math, Number Sense & Numeration, Problem Solving

Baking

Are you still baking bread? At the beginning of the world-wide shutdown, everyone was baking bread and cookies and their own pizza. We are still doing this – we were doing this before. We’ve slowed down a bit because it’s been too hot to turn the oven on. But yesterday I made some bread and today my daughter is baking cookies.

She wants to do this all by herself. I have a recipe that’s meant to be easy for children to follow, and she has a lot of kitchen experience for a 9-year-old. She’s only needed help so far with the “1 slash 2 cup” of butter. We’ve talked about 1/2 dozens of times but it still eludes her. I showed her how to use the markings on the butter to figure out 1/2 of a cup. She then needed help with 1/2 cup of honey. Partway through pouring she realized she had the “1 slash 4” cup and thought it was going to be too much because she only needs “1 slash 2”. We’ve talked about this a bunch too, but in the moment she was confused again.  I coach her through it.  “1/4 is 1/2 of a 1/2.  So if you have 1/4, you have 1/2 of what you need.  So what do we need to do?”  She figures it out, I pour her another 1/4 cup of honey, and she’s back to working on her own.

I’ve been thinking a lot about baking and the learning that goes along with it. Little of it actually shows up in our curriculum. There’s problem solving, some collaboration (her brother doesn’t like chocolate so this is always part of our conversation when making cookies), communication, following instructions and, of course, measurement and fractions. At home this type of learning is very important to me. I want my children to head off to university with the ability to cook more than Kraft dinner, grilled cheese and scrambled eggs. The curriculum connections are a bonus. At school I cook or bake with my class maybe twice in a school year (less if there are students with allergies or special dietary needs in the class.)  I learned to cook at my grandma’s house, at my parent’s house, in Home Economics classes, and in neighbourhood 4H clubs.

If I was in charge of the curriculum, I’m not sure what I would eliminate in order to make space for cooking in the elementary grades.  I’m not sure there is anything we should exchange for cooking time. Secondary students still have the option of doing catering courses so they can learn to cook. Mostly I feel like learning to cook is part of how we pass our family and cultural traditions and values down to our own children.  I know some parents don’t teach their children to cook, but maybe that needs to be up to them.  Maybe this is one thing the schools have let go of for good reason. If I cook with my class it’s because we have a connection to something we’ve read about, or it’s a snow day and we need to fill the time with a worthwhile but fun activity.  I don’t feel compelled to teach them life skills like cooking or sewing.

 

 

math, Math Workshop, Mathematical Processes, Problem Solving

NOMA Summer “Book” Club #1

Today we at the Northern Ontario Math Association (NOMA) had our first summer book club meeting.  Instead of reading a book together, we are finding resources on the Internet we can read for free – things we can get without having to wait for delivery!

Today we discussed a webinar found on TheLearningExchange called “Teaching Math Through a Social Justice Lens”.  I highly recommend this learning series. It is basically a problem-based math teaching approach. Students are using real-world numbers to think about real-world problems with a social justice focus.  In this exact case, the students were mostly focused on an inquiry that had them wondering about their shoes – where in the world do they come from, who makes them, how much are those people paid to make them, etc.

Preparing for this has had me thinking about some social justice issues I could cover in my primary class.  We study water in science, so it would be interesting to do something with water bottles – collect data on the number of bottles used in our school, how much we save by using refillable bottles, what is the environmental impact on not only using them but having them delivered to your local store, what is the financial impact on buying disposable water bottles…etc.   I definitely need to think more about possible topics, but I also want to make sure I am paying attention to what my students are interested in.

The great thing about a book club is that other people think of things that I don’t. In our conversation there were a few important things that were brought up.  Some of the issues might be upsetting to families who feel the teacher is trying to push their own political agenda.  Some issues might be upsetting to students (we talked about all the amazing data related to Covid-19, for example, which our students might not be ready to analyze in the next year…or more!) And we have to make sure we are still teaching math and not just doing these projects that use the math. We want them to have a certain sense of exploration and problem solving, but we also need to make sure they know how to do all the necessary calculations for their particular developmental needs and grade level.

One of the big hurdles for me in my own thinking and teaching has been how to come up with projects that have my students doing math, literacy, science, social studies across the day instead of each happening in their own separate, compartmentalized time block. I have this figured out with literacy, but math…I’m still working on it. As I watched this webinar I feel like I have a new understanding of how to create inquiry problems that students could work on all day and still hit all the topics.  Now, I do think I wouldn’t jump right into this in September (though maybe with the right problem I could…) and I definitely think I will need to still have a time set aside on most days when we are focused on learning to do calculations.  But I’m thinking of some social justice and global citizenship issues that could really take over the class (in a good way!) for a solid week.

