Math Curse

As I was reorganizing my classroom library this summer, I realized in the middle of building the shelves that I was doing a whole lot of math! AND, it was math that my students would be learning throughout the year!

Problems lead to questions, which lead to answers that can be solved mathematically.  Why not share this with my students at the beginning of the year to show them that I, too, do math... even during the summer. A bonus is that a bulletin board is also created so it's not left blank. :)

Since I read aloud Math Curse at the beginning of the year and do an activity with it already (students find and write their own math problems they find throughout the day), I figured it would be a good board to display.

The board features all the questions and problems I encountered through this one task of making bookshelves:

Here is where my problem starts:

Revamping Math Centers

I'm a big proponent of math centers for their small group appeal, novelty for the kids, and more activities to refuel their brain when they transition.  I'm also a proponent for whole group instruction when it's necessary because, to be honest, there are notes/certain lessons that I don't want to teach in small groups over and over and over and over and... you get it.  I want to spend my small group time focused on needs of students.

Anyway, I enjoy centers and have always thought that when I did them, they were done pretty well and I put a ton (probably too much) thought into what the specific activities were.  But because they took so long to plan, I didn't do it as consistently; only when I felt they were needed or when I had enough activities.  That was my biggest problem.

What do I want?

• centers weekly, not whenever (it will also aide in the math planning process & build practice time)
• go-to activities (so I'm not always thinking of activities for that station) that review, promote thinking, practice fluency of basic skills, etc.
• more differentiating (really able to meet with my high kids more often)
• not get rid of my whole group time (I need this independent time to target my low kids more often... which is why I wasn't getting to my high kids as often)

Luckily, as I was contemplating all this, I got an idea from a great teacher in my district during a training held in her room. She had a math rotation chart up, but the colors didn't go in order from one rotation to the next.  Talking to her about this, I got many ideas and tweaked it to match my room.

 Lo and behold, this is what I came up with:

First, let's talk flexibility:

• The top activities are taped on, so they're interchangeable...and I could use this chart for non-math centers in the future (I'm all about not redoing everything).
• Group names are also taped onto the bottom crayons to allow student movement based on concepts currently being studied.

Major Qs after people see this:

• Why is there an "x" on the tutor station?  I don't have an aide during that time.  She is actually not even there for the full 3rd rotation.  Therefore, I strategically planned my lowest kids with her during rotation 2 to get her the full time.  My middle kids are with her during the 3rd rounds.  She has plans and knows that when she has that 3rd round of kids, she should be doing her guided practice during the first 10 minutes and check for understanding before leaving and having them do the rest on their own.
• Why do you have only 6 groups but 7 stations?  This is because my tutor is not with me at all times.  A problem solving group could be used for my higher, independent kids who don't need her (since she's not with me full time anyway). Also, I am able to be flexible and add in or take away stations I don't need that week.
• Why don't the crayons go in order diagonally? This idea I got from that teacher in my district. Not every kid will hit each station.  My lower kids will probably not hit enrichment.  Some students need to build fluency with basic math facts more often than others. I organize where they'll go weekly and that sets my math plans for 2 days!
• How often do you do centers? I'll do centers twice a week (3 rotations/day). Other days are whole & small group break outs.

Here is a picture of my computer spreadsheet for 2 different weeks where I moved groups around:

BRIEF description of each station: (they can change anytime)
Computers: Greg Tang or other related sites on my class webpage; I'm also trying to implement Think Through Math this year as a more structured go-to computer station where I can assign pathways related to our current unit
Teacher: Based on the group I see, I may go over tests, guided practice problems, introduce different manipulatives, give math problems with difficult number sets, or move on
Fluency: reinforce basic operational skills with Equation Station Puzzles or Kakooma sheets found on the Greg Tang site
Tutor: more practice with middle to low groups
Problem Solving & Logic/ Hot Dots: If it's a review week, we will do Hot Dots (also sold on Amazom) and/or save this station for problem solving.
Review/Enrichment: more practice or enrichment work for high kids
Marcy Cook: See this post about Marcy Cook


How I organize stations:

Most stations have a manila folder (I'm working on something less lame as this is just a post it!) with colored construction paper folders inside (according to group color) to hold student material.  Students are taught to return papers back into their colored folder in case it is an activity that can continue next week. Also, I am able to see how much each group completed, check for understanding, and see if I can use the material in a teacher/tutor station to continue/review.   

