About Me

My photo
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, December 19, 2013

Twelve Days of Christmas: Experimental Probability (5th Grade)

Twelve Days of Christmas

Today we combined the data from all three class to find our total experimental probability.  I explained that the more data we gather the more accurate our percentages will be.  Instead of looking at just 100 pulls, we are now looking at the data from 300 pulls.  We just the following spreadsheet:

First, we determined our fraction, then we used calculators to find the decimal, and then converted our decimal into a percentage.  As we worked, we were comparing our data to the theoretical data (what SHOULD have happened).  If it was exact, we circled it.  If it was a 1% difference, we placed a check mark.  If it was more than a 1% difference, we placed an 'x'.

As you can see, we had two pieces of data that were exact.  We had 6 more pieces that were a 1% difference, and only 2 that were more than a 1% difference!  We discussed our data and drew a few conclusions:
  1. Our experimental data as a 5th grade was much closer to the theoretical data.
  2. If we had a fourth classroom in 5th grade and were able to add another set of data our experimental data would probably be even more closely related to the theoretical data.
The kids did a final circle graph.  Then they were asked to compare the 5th Grade Experimental Data Graph to the Theoretical Data Graph and describe an observation.


This will be my last post until January 6.  

Wednesday, December 18, 2013

Twelve Day of Christmas: Experimental Probability (Class)

Twelve Days of Christmas

Today we moved from theoretical probability (what SHOULD happen) to experimental probability (what DID happen).

We sat in a circle.  I had a container with 364 beads.  There were 12 different colors.  Each color represented a gift (black for partridge in a pear tree), and there were the same number of each bead as gifts given (12 black for the 12 days "my true love" received a partridge in a pear tree).  We passed the container around 100 times to see how many of each "gift" we pulled.  We recorded our data on our Experimental Probability spreadsheet:

Once we had our data, we turned the information into a fraction, then a decimal, and then a percent.  It was much easier today because we were dealing with a denominator of 100!  So a fraction of 3/100 = .03 = 3%.... no calculators needed!  The interesting part is that each classes' data is different because you are dealing with luck!  So the data we gathered in each class is below:

 To finish off the day, we created a new circle graph that shows today's percentages.  Each class' graph will be different.  

Finally, the classes were asked to complete an exit ticket.  They were to write two generalizations comparing the Theoretical Probability Circle Graph to the Experimental Probability Circle Graph.


  1. Complete the circle graph/exit ticket
  2. Countdown 2.3

Tuesday, December 17, 2013

Twelve Days of Christmas: Theoretical Probability

Twelve Days of Christmas

Today we began discussing probability (the likelihood an event will happen).  I explained that we are going to put all 364 gifts into a jar (in the form of pony beads) with each gift being assigned a color.  Our question today was, "What is the probability we would pull --- from the jar?"

To determine the probability we worked through THEORETICAL probability.  

Theoretical probability is what SHOULD HAPPEN.  

We completed the following spreadsheet to find the theoretical probability of each gift:

First, we look at the fact that "my true love" was given 12 partridges in a pear tree out of a total of 364 gifts.  We have the fraction 


Second, we turn this fraction into a decimal.  To do this we use division.  I had to discuss with my classes that a small number CAN be divided by a larger number.  When we divide a smaller number by a larger number we get a decimal (we used calculators)

12 ÷ 364 = 0.032967

We do not use the entire decimal number, we just want the number to the hundredth's place. 


Third, we turn this decimal into a percentage.  Basically, percent means "out of 100".  Since we have our decimal to the 100ths place, we drop the decimal point and we have our percent:


This percentage tells us how many times we SHOULD pull a black bead from the container tomorrow.  We SHOULD pull a black bead 3 times from the container because we will be pulling a bead (and returning it) 100 times.

We did this for each gift he gave her.  Our completed spreadsheet looked like:

Finally, we turned all of our percentage data into a circle graph.  This will allow us to visually see the patterns that developed in our data.

