Friday, December 2, 2016

Getting students ready to divide and tackle remainders!

division fact games
It's division time--and I am always shocked at how students freak out about division...and how much "harder" it is than multiplication.  I always promise them that I can make it easier for them! I posted a picture on Instagram the other day and I had a bunch of requests for more details on the "Herding Game"!

To begin, I wanted students to really understand the idea that multiplication and division are so linked that we can almost use them interchangeably in our minds—but that our math language needed to reflect what we are doing.  What do I mean?  We often teach students what many call “turn around” facts.  We tell them that 4 x 3 is the same as 3 x 4.  But is it?  Is four boxes of 3 pies the same as 3 boxes of 4 pies?  No it isn’t.  They both represent 12 pies—but the situation is totally different.  To help students see this, I made up a game a few years ago...and it has proven to be super effective--and FUN!

I told the students that they were going to be a “herd” of animals today and that I had researched a whole bunch of animals that traveled in herds.  I also let them know that when animals who travel in herds are threatened, they sometimes break into smaller groups to protect each other.  I told them that I was going to break them into smaller groups today and then we would write the mathematical equations that we discovered in the process.  We counted our “herd” and found that we had 22 animals this day.

I taped off an area of one of our empty classrooms (this would have been fun to do outside as well with a chalked off area) to have as our “holding pen” for extra animals that couldn’t find a group.  I also put some animal “tokens” in the pen so that each child who ended up there took a token—and the token was a “get out of the pen free” card so the same students didn’t always up there.  For some reason, some students WANT to land in the holding pen so they don't actively participate in the herding...so once is enough!

Here's how we play.
teaching remainders
First of all, I called out a type of animal (buffalo, giraffes, zebras, wild boars, cows, bison, elephants…) and the size of the group I wanted them to form.  For example…

“Elephants—form groups of 5!”

The students scampered to make their groups, and I asked for help writing the equation on the board. I had to help a bit, but with coaching, we got it.  I asked,“So I just formed four groups of 5?"
I wrote 4 x 5 = 20.  "What about the leftovers?"  I wrote (4 x 5) + 2 = 22
We tried again.  “Giraffes—form groups of 2!” Students quickly paired up and we wrote the equations.
22 ÷ 2 = 11
11 x 2 = 22

No remainders this time!

The students were getting the hang of the game so I decided to move to the next steps.  “Buffalo—form groups of 7.”

The students struggled a bit to make their groups—but eventually the leftover buffalo found its way to the holding pen.  We worked
to write the equations this time. 22 ÷ 7 = 3 groups with 1 remaining
(3 x 7) + 1 = 22.  We tried again..."Make 3 herds of antelope!" (Different than herds of 3, right?)
teaching about remainders
teaching remainders
Everything was going beautifully--until one of our specialist teachers showed up...so we had to redo the game a few times with 23 animals!
division and multiplication
We continued with several more rounds until I could see that the students were getting the hang of it!  We wrote down some of our rounds on the board (when I remembered!) and then I asked them to try to do some mental math to determine what would happen if I asked them to make groups of 9…then groups of 6.  They did a great job!  I knew that I had given my entire class enough to go on—and I was ready to continue the work with my more struggling students back in the classroom.

While my other students were working on some multi-step problem solving, I pulled some of my struggling students to try our “herding” activities in a smaller group.  I made some cute little animal tokens to use as counters and we started working to tell herding stories. I wanted to see if they could apply the skills of the game a little more independently and could make the shift to recording their math equations on their own.
teaching remainders
Much like the game, I told herding stories but this time gave each student a baggies of animals—and I was able to change the number of animals in the herd at will.  So the questions began…

“You have a herd of 12 animals.  Divide them into 3 groups—what do you get?” 
“You have a herd of 16 animals.  Divide them into 8 groups—what do you get?”
“You have a herd of 20 elephants.  Divide them into 5 groups—what do you get?”

We did several rounds where the groups worked out with no remainders, but after a few minutes, I moved to working with remainders. Students started really seeing the connection between their multiplication facts and the division problems! We kept track on the recording sheet to make sure that we were getting the practice with the math language and grouping concepts. I really started seeing light bulbs go off!

As a follow up, I introduced "The Pretzel Game"...perfect for practicing these division with remainders situations.  See what you think and give it a try!  I probably should make more copies of this...I only have two right now and my students are clamoring for it!
math game remainders
If you want to see more, here are the two resources I used to get this division unit going!