I’m also still trying to wrap my head around having students part-time in school and part-time at home but still working and I think this integrated approach would be a good way to have them working at home on things besides worksheets.

I’m still thinking through all of this!  But the book club was a good way for me to consolidate some of my thinking…and it gave me more to think about!

 

Relevant article:

Caswell, B., Stewart Rose, L., & Doura, D. (2011). Teaching Mathematics With a Social Justice Focus. Inquiry into Practice: Reaching Every Student Through Inclusive Curriculum, 81–88. https://wordpress.oise.utoronto.ca/robertson/files/2017/03/Teaching-Mathematics-with-a-Social-Justice-Focus.pdf

 

math

At home math: #2

I was busy in a webinar on a Friday so the computer was teaching my children for me. My son came to get my phone, the returned a minute later asking me what the clock in the picture said. “HURRY! I’m going to lose the battle!” I was focused on my webinar so it took me a few seconds to figure out what was going on.

My class uses the iPads to play “Dreambox” a couple of times each week. That feels like enough screen time to me. I haven’t bothered to use other tech-based games and activities even though I know there are some really good ones out there. Fast forward to March 2020 and everyone was prepared to carry on with their online math games. I can make assignments and track their progress. I can even see where a group of them, or individuals, are struggling and provide videos walking them through what to do. It’s great!

Fast forward to April 2020 and I could see that my own children were no longer subject to the same screen time restrictions normally in place. Thinking that perhaps this was true for my students and that all of us could enjoy some other math activities, I signed up for Prodigy and added my son to my class (my daughter’s class is already signed up on their own.)

Here is what I like about Prodigy:

Kids can find their friends in the game. It’s fun even though they can’t actually chat or anything.

I can give assignments. This week everyone is working on telling time. The questions will still be a mixed bag, but there will be a focus on time.

There are virtual manipulatives available for students to use to help solve problems.

I usually don’t use Prodigy because it’s more game than math, but that’s exactly what appeals to me now. My son will happily play for the duration of my meetings or webinars.

When we return to school I’m not sure Prodigy will be in rotation in room 16. I think I’m going to be even more conscientious about overdoing the screen time, and I really am committed to Dreambox.

math, Problem Solving

Math at Home: Week 1

Every day we do math at our house. That’s not new. But this week we are going to be more serious about addressing some gaps. I get to be a one-on-one teacher for my children, which they need.  Well, really every kid needs it!

We started working on printing numbers correctly last week. One of my babies has some bad habits and the numbers are backward all. the. time.  Last summer we painted a chalkboard wall in the basement and it’s come in very handy many times.  It is now part of our makeshift classroom.

My son, who is in grade 2, is working on number lines.  He is very good at mental math, but doesn’t have a way to visually represent his thinking. I thought long and hard, but try as I might I can’t remember all the lessons from the Context for Learning units.  However, I do know that Antonio is 2 years younger than his sister and there are a lot of interesting math conversations that can come from this.  The sister is 10, and Antonio is 8, and Dad is 40 and Mom is 38 and I can’t remember right now how old the grandparents are.

Today we talked about how far apart Antonio and his sister are on a number line.  Then we talked about how that would look at different times in their lives.  How old was she when he was born?  How old was he when she was 6?  How old will she be when he is 10?

See the trouble making the jumps on the number line?  That’s a handwriting issue, but it’s effecting his math so we’re working on it!   Tomorrow we’ll continue working on this before we move onto finding the difference between the children and their parents.

We also did some counting.  Spencer needs practice skip counting so I have him counting his cereal and candy.  He doesn’t mind.  We do it only once per day, not over and over. When we worked on 3s today I modelled it for him first then he repeated what I had done.  We’ll see how it goes later.

My grade 3 daughter is ready to practice the 7 times tables.  We started by going over everything from 1×1 up.  We played Multiplication War last week.  This week we are going to do that some more.

Both kids are working on Dreambox for a few minutes every day.

math

The good and the bad

Some weeks I feel like the windshield, and some weeks I feel like the bug. This was a bug week so I’ve decided to find some wins to focus on. We worked hard last week, and mostly it showed. Today, Monday, I was so glad I spent the weekend reflecting on what had gone right last week instead of staying stuck in a negative reflection cycle.

Each of the above pictures shows a moment I captured on my camera because something was going well. I had a lot I left on the camera roll too. I started taking photos during math because it can be difficult to document student work in the moment. My phots help me go back and document later. I often take videos too so I can spend some time reflecting on conversations later. It helps me think about my students. It helps me refine my questioning and conferring practice, too.