DIFFERENTIATE: I felt that in the few weeks I have tried this, I have been able to differentiate so much more.  The high kids tend to be the ones left out, moving slower than they should.  For example, in this Review/Enrichment center, I have different activities in their folders based on abilities.  My red group is high and this activity  has them explaining their thinking with specific math vocabulary words.  The words have a fractional point value.  They add up the point value of the words they used in their explanation when they're done (still adding mixed numbers, but more in depth). My purple group is lower and needs more basic practice with the word problems we've already worked on that they haven't finished (they'll solve in their math notebooks). 

Thanks to friends and donors from DonorsChoose for these Hot Dot cards and pens.  I think the kids will really like the immediate feedback from the talking pens.  Don't you worry... I have plans for what to do if they misuse the pens.  ;) White boards are provided to help write down thinking if needed.  The manila folder holds groups' colored folders with their tracking sheets.

See this Marcy Cook post for more info about my set up.

And because it's my blog, here's a picture of my ultra cute baby working with me as I set up my math centers.

Marcy Cook Math

So I remember when I used to complete these as a kid.  Who says that what we used to do is totally out?  I purchased eight Marcy Cook Tile Packets to use as a center in my classroom (more about revamping my math centers in another post).

When I purchased, they were $15/packet, which isn't too bad, but can add up since I bought eight! However, I think it will be money well spent.

Depending on your students & the packets you purchase, these can be good review, fluency building, or challenging activities.

The "greater, equal, less than" packet that I purchased was purposeful as a starter to get my class thinking while figuring out how to use the materials.  As you can see, it still creates logical thinking and problem solving skills, as students are required to use all 10 tiles to complete the card activity.

What comes in each packet:

• sheet with suggested ways to use materials
• 20 card sheets
• reproducible student tracker sheet
• answer key
• directions and example cards

What you'll need to purchase:

• Quiet Tiles made of vinyl (or make your own 0-9 tiles)
• They are $1 each, not a dollar for four... I was obviously confused by this description: The strips ($1.00 each) come in four different colors  (I purchased 3 thinking I'd get 12, but alas, made a couple number squares out of construction for now.

student tracker sheet

How I set up the Marcy Cook station:

• I put each set of number tiles in a resealable baggie (5 total since that's the maximum number I have in a group)
• I placed the answer key in a plastic sleeve (so students can self-assess) and the direction/sample card on the back (I sadly have no prep volunteers this year, so spending all that time laminating is out for me).
• I copied the student tracker sheet and placed them in the colored construction paper folders (these are group colors...that way students won't have to dig to find their sheet each time they come to this station). 

As we work through them and students work at different paces, I will have to figure out how to put more than one card pack out at a time.  20 cards to start will suffice for now.

I'm super excited to see how the kids respond to these tile activity cards.  I anticipate it being difficult for my lowest kids, but they will hopefully get better.

Worksheet Turned Math Center

Ok, the week I did this lesson, I was being WORKED!  Stressful week, too much on my plate, irritated easily, emails galore, always feeling behind, beating myself up for not having better lessons because I planned it last minute... ever happen to you?

Well, this is not the best lesson I have ever done, BUT it turned a would-be worksheet into small centers and allowed students to move more often.  And since not every lesson can be so amazing, I thought I'd share how I tweaked a bland lesson into a more fun one. I thank the combination of "last minute planning" and "beating myself up for not having better lessons" thoughts the day before.