Monday, November 21, 2016

Team Challenge: Subtraction with Regrouping...and FUN!

computation practice
Just a quick "photojournalistic" post today to show you what fun we had with a class warm up today!  Our goals?  To continue working on our subtraction with regrouping fluency and accuracy--and to be able to look for errors and fix them.

Here's what we did.  You could easily do this with a set of cards you make...but I used the cards from my Precision Practice resource (this activity is listed at the beginning as one of the extra activities) because we had just used the cards a few weeks ago and, in typical fashion, they were not yet put away!  I have probably used them 8-10 times since the start of the school year in different ways--but this was a new one for us!

The directions were simple:  Students worked in pairs to draw two cards (I used 3 different levels of cards and students picked their own level of challenge--3 digit, 4 digit, or 5 digit).  Each child found the difference between the two cards, and then compared answers.
collaborative work

accountable math talk
If they both got the problem right, one teammate went to the smartboard and added two tallies to our "class challenge". If they did NOT both get it right but were able to work together to figure out where the error was, they got to put up ONE tally.  I really stress how important it is to be able to make mistakes--and to be willing to hunt out how to fix them so this activity was PERFECT for that!
cooperative learning
I set the timer for 15 minutes and the teams worked to earn as many tallies as they could in 15 minutes.  When they finished we looked at the tallies, estimated how many there were, and then made groups of 10 to get the grand total.
cooperative learning
We could have done a subtraction practice sheet--but WHY?  Students got a ton of practice...and the added benefit of troubleshooting mistakes.  It was a great kick off to get our brains ready for our lesson today--subtracting across multiple zeroes.  Give it a try and see what you think!  My students asked when we could do it again!

Looking for the Precision Practice resource that I used?  It includes this and many other activities to practice addition and subtraction in challenging and unusual ways.  Just click the image below to see more. (Also available in multiplication)

Saturday, November 19, 2016

Subtraction Observations...the power of working one-on-one with students

math assessment
As you know, formative assessment is a critical part of the teaching/learning cycle. Without knowing what our students know and can do, it is very hard to make sound instructional decisions.  I use exit slips (and entrance slips) ALL the time to try to keep a clear vision of what my students can do--and what more we need to work on.

There are, however, times that I believe a paper and pencil assessment can only give us part of the information we need.  Giving students a few subtraction problems to do can tell us if they CAN get the right answer...but it doesn't always show us HOW they do it or where they may be getting off track.

For something important like the standard subtraction algorithm, it is critical to see where students who are struggling are going wrong.  This is what I wanted to do on Friday before we move into bigger numbers and lots of 0's!  Although you can do this with only students you are worried about, I truly wanted to watch each of my students solve two problems so I could look for the following things:

1.  Accuracy 
2.  Fluency
3.  Efficiency
4.  Confidence

I kept a recording sheet right next to me and as they worked, I watched every step they took, asked questions if I couldn't tell what they were doing, and then jotted down what I noticed.  Did they get it right?  Could they do the algorithm AND use correct subtraction facts to get the right answer? After all, we DO want students to get the right answer, don't we?

But getting the right answer is only part of the deal--if this was all I was concerned about, I would just give them a paper and pencil assessment (which I will be doing often over the next week or so!).  I really want to get a sense for students' fluency (speed at which they work) and efficiency (are they using notation and strategies that make sense and contribute to fluency?).  I also wanted to know if they could EXPLAIN what they were doing...not just do it.  All of these things work together to show me their overall CONFIDENCE with the skill.  I have to say--it was time well spent!

Throughout the day, I pulled students one or two at a time (two if I was 100% confident in their skill level) and watched them work the two problems.  I watched them like a hawk to see if they were REALLY having to think through the steps or whether it was smooth and natural.  I jotted down my observations, used the time as a coaching session for any mistakes that were made, and noticed something really important in about 1/3 of my students--how one sentence I had said during a lesson might have gotten them confused!
math assessment
So here's what I learned about how important MY language is with students!  The other day during my mini lesson, I mentioned to students that it "can be a good idea to look at ALL the numbers you are subtracting from to see if trading will be needed."  Harmless, right?

Well...something I discovered in my assessment interviews was that I had a number of students who started this problem by doing just THIS--looking at EVERY place and crossing off everything needing a trade right off the bat!  I was confused...in all of the modeling I had done, I carefully and methodically went place by place--if we needed "ones", we traded for a ten.  If we needed "tens", we traded for a hundred--one step at a time.

