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.

## Wednesday, September 30, 2015

### Hands on Equations (Day 5)

We continued our study of basic algebra using our Hands-On Equations manipulatives.  We added a new twist today, we threw in subtraction!

On a problem such as:

5x - 3x + 2 = x + 5

Students first need to subtract 5x - 3x before setting the equation up on their scale.  Since 5x - 3x = 2x, the student only places 2x + 2 = x + 5 on the scale.

Then we followed the same procedures.  We brought down one "x" from each side leaving:  x + 2 = 5.

Next, we worked with the constants, removing 2 from each side leaving:  x = 3.

We replace the original equation on the scale:

2x + 2 = x + 5
2 x 3 + 2 = 3 + 5
6 + 2 = 8
8 = 8

We practiced a few more examples, and then students worked together or individually to complete 10 problems.  To view our examples, please following the link:  Hands-On Equations Day 5.

## Tuesday, September 29, 2015

### Hands on Equations (Day 4)

Ms. Colson is also in charge of teaching Social Studies this week.  While we love teaching this subject as well as math, this does cut into our math time.  So, we were unable to get to the practice part of Lesson 4 yesterday.

Today, the kids worked with The Subtraction Property of Equality using both pawns (variables) AND cubes (constants).  It was nice to see that there weren't any issues with remembering the lesson from yesterday.  The kids are just that strong in their understanding of algebra using pawns and cubes.

## Monday, September 28, 2015

### Hands on Equations (Day 4)

We continued working with the Subtraction Property of Equality today using the Hands-On Equations manipulatives.  Yesterday our focus was using the property with our variable "x" (also known as the pawns).  Today, we continued this portion of the property, but we also used the property with our constants, which are the known numbers (the number cubes).  For example:

• Pull down one pawn from each side of the equation leaving:

3x + 2 = 2x +9

• Pull down another pawn from each side of the equation leaving:
2x + 2 = x + 9

• Pull down another pawn from each side of the equation leaving:
x + 2 = 9

• Now pull down 2 from each side of the equation leaving:
x = 7

• We have just solved for x.  Now, we replace our manipulatives to show the original equation:

4x + 2 = 3x +9

• Replace "x" with the value "7" and solve:

4 x 7 + 2 = 3 x 7 + 9
28 + 2 = 21 + 9
30 = 30

I have made a short video demonstrating this lesson, just follow the link:  Hands-On Equations Day 4.

## Friday, September 25, 2015

### Hands on Equations (Lesson 3)

We worked on Day 3 of the Hand-on Equations.  Today's focus was teaching the Subtraction Property of Equality.  Basically, you set up the equation and remove pawns from both sides of the equation allowing the scale to remain "balanced".  Once this removal has occurred, one side of the equation is usually a number.  This allows solving for the variable "x" to be much easier to determine.

For a better explanation, please watch the video, "Hand-On Equations Day 3," I made for my students who were absent today.  I think you will get a much clearer understanding of the process watching the video vs trying to make sense of pictures!

## Thursday, September 24, 2015

### Hands on Equations (Day 2)

Our second day to work with algebra and WOW!  I am not getting any kind of payment, but I highly recommend Hands-On Equation to introduce algebra painlessly!  Day 1 was all about placing pawns and cubes on the scale and determining the value of the pawn.  By the end of the class we were calling the pawn "x".

Today I reviewed our learning from Tuesday, including reemphasizing that the scale is just a visual to remind us that both sides must be equivalent because the scale must ALWAYS balance.  We moved into exploring placing equations visually on the scale and then solving for "x".  For example:
2x + x = x + 8

I explained that when a number and the variable are touching, this means to multiply (2x) and that the student should place that number of pawns on the scale touching one another.  I also explained that a number standing alone in the equation was represented by a cube.  Then I handed each child a sheet of equations and let them go.  WOW!

My classes were solving equations like 4x + 2 = 3x + 9 without even batting an eyelash!  Unbelieveable!

To view the lesson, please go to:

## Wednesday, September 23, 2015

### Hands on Equations (Day 1)

We moved into a new unit of study today.... ssshhh... basics of algebra!  Since algebra can be so abstract, I wanted to give the kids a good foundation to build upon.  I found a program called Hands-On Equations that has been around for many years.  This program has all kinds of data supporting its success.  Basically, the concept behind Hands-On- Equations is to begin working with algebra concretely (with manipulatives), move to pictoral (draw pictures), and end at the abstract level (equation).

Today we worked concretely, with manipulatives (see above)!  We began by noting that since we are working with a scale, both sides of the scale must be equal for the scale to balance.  I explained that this whole idea is what math is all about.... both sides of an = sign, should EQUAL (balance)!

1. We practiced working with the idea of placing a number cube on the right side of the scale and a pawn on the left.  We discovered that the pawn's value was = to the number on the cube.
2.  Then we moved to placing a number cube on the right side of the scale and having two pawns on the left.  This time the pawns' value, which was equal, added TOGETHER would equal the value of the number cube.
3. Then we moved to having pawns on both sides of the equation.  This meant that a little more trial and error was involved as we worked to determine the value of "x".