Not every day at school feels like a win. Lots of them feel really hard. But there’s good to be found if I look hard enough.

math, Patterning & Algebra

Money (or “Learn to get along with your classmates!”)

This week we learned more about money.  We started “Trades, Jumps and Stops”, a Context for Learning unit and the first thing students do in that unit is count some money.  On the first day, I did a Number Talk, which was definitely not a Number String! I had 50 cents in my pocket and I told the class about the 50 cents.  Then I asked, “Can you tell me which coins I have?” We wrote down 5 or 6 different combinations of coins that are equal to 50 cents.  Then I told them I had 4 coins and they immediately knew which of the options they’d given was correct.  But by “them” and “they” I mean it was only about 3 or 4 students.  Granted, we had a lot of students away due to illness but it was clear that we needed some practice with counting money and making amounts in different ways, so we took a pause from the unit and did that for a couple of days.  By Friday we were using the piggy bank cards, which we need later in the unit, to count out coins, adding up two different amounts to get a total, and comparing them to our partner. This is a detour from the original content of the unit, but I didn’t feel like we could go forward successfully without solidifying this skill. Or set of skills I guess.

I am happy to report that everyone was counting by 5s and 10s, and many were adding up quarters too!  This is because we have progressed as mathematicians!  It is also because I only gave each group 5 pennies so they didn’t have the option of counting out a very big amount by ones.

This week I am also reflecting on how well we are collaborating when we need to.  For the last several years I have done a lot of work with intentional learning partners.  I assign my students to a triad and those people are their partners for the entire month whenever they need partners. In the beginning, I assign them to a partner, or I use a random system for matching students.  As the months go by, I start to ask for their input and ask them to do some self-assessment of their ability to be a good partner.  By the 5th month of school I would not be doing random assignments anymore.

This year is different. On Thursday I pulled out our partner matching cards and I immediately thought, “Why am I still using these?  Why don’t I have partner assignments ready to go?”  Intentional learning partners are meant to match students who will be able to actually help each other out and collaborate together.  Peter Liljedahl does the opposite and has students work with different students every day.  But his work is mostly focused on older students.  I believe that in the primary grades the students need different social things than they do in the higher grades.  For example, practice putting up with each other’s oddities in order to learn some tolerance, practice noticing someone else’s preferred work style and then trying out some tips from that person, and of course they need to learn how to take turns.  They also need to be matched with someone who is close in ability.  Maybe not the exact same ability, but in a split grade class I can’t have my most accomplished grade 3 matched with a grade 2 who is really struggling.  Or worse, a struggling grade 3 matched with a grade 2 who is sailing along! I take all of this into consideration when making matches.

So, why not this year? Well, I think there are a few reasons.  First, we have an attendance problem.  I don’t want to say too much about that, but some kids are away a lot. Second, we have a few kids who are really struggling with being told what to do.  I’m quite concerned that I will assign them to a partner and they will make such a fuss that it will ruin the class period/day/week/month.  Or worse, they will want to be partnered up with someone I do not want them to be partnered up with and I will not partner them up with that person because I am the adult and IT WILL NOT END WELL!  It all seems like a better idea to say, “Sorry, not my fault.  Talk to Fate! She’s the one who picked your partner.” or, “The cards decided, not me.” (which is what I am most likely to say.) We’re a little behind in some of our executive functioning skills and random partnerships let us work on some of those areas while avoiding some of the more volatile ones.  And as I’m writing this I feel like maybe I’m taking the easy way out because I’m exhausted from all the emotional stuff that goes with teaching.

And now I’m going to spend the day thinking about maybe putting some more time into developing the executive skills that will allow everyone to manage frustration in a way that does not make Mrs. Corbett want to cry every day on the way home from school.

But we can all count money, so HOORAY!

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This is the “cheat sheet” for the partner matching cards I use.  I got them from Teachers Pay Teachers.  There are individual cards which are handed out randomly and the students have to find their partner. I use the big heart as our “pick your own partner” card for the days when we have an odd number of students in the class.

math

Time after time

This week we had some fun with the clocks.  I had mini clocks for every child to use.  We worked on time to the hour, time to the half hour, and then time in general.  One of the things I am really enjoying about following the curriculum spiralling document is that I know we’ll be back to this again later, so I’m happy about what happened this week even though not everyone can tell time.  We’re good with time to the hour, and mostly to the half hour.  We’ll need a lot more practice with all the in-between times though.