  1. Complete the bar graph
  2. Countdown 2.2

Monday, December 16, 2013

Twelve Days of Christmas COSTS WHAT?!?!?

The Twelve Days of Christmas

I love this week!  This is one of my favorite math weeks.  We began by exploring how many gifts "my true love" received in the song The Twelve Days of Christmas.  While the number is impressive, my kids minds are blown by the total amount spent on the the gifts!

To begin, I show my classes The Twelve Days of Christmas pop-up book by my favorite pop-up book author, Robert Sabuda.  Then I posed the questions:

  • How many gifts do you think "my true love" received?
  • How much money did he spend on "my true love"?
To find out, I had gone to the Christmas Price Index.  This site is updated the first Monday of each December.  It gives the current price for each item as well as the total price of the collective 364 gifts.

I did not want to just go through the index, so I created a power point along with a spreadsheet for us to explore the answers to these questions.  The spreadsheet keeps track of the number of days each gift is given, the cost per day, the total for all of the days, and the number of gifts given each day.

My kids were more than surprised by the amounts some of the gifts cost!  They were also surprised by the number of gifts given (364).  However, they were most taken aback by the total amount he spend on "my true love".... a whopping $114,650.89!  

Our completed spreadsheet:

Who knew math could be fun?!

HOMEWORK:  Countdown 2.1

Friday, December 13, 2013

Problem Solving with Algebra Model

Today my students had to put their thinking caps on.... they had to solve 8 word problems independently.  However, they had to use the algebra model that we have been working so hard on this week.

This process still stretched their problem solving skills as they had to search the problem for the clues given to solve it!  They need to realize that they are really just solving a puzzle and need to find the pieces that complete the puzzle without forcing pieces in that do not work!

We will be moving on to a new topic next week....one that is holiday themed.  It is one of my favorite weeks in math!  As usual though, don't be surprised to see problem solving happening daily!

Have a great weekend!

Thursday, December 12, 2013

Solving Word Problems using our Algebra Model (Day 2)

We worked with solving word problems using the algebra model that we have been focusing on for the past few weeks.  It is a slow process, but it seems to be helping students to focus on the meaning of the problem.  

For many students the most difficult part of math is decoding the problem (what is being asked, what parts of the problem are needed, which parts are not needed, which operation(s) should I use, which one should I do first.... ).  Many of my students assume a problem is "hard" because there are words.  Wouldn't all of us love to have math thrown at us in ways like "What is 4 + 4?"?!?!  Instead, we spend our entire day solving mathematical problems that are multi-step word problems.... we just don't write them down.

Think about it.  As you are going through the grocery store, more than likely you are on a budget.  You know how much you have to spend and you have no intention of going over (no matter how much your child wants that sugary cereal and is letting the entire store know!).  So, as you walk the aisles and place items in your cart, you are either keeping a mental estimation going, or you are using the calculator on your phone.  This is problem solving.

Math does not come at us in the form of algorithms.... it comes at us as a multi-step problem we have to work through.  The same is being asked of our kids.  The expectation is that students should be able to work through a real life situation (most of these situations ADULTS don't have to go through, much less a 10 year old) and be able to determine the best possible way to solve the problem and achieve the correct answer.

After looking at the data between the released STAAR Math Benchmark that I gave on December 2 (which is full of 50 problems, most of them very difficult multi-step and many-worded), and the Renaissance Place STAR Math that they took online yesterday (34 problems, with few examples of word problems), I noticed a pattern.  My students performed much higher on yesterday's assessment.  I feel that it was because they were faced with straight algorithms that they understood instead of monster word problems that they have to wade through for meaning.

Please encourage your child to read.  Please.  The more exposure they have to written material the larger their vocabulary will become.  The larger to vocabulary, the easier it is to decode meaning.