Finally, we worked through a series of equations.   Students set up their math equation using the scale, pawns (our variable:  x), and the number cubes (our constant).  For example:

Working together, and using trial and error, students were successful in determining the value of x.  For example, to solve the shown equation:

• x = 1 so 1+8 = 1 x 3 NO
• x = 2 so 2 + 8 = 2 x 3 NO
• x = 3 so 3 + 8 = 3 x 3 NO
• x = 4 so 4 + 8 = 4 x 3  YES
The value of x (each blue pawn) is 4!

If you would like to watch the process, please watch the video:  Hands on Equations Day 1.

I know that a class was a success when students want to do more... we were VERY successful today!

## Tuesday, September 22, 2015

### Division

Today, Ms. Colson completely took the reins.  She will be teaching full days through the end of next week.  She is doing a terrific job!

She continued our work with division by having the students play a Kahoot that required them to solve division problems.  They did a great job, but were a little disgruntled by the time limit imposed by Kahoot.  The longest amount of time possible is 2 minutes.  However, the kids worked very hard and their grit and determination allowed them to have success with division!

After the Kahoot, she challenged the students to create a poster, poem, song, etc. that would help them remember the steps to solving a division problem:

We will add these to the students' journals as a helpful reminder to the division steps.  Finally, they worked on a Countdown to STAAR as their spiral review.

We will be moving on to a new topic tomorrow, but just know that we will continue to divide using our spiral reviews!

## Monday, September 21, 2015

### Division

So we continued working with division today.  This will take some time, two days of division does not a division guru make!  Part of my strategy affording students the many repetitions of the many concepts we are to master is to work on a spiral review daily.

However, we must teach the concepts before we can review them.  So, we warmed up our brains and then we took notes on division.  It is important for my students to know the parts of a division problem, so we noted the divisor, dividend, and the quotient as a standard algorithm.

Then we reviewed the steps to solving a division problem:

D = divide
M = multiply
S= subtract
C - compare
B = bring down
R - repeat or remainder

I also require my students to use grid paper to help keep the digits in their proper place.  My final strategic piece, is the use of a notecard.   This is used to hide all of the digits that I am not working with.  Even with all of these pieces, four digit by two digit division is still hard!  It is a process that needs to be repeated over and over for it to become rote.  Hence, the spiral review!

## Friday, September 18, 2015

### UIL Emphasis

Today we spent a little time talking about our UIL competition that will happen in December.  I coach the Listening competition, which is brand new to 5th graders, so I wanted them to see what it was like.  So, we listened to a story about Wilma Rudolph that was about 7 minutes long, then we took the "test" that was timed for another 10 minutes.  I showed them how a Listening test was graded and then I asked them to let me know if they were interested in being a part of that competition by placing  a "yes" or "no" in the corner of their paper.

I also discussed the other 10 competitions available to 5th grade and asked them to fill out a form showing us which competitions they were interested in.

Next, we took a moment to FINALLY fix our problem with posting to Kidblog.  Now we will be able to post AND read each other's work!

Finally, we completed our Spiral Review for the week and then worked on long division on Khan Academy.

## Thursday, September 17, 2015

### Ian's Job (Day 2)

We finished working with Ian's Job today.  We focused on the amount of money Ian's job was paying him to cover expenses for his travel to and from work.

Since we were dealing with LOOOONNG division, I felt we needed a little more guidance today.  I began by reminding them of the mnemonic device for division:

I added a few extra steps:  Divide, Multiply, Subtract, Check, Bring Down, REPEAT or REMAINDER.  Then we used grid paper and an index card to help us break the problem into even smaller steps.

After reviewing long division, we finished up Ian's Job, completed a Countdown to STAAR review, and then students got on to Khan Academy to work through the LOOOOONG division activities and videos.  More practice tomorrow!

## Wednesday, September 16, 2015

### Mistake are expected!

Today we needed to take a step back.  On Monday, we had played a Kahoot using 3-digit by 2-digit multiplication, on which the kids did an excellent job.  However, when given six problems to complete, I had quite a few students do poorly.  This concerned me, but after looking more closely at their work, I realized that, feeling overconfident, my students had rushed through these problems making "silly" mistakes.

So, today we focused on what mistakes are.... Mistakes are to expected, mistakes are to be respected, mistakes are to be corrected, and mistakes are to be inspected.

I began by reminding my classes that mistakes are expected AND necessary for us to grow our brain!  I also reinforced the belief that mistakes are to be respected and so are the people that make them.  We ALL make mistakes!  I explained that we were going to spend the day correcting the mistakes, in order to inspect the mistakes made.  We would use this new understanding to ensure that we did not make the same mistake again!

Initially, my students were apprehensive, but when they saw and understood the mistakes they made, synapse fired and their brain grew... right in front of me!

