Multiplication Worksheets

I think last time I posted I said I’d be posting more often, so I feel like I need to point out that once a month is “more often” than once a year. So if you were expecting to come here every week I’m a little bit sorry to have disappointed you.

One of the reasons I wanted to learn how to make math resources for myself is because I never quite like the things that are available to me on the Internet. I mean, they’re okay I guess, but I usually end up feeling like they could have been more interesting. One of the first things I learned how to make are these “cut and paste” activities. They don’t take too long and I can customize them pretty quickly now that I have a template made. In addition, I like that it gives my class some practice cutting. The thing I had not anticipated, but love, is that they have learned how important it is to organize their answers before they start to glue them down. The first time we did one of these they were gluing too soon and regretting their choices. Now, however, they place the strips where they are pretty sure they belong, then double check everything before gluing them down. I love listening to the conversations they have when two people who sit beside each other aren’t sure if they have something right.

The next thing I learned how to make are these fun mazes. I have plastic covers that the papers slip into. I printed five of each maze style, then we passed them around all week for morning work. You’ll see some commonalities, so nobody was exactly sure which maze they were getting. They couldn’t fake their way through it! They had a great time doing them. They love using the dry erase markers to colour so this seemed fun to them. I have set these aside so that we can do them again in a few weeks for a review. Here is a picture of what it looks like when one is complete:

Speaking of reviews, the last thing I am posting today is a scavenger hunt. I think I mentioned in the money post that we LOVE LOVE LOVE scavenger hunts. I made this one as a review of all the things we have learned so far. It’s much more fun that doing worksheets for sure. Every child gets a recording sheet, copied front to back, and they wander around the room with clip boards looking for the equations they need to solve. I’ll definitely be making more of these reviews because it was so much fun. I was able to sit by one or two questions and observe every child as they came to that question. I have great notes! Most of them worked in self-selected pairs and they had great conversations about their strategies. I was initially thinking that 40 questions would be a lot and that we’d spend multiple days on this. I was prepared to shut it down if it was too much. However, they loved it. When I could see that some of them were more than 75% finished and others were less than 50%, I started observing them more closely. There were some students who were struggling with things we had left behind while working on multiplication. They had it while we were focused on it, but lost it when we moved on. That let me know that addition and subtraction need to be on constant repeat in our Number Talks, or in our morning work. This has definitely helped them.

We are moving on to division when we return after the holiday break, so I am already working on making my division worksheets, then it’s on to fractions.

multiplicationmazesDownload

multiplicationcutandpasteDownload

scavengerhuntreviewDownload

Show Me The Money!

I’ve been super busy.

That’s the only thing I can say. I’ve neglected the math blog once again. I think of it often, but never quite find the time to update.

I’ve got some spare time right now, so here it is. The update.

I’m teaching grade 3. I love it. Having a straight grade is so nice.

Now, on to other things. This summer I took a quick webinar about how to make my own math worksheets. (more info here) It was a lot of fun and now I am making them all the time! I’m going to start posting some here. The webinar was intended to teach people how to get started making and selling resources on Teacher’s Pay Teachers. I can’t be bothered with that. I have a lot of issues with that website and prefer to give away resources. I am adding a copyright, however, because I don’t want to find out someday that someone is selling my stuff on TPT.

Here is some stuff I made to use to teach my grade 3s about money.

We did this activity for the first time today. I put piles of fake money out (bills only today) around the room. I had a number label for each pile. Every child had a recording sheet. They went around the room finding the piles, counting the money and recording their total. I let them choose if they would work alone or with partners, and they did a little bit of both. Some people started with one partner then moved to another. I spent a lot of time watching and taking notes. We’ve done a number of these scavenger hunt activities at this point and they love them! I like to watch them help each other out, correct each other’s mistakes, and show each other the strategies they use. Today everyone was able to count the money without difficulty, and there were a few different strategies they shared. Sometimes they started by sorting the money into groups (e.g. put all the fives into piles of $10). Sometimes they had to count more than once to be sure.

On Monday, we are going to review the values of the coins, then we’ll repeat this with piles of coins. On Tuesday we’ll have mixed piles of coins and bills. (That’s assuming everything on Monday goes okay!) Finally, probably on Friday, we’ll have some more complicated piles with larger amounts. On that day I’ll most likely ask them to choose ten piles to count because sixteen will probably be too many. We’ll see!

I’ll be back soon with more of the things I’ve created. I like them and they’re working well.