First, I took the 8 problems on the worksheet and called them tasks.  I then copied the question as many times as they would fit onto a sheet of paper, copied them on different colored paper, & cut them into strips.  My plan was to have them keep these work examples in their math notebooks. (If you weren't doing that, I assume you could leave space below for them to solve & then cut the paper.) I found by doing this, I also saved lots of paper!

I then placed each task in a different place around the room with a task number and glue bottle.

Students' jobs were to start at a task (didn't all start at #1) and move around the room at their own pace.  They glue in the strip, complete the work, get checked, and then move on.  

Of course, because they are working at different paces, some will be moving to a different station faster than others, and that's okay.  This would be the case anyway with a worksheet.  I had an activity ready for early finishers in addition to using them as "tutors" for those who need more help.  

For next time...

• One thing I did NOT do and should have was start my lower students at the same station so that I and/or my math aide could help them all at once on skills they needed and moved them together from station to station.  
• I will think about putting in an answer key at each station so students can self check.  I did originally want to do this, but knew many students would check incorrectly.  This is because we are modeling and I wanted to check for accuracy.  Perhaps I will only put in answer keys at some stations so I won't be so bombarded by checking answers.

Fraction February - Hands On # Line of Division w/Remainders!

Ok, I thought this went really well, especially as an introductory lesson!  AND, it's still Fraction February!

I had taken notes and planned how to teach the modeling of division of whole numbers by fractions WITH remainders, and we're finally here.  I knew this would be a difficult concept for the reasons I mentioned in this other "Fraction February" post. Therefore, I wanted a way for students to "see" the model in a way other than following my notes under the document camera.

Here's the problem:  Mrs. H had 2 pounds of dog food.  Her dog eats 3/5 pound per meal.  How many meals will she be able to feed her dog with the 2 pounds?

They had already modeled division problems like this where the answer fits in evenly, so they knew the process.  We had also talked about the "pattern" they see in the division... essentially, what is the algorithm?

When I gave them this problem, they all did exactly as I expected.  They drew a number line and did everything just right, but got stuck at the leftover spot.

NOT the correct answer.

Some answers they came up with were simply "remainder 1" or "1/5," the latter of which I knew was going to be the most common.  When I asked what 1/5 represents/means, they said it's how many pounds are left in the bag.  Then I said, "Yes, 1/5 means the pounds left over, but that doesn't answer my question.  The question is how many MEALS I can get out of a 2lb bag, not how many pounds are left."

Since they have already figured out the "pattern" to the algorithm, we just did it.  Yup, we multiplied the inverse of the 2nd number to get 10/3, which was 3 and 1/3.  I asked if they could see the whole 3 in their model, which they all could.  When I asked where the 1/3 came from, I got silence.  I even questioned, "In the original problem of 2 divided by 3/5, fifths is the unit we're working with... so where did we get this 1/3, which is the correct answer?" About two of my highest math kids could tell me, but that was it. I could tell the rest of the room didn't get it based on their explanation, which needed to be refined.  So we did this hands on number line whole group.  This picture below was the end result.

I pulled popsicle sticks to have each child do each part.  They had to work together to partition the number line as evenly as possible.  Note: Our #line went all the way to 3 for the purpose of "seeing" the remainder.  They labeled the whole number & fractional parts on the bottom of the #line. The chalk was used to show the 3/5 jump for every meal.  Then we labeled the #line by meals on the top.

Fraction February - Multiply Fraction by a Fraction

So I've already taught this unit, but never blogged about it.  And since it's Fraction February, what better time!  I taught it directly after teaching multiplication of decimals by decimals and multiply decimals with thousandths grid since they are so related.  Even though I knew this would be much more difficult than using the hundredths grid, I wanted to jump right in when the process of the math was very similar.

I decided to teach it from the basic progression... starting with more of an enactive (hands on) way of solving, to iconic (visual) before moving on to symbolic (algorithm).

Enactive Modeling of Multiplying Fractions by Fractions

I made these fraction squares on a Smart Notebook file before printing out onto transparencies.  I couldn't find any online that divided up a square in the SAME direction.  For example, fourths were quartered into 4 squares, but that would not work for my purposes here.

