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Welcome to my math blog! The purpose of this blog is to help you stay informed about our learning and experiences that have taken place during our math class. I have also included links your child (and you) may want to use in order to supplement math learning in 5th grade.

Thursday, October 31, 2013

Great Pumpkin Caper

Every year my math classes get to enjoy "The Great Pumpkin Caper."  Oh.... they think we are going to do something like a pumpkin carving contest, or eat pumpkin seeds, or do some other non-mathematical activity with the pumpkin.  Little do they know!  Today was all about math!

To begin, each group gets a pumpkin, a piece of butcher paper, and a recording sheet entitled "The Great Pumpkin Caper."  I explain that we are going to explore our pumpkin using math (at this point there are usually groans).  I explain that we are going to begin by making a few predictions about the pumpkin and then we will work to find the actual answer to the questions.

The questions we are answering were:

  1. How many pounds does your pumpkin weigh?
  2. What is the circumference of your pumpkin in centimeters?
  3. How many lines does your pumpkin have around it?
  4. Will your pumpkin sink or float?
To find out how much a pumpkin weighs, we have to get a little creative.  I have a scale, but it is difficult to get a precise measurement if you just sit the pumpkin on the scale.  Instead, I have a volunteer stand on the scale (knowing we will learn their weight) and we determine the weight of the child.  Then I ask the child to hold the pumpkin.  We determine the new weight, and find the difference between the two weights.  This is the weight of the pumpkin.  

To find the circumference for the pumpkin, I have to do a little prep work with the kids.  First, I ask them to define circumference (distance around a circular object).  Then I ask them how they plan on finding the circumference of my pumpkin since my rulers don't bend (I do not offer tape measures).  They problem solve and decide that we need string to go around the pumpkin, cut the string, and then use centimeter rulers to find the length of the string.

The most enjoyable part of the day is watching the kids' faces as we discover whether a pumpkin sinks or floats.  Invariably, about 90% of my classes believe the pumpkin will sink.... it is heavy after all!.  When they see that the pumpkin floats, no matter its weight, the look on their faces is priceless!  (I would include pictures, but it would take away from the moment if I aim a camera at them!)

The greatest portion of the day is spent working with the seeds.  I want the kids to make a REASONABLE estimate for the number of seeds in the pumpkin.  So, I cut open the pumpkins and have them take out the seeds making a large pile (pulling off the pumpkin guts).  Then I give each group a scoop (1 tbsp) and have them make piles of pumpkin seeds.  When all of the seeds are in smaller piles, the kids count the seeds in one pile.  Then they multiply this number by the number of piles.  This gives them their REASONABLE estimate.  Finally, they have to count all of the seeds in each pile.  I have them keep track by writing the number of seeds in each pile with chalk beside the pile.  Finally, they add their piles together.  Hopefully, when they compare their estimate to their sum they find that they are fairly close.

At this point we are just about out of time.  I have time enough for them to answer the following:

  • Three things I discovered about my pumpkin.
  • Two things I measured.
  • I thing that surprised me and why.
Tomorrow we will put all three classes' data together and discuss our estimates.

HOMEWORK:  xtramath.org

Wednesday, October 30, 2013

Last Day Long Division

Don't get too excited.... we are just moving on.... it will be back!

I did a little differentiation today.  All that means is that I had kids working at different levels.  Basically, I had three groups.  The first group worked in Content Mastery to get the little extra help needed.  The second group worked with me.  I was just a sounding board!  I was very pleased with how well my kids worked!  They seem to have it down!  The third group worked on the computer doing  xtramath.org  and  khanacademy.org.  These kids had division down yesterday HANDS DOWN!  So, instead of making them do more of the same, I allowed them to work on programs that meet them where they are mathematically.

There is HOMEWORK tonight.  Usually I do not have homework on Wednesday because we are all in the computer lab, so xtramath gets done.  With needing to finish up our long division, we did not get to the lab.

Tomorrow is the GREAT PUMPKIN CAPER!  Please be sure to check out the blog.... loads of pictures!