Because seeing this "crazy crossing out" got me curious, I started asking questions...and students all came back to that line--that I had mentioned to look at ALL the numbers to see if they would need to"regroup"--and if they did, they got them ready to trade!  Although some could do this "cross off" and keep their brains organized--most of them went WAY over to the thousands and started working from there--with obviously unsuccessful results!  So, despite my careful (and repeated!) modeling (even with manipulatives), they took hold of that one sentence and went down a dangerous path.
assessment
When I saw what these students were doing, I realized how they misinterpreted my suggestion--and I NEVER would have seen it if I wouldn't have been working with them one-on-one and making those careful observations.  I also would not have seen it on an exit slip--I would have seen the wrong answer but would not have seen the order of steps they took.

So what were MY next steps?  I went back to those other students who had been doing the multiple cross outs and we worked together to correct the misconception.  By the end of the day, I knew which students were extremely fluent and confident and ready to move at a faster speed, which students understood the concept and just needed fluency work, and which students needed a variety of different misconceptions corrected--whether due to MY miscommunication or other errors they  might have been making!  I know now exactly where each student is in their learning--and I know how to group them next week.  As we continue, I will do more observations with students who are struggling so I can continue to guide them with "just right" instruction.  We will also be doing frequent exit slips to check for accuracy and fluency as the problems we do get more and more complicated.  Thanks for stopping by!

Thursday, November 17, 2016

Sharing Our Blessings

If you followed me last year, you might remember that a group of bloggers and I hosted a fun Thanksgiving giveaway to say "thanks" to our followers...and we have decided to do it all over again this year!

At this time of year, I think many of us are reflective about all that we have.  I know I am thankful for so many things...and no matter how difficult life can get, this is the perfect time of year to reflect on all that we have that we are grateful for.  I am so blessed to have TWO jobs I love--teaching by day, and creating resources and blogging by night!  I have a wonderful family and great friends...I have a more-than-ample roof over my head and go to bed with a more-than-full belly every night.

Today I am joining together with some other wonderful bloggers in a special link up to celebrate all our blessings--and to show our gratitude to YOU by offering some special gifts to make your lives easier at this busy time of year.  We have a couple of fun things planned for you.

First of all, each one of us is offering up a gift for you--we are taking one of our products and making it free for you, our loyal readers!  Just stop by my store on Sunday, November 20 or Monday, November 21 and grab this for free--and check out the other 7 versions as well! This offer is only good for those two days, so mark your calendars!

When I use word problems (which is nearly every day), I like having a variety of formats to choose from--and this (as well as many of my other sets) has three different "looks" to choose from.  This is one of 8 different seasonal sets --so check out the others if you like what you see!  Just stop by my store and search for "Seasonal Word Problems" or click the image above to see more!

Also, we would love to give a little more, so each blogger in this "hop" is also giving away a $25 gift cards to Teachers Pay Teachers so you can load up with even more great resources for your classroom. Because there are FOURTEEN bloggers involved, you have 14 chances to win!  See below for details. 
We wanted to keep our giveaway in the spirit of the season as well, so entering is easy...you have three chances to enter mine.  The first is asking YOU to share a picture or comment about YOUR blessings on social media...your Facebook page, Instagram, or Twitter.  Use the hashtag #sharingourblessingsTpT .  I'll do my best to visit and check them all out!

A second way to enter is to subscribe to my newsletter--which you can do by checking out the top right corner of my blog.  If you already DO subscribe, just leave your email address and let me know that you already subscribe.  Finally, you can subscribe by following me...on TpT, on FB, on Bloglovin'-or all of them if you wish!  Just let me know your follower name and where you followed me.
So...sound like fun?  Then don't forget to check out all these other AMAZING bloggers who are participating as well.  Think of all the chances to win and all the wonderful "gifts" you can receive.  Don't forget to come back on Sunday to pick up your copy of my Winter Word Problems, completely free!


Wednesday, November 16, 2016

Math Workshop Thanksgiving Style

So often, I get questions like, "What does math workshop look like in your classroom?" and it's always such a tough question to answer--because it changes all the time.  So I thought I'd tell you about my plans for the next week or so leading up until Thanksgiving--and see if you can picture what I'll be doing!  Maybe in a month or so I'll do another post and show another "twist" on math workshop organization!

For the next week or so, our curriculum has me scheduled to work on subtraction with regrouping.  As you can imagine, I have students at ALL levels of sophistication with that skill--so there is no real way I can teach for a week or more whole class!  My goal is always to maximize the amount of time students spend on "just right" instruction, so here's what the next week will look like.

