Thursday, April 11, 2013

Technology: Finally!

We have Technoooooolllloooogy!!!! (Said in my best "Oprah's Favorite Things" voice).  Because we were able to build all new schools, we also received all new interactive whiteboards, as well as speakers in our ceilings and MICROPHONES!  If you know me at all, you know I love to sing, so my poor students always catch me singing into the microphone.  It always lightens the mood, especially during testing prep when things can get a little tense.

Today, I decided to slow things down a bit and let the students use the interactive whiteboard to show their answers on their homework.  Normally, I would just slide their paper under our document camera, but he's been feeling a little under the weather lately, so we've had to do without (I feel LOST without it, but we make do!).  We have been doing a lot of reviewing lately, as well as making connections between all the different areas of math, so last night's homework involved circle graphs, fractions, and percents.  We can ALWAYS review that!  They were given four frequency charts with information that they had to put into circle graphs using the fractions given.  Here are some pictures of a few of the students recreating their graphs;

Ben was the first brave soul to give it a try!  Pretty good!

Paige and TeShon hard at work!

The last class of the day seemed to have a hard time deciding which fraction was larger; 3/8 or 1/4, so we decided to use the highlight feature on the interactive whiteboard to give us a better visual.  As we were highlighting, I heard lots of  "ohhhhh!!!!!!"  The visual really helped, and it was so much easier with the interactive feature.  Check out the picture below!

 I can't wait to start  utilizing our new technology in the future!  Woo!

Tuesday, April 9, 2013

Probability: Math Notebooks

Today's Math Notebook was inspired by the WONDERFUL Mrs. Runde over at Runde's Room, although, I catered it to our needs.  I really liked how she had her students write out the learning goals and task before starting, so I decided to try it.  I always let the kids know what our goals for the day are, as well as have our "I Can" statements posted clearly in the room, but this is the first time we really put it in writing as a class.  We have been working with probability, so I decided to make a spinner as well. I also liked how she had the kids figure out a way to divide their circle in ten equal pieces as a nice review on dividing as well as remembering how many degrees are in a circle!  We also love working with protractors, so it was a nice review.   (We also had the chance to review equivalent fractions AND percents!  All in one activity! YAY!) Below is our page:

Because our goal was to compare theoretical results with actual results, and to make predictions, our notebooks ends up steering away from Runde's a little bit.  We have been having trouble creating frequency tables lately, so here was a great opportunity to do so.  I was going to have them do their experiment 20 times instead of just ten, so we based our theoretical results off of 20 (and reviewed equivalent fractions at the same time!)  I also had them come up with a prediction of what they thought would happen, based on their theoretical results.  Then, it was spin time!  They recorded their results in their frequency table and wrote out their conclusions based on their actual results.

Lastly, we met to talk about the reasonableness of certain results.  We used our theoretical results to determine if the actual result was reasonable or not.  Before this lesson, only 50% of my students answered a "reasonable or not reasonable" question correctly.  After this lesson, we were up to 87%!  I would say we succeeded!  :)

Algebraic Expressions and Math Notebooks

We covered Algebra way back in October and did a really great foldable for the four steps to follow when solving a problem with unknowns.  We came back to it today, both as a review, and to extend our thinking to expressions and patterns.  Our learning target for today was to introduce the use of algebraic expressions to represent situations and describe rules.  First, we watched this StudyJam on Function Tables, as well as one on Addition and Subtraction Equations and Multiplication and Division Equations.  We also did a sample problem in our notebooks, as shown below.  The problem reads:

Joe and Maria are 5th graders.  Joe is two inches taller than Maria.  

I asked the students to put this information into a function table and give me some measurements for Joe and Maria.  I reminded them to make them reasonable measurements for 5th grade students.  Of course, everyone had different answers, and all were acceptable as long as Joe was two inches taller.  Next, I recorded some of their measurements on the board and asked them to explain how they came up with Joe's height.  We also noticed that our function table was similar to the In and Out boxes they have become so familiar with using Everyday Math.  I asked them what the rule was for this table.  Of course, they all said "add 2!"  Then, I encouraged them to tell me the rule for finding Joe's height based on Maria's if we use m for Maria.  This was a little tricker, but with a little prompting, they said "m+2!" Now we're talking!

Next, we wrote some sample problems in our notebooks and came up with expressions to describe the problems (EDM 10.3):

After some more practice independently, I gave the students an opportunity to write their own problem situations that would require the use of a variable.  I forgot to capture this in a photo, but they did a really great job!  Being able to write their own, and accurately, made me feel confident in their understanding of expressions.