HOMEWORK:  xtramath.org

Tuesday, October 29, 2013

Working with Long Division

Not too much to share today.  The majority of class was working with solving division problems.  The classes were expected to estimate, divide, and check each problem.  

At the end of class I did ask the classes to complete an exit ticket.

The classes were asked to complete the following sentences:

One thing I accomplished today
What I did to participate
I want to know more about

The purpose was to have each student evaluate their work in class.  Division is hard!  I wanted to see how they felt about their work in class today.

HOMEWORK:  xtramath

Monday, October 28, 2013

Decimals on a Number Line AND Long Division

We have been working on placing decimal numbers on number lines for a few weeks (every Monday during warm up).  Today, I wanted to gather all of that information into our journal.  I wanted the kids to be able to look up how to place decimal numbers on number lines just in case they forget between now and the next time they are asked!  :-)  The completed page is shown above, but if you would like to see the process, please watch the video at:  Decimals on a Number Line.

The most difficult concept to get across is that you are "zooming" in, or magnifying, a portion of the number line as you work with decimals.  For example, to "see" 10ths, you have to magnify the whole number section that would contain the 10ts.  To "see" 100ths you have to magnify the 10ths section.  To "see" 1000ths you have to magnify the 100ths section.  To help get the idea across, I shared the book "Zoom" by Istvan Banyai.  Each page "zooms" out to show a larger portion of the scene (this is just a small example):

As if that wasn't enough to do.... we also worked with long division.  Today was just a walk through reminding students of what is expected when solving a long division problem:

  1. estimate:  page 8 in journal
  2. divide:  page 10 in journal and Robotic Parts video
  3. checking answers to division:  page 11 in journal and checking division video

I am spending a considerable amount of time on this concept because it is difficult for the kids and they need time to practice.  So, tomorrow we will continue working with long division.

HOMEWORK:  xtramath.org

Friday, October 25, 2013

Robotic Parts (Checking Answers)

Our work with long division continues.  We actually began by completing the final question from the worksheet yesterday.  This was a good way to remind ourselves of the steps:  1) estimate, 2) divide.  I also wanted to but this back into their heads for another reason.  I wanted them to write me an "Exit Ticket" answering the prompt:  

Justify why you believe it is helpful 
to estimate the quotient to a long division 
problem BEFORE solving the problem.

Next, we took a little detour from division.   I felt like they needed to know how to check their answers to their division problems before we move on to working independently!  So, we began by creating a foldable for our journal.  To see the video about the foldable, please follow the link:  Checking A Division Problem (Foldable)

Next, we used these notes to help guide us with finding the answer to our division problems.  We used yesterday's assignment "Robotic Parts" and found the answer to the robots' right hands using our new knowledge.


Have a great weekend!

Thursday, October 24, 2013

Long Division (Robotic Parts)

Long division.... one of a 5th grader's biggest nightmares (right up there with fractions)!  I attempted to make the idea easier by requiring the classes to estimate their answer to the division problem BEFORE working with the algorithm.

The process is involved, but the outcome was encouraging.  To see how to estimate a 3 digit by 2 digit division problem and use this estimation to help solve the actual division problem, please watch my video by going to: Robotic Parts (Long Division)

Today was just the beginning of our time with long division.  My goal is to take away my kid's fear of long division!

HOMEWORK:  xtramath.org

Wednesday, October 23, 2013

Computer Day (say it like a camel!)

Every Wednesday is our math computer day.  Since there isn't much to tell you if I just let you know we went to the computer lab, I decided to remind you about our daily warm up.

We always begin the class by completing our warm up.  Each day hits specific skills that are important for 5th graders to understand.  As a reminder, this includes working with the number of days we have been in school.  As of today, we have been in school 41 days.  

