But...that was intentional...

It's okay to disagree with a fellow teacher.  It's okay to not want to deliver a lesson the same way as another teacher. It's okay to put your own spin on things.  Some things should be the same (the assessments, the vocabulary, the definitions), but we aren't going to teach the same way.  That's okay. I have a difficult time following instructions or lesson plans verbatim, even when I'm the one who wrote them.  Don't get me wrong, I am always meticulously prepared for my day.  I just also take advantage of teachable moments.

However, I do get a little frustrated when it seems almost every instructional decision I make is questioned.  I've got a lot of background working with special ed kiddos and with the pacing of units.  Things are sequenced intentionally to help students make connections between background knowledge and new content.  The use of manipulatives (hands-on materials) during the first few days of a unit is quite necessary.  Students, even my fifth graders, need the concrete examples to investigate a concept.  They need experience in the concrete before moving to representational and abstract understandings of content.

We are starting division on Monday.  The standards quite explicitly state do not teach the standard long division algorithm. This is not to be introduced until sixth grade because students don't have the number sense nor mathematical understanding to reason through what is occurring.  

Here it is, straight from our professional development department:

I'm not really sure how much more clear this could be, but there were still debates about what it means.  

The first few days in our math unit has a lot of investigation by the students.  I'm giving them a bunch of paper clips to sort into smaller groups.  Some problems will divide evenly, some won't.  

I want them to tackle it. I want them to struggle.  Some kids will count those 48 paper clips into the groups one at a time, driving their partners bonkers in the process.  Some will make the connection to multiples and give away larger groups.  Some will use their multiplication facts to estimate the quotient.  Some will see division as repeated subtraction while others will see it as repeated addition up to the dividend.  

That's okay.

I want my students to understand what they're doing.  I want them to make connections.  I want them to discover how division is related to the other operations and take ownership over their strategies.

My math unit is scaffolded intentionally.  The first day is exploration.  The next introduces vocabulary terms, goes over making sense of the problems (hello math practices), and has student generated strategies.  Direct instruction doesn't begin until day 3 after students have had ample time to investigate sorting and making groups with paper clips and cubes.  From there, we'll move to hundreds grids and talk about regrouping.  We'll make the connection from the physical orange flats, rods, and cubes to the paper versions and drawings, thus moving from concrete to representational. From there, we'll move into number based strategies that build upon other operations, powers of ten, place value, and multiples.  Again, scaffolded from representational drawings and grids to strictly numbers (abstract).  There's a plan.  It took hours to design, but I'm really excited about it. The plan, which spans thirteen instructional days, scaffolds so students will feel successful and anticipates common misconceptions.

However, another teacher entirely disregarded the plan...and told me about it, gleefully.  She had them try one problem with manipulatives and then gave them the algorithm.  I'm so disappointed and feel sad for her students.  I'm sad they lost the opportunity to make their own discoveries. I'm sad they lost the chance to feel ownership over the concept. I'm sad they lost the opportunity to have a meaningful struggle with the tasks.

Her justification? They'll learn it next year and she's doing the sixth grade teachers a favor.  Besides, the standard algorithm is just faster.

I'm aware it's faster.  Faster yet? Whipping out my phone and using its calculator function.  But what's the point in that?  What do they learn when they're just handed the short cut?

I'm standing my ground on this one. My goal is not to teach math.  Yes, you read that correctly.  My goal is not to teach math.

My goal is to have my students understand math.  I want them to know what they're doing, why they're doing it, what happens to their numbers, and why their problem works out mathematically.

I'm making critical thinkers and problem solvers, not robots.  I'm aware it takes more time, but this mindset also encourages stronger students and that's my ultimate end goal.

Math training, days 2 & 3

After tackling my homework for math training, grocery shopping, and spending several hours leveling my library (such a daunting task), I didn't have the energy left to process what I'd learned.  

However, today I was home much earlier so I could reflect on yesterday and today's math trainings.

Days 2 & 3:

We talked about multiplication.  We talked about it...a lot.  Perhaps it's because I teach fifth grade and have taught inclusion, but none of the strategies mentioned were new information.  I grasped the concept right away and helped my neighbor make the same mathematical discoveries.

However, I did learn a few new things over the past few days.  Here are my "ah ha" moments:

The minuend is the first number in a subtraction problem and represents the amount you start with.  The subtrahend is the amount that is being removed or subtracted.  

This discovery raised an interesting question within our group.  Why is it that other math vocabulary terms (addend, sum, factor, product, quotient, etc) are well-known but minuend and subtrahend aren't?  Why can teachers (and hopefully their students) use the correct vocabulary for the other operations, but stumble on subtraction terms?  I know I'll be incorporating these terms into my math instruction!