1.  Pretesting and regular formative assessments

Although I don't  do them every day, doing quick progress checks are SO important to me.  Based o what I find, I can group students in different ways on different days to make sure that everyone gets as much "just right" instruction as possible.  Everyone leans at different rates--and waiting until the end of unit is simply not an ok time for students to get feedback on their performance.  These quick checks literally take minutes and can help me see who is getting it--and what types of mistakes students are making.  This error analysis is so important in helping us streamline instruction.
addition and subtraction exit slips

2.  Full class and partner warm ups

To warm up our brains each day, I make a choice of a warm up activity.  Some days it might be a number talk, other days it may be a review problem or two--but one of my favorite warm ups is a challenging word problem!  I LOVE using word problems to warm up because it sets the stage for thinking all day!  I often have them try a problem alone first where they try to implement all the strategies I have taught to "dig in".  After a bit of work time, I offer up the option to pair up to continue.  Some choose to keep working on their own, others like the collaborative part.  I circulate and check for understanding, encourage organization and precision, and hunt for interesting work to share under the document camera. What problems am I using?  Thanksgiving problems, of course!  I love these because they are filled with cool facts--and each has two levels of challenge.  I use several as warm ups, and then the rest of them get put on the wall in a pocket chart for students to do when they have time--or as a rotation in math workshop.  I try to have other problems available that might be more "accessible" as well--so that those "wall problems" are not seen as something for only my top students.  ALL students can easily access word problems to do during their math choice times.
Thanksgiving problem solving
These Thanksgiving problems are fun because students LOVE some of the cool facts they include--and each has an "extra" part to allow those students who are ready to add a level more challenge!

3.  Small group, targeted  instruction

 For these weeks, the lessons focus on subtraction...starting small (even with base 10 blocks for some) and then eventually moving through subtraction across zeros with increasingly large numbers and money problems. I definitely will need to be grouping over the next week or so--and I am planning on two different approaches to this.  Some days I will be splitting my class in half and teaching the concept at two levels.  This allows me to spend more time with my struggling students and to use more hands on teaching methods to help build their conceptual understanding.  When I do this, I do NOT meet with my two groups for equal amounts of time...my mini lesson for my "on track" students might be 10-12 minutes followed by some supported practice while my strugglers might get my full attention for 25-30 minutes.

Other days I might teach the lesson to the entire class (I did this today) and then I either assess or have students self-assess and I follow up the lesson with a second "reinforcing" lesson.  I often call this "coaching time" where I invite (or mandate!) students who might have struggled during the minilesson to come do some additional work with me.  Students who are ready to roll can do some independent practice, make sure they are on track, and then move to some differentiated activities that are a good match for them.

4.  Differentiated activities during workshop time

So...if I am only working with a part of my class at a time, I need some quality independent or cooperative work for them to do.  I have a HUGE problem with doing math "fillers", so I am always looking to find engaging work that my students love and ask them to really apply math skills--or to practice fluency on skills they need.  Here are some of the options we will be using during that workshop time.  Some things may be required (like my top students are required to work on this Thanksgiving Feast Thinker Task and some of my students needing fact fluency are required to do some of the fluency games), and other activities are offered as choices.  Here they are!

First, this is an differentiated problem solving task that has many parts--so students who solve the first part can continue on.  Almost all students choose to work together and I just LOVE the conversations they have.  They truly "teach" and coach each other as well as any adult can...and they really are pretty independent so I can focus my attention on specific students or groups.
problem based learning
Thanksgiving math problems
The next option that I have ready for my students is a set of Thanksgiving games...it comes in both addition and multiplication--and each of THOSE has two levels of challenge.  My students LOVE this game (We started it last week) and they get tons of fact fluency practice.  It's also a super easy one to copy and send home...just a few dice and markers (even pennies or paper scraps) and they are ready to roll!  I have had students begging to stay in for recess to play!
Thanksgiving addition game

Thanksgiving math game
One third choice is another fluency practice activity I call "Toss and Solve".  Students have laminated cards that look like this--from two digit on up to 4 digit.  They roll dice to make the bottom number and then work to solve.  They can either check their work on a calculator or two students can each solve it, compare answers, and then work to solve any discrepancies.  I LOVE having students hunt for errors...and brain research says this is a great way to build those brain connections!