On Monday one friend reported that he won’t ever need to learn to tell time on a regular clock because he’ll just look at a phone.  My own son, who is in grade 2, has discovered he can say “Hey Google, what time is it?” and have his question answered.  But analog clocks are everywhere and we really do need to know how to read them.  Not to mention all the “other” math that connects to clocks!

We did a bit of work on elapsed time.  I told them about my morning and had them move the clock along.  I got up at 6:00 – they showed me 6:00 – and it took me 15 minutes to get dressed – they showed me 6:15.  On and on we went as I made lunch for the family, tidied up the kitchen, and finally pulled into the school driveway at 8:00 (30 minutes before school begins!)  The real test came when I started saying to everyone, “I can’t see the clock.  What time is it?”  and “Mr. so & so will be here at 12:20…how long until you go to gym?”  I really can’t see the clock from where I sit by the chart stand and now I shouldn’t need to get up to check it.  And even my most reluctant friend realized it might be to his advantage to learn to answer his own “how long until…” questions on his own.

We have been talking about the larger “time” picture all year long.  We have the whole calendar displayed on a bulletin board and we’ve been talking about how time is passing all year.  We count how many days until things happen – birthdays, breaks, days off, holidays, Friday.   But this was our first week of talking about the hours and minutes in our day.  They have had this before.  This isn’t new.  Reading the clock should be something that many of them have done before.  But now they’ll have the skills to do it all the time.

 

 

math, Number Talks, Patterning & Algebra, Spatial Sense

Math on the Move

This was our math class this week:

Last Spring at the OAME conference, I bought a book called “Math on the Move” by Malke Rosenfeld.  My friend, who was at the conference with me, attended a workshop about the book.  We talked about it a few times.  She tried it out with her grade 2 class last year, and I read it over the summer. Then in December we had a day when we could sit down and do some planning together.

The premise of the book is that there is a lot of math students can learn while moving around.  This past week we learned about patterns in math while dancing. The squares on the floor, made with painter’s tape, give everyone a designated space to work in.  They also give everyone signals for where the feet should be at a given time.  I added the blue tape line because our previous work with directional words and spatial sense activities let me know that left and right are still tricky for quite a few of my people and I thought “blue side” would be less tricky. I still used the words left and right, and gradually stopped saying “blue line” over time. We worked with 4-count repetitive patterns all week. We got over some self-conscious feelings about dancing where others can see us.  We resisted the urge to pick the painter’s tape off the floor even though it was getting pretty scuffed up by Friday.  I like the way this activity integrates spatial sense, patterning, dancing, and self-regulation!  It was super hard for some children to follow dance steps instead of dancing free-style.  It was a lot of fun, and this can be quite dysregulating for some children. I had specifically planned to do this during the week we returned from Winter Break because I knew they would need to ease back into the routine of school.  I think this helped many of them.  I’m confident, based on the rest of our days, that sitting down and focusing on some table activities would have proven to be a challenge!

We have been using “Banana, Banana, Meatball” on Go Noodle for a few months during our DPA.  I used this to launch us into a study of patterns and dance in music.  The class, mostly, can do the moves.  It’s just hard to keep to the right pace.  However, everyone could follow the patterns, talk about the patterns, and create their own patterns.  We also watched some other music videos and danced to the music.  Turns out all dancers follow the same moves we were using.  There are patterns everywhere!

We didn’t get as far as I wanted in one week. I had hoped to have everyone using some boxes to record their moves so others could follow the pictures (this is all explained in the book.)  We will get there eventually, but it didn’t happen when I thought it would.  I’m not in a rush though.

To support our pattern learning, we were also using some “Eyes on Math” images for Number Talks this week.  Marian Small wrote this book several years ago.  I use it every year and I love the way the images get students thinking about noticing the math in the world around them.  This week we looked at a picture of a parking lot.  Cars were leaving a person was counting how many cars were left.  We had to figuring out how many cars were left as each left (shrinking pattern.)  On another day we  wondered how many eggs would be left if mom takes them away 2 at a time.  We talked about several different ways to figure out how many bicycle wheels were in a picture (growing patterns.)  We worked on a few money problems too!

While we were doing the Number Talks, we also talked about how to solve a problem.  In other words, the problem is up there on the board, or on the paper, and you need to read it and figure out what to do in order to find a solution.  How do you do that?  This is one of the times when I did some direct, explicit instruction.  I know how to solve a problem. I know how to break it down into steps.  They don’t.  I told them. I made a chart, we practiced, now some of them know what to do and more of them are going to know what to do after we do some explicit practice next week.  When I start the next Context for Learning unit they should be better equipped to work independent of me.