"Give One, get one, move on" strategy

The page is divided into four sections.  Students solve the problem in the first quadrant, which is labeled "give".  After time to process the problem, students then will stand up and find three other people to "get" strategies from.  The students will work in pairs to explain their strategies to one another.  Not only does this allow for movement, but students can explain their thoughts to one another.  During this time, the teacher is monitoring as an informal assessment to see what students are grasping the content and which ones still need a little more practice time.

The next classroom tweak deals with these manipulatives:

Found in almost every elementary classroom, I always called these "ones", "tens", "hundreds" and so on.  Most teachers do.

However, in doing so, you're limiting students' understanding of the relationship (powers of ten) between the manipulatives.  

These will henceforth be referred at as units (smallest), rods (long ones), flats, and cubes.

By doing so, a teacher is able to stress the relationship between a value being ten times larger or smaller than the value next to it on a place value chart.  

Referring to these as units, rods, flats, and cubes also allows for the manipulation in upper elementary.  If my "one" is now the cube, I can use these manipulatives to represent a tenth (flat), a hundredth (rod), and thousandth (unit).  I can also regard the unit as a thousand, then have students prove the other values. (Rod would be 10,000, flat 100,000, cube 1,000,000).  

Finally, we played close to 100 (from Investigations).  While this game was not new to me, I did appreciate the discussion about its importance in the classroom.  In playing this math game (and others), students are provided the opportunity to practice many math skills such as estimation, reasoning, critiquing the reasoning of others, operations, and place value.  These games take minutes to learn, can be a good task for students if they finish early with an activity, and can be used as homework.  I know my students would much rather go home and play a math game as their homework then fill out a worksheet.  

Close to 100 also reminded me of another quick math activity:

What an easy way to get their brains working during the first few moments of the day!

Stay tuned for a recap of days 4 and 5!

20 Wins

I first heard about "20 wins" from a math professor at UNLV and have used this math strategy game every year with my students.

The essential premise is students play using the digits (0-9) and try to make 20 with any four connecting corner boxes.  They can use any operation.

I modeled with my students (me against them):

Before l let them loose!  

They loved it!

You can download one here for your students!  I included extension suggestions!

Math Centers Bundle

Since I teach my math in small groups, my students need a center to keep them engaged and on task when they're not with me.  We don't have enough iPads or computers to go around, so I compiled my dozen favorite math games for students to play.  I bundled these centers and you can grab the 20 page packet here.

These games require very little teacher prep beyond gathering supplies (cards, dice and for some, candy) and printing the materials.  They can be scaffolded and incorporate any operation(s) depending on the grade level.  Some can even be sent home as homework to practice with students.

My students, which were almost all English language learners and about half had individual education plans, excelled at these.  I rarely had behavior issues because they knew if they were off task, that meant they were choosing silent book work instead.

Hope your students enjoy these stations as much as mine do!

Math Anchor Charts and Ideas

I love great math ideas.

Here's an easy center to make, it just requires sharpies, a plastic bag, some patience and old water bottle lids (yay upcycling!)

This center can easily be differentiated for any grade level depending on the operations that are used.  For fifth grade, I would use parentheses and all operations signs.  This would be great for making algebraic expressions, practicing multiplication and division, finding unknown values and using decimals to show place value.

Students could easily bring in lids to help you collect the supplies.

With the Common Core, fifth graders have to review geometric shapes and classify them into a hierarchy.  This is a great example of an anchor chart that could help students:

Before we go into 3D shapes, I would review 2D shapes on the geoboard.  Most classes have a set of the old plastic boards and rubber bands, but there is a great free app on the iPad that allows students to virtually manipulate geoboards.  As a bonus, you can expand the board from the traditional 5x5 to a much larger 10x10 board, allowing for more room to make shapes.  This app could be used as a formative assessment where you call out a shape (ex, right scalene triangle) and students make one to show you.  

Plus, there are different colored rubber band options with the app :)

This is a great freebie I found on another teacher's blog:

I've used it in my classroom and it's a great center to review number sense.

You can also use cups to review place value:

For a review of area and perimeter, you can use graph paper, markers and dice for this easy game of war.

Students roll the dice, then create the corresponding array.  Students must strategically place their array on the grid and try to stump their partner.  I like that this is a nice model of how repeated addition and multiplication are the same.

This can easily be differentiated for lower grades by having students add the dice rather than multiply them. 

This is another great (priced) TpT center that my students enjoy:

Plus, it's pink and polka-dotted!  Grab yours here for a buck! 

Happy math time!