I have a recording sheet that students use--or they can simply do their work on the cards or in a math spiral.  Although this is a more traditional computation practice activity, it's far more fun than a worksheet--and when you involve partners and error analysis, it's WAY more than a worksheet!
addition and subtraction activities
Remember, too, that there are always word problems available as well, so students really have several choices during this short unit.  I work hard to help my students make just right choices, but there are times when gentle reminders are needed!

When I am not teaching my small groups, I am circulating and coaching as students do these different activities--and my goal is also to pull a few intervention groups along the way as well.  I still have a number of students FAR below grade level who need work on basic number sense and fact strategy work, so while students are busy during math workshop, I have time to pull them and work on their varying needs.

Thanks for stopping by and taking a peek at my next week and a half or so of math workshop as we dig into our subtraction with regrouping review.  If today was a sign, I know I am going to have a pretty sizable group needing enrichment during this time--not a bad problem to have, right?

Interested in any of the resources mentioned above?  Just click the photos above or these images below.  Thanks for stopping by!

Thursday, November 10, 2016

Google Drawing Tools and Scientific Drawings!

Google drawing tools
One thing I like to do every year when I study electricity with my class is to take the time to teach them how to use drawing tools on a Google slide.  Most have had very limited experience with this--but take to it quickly and use it often throughout the year.

As we have worked our way through our lessons on safety, how light bulbs work, conductors and insulators, and different types of circuits, we have been reading books and articles, taking notes in our interactive notebook, building circuits and testing out hypotheses--and I wanted to give them a technology connection to let them show some of what they have learned.

We reviewed the different types of circuits--and the point of "scientific drawings"--to convey information graphically with pictures, symbols, and labels.  I showed students the following Google tools:

  • Drawing shapes, changing color, changing line color and thickness
  • Drawing different types of lines
  • Creating and resizing and moving text boxes
  • Selecting shapes and changing their size and rotating them
For a few students, I showed them about "ordering" their shapes as well--so they could "hide" their wires and so on.  I showed them these skills on the projector and then sent them off to get creative!  I encouraged them to coach each other and to think of different ways to use the shapes and lines to create a drawing that would clearly show either a series or a parallel circuit--and off they went!


electric circuits

Google slide lesson
I loved watching the students dig in and help each other!  I walked around coaching, asking questions, and trouble shooting but overall I was SO pleased to see how much initiative students took to "try" on their own and to ask desk group neighbors before asking me.  Each student found their own way to show their circuits--some very simple, some more complicated--and not all 100% accurate...but they learned a ton, talked about science and technology, and were VERY proud of their work!
scientific drawing
We think they turned out pretty cool!
electricity project
You could certainly do this lesson with pretty much any science content...drawings of plants...simple machines...the water cycle.  Get creative!  If you are teaching electricity and want to see more of what I do with my class, just check out my resource that can supplement a textbook or a hands-on kit.  See what you think!

Tuesday, November 8, 2016

Getting Students Thinking about Fractions

fraction unit

Just wanted to share some fraction fun from our first day of fraction review!  I like to dig in by really getting students thinking--no fill in the blanks for THIS review! Check out what we did today to kick off our fraction studies.

One thing I love to do is to start off lessons with discussions... we start in discussion pairs and then share out key ideas with the entire class.  These "Discussion Starters" are simply true statements that might be interpreted in different ways and can get students talking about what they might mean and to think of examples.  We practice our math talk too--adding on to what others say, asking or clarification, and so on.  We had some GREAT ideas shared!

teaching fractions
After we got our brains warmed up with key ideas--like that fractions have equal parts, can be shown in different ways (on a number line, with shapes, with collections of objects, etc), I sent my students off with small groups to find different ways to "make" representations of different fractions--halves through eights.  
fourth grade fractions
As students were working, I put out a stack of post it "flags" for students to use to mark contributions they want to talk about...for whatever reason.  LOTS of discussions going on at this time!  Love it!  
fraction activities
So...as students marked certain "samples", I picked a few to redraw and share under the projector--and the debates began!
fraction unit
I just love inviting students to come up and try to use their reasoning and math language to explain their ideas in front of the class...and have their classmates agree, add on, ask for clarity, or respectfully disagree.  The fun part?  We didn't come to any FINAL conclusions...math class doesn't have to end when the bell rings!  Let them think and stew on things overnight.  Seriously.
fraction reasoning and thinking

If you like this lesson, you might enjoy my fraction unit--16 lessons that promote deep thinking.  It includes tons of activities, assessments, discussion topics, and more!  Check it out and see what you think--teaching fractions can be fun!
constructivist fractions