Capacity: Interactive Math Notebooks

Capacity is always fun!  Unfortunately, when moving to our new building, all the containers I had saved for this day were tossed thinking it was trash!  Can you believe it? Someone thought our old milk cartons and jugs were trash!  Anyway, I'm lucky to have a mom who also teaches 5th grade math (you should hear our phone conversations....very animated!) and because she had taught capacity the week before, she was willing to lend me her collection.  Saved by mom (again!).  After a lot of spilled water and "do you predict this container will hold two or three of these?" we moved into our notebooks to record our thoughts.

First, we wrote down the Big G.  Why didn't we have this when I was a kid??  I never remembered what the Gallon Bot was and it was way too difficult to recreate, but the Big G is EASY!  It's truly how I remember my conversions.  Here is a picture:

Next, I gave them a moment to free write.  I really wanted them to write down everything they knew about capacity, so each student's page is very different, but many chose to write down conversions based on the Big G.  I walked around making sure that they understood how to read it.  Here is one example:

Of course, there's also an anchor chart hanging in our room of the Big G that we refer to often, but I didn't feel the need to post it here because it is the same as the notebook page :)

Measurement and conversions: Interactive Math Notebooks

Again, I'm behind on posting this! Where does the time go?  We did measurement back in March, and while we did a lot with it, I'm just going to outline what we did with our notebooks in this post.  We began by discussing the two systems of measurement.  We decided the best way to organize this information was in a T chart (we REALLY like those around here!) and we wanted to keep all the types of measurement (length, capacity, weight) together as well.  Here is the list we came up with:

Next, we brainstormed some of the basic conversions we remembered for length for each system and wrote them down.  Lastly, we took notes on an easy way to convert between units of measurement.   A BIG "thank you" to my coworker Adrienne, the 4th grade math teacher, for sharing her mnemonic device!  Some of my students remembered it from last year!  She taught us that there are two ways to change units: to multiply or divide.  When converting from a Big unit to a Small unit, you Multiply, so we think "Best Soccer Mom."  When converting from a Small unit to a Big unit, you Divide, so we think "Silly Babies Dancing."  We always giggle at "Silly Babies Dancing!"

Below is the anchor chart hanging in our room to serve as a reminder.  Another "thank you" to Adrienne!  I got this straight from her!  Thank goodness for kind coworkers willing to share and kick around ideas with!

Surface Area: Interactive Math Notebooks

We didn't spend a lot of time on Surface Area after all the time we spent on area, perimeter, and volume.  I really just wanted the kids to understand the concept of it, not necessarily how to find it.  We will get to that later in the year.  So, in order to demonstrate the idea of surface area, I wrapped a box in wrapping paper to show that we needed to know how much paper to use to cover the box.  I also gave each student a net for a rectangular prism and asked them to color just one side to represent wrapping paper.  Then out came the interactive math notebooks!  We creased each net and glued them into our notebooks so that when they flip to that page, they can easily fold it back up to look like a 3-D shape!  Here is an example:

Because we just finished up volume, we made a T chart in order to make comparisons between volume and surface area.  I told the kids to think about a tool box or toy box to tell the difference.  Here is what we came up with as a class:

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 Well, there ya have it!  A quick and easy day!  Thank goodness for math notebooks!

Wednesday, April 3, 2013

Pi Day!

March 14. Finally. An ENTIRE DAY dedicated to MATH!  And it's PERFECT for 5th grade!  I started getting the kids excited about Pi day early in March.  Some knew that pi = 3.14, but they really didn't know much more than that.  I could feel the excitement as they entered the room that Thursday morning.  I only had 90 minutes with each class and each minute was accounted and planned for, so we got right to business. Here is an outline of our activities for the day!

1. Quiet morning activity: Write as many digits in pi as you can around a paper plate

I used a paper plate for two reasons: I have 75 kids and they are CHEAP! And, of course, it's a circle.  The directions were on the projector when the kids walked in and they quickly figured out they needed to sit as close to the board as possible so as not to miss a single digit.  I only gave them about ten minutes to make their paper plate.  I wanted them to have something to take home to show their parents as well as something to study from for our Pi contest.  More on that later!  This activity also got them wondering what the heck pi was!  Here are some paper plate making shots:

Allison ended up getting 4th place in our pi contest!

Busy at work making their paper plates!

2. History of Pi

We found a short history of pi in our books, and discussed it briefly.  Many kids were fascinated by the fact that the definition of pi has changed so much throughout history (their teacher was fascinated too!).  I could feel the excitement building now!