  • We turn this into a decimal (.41)
  • create an equivalent decimal (.410)
  • create our fraction (41/100) 
  • go find the factors of 41 (1, 41)
  • We determine if 41 is prime or composite (prime)
  • We name its prime factor (41)

  • We locate the greatest common factor of 41 and 100.  (1)
  • We create an equivalent fraction.  Since we cannot simplify 41/100, instead we create an equivalent fraction by using multiplication.  So, if we wanted to multiply by 4, our equivalent fraction would be 164/400.
On Wednesdays, we find area.  However, in order to find the area of our square today, we had to use its given perimeter (24 cm) to determine the dimensions of the sides.  We chose to use the formula for perimeter to help us:
  •  P = s x s
  • 24 = 4 x ?
  • so the side = 6  
Then we used our formula for area (A = L x W) to find the area of the square:
  • a = 6 x 6
  • so the area is 36 square centimeters
Our final warm up activity was to use our 5th grade graph to work with range, mode, mean, and median.

  • Range is the difference between the largest and smallest number:  13-2 = 11
  • Mode is any number that has a repeat:  13
  • Mean is the average, so we added (54) and then divided by the number of pieces of data (7) and got a quotient of 7 remainder 5.  We then had to determine how to round our answer.  Since the remainder (5) is more than 1/2 of the divisor (7), we knew to round the mean to 8.
  • Median is finding the exact middle number of making out the least and the greatest numbers.  This left us with 7.

Before heading to the computer lab we answered our new graphing question:  

What is your favorite part of Halloween?
  • costume
  • trick or treat
  • carving pumpkins
  • eating candy
  • Halloween party
  • other

Finally we headed to the computer lab.  We began by completing an xtramath exercise.  Remember, once your child has passed the multiplication portion of xtramath, he or she is finished with xtramath as homework!

Next, the kids worked with khanacademy.  I like this program.  It allows your child to work on closing any gaps in their math and then allows them to progress at their own speed!

Tomorrow....long division!

Homework:  NONE

Monday, October 21, 2013

Who Stole It? (Single Digit Division)

We began by asking a question... "Is Division Easy?"  (See the video at:  Is Division Easy)  I had the students create a journal page and we answered this question with another question...  "Does McDonald's Sell Cheese Burgers Really?"  This second question is really an acronym that is meant to help students remember the steps to a division problem:

  • D - divide
  • M - multiply
  • S - subtract
  • C - compare
  • B - bring down
  • R - repeat or remainder.
We also added a few division vocabulary words:
  • dividend - what is being divided
  • divisor - what we are dividing by
  • quotient - answer to division problem
Finally, we defined division as the opposite of multiplication.  We also noted that division is actually separating into equal groups.

Since, today's focus was on division, we used the paper from Friday called "Who Stole It?"  On Friday, we had used these division problems to estimate answers (see Friday's blog).  Today, we worked the problem and compared our answer to our estimates to see if our quotients were reasonable.... THEY WERE!  See video:  Who Stole It? (Division)

My goal is to show students that if they will estimate their answer before solving a division problem, then they can use the estimate as a starting point!  Knowing where to begin when solving division is half the battle!

Homework:  xtramath.org

Friday, October 18, 2013

Estimate Single Digit Division Using Compatible Numbers

Wow!  What a quick day!  We did have 40 minute classes, so I was able to work with the classes on estimating the answers to a single digit division problem.  If you would like to see the process, please watch the video at:  Estimating Single Digit Division using Compatible Numbers.  Oh, please excuse the intercom interruption... it's just part of the day!

Otherwise, we had pep rally, PE, and lunch and then we were out the door!  Have a great weekend!  Go BULLDOGS!

Thursday, October 17, 2013

Estimating with Compatible Numbers

Our topic today was compatible numbers (as shown above).  We focused on note-taking and making a foldable in class and will use this information starting tomorrow when we begin our unit on division.

To begin, we made another foldable titled "Zero Is A Hero:  Division".  One half of the paper focused on estimating quotients to division problems with one digit divisors.  I made a video of this session and it is available on youtube at:  Zero Is A Hero: Division (part 1).

The second portion of the foldable focused on estimating quotients with division problems with multiple digit divisors.  This second video is also available on youtube at:  Zero is a Hero: Division (part 2)

Compatible numbers are extremely helpful when we work with division using multiple digit divisors.  It will help determine a reasonable starting place.

Homework:  xtramath.org