started the “Trades, Jumps and Stops” Context for Learning unit quite some time ago. A variety of inclement weather days has interrupted us a lot, so we are behind where I thought we’d be at this point. That might be part of the issue I’m having with this unit.  I’ve not taught it before, so that has to take a bit of the blame as well.  And finally, I’m thinking I might have misjudged our general readiness for this unit.  But I talked to my down-the-hall neighbour who is also doing the unit and she concurred:  It seems that some kids are easily getting it, and some are really, really having to work hard to get it.  There’s not a lot of in-between here.

Day 4 of the unit begins with a mini-lesson that we needed quite a bit of time with.  I was to fill 2 separate bags with a certain amount of coins in each, plus a “mystery” coin.  We have had a bit of trouble adding up coins, so I decided to stretch this out a bit instead of trying to get through it in 15 minutes.  Instead of putting the bags out of reach, I gave the coins to kids.  I started by explaining, “X and Y have some coins.  They have an equal amount of money, but they have different coins.  I want to see if you can figure out which coins they have.” On the first day only one child had a “mystery” coin (a poker chip!), but on the second day both kids had one.  The children holding the coins were very excited to be given this job. It gave them practice identifying the coin by name and value.  Have you ever thought about how we interchangeable use “dime” & “10 cents” when talking about coins? Some of the kids are still calling this “The Boat”.

We unpacked the bags a bit at a time.  I don’t have pictures of the whole process, but this is how it looked in the end.  Obviously our mystery coin was worth 10 cents this time.  This is the beginning of the children learning about a variable, and I think they did OK!

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On the second day, we talked more about the signs < > and =.  We added up the coins in chunks, as suggested in the lesson, and then decided if we needed to have a < or a > or if we finally needed the =.  This time, instead of adding them up as a group, I had the students work with partners.  We knew that X had 40 cents, and Y had 5o cents, but how much would they have once they each got another quarter?  This partnership was trying to make a number line across the bottom end of this photo, without actually making the number line.  It’s a step in the right direction for them!

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They wanted to have the numbers in a long line, but couldn’t hold all those totals in their head. Writing them above helped them work on the math and compensated for the stress load on their working memory.

We had lots of people able to do this:

Finally we made it to the mystery coin.  We knew how much money everyone had in actual coins, but what was that mystery coin worth? This led to one of those really cool moments when I felt like (most) everyone was excited about the math.  You can see here where I recorded some of the different responses to the value of the mystery coin.

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img_3311.jpg

I was even able to use a double number line to show two of the answers, and since that is the goal of this unit (developing an understanding of the double number line is in fact the very next lesson we will do!) I felt very good about that.

The next day I needed a Number Talk to reinforce the understanding of the variables.  I didn’t really NEED to do it, since this doesn’t come into the curriculum until a later grade, but they were excited about it, and it certainly can’t hurt them so we did it anyway. I found some images on Math Before Bed and use them for our Number Talk.  I feel like they really help to reinforce the student’s number sense because there is more than one way to make 10, or 12, or any number really.

The weather here is terrible today (Sunday) but I’m hopeful there will be plenty of actual school days this week when we can move forward with this unit.  I don’t want to lose our momentum!  Next time I do this unit, however, I am going to maybe wait a bit.  Of course, the thing that keeps getting me through is that I have to trust Cathy Fosnot! She says this will work, and she has seen it work with many, many children, so I am going to go ahead and finish the unit.  The students are mostly getting the ideas behind the math. Some of them are actually in need of more practice with adding up money.  I am going to make sure we have a day this week when we have some activities that require counting money and we’ll rotate through those to give everyone lots of practice. Often these blogs help me think through what has happened and what needs to happen next!  Time to stop writing and plan my money counting activities.

Geometry, math, Math Workshop, Number Talks

Real Geoboards vs. Virtual Geoboards

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

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

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

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

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

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

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

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

 

math, Math Workshop, Number Sense & Numeration

Games

This past week I had a chance to think about, and talk to colleagues about, how my family did math at home when I was a kid. My answer: we played games. I don’t recall having much homework until high school. I always got off the bus (5th grade and up) by myself and had about an hour before my mom came home. I typically did my homework while watching Days of Our Lives.

After dinner, however, it wasn’t uncommon for us to play Rummy, Gin Rummy, or Uno. We also enjoyed Yahtzee and Monopoly. If nobody was into it, I’d play Solitaire by myself (yes, I was a kid before it was possible to start a game online with someone.) When I was a teenager my dad taught me to play Black Jack. (It’s much less stressful with my dad than it is in Atlantic City for sure!)

Now I like to play games, in class and at home with my own children. Some of our favourites are War, Addition (or multiplication) War, and Tens Go Fish. You can play any of these with a standard deck of cards. Remove the Face cards if your children aren’t ready for adding, or multiplying, 11-13!

Today in class we did 100 chart puzzles. I copied 100 charts on card stock and cut them apart. Since I made these I have been using a 120 chart in class, but I couldn’t let the game go to waste. I suppose I should pass it off to the grade 1 class and make a new set. It was easy, and cheap. I’ve got nothing to lose. You can see here that some of my puzzles are more challenging than others.

Besides practicing math, games are a great way to practice taking turns, and losing with grace. These are important skills for kids to learn too!

math, Math Workshop

Communication

Communicating about math is a whole skill set of its own.

Case in point: each of these pictures is supposed to show you how 3 children would share 10 granola bars.

I’ll probably write at some point about the actual math. But I was most struck by the issues we encountered with communicating their thinking in writing. They basically got correct answers, but I’d never really know that with a couple of the groups if I hadn’t talked to them, and if I hadn’t helped them through the communication piece.

We’ve done a bit of this, and it’s clearly one of the things I need to focus on. I give them paper and ask them to communicate their strategies; “Show me how you got your answer!” I say, and I get little cartoons of kids writing the correct answer on a paper. Seriously. I’ve been doing a lot of modelling of writing to record our discussions during Number Talks and Number Strings. Alas, we still find ourselves in murky waters.

To be clear: it’s not just this year that my students have struggled with this. They are 7 and 8 years old…some still 6 at this point in the year! Writing is a skill they are learning. And by writing I mean printing letters and numbers, translating a stream of consciousness into written words, pictures, and numbers, and doing all of this while remembering what it is that needs to be said. They, pretty consistently across the class, thought they could write 3 names on that 10th granola bar and be done. They kept saying, “What is this big paper for?” And I kept pointing to the front of the room where our last set of math posters was still taped to the board.

I’ve had students who use manipulatives to show how they got an answer, but then not have the words to explain. They just point and smile.

I know we’ll get there! I will keep demonstrating. I have given everyone a small math journal, and for the last question during a Number Talk I ask them to write their strategy. I think it’s helping. Actually, I know it’s helping! We’re only in the middle of October. There are a lot of days left to practice mathematical communication skills.

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.