HOMEWORK:  Countdown 8

Wednesday, December 11, 2013

Computer Day

We had class in the computer lab.  We began by taking the Renaissance Place Star Math assessment.  This assessment gives me an approximate grade equivalent, a percentage score, and an idea of their algebra readiness.  I will be comparing this data to the scores given to me from the end of their 4th grade year.  This will give me an idea of who is in need of intervention.  If you are interested in seeing your child's results, please let me know!

Next,  students did xtramath.org and then worked on khanacademy.org.  Students are trying to master skills so that they can earn rewards for the Khan Club.


Tuesday, December 10, 2013

Solving Word Problems with Hands-On Equation Models

We started late again today.... the ice has been something else.  It was 20 degrees last night....

However, we were able to have normal classes today, well, pretty much.  I was very excited to get to connect our Hands-On Equation models to word problems!  

I spend the entire school year giving my students strategies that they can use to help them solve problems.  Very few things make any 5th grader happy to have to solve a word problem.  I am not saying that they are now thrilled to meet up with a problem with more than 10 words to it, however, they are becoming more equipped to solve these problems through a variety of models.

We have worked with

  • Open Number Line models
  • Strip Diagram models
and today we worked with (for lack of a better name)

  • Algebra models (pawns and cubes)
I was very pleased with their reaction to seeing how a word problem could be broken down into a model that they are comfortable using.  We did 9 problems as our introduction today and will work with additional problems tomorrow.

I made a video of the introduction to our lesson today.  You can view it at Solving Word Problems with Algebra Models to see how turning the words into a visual model helped break the idea that word problems are "hard".

Also, if you would like to see the types of questions (mostly words problems) your 5th grader will have to solve (in 4 hours) the day of our Math STAAR, please visit the TEA website.  Choose the Grade 5, 2013 Mathematics link.

HOMEWORK:  Countdown, p. 7

Monday, December 9, 2013

Snow Day (Part 2): Late Start

We began school at 10:00, had lunch at 11:45, and lost our music kids from 12:30 - 3:30 as they practiced for their play that has been postponed to this evening.  So.... weird day.

Friday, December 6, 2013


In Texas.... it's a BIG deal!  Actually it wasn't even snow.... ICE and lots of it!

Thursday, December 5, 2013


We briefly touched on patterns today.  We have just survived two LONG days of benchmark testing for math and reading.  So, I decided to take it easy on my students today.  We worked with numerical patterns and then watch Eddie Files:  Patterns: "The Big Concert".

There are numerical patterns:

There are patterns in nature (These are my favorite!  Google "Patterns in Nature" and enjoy the images!):

There are patterns in art:

There are patterns in clothing:

There are patterns in music:

There are scientific patterns:

Patterns surround us in life.  Just keep your eyes open and you will find them!


Wednesday, December 4, 2013

Computer Day

We had class in the computer lab.  Students did xtramath.org and then worked on khanacademy.org.  Students are trying to master skills so that they can earn rewards for the Khan Club.


Tuesday, December 3, 2013

Math Benchmark

My students took a math benchmark today.  This benchmark was the released STAAR test that my 5th graders took last year.  I give benchmarks for a number of reasons:

  1. Benchmarks allow me to see where my students are strong and any area of weaknesses that I need to address.
  2. I am able to use the data to determine any intervention that needs to take place in small group settings and at a more individualized level.
  3. The kids are able to see the types of questions they will have to answer in April (50 questions that must be completed in 4 hours).
This is the first benchmark I will do over the next few weeks.  We will also be taking:
  • Study Island Benchmark - Students were given this exact assessment at the beginning of the year.  I am looking for growth.
  • Star Math (not to be confused with STAAR) - Students took this at the end of 4th grade.  I am looking for growth.
  • MStar (algebra readiness) - Students were introduced to this assessment in September.  We will take the second installment in January and a third installment in May.  I am looking for growth in their algebra readiness in preparation for Junior High.

HOMEWORK:  Countdown p. 6