## Tuesday, September 15, 2015

### Ian's Job (Estimation w/Multiplication)

We began a new performance assessment today called Ian's Job.  In this activity, students are asked to determine if an estimated distance is reasonable.  Next, students are asked to find the actual distance he will travel.  Finally, they are asked to compare their estimate to the actual.

To finish off the day, we spent about thirty minutes reviewing concepts using Countdown to STAAR.

## Monday, September 14, 2015

### 3 x 2 digit multiplication

We began our day by warming up our brain.  I happened to come across a critical thinking activity that uses multiplication.  This activity was from:  Groundworks:  Reasoning about Numbers (Creative Publications, 2005).

Next, we had to do our estimation180.  At this point, I think the kids would revolt if we tried to skip it!

I gave a short pretest on 3 x 2 digit multiplication using a Kahoot and was extremely pleased with the results!  Therefore, we spent little to no time reviewing the process and completed six problems.

We used the last 30 minutes of class working on a Spiral Review to review specific skills.  As we learned in the beginning of the year, if we do these math skills a little every day, we grow our brain!  I found it on Teachers Pay Teachers.  It is specific to Texas TEKS for 5th graders.

## Friday, September 11, 2015

### Substitute

We worked on multiplication using Khan Academy.

## Thursday, September 10, 2015

### Frank's Project (conclusion)

We completed "Frank's Project" today.  We began with a guess my number warm up and an estimation180 activity.  In order to complete "Frank's Project," we needed to conclude our Project Summary.  This included finding the difference between Frank's budget and the bid given by each company.  Then we had to write a recommendation based on the company that would save Frank the most money.

Once the project summary was completed, students were asked to solve six addition and/or subtraction problems.  The interesting part of this activity is that students had to use a code to determine the numbers to compute.

As students completed this assignment, any time left was given to working on multiplication through Khan Academy.

## Wednesday, September 9, 2015

### Frank's Project Day 2

We continued with "Frank's Project" today.  As usual, we began with brain warm-ups.  Today we used   101qs.com  and estimation180.com.  Then we located our project summary in our Google Classroom in order to continue working on it.

Students began by creating the second table for Construction Corral's bid, filling in the actual bid costs, estimating those costs, and finding an estimated total.

Next, they were asked to compare the two estimates and determine which construction company they would recommend to Frank at this time.

(b) Compare the two estimates.
Explain which company’s estimate appears to be the least expensive.

Finally, the were asked to compute the actual costs of each company's bids.  This was our stopping point.  Students worked at their own pace to complete the pieces of the project summary.  As they finished, they began working on multiplication through Khan Academy.

## Tuesday, September 8, 2015

### Frank's Project

Today we began a real-world estimation project called Frank's Project.  However, before beginning the project, we needed to warm our brains!  I challenged the kids to find:  Which one doesn't belong?  There are many plausible answers to this problem!

Next, we worked on our estimation180 for the day:

Then, we played a Kahoot to review estimation and the three types of estimation we had discovered last week.  Now it was time to begin the project.  I began by reading through the instructions with my students:

We walked though the project and analyzed what we needed to do to be successful.  A project of this size appears to be overwhelming to 5th graders (they are just 10 year old), but after we looked carefully, we realized that we were estimating, adding, and subtracting.  All of those words and scary looking information and we were being asked to do something we were very comfortable with!

We discussed the type of estimation we thought was most appropriate to use (front end estimation), then we had a discussion about how we should keep track of our estimates in an organized manner.  The consensus was to create a table.

The remainder of class was a combination of math and technology as we had to learn how to create a table in Google Docs.  All of the classes were successful in creating the first table:

We were not able to get quite as far as I had anticipated (the mantra of an educator), but I loved that the kids all groaned when told time was up!  We will continue working on our project tomorrow!

## Friday, September 4, 2015

### Estimation Round Up

Today Ms. Colson finished up her week on Estimation.  She opened with our brain warm-ups.  The first was having students create math analogies using a resource from Teachers Pay Teachers:

Next, she asked the students to complete an estimation180 to estimate the number of tissues in the cube.  We discovered yesterday that there were 10 tissues in the small package.

Her next step was to have students review the three types of estimation:  rounding, front-end, and compatible numbers.  She had them complete a "stick it together" activity.  Each student was given a sticky note on which to solve a problem.  They compare their answers and choose the "best" answer to place in the middle.

The groups that worked with me over the past two days were able to share their Kahoot with their classmates.  Fun, fun, fun!

To finish the day, the students took a post assessment on Estimation.

## Thursday, September 3, 2015

### Estimation: Compatible Numbers

Today's focus was Compatible Numbers.  While Ms. Colson worked with a majority of the class, I worked with the small group of students who pretested out of Estimation.

Ms. Colson began with students solving a Guess My Number activity.  Next, she asked the students to solve their estimation180 for the day.  She then led the students in working with compatible numbers by modeling and practicing the concept.  After finishing the practice, she had the students play a Kahoot in order to test their knowledge.  Finally, she asked the kids to fill out an exit ticket to reflect on their learning today.  The misconception we addressed was the fact that most