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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.

Monday, November 30, 2015

Personal Financial Literacy: Choose a Home

So this week is going to by CRAAAAZZZZEEEE!  It began today with having 50 minute classes and a Science Benchmark!

The time I did have with each class was spent working our our budget.  To recap, we had each chosen a career, we then took out our income tax to find our net income, then we divided that by 12 to find our monthly net income, and finally, we took out 10% to put into savings.

It was time to start delving into expenses.  I introduced the day by discussing fixed and variable expenses.  Then I explained that with our expenses comes TAXES, yes, more taxes.  We defined property and sales taxes in our journal noting how each tax is used and where it comes from.

We noted that people are supposed to determine a maximum housing (including utilities) budget that does not exceed 35% of the monthly income.  Students used their monthly net income, multiplied it by 35%, and determined their housing allowance.  My military career students were about to keep their housing budget at "0"!

For the sake of time, I had students use the housing page given in the teacher guide to locate the house (plus utilities) that fit in their budget.  We added these to our budget sheet, but ran out of time before we were able to determine our ending balance.  So, that is where we begin tomorrow!

Friday, November 20, 2015

Autumn Trees

It is the day before our Thanksgiving Break.  My students have been working hard for me and I wanted us to just take a moment and reflect on what we like about Autumn.

So, on Thursday, I had the kids work on a paper called "Autumn Five Senses".  I had them write three things that Autumn TASTES like, SMELLS like, LOOKS like, FEELS like, and SOUNDS like.  These didn't need to be sentences, just ideas.

Today, we took those ideas and created our Standing Tree of Thanks (I found them at Oriental Trading).  On each leaf we wrote one of our ideas (for example:  Autumn takes like dad's hot chocolate) and then used glue dots to affix the leaves to the tree.

The kids were very proud of their creations and I hope they are proudly displayed at their Thanksgiving dinners!

Thursday, November 19, 2015

Personal Financial Literacy: Savings

Last night, I opened all of my students' Personal Income Tax documents that they were working on.  I went through each and checked for accuracy of addition.  I had already checked the accuracy of their multiplication on their grid sheets (where they show their work), but used the SUM formula in Sheets to check their addition (so much faster).  On each page, as I found an error, I corrected it in red.  This allows my students to see where errors were made, but it also allowed me to input correct information to use today.

So, today, we used the total amount of taxes found yesterday and subtracted it from our GROSS income.  I explained that the difference (answer to the subtraction problem) was the amount of money they actually got to take home!  Students were not pleased to see how much their income decreased!

I also had to explain that this is not the amount of money we take home each month!  Our next step was to divide our net income by 12 to find our monthly net income.  I did check both their subtraction and division numbers as they completed them since I wanted correct information placed on their Personal Income Tax form.  I was very pleased with the number of students who divided PERFECTLY even though they were dividing a HUGE (by their standards) number by a TWO-DIGIT divisor... oh the horror!  We placed this information on our budget sheet to be used as we contemplate our month expenses.

At this point, they were able to "turn in" their completed document and we finished taking our notes about gross income vs net income.  I even showed them a pay stub to see how gross and net income were shown as you receive a paycheck.  To finish off this part of our day, I asked the kids to answer the following prompt:

Summarize what you have learned by explaining
the role TAXES play in your gross and net income.

We also worked with the idea of keeping a savings account.  To begin, we talked about the necessity of a safety net for unexpected things that happen in life.  We referred back to the information we had seen that suggested putting 10% of each paycheck into savings.  So, our next step was to find the amount of 10% of our monthly net income.  We added this information to our budget sheet and subtracted from our beginning balance (monthly net income).

To show how savings can grow quickly, we found out how much we would save over 6 months and then 1 year.  We also discussed putting the money in an account at the bank where it could accrue interest.  They were very "interested" in the idea of getting free money, even though .04% a month is not much.  However, they did realize that, since they received this monthly on the new balance, this added up pretty nicely!

This project is terrific!  It is of such high interest to my students they do not complain about the amount of math they are completing!  

Wednesday, November 18, 2015

Personal Financial Literacy: Personal Income Tax

I very much enjoyed today's lesson on personal income tax.  Yesterday, my classes had chosen a career and found the average salary for that career.  Today, we started chinking away at that salary by finding the income tax they would be due.