Fraction February - Division of Fractions by Whole Numbers

Ahhh, since there is no commutative property in division, it DOES matter whether the fraction or the whole number is written first.  Unlike the ease of multiplying fractions, students need to be very careful when reading division of fraction problems.

Anyway, division of fractions by whole numbers is a much more difficult concept, so I taught it after students grasped division of whole numbers by fractions, as detailed in my previous post here.

What's difficult about this is that students start with something less than one and then have to further divide it into smaller pieces.  In doing this, they need to be able to determine equivalence in order to represent the answer in relation to the whole.

I will be using the same theme of the dog food example as I did with my other division of fractions notes.  I plan to stick with it so after we learn all division of fraction types, students can compare/contrast the different ways the problems are worded, how you would write the equation, and how they will be solved based on the question asked.

Fraction February - Division of Whole Numbers by Fractions w/ & w/o Remainders

We are learning to model division of a whole number by a fraction on a number line.  The first day went much better than I expected!  Woo hoo!!!

While planning, I had to be VERY purposeful about what number sets I used.  Not all division of whole numbers by fractions turn out so evenly on a number line.  I wanted students to be able to grasp the modeling and understanding first before introducing number sets that would not be so "nice" to them.

Therefore, as I planned for number sets, I determined...

1. what denominators I wanted them to work with.  I'm not one to get all crazy and give them thirteenths!  
2. what numerators with that unit size will go into which whole numbers perfectly.  These will be the number sets I use first.  (Basically, if you invert & multiply before dividing and it comes out as a whole # answer, the number set works nicely for modeling.)  I tried not to use such a big whole number.  Here are just a few:
• 2, 4, or 6 divided by 2/5
• 3 or 6 divided by 3/5
• 4 divided by 4/5
• 2, 4, or 6 divided by 2/3
• 3 or 6 divided by 3/4
• any whole # divided by 1/any unit size works

These are notes we took for dividing a whole number by a fraction (when they are "nice").  Since students did a pretty good job of explaining reasoning for each step when multiplying fractions by whole numbers as mentioned in this post, I decided to add reasoning in their notes this time around.  I noticed a mistake... Step #5's reason should be that I count the number of jumps because that represents the number of meals the dog ate.

Fraction February - Multiply a Fraction by a Whole Number

Well, we've been doing fractions for awhile, but Fraction February happened to sound nice.  We just finished the unit on multiplying fractions by whole numbers and I wanted to share how it went.

First, I had to go over what is an improper fraction, what it means, and how to model it different ways.  This is key because student answers to multiplication of whole numbers by fraction problems may result in improper fractions. I also want them to be able to write answers in mixed form.

I didn't formally teach students they could divide the fraction to get the mixed number.  Students know that the fraction bar is essentially a division sign, but I want them to understand the concept of decomposing and seeing their work in their model first.

Baby Name Revealed using Coordinate Graph Hidden Messages!

The best part about reading others' blogs are the cool finds, especially when they relate to your specific grade level and standards.  Fifth grade Common Core math requires students to master coordinate graphing within the first quadrant.  I always move to all four quadrants with students who are ready, though.  So anyway, I was reading posts from Teaching in Room 6 and am totally PSYCHED with what I found!!!

Multiply Decimals with a Thousandths Grid... I'm Dizzy!!!

Be warned!  Coloring in this model made me dizzy!  And I don't think it had anything to do with being pregnant.

We have a week before Thanksgiving Break, so I decided to not start something so new for math, but expand.  We just finished multiplying with whole numbers, whole numbers by decimals, and decimals by decimals - modeling everything!  You can read about those concepts and get some downloads here. So I thought expanding to using the thousandths grid would be a nice way to end a unit, mixed in with some Thanksgiving themed math of course!

Anyway, here are the notes we took together:

Folded Cover of Math Notes... I would have typed it, but thought about it last minute at the copy machine.   So this is what they get.  It works.