Next week our math focus will turn to telling time.  The turn of the year is a good time for that.  But we will come back to our dancing a few times.  We’ll talk about more Eyes on Math images and practice solving steps. And we are going to do an art project that uses patterns.  I’m excited to see what happens when we get started on this.

Geometry, math, Mathematical Processes, Problem Solving

Geometry

Teaching geometry in grade 2 and 3 isn’t all that exciting.  I mean, we have to make sure everyone can identify their shapes, can name a few attributes of those shapes, can manipulate those shapes and make things. It’s not all that interesting when we first get started.  Well, I should say that it isn’t all that interesting to me.  The kids love it!  And they think it’s awesome and the pattern blocks feel nice and everyone feels really confident about themselves during math when we are talking about geometry.  That makes it a great topic to work on during December.  December is a crazy month with a lot of different things happening and emotions running around so it’s nice to have geometry to come back to.

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I promise next week I’ll have a lot more to reflect on.  We are moving on to 3D geometry and angles.

We spent some time using the Spheros this week as well.  My friend and I spent some time writing up an instructional unit that involves math and science expectations.  This past week we mostly spent time playing with them.  Luckily one of my students from last year, who is also in my class this year, remembered some important things like how to charge them. There are so many steps involved in using tech!  Even though they aren’t complicated steps they still take up a lot of time, and can cause a lot of trouble if any of them are not followed.  Which is the whole point of learning coding, I suppose.  Try something, fix up the problems, try it again, fix up the problems, repeat.

Like I said – nothing too exciting.  But everything we did this past week set us up for some bigger learning in the next week.  The weeks when we go back and remind ourselves what we already know are quite often as important as the weeks when we are learning new things.

math, Number Sense & Numeration, Number Strings, Number Talks

Subtract

I know it’s only Tuesday, but I’m in a “celebrate the little things” frame of mind.  It’s helping me cope, which is pretty important for teachers under stress.  And other humans of course.

This week, only 2 days old, I am teaching area and perimeter.  But I like to continue with Number Talks even when we’ve moved away from the computation portion of our work. Yesterday I started with one from Sherry Parish’s “Number Talks: Whole Number Computation” book. I chose one from the grade 2 section:  20-19, 20-14, 20-12.  We talked about how we could use all of our strategies from the math wall, but that counting up seems to work better than counting down.  We used the math racks for this activity, and I celebrated my own ability to say “subtract” every time instead of reading the problem as 20 TAKE AWAY 14.

Then today, we started with 20-19 (because one thing I have definitely learned from Cathy Fosnot and her Number String work is that starting with a helper problem is very important – this is not part of the Number Talks book work.)  Everyone remembered or quickly figured out that the answer is 1.  Then I wrote 30-19.  They weren’t so sure at first.  It took us a while to get to 11.  Some kids wanted to count all the way down (their go-to strategy).  Some wanted a math rack so I pointed out it doesn’t have 30 beads so what would they do, they didn’t have a plan. Some made random guesses AS ONE DOES!  We started to talk about our potential answers.  I purposely called on a student that I knew had the right answer AND that I knew could explain the thinking to share.  This child did a great job of noting that the helper problem was helpful.  If we think about how 30 is just 10 more than 20, but we still subtracted 19 then the answer should be 11, or 10 more than 1. I pulled out the math racks. I showed them 30-19 using a 20 rack and a 10 rack.  This way I could show how I added 10 more in but didn’t remove any more than I had the first time, leaving 10 more remaining after I “took away” or “removed” the 19 beads on the rack. After we did 40-19, someone noticed a pattern.  This is honestly the thing that makes me happiest sometimes.  Some groups of kids will notice patterns right away and then stop puzzling over the math because they have found the short cut.  But this class always takes a bit longer to see the pattern.  It’s fine with me, because we have a lot of good conversations along the way.  But I’m also glad when the pattern becomes part of our conversation too.  Even after this child thoroughly explained the pattern, some were skeptical.

Along the way I was drawing the number lines.  I decided to draw a new one each time because I wanted them to clearly see how each time the 19 didn’t change, but our starting and ending point did.  I also wanted to highlight the iterated units.

We talked about each of our strategies:  does it make sense to count up?  to count down?  to try and “take away” something?  to think of an addition problem that would help?

Two weeks ago I blogged about a moment when everyone was working independently.  It has rarely happened since. But it is happening, throughout our day.  Slowly but surely we are edging forward, and today’s math was a reminder to me that we are indeed doing good work. Not every day is easy.  In fact, today wasn’t that easy.  But this was my shining moment.

We’ll continue on with this tomorrow, but I will use some other number besides 19.  I am also going to write out today’s work on a chart paper because I think it will help us going forward and, therefore, deserves a spot on the math wall.