The Project-Based Unit (above) is very timely and used the 2016 Tax Brackets to make this even more pertinent.  To begin, I had students find 10% of their salary to take away for various payroll taxes.  Next, we began to find their income tax.  Now, this part of the lesson got a little touchy as every child had a different salary.  So, we all began in the same place.  We all had a salary higher than the 10% tax bracket, so we were all able for find 10% of $9225.  Then we had to subtract $9225 from our salary before heading to the next tax bracket.  In the second tax bracket, the salary goes to $37,450.  If students salaries (after taking out the $9225) were below this, then they took the difference and multiplied by 15%, it it was over, we had to find 15% of $37,450 and subtract again.  For some students, their salaries were finished after the 2nd tax bracket, but I did have a handful in each class that went to the 5th tax bracket!  These students were a little more self-paced and able to work without my immediate help.

After finding all of the taxes taken from all needed tax brackets, we added up our taxes (including payroll) to find the total amount taken from our gross income.  Then we subtracted the taxes from the gross to find our net income.  This was more painful than I thought, as I had students who have gotten used to not lining up the decimal when they multiply, so they didn't line up the decimal numbers when they subtracted.  It makes quite a difference in the answer!!!

We stopped at this point as we were out of time!  We will pick up right where we left off tomorrow!.

Tuesday, November 17, 2015

Personal Financial Literacy: Taxes

We continued our Project-Based learning activity on Personal Financial Literacy today.

Last night for homework, I asked the students to choose a career they are interested in pursuing.  I explained that the difference between a career and a job is the training, usually through college, you receive.  Once everyone had shared their choice, we looked up the average salary for that career in Texas.  I explained that some jobs pay more in other states, so we want the salary for Texas.  I also explained to my boys who wanted to be pro ballplayers and golfers that they would not begin as a Napoli or Spieth.  I asked them to find the average salary of the average pro (if there is such a thing).

Once we had our salaries, I explained that this was their Gross income.  That this amount (split over the year) is what they would receive BEFORE taxes were taken out.

I began by explaining about payroll taxes.  I explained that they are taken from your check monthly by the federal government (IRS).  I began with income tax and explained that this money is used by the government to pay for government jobs, buildings, memorials, etc.  Them we moved on to Social Security and Medicare.  I explained that these taxes were taken from our paycheck each month and held for our use once we retired.  I also explained that employers also match these funds, helping them to grow more quickly.

I then revisited income tax.  I pointed out that income tax is taken from paychecks monthly, but that if the government determines that enough income tax was taken out of your paychecks, you may have to pay an additional amount on April 15.  We also discussed some deductions that are available to help keep the owed income tax down or result in a refund.

At this point, we ran out of time.  So, we will continue with Gross vs Net income tomorrow.  

Monday, November 16, 2015

Personal Financial Literacy: Budgets

We began our Personal Financial Literacy unit today.  I  found a Project-Based Learning activity on Teachers Pay Teachers that I am excited about using:

Basically, we began our project by discussing budgets. We talked about the need for a budget and the importance of a balanced budget.  We talked about budgeting for needs vs wants

 I also had the kids create a budget spreadsheet on a Google Doc.  I decided that teaching them some of the tricks in a Google Doc is easier than introducing them to Sheets right now.  Maybe later this year.  Since my additional focus will be adding, subtracting, multiplying, and dividing decimals, I did not want to show students how to use a formula in Sheets just yet.

The homework was to decide on a career that they are interested in having as an adult.  We will use this information tomorrow.

We finished our day by answering the prompt:

What conclusions can you draw about the importance of keeping a budget and maintaining a balanced budget?

After finishing the prompt, students worked on completing a Countdown to STAAR. If they had time, they began researching career ideas.

Thursday, November 12, 2015

Decimal Operations: Multiplication and Division Word Problems

Today we had to put our thinking caps on!  It began with a "Guess My Number" warm-up question.  The students have to use a set of clues to determine the number.  Then we moved on to our estimation180 problem.  Today's picture showed a roll of dimes in a glass container.  The students needed to remember that a roll of dimes is $5.  They also needed to remember the number of rolls of pennies that filled the same container.  Using this information, they should have been able to come to a very reasonable estimate of the value of the dimes in the glass container.

Our activity today was to work with multiplying and dividing decimals found in word problems.  As always, I am working to keep students interested in solving math problems and handing them a worksheet seems to shut off their brains!  However, I did have a group of students in each class that needed a little more attention, so they took their problems to our Content Mastery to help conquer division.  The rest of the class found these same problems on quizizz.com .  

Once students had completed the questions online, they were to create a word problem of their own using the Ticket Prices from the word problems they had solved.  They were also asked to write the equation for their problem and solve the problem showing their work.