You can download the recording sheet and labels for the piles here. I’ve also posted some cut and paste activities for counting coins. We haven’t used paste EVER in my class and I don’t think it’s even sold in stores anymore, but “paste continues to be what “cut and paste” remains in our lexicon so there you have it! Finally, I’m posting some word problems were’ going to work on in group using vertical nonpermanent surfaces, which you can read more about here.

money-counting-activity-1Download

word-problems-moneyDownload

coincutandglueDownload

Synchronicity

Bigger, Better, Best by Stuart J. Murphy

We’ve been working on multiplication and we’ve been having a good time doing it. It has taken about two weeks longer than anticipated, but I’m going to mostly blame snow days for that.

About a week ago I walked into the library and the book above was on display. It’s been in our library for a long time, judging by the state of it, but it’s a new to me title. I love these Math Start titles, and was so happy to discover that this book was going to help us move on to finding area.

In the book, the children are arguing over who has the bigger bedroom. They solve their fight using math. To measure their bedroom windows, their mom suggests using sheets of paper, and to measure the whole room they use sheets of newspaper. One child’s window takes two rows of paper with six in each row. The other child’s window is four rows of paper with three in each row. That lead to a fun discussion.

Then I set them up. We have several different kinds of tables in our classroom and I asked them to help me figure out which kind of table has the bigger top. We brainstormed a list of tools, and “sheets of paper” was added as a measuring tool. They also wanted sticky notes, but I only have tiny sticky notes so we decided to pass on trying those.

Next, everyone got to work.

Everyone used their favourite tools to measure, but only one team used the sheets of paper. On the second day, we used the photos I took to have a “mid problem” math congress. I focused on the snap cubes and the sheets of paper, so on the second day when we took up the measuring again, more groups used those two tools.

One group was really finding the area, as opposed to other groups that got sidetracked with finding the length and width. It’s okay and we’ll work it out, but I really wanted to focus on the concept of area so we talked about this one a lot. We have several rectangular tables like this. As you can see, it takes two rows of paper with six sheets in each to cover the top. We did get them lined up pretty exactly, even though this picture doesn’t show that well. But we had a problem…

…it was really hard to lay out the paper on the trapezoid shaped tables. They arranged and rearranged but couldn’t quite get it. They then started to try measuring the leftover bits with other tools and we were finally saved by the bell and they had all night to figure out what to do.

The next day, this group was at it again. They tried several different layouts but couldn’t figure out what to do about the gaps. I stepped in to help. I put down a piece of paper so half was on the table and half was off. Then I took a pair of scissors and cut it. “There,” I said. “So we know it is ten pieces, plus at least two halves, so we’ve used eleven pieces so far.” This was met with silence, then they got to work. They needed a bit of help with some of the wee corners, but in all, we finally figured that it took thirteen pieces of paper to cover the top, and we would need a bit more so clearly this brown table has the larger surface area.

Unbeknownst to me, one of our kindergarten teaching teams has been hoping to get a different table into their class. On the second day of this investigation, my colleague posted a request asking if anyone had a smaller table they would be willing to trade. I showed this to the class and told them that I asked if by “smaller” she meant shorter or smaller area on top. She meant shorter, but also needed the table to fit in a certain spot, so the surface area needs to be just right too. They then set out to measure the height of all our tables, especially the one with the smallest surface area, so we could see if it would be a good trade. Not wanting to disturb the kindergarten class, I took just two of my students to measure her table so we could compare.

Are you dying to know the results?? Well, I think we’ll need to trade her for one of our adjustable tables. Her table and our adjustable tables have the same surface area, and the table we have that has a smaller surface area is the same height! I’m going to try to have the children present their results to the kindergarten teaching team one day this week so they can decide. It will be a good chance for my students to practice communicating.

There were so many good things that happened: we got to talk about using the snap cubes in groups of 5 so they are easier to count; we had reminders about centimeters and meters; we did some mathematical modelling; we had conversations about why the centimeter cubes need to be in a straight line (see how it curves in one of those pictures?); we had lots of opportunity to practice communicating our thinking and solutions.

This week we will spend more time talking about area specifically. We will also be talking about why it takes fewer snap cubes than pieces of paper to cover a table, and why it takes so many centimeter cubes compared to snap cubes.

Stay apart

I started my school year with three students. We had a staggered entry and my two grades straddled the split between who started Wednesday and who started Thursday.

I was thinking a lot about physical distancing. Kids don’t really know how long a metre is – they really truly don’t! A metre, a mile, a moose – these units of measure are things they are still trying to figure out. In addition, they are busy figuring out where they exist in space. They aren’t all really sure where they end and someone else begins.