3. Measurement of circles and discovery of pi

We briefly discussed using centimeters in our measurement and getting right down to the exact millimeter so that our measurements were as accurate as possible.  This was just a review for them.  We also discussed measuring diameter as going right down the center of the circle as well as reviewed what ratio meant since we were finding the ratio of circumference to diameter.  We did one example together, and off they went about the room.  I had a table full of circular objects for them to choose from, and a chart from to fill in as they went.  While they worked, I walked around and discussed findings, as well as helped troubleshoot when I could tell their measurements were off.  
All the lovely objects we have to measure!  Yes, that is my soap from my bathroom, and my coffee mug :) 

"Ms. McHugh, did you even wash out your mug?"  

Pretty accurate I would say!  

Partners hard at work measuring and loving every moment of it!

What a great day!

4. Discovery

Once we were finished, we had a lengthy discussion about what we learned.  Ultimately, I wanted them to see that the circumference of a circle was about three time its diameter.  We used our knowledge of finding the unknown (all our algebra work is paying off!) to figure out that if you don't know the circumference, but you do know the diameter, you can use pi to help you find it.  There were a couple ah ha moments at this point.  I literally saw the understanding unfold on Ivy's face!  It was neat to see her go through the process of understanding using our measuring activity and finding 3.14 was (about) the ratio each time, to knowing that she could always use that to find circumference.  These are the moments people!  The ah ha moments! :)

5. Short video

We always try to wrap up with a short video from StudyJams, and today was no different.  It gives them a chance to listen to someone else talk about what we learned and they do a great job of putting concepts into real world situations.  If you haven't checked out StudyJams yet, I encourage you to do so!

6. Cookies

On a day like today, you have to have a fun treat!  Every student received a cookie, but don't worry, we found its diameter and circumference first!  YUM!

7. Contest time!
Lastly, I held a digit reciting contest.  I gave them until the next day to see how many digits they could memorize in pi.  It was completely optional and just for fun.  I was so impressed by how many students really got into it, and memorized WAY more digits than I ever could!  Our winner was Cale: he memorized 78 digits!  WOW!

All in all, this will stand to be one of my favorite days of the year.  I think my students would have to agree!

An Exploration of Volume

Ok ok....So it's April and I taught volume almost a month ago.  Things can get pretty hectic this time of year, what with preparing for the OAA and making sure my kids are in tip top shape to show what they know!  Now that we're on Spring Break, I can finally sit back and reflect on what we've been learning and where we need to go after this.

I truly feel that math should be a hands-on experience for kids of all ages.  It shouldn't stop in 3rd grade.  All too often, we get caught up in making sure they know how to do it on paper and apply formulas, but kids need to be able to touch and feel what they are learning to really grasp it and understand it.  I always try to give them thorough hands-on experiences before teaching them the "math" part: formulas and equations.  So far, I think we've been pretty successful.  But, as in most cases, time is always an issue.  We just have to keep moving, moving, moving!

As will area and perimeter, we did an exploration of volume.  Many of my students had remembered the formula for finding the volume of a rectangular prism from 4th grade, but I wasn't really sure they understood or remembered WHY you multiplied LxWxH.  Thanks to Everyday Math, each student had the net of two different open rectangular prisms in the back of their math journals.  We made predictions for how many cubes we thought would fit into each.  These predictions actually gave me pretty good insight as to where each student was in their understanding of volume.  Then, of course, we began filling!

 We started by just filling the base of the prism and finding out many cubes that was.  I wanted them to see this as the area of the base: of course, some did, some didn't.  We will keep working on this idea of area! (Too often, their idea of area is just a rectangle on a page....must change that thinking!!).  Then we added another layer, and finally a third.  This allowed them to see that we were adding the area of the base however many times tall it was.  For the second prism, we only filled the base and predicted what the volume would be based on the results of the first prism.  From this, we developed the formula for finding the volume of a rectangular prism!

As an extension, and because we had a couple extra minutes at the end of class, I had each student build a rectangular prism on their desk with a volume of 24 cubic centimeters.  I didn't give them any more specifications than that.  After a minute or two of building, I began recording different lengths, widths, and heights that I saw around the room.  Once they saw all the possibilities, hands flew in the air.  They remembered what we had learned about multiplication being part of the commutative property and knew they could use the factors of 24 to build many many different prisms, all with the same volume.  Ah ha moments are the best :)

Lastly, here is the anchor chart we came up with.  They wanted me to point out that volume is "all about the threes":