Finally, we worked on a Countdown to STAAR and then on either multiplication or division of decimals on Khan.

Wednesday, November 11, 2015

Decimal Operations: Division by 2-digit divisor

Division....'nuf said!

I did my best to make division "fun" today.  Division is not fun, not to a 5th grader, so I had my work cut out!  I know that division is hard, in the minds of an 11 year old, so I knew there was no way that I was going to assign a set of 20 problems from a worksheet.

So, I took a worksheet called "On Board with Columbus" from The Mailbox Teacher's Helper Oct/Nov 2011 edition.

First, we did problem "A" together as our example.  Now, keep in mind, my students have been dividing all year.  We have done whole number division and now decimal division.  I wanted practice, this was not an introduction.  So, I had each student pull a card that had been labeled B-T.  This was the letter they were to start with on the worksheet.

Once they had solved their problem, they were to go into the hall and find the little piece of red paper with a QR code with their answer on it.  When they found their answer on the piece of paper, we used my phone to scan the code to determine the next problem to solve (kind of like a scavenger hunt).  The final piece of good news was that they were only being asked to solve 5 problems.  The kids really enjoyed this activity!  They liked the "chance" involved and willingly worked their problems.

Tuesday, November 10, 2015

Decimal Operations: Division

Today we started delving into decimal division.  The kids were quite surprised to discover that decimal division is exactly like whole number division, albeit you have to place the decimal in the correct position.

To introduce the topic, we watched two Khan Academy videos.  I wanted the students to see someone else's perspectives on solving these types of problems.  The videos detailed the placement of the decimal point and solving the problem "completely" so that there is no remainder.  

After viewing the videos, the students completed an activity on quizizz.com involving division of decimal numbers by a single digit whole number.  I had assigned 5 problems and wanted to see how students performed as a type of pre-assessment.  Overall, I was very pleased by the ease with which most of my students solved these problems.

Once students completed these problems, they completed an xtramath.org exercise, a Countdown to STAAR, and finally, worked on Khan Academy.

Friday, November 6, 2015

Decimal Operations: Add/Subtract/Multiply using Quizizz.com

I took a time today to do a quick assessment using www.quizizz.com .  I found out about this type of "game" at the workshop I attended last week.  This format is very similar to using a Kahoot, with a few differences.
  1. Kahoot has a two-minute time limit, while Quizizz has a five-minute limit.
  2. On Quizizz, students are not waiting for each other to complete a question, they are moving at their own pace.
  3. There is an element of competition, however, there seems to be less stress in that there is more time available and people aren't waiting on you.
I gave it a try and loved it!  I will still use Kahoot, don't get me wrong, but the kids were much more relaxed while being able to solve word problems.  I used a worksheet called "First Come, First Served" that I have from The Mailbox Teacher Helper from April/May 2013.  As usual, the format of an online "game" kept the kids much more engaged than filling out a worksheet.... it also saves paper!

Thursday, November 5, 2015

Decimal Operations: Multiplication Would You Rather

With our decimal multiplication today, I posed the Would You Rather question: 

I posted this activity on Google Classroom along with a Google Doc for the 3 Act Math information.

Using the information given from the prompt, students soon discovered that the plans were of equal value, with the exception of Option E.  It was a total savings of $.01!  We even discussed the fact that trading in your phone early saves you no money, you are still expected to pay the entire amount!

During the process of multiplying, I wandered the room to ensure success.  I found common multiplication errors, forgetting to bring down the zero, but I also saw misalignment errors.  Students want to line up decimal points when multiplying!

Wednesday, November 4, 2015

Decimal Operations: Multiplication 3 Act Math

We moved into multiplication of decimals today.  I wanted to make this intro a little more entertaining, so we did a Kahoot and a 3 Act Math activity.

To begin, I had to explain that all of the emphasis I put on lining up the decimal point when adding and subtracting decimals, goes out the window when we multiply decimals.

I explained that we have a new set of rules:

I decided to allow the classes to "play around" with this new set of rules by playing a Kahoot.  I created a survey with 4 problems.  I chose to use the survey format because there is no stress on being right and winning... helps calm the nerves!

After completing our quick activity, I had the students create a new Google Doc in their math classroom to help them solve our 3 Act Math problem.  I began by having them watch an Esurance Commercial about saving a ton of dollars.  This was the "hook."  

Once we viewed the commercial, I asked the students what they wanted to know after seeing this commercial (Act 1).  It took a little guidance, but we finally go to "How many dollars are in a ton?"  At this point, I asked them to make a prediction.