I decided to start off by asking them how big a meter is. I wanted them to have a frame of reference and a benchmark for how far apart they should be from one another.

We watched a video about the importance of staying 1 metre apart from each other. I said to the three, “Do you know what a meter is?” They did not. Makes sense since they are in grade 2. I asked, “Can you find some things that are as long as this meter stick? Some things that are 1 meter long?”

We then spent an hour measuring stuff in the room and in the hall and then we had to go outside for another thirty minutes of measuring because my three friends were obsessed with holding the metre stick up to things and asking, “Does this count?” Sort of like when we were driving across Ontario in August and my own children were obsessed with asking, “How much longer?”

Some really cool things happened during this time. We found out that you can stand at certain spots beside our tables and be a metre apart, but if you stand at other parts you are not a metre apart. We discovered that three floor tiles are equal to 1 metre. This was true for the white tiles in our classroom, the white tiles in the hallway, and the blue and yellow tiles in the hallway. We discovered that 2 1/2 bricks on the hall wall are 1 meter long. And the ladder on the play structure is less than a meter. So is the storm drain.

I spent a lot of time asking them if they were a meter apart and they had to use these benchmarks to figure it out.

The rest of the class joined us the next day and I couldn’t take 20 kids out to measure stuff in the hall so we used the photos from the day before. They had to basically memorize the two benchmarks we focused on and they were sort of good at it. They were very good during the lesson! They were less good at doing this in the wild. They even had trouble with the “Superhero arms” measure of distance. They are kids after all.

So I’m plotting my next step now. In the new curriculum both grades need to do some work with centimetres and meters. (E2.2) For now I am going to be content with helping them develop a feel for how long a metre is. We have moved into doing some work with figuring out how to use manipulatives, especially now when sharing has become complicated.

Calendar

I’d normally have the first week all organized by now.  I’ve been going through my notes (mental and written down) as I try to plan out what my first week of school will be like.  There are quite a few of my old tricks that won’t work this year because of “you know, social distancing” as my son likes to say.  And, truth be told, I could still get a big assignment change so I am not putting too much effort into getting excited about exact plans. But there are certain things that can happen no matter what my assignment turns out to be and no matter who will be in my class.

Last year, I added a new calendar routine to my class and I really liked how it all unfolded.  I had the whole year on the board at once, and I loved how the students used it to count “how many days until” things would happen.  I’m not usually one for celebrating birthdays in class, so I wasn’t expecting them to do their favourite thing:  add their special day to the calendar.  We added the holidays together as the approached and talked about how some holidays are always on the same day (Feb 14 = Valentine’s Day) but others float around according to the cycles of the moon (Passover). This is a grade 2 social studies expectation and I liked how that became part of an ongoing conversation in our room.

This year I have decided to do it a bit differently.  Instead of printing a complete calendar, I found some blank calendar pages here.   I am going to fill out September (maybe only the first 2 weeks?) and then get kids to help fill out the rest.  I made a poster to post beside the calendar:

You can have a copy! 

I want the students to fill in the dates on their own because there are so many patterns to the counting on calendars.  If they are filling out the dates themselves I think it will help them see the patterns. During the first week, maybe in the second week, we are going to work on this together.  I still haven’t sorted out all the details though because, “you know, social distancing!” is going to effect this for sure. Maybe the students can have their own mini version to work on at their desks.  (I keep reminding myself that some kids are going to really love working alone at their desks!)

I’m going to keep this at the front of the room because we referred to it so often!  I want it up close.  I know things will be different now because we can’t have any carpet time, but we didn’t really use it for that anyway. It was just an ongoing topic of conversation all year. Kids like to know when things will happen. This helped with that. I’ve been reading a bit of executive function skills and some of these are the ability to organize, to be able to plan things, and of course manage time. I know that I personally need a calendar or day book for this, and I really do much better if I have written it down.  My phone calendar is great for reminders, but I still need to physically use a pen and paper to write it down before a scheduled activity is in my brain. I need to know when something is due and then I need to write out a plan for how to do that slowly over the course of a week or more.  I need specific small deadlines (because one of my executive functioning strengths is that I am goal oriented) to keep my on track. The wall calendar seemed to provide support in all of these areas for the kids in my class last year, and I suspect it will help this year as well. 

So…20 minutes of each day of the first week…sorted!

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.

 

 

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

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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.

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.

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.

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!