Inside of the notes:
I blew up the thousandths grid so that it was easier to see.  The green was hard to see in the examples, even under my document camera.  I'd use a darker color next time.  Helpful tips: having SHARP colored pencils made it easier to color the thousandths.

I also gave some problems like the ones on the right that they could practice with.  Making sure students write the numbers in the correct place was crucial.

Here are the pdf copies of the notes and problems I gave students: Model with Thousandths Grid

For this concept, I did not start with contextual problems  We had been doing SOOOO much of that with decimals by decimals using the hundredths grid and they GOT it!!  Woo hoo!  For this concept, I really wanted them to be able to figure out place value first.  For example, students may accidentally write .7 when it is in fact .07 that they counted.  The thousandths place also got tricky.

I plan to give them contextual problems on an 11 x 17 sheet of paper like the picture below tomorrow.  It is double sided, so 12 problems were more than enough since we will be in centers this week.  They start this in one center and then continue with me at the next center (so I could see/help) before doing other fun Thanksgiving review stuff.

The word problems I used can be found here: Thousandths Grid Word Problems

By the way, do you ever look on Pinterest or Teachers Pay Teachers and feel like you're never doing anything cute?  I'm making all my word problems, finding models, creating lessons/notes, lessons, quizzes, and enlarging, reducing, and/or cutting and pasting things to be copied the way I want them that I barely have enough time for cute.  Phew!  Talk about late nights.  Oh Common Core!  But hey, they are getting it!  And I am here to share it FREE.  :)

Oh Math Planning... How I Love and Hate You

Ok, I am a total math girl, especially 5th grade math.  The rigor and content is just so exciting!  It's right about where even adults have a difficult time with the math.  I'm sure most of you teachers (and non-teachers) have heard of the Common Core Standards.  The Common Core math is our district's focus since it is a shift when it comes to the depth of knowledge kids are expected to comprehend certain concepts.  Modeling and explaining WHY things work takes time, energy, and effort (students and teachers).  I love planning it, and I hate it for the time it sucks out of me.

Yes, there's stuff out there, especially on Teachers Pay Teachers, but not all of it is Common Core aligned, even if it is labeled as so.  FRAUD!  You have to really look at it.  I've seen things called "Common Core" and it's just a worksheet with problems and maybe one number line.  No, not Common Core.  And if it is pretty Common Corey, it's usually more expensive because it's good.  I don't know about you guys, but I can't spend an arm and a leg on one unit, much less a bunch of units!  Plus, after the time it takes me to sift through everything, I realize that I could have created something myself.  No, it wouldn't be with the cute graphics or pictures, but it would be what my kids needed specifically this year.

I am in no way saying I'm a Common Core expert, but I am doing the best I can with not as many resources available.  I teach them the algorithm when appropriate and model the others when necessary.  With 5th graders (compared to primary), they're really getting the short end of the stick since so much of what 5th CC builds on is what they really "know" from the previous years, such as the 3rd and 4th grade fraction units.  However, since CC didn't really roll out for our district until last year and teachers are still experimenting, I have to know that pre-teaching 3rd of 4th grade concepts is necessary to continue with what I need to do sometimes.

What I like about creating my own stuff is that:
1) I can use their names in contextual problems
2) I include things they're interested in
3) It's electronic so I can change and reuse as needed for future years

So anyway, enough rambling.  I wanted to share a few concepts we've been working on.


ADDING & SUBTRACTING WHOLE NUMBERS & DECIMALS
With adding & subtracting, I did this with whole numbers and decimals together, emphasizing lining up by PLACE.  By 5th, they should be able to do this with the algorithm, so I didn't spend too much time on the other models.  It's not the main focus for 5th grade... although you wouldn't believe the amount of kids who can't add or subtract with regrouping by the time they're in 5th.  It's shocking!

I added tree diagrams in, but really didn't push it, since the algorithm is much more efficient & they should be doing that by 5th anyway.