Act 2 is about gathering information.  I asked the students what we needed to know in order to answer the problem.  Students knew there were 2000 pounds in a ton. So, they wanted to know how much a dollar weighed.  We discovered that a dollar is about one gram.  Well, now we need to know how many grams are in a pound (453.594).  

Act 3 is using the information to solve the problem.  The students explained that there are $453.594 dollars in a pound so we needed to multiply that by 2000.  We chose to multiply 453.594 by 2 and then add our three zeroes.  At this point we used our new found information to place the decimal in the correct spot, add our place value commas, and voila.... the number of dollars in a ton!

Tuesday, November 3, 2015

Decimal Operations: Add/Subtract Money

As usual, we began our class with a few math warm-ups. 

  • First, we completed a "Which One Doesn't Belong?"  Students look at four items (numbers, shapes) and choose the one that does not belong.  There are many answers to these problems, students just have to be able to justify their thinking mathematically.  
  • Next, we completed our estimation180 for the day.  Today we were estimating the value of a roll of nickels.
After warm-ups, we move into framing our lesson by looking at the class and student objectives for the day.  I also explained the TEK we are working on for the day.

Now it is time for a mini-review (formative assessment).  I have assigned students a problem on goformative.com to solve.  Today's problem combined the addition and subtraction of decimals with the Order of Operations.

Below is a student example of "my favorite no" (on the grid paper).  In blue, you will see the steps the students needed to take to have the correct answer (please excuse the writing... it is not easy writing with a mouse!).

From there, we reviewed our vocabulary from yesterday and then moved into practicing solving decimal addition and subtraction problems.  We focused on word problems that had to do with visiting a barber shop, finding total costs, paying bills, and determining change.  We used a page from The Mailbox Teacher's Helper Feb/Mar 2008 entitled "Checking Out."

As part of the activity, I required the students to write the number sentence they were to solve and show their work on grid paper.  To challenge the students' higher thinking skills, I required them to create their own word problem, write its number sentence, and solve it.

To view my instructions, please view the video:  Checking Out.

Monday, November 2, 2015

Decimal Operations: Add/Subtract using 3 Act Math

Our focus is shifting to working with decimals and all operations.  Today, we focused on the addition and subtraction of decimals.  In fact, all of our activities centered around this idea.

We began with a "Would You Rather" question:

Next, our estimation180 prompt was also about pennies:

I wanted to do a little formative assessment about student's prior knowledge of adding and subtracting decimals, so I began with a common misconception.  The misconception that I see in student work is that decimal placement is not important.  I have many students who do not line up the decimal.  So, I began with a formative assessment.  I had the students use a "quick code" to logon to goformative.com and complete the following problem:

Students used the "pen" to write the numbers on the grid (one digit per box), line up the decimal points and subtract.  While I did have a number of students complete this formative assessment correctly, I also had a number who made common errors:

  • This student knew where to place the decimal on a whole number, but did not put in zero place holders so that he did not subtract correctly, he just brought down the digits.

  • This student forced the numbers to fit in a way that made sense to her.  She did not know where the decimal point went on a whole number.
What I like about goformative.com is that you are seeing student work in real time and can work with students immediately to correct errors.  To go over some of the errors, I used the idea of "My Favorite No."  This is a procedure where incorrect student work (anonymous) is shown to the entire class and the class works together to make the corrections.  I want students to understand that making mistakes grows our brains and to be comfortable with making AND correcting mistakes.

After completing my own version of "my favorite no," I had the classes take a few notes about adding and subtracting decimal numbers.  These notes included a few new vocabulary words:

To finish out our math class, I introduced my classes to 3 Act Math.  While not all of the activities can be used in my classroom because they are for higher math classes, there are a few sites that I really enjoy that employ this technique:

The activity I used today came from "Mr. Kraft's Wikispace."  It is titled Cheap Chicken Sandwich.  Basically, the students were to determine if the "meal deal" was the best way to purchase a chicken sandwich, fries, and drink.  This type of problem solving is also similar to working with perplexities, which is also discussed by Dan Meyer on various internet sites.

I have my own version of 3 Act Math:
  • Act 1 - Question
    • Students see the problem in an engaging manner and develop the question that is to be solved.
  • Act 2 - Gather Information
    • Students determine the information they need to solve the problem and then finds the information.
  • Act 3 - Resolution (Attack)
    • Students use their information to solve the problem.

We discovered that, in this case, it would be cheaper to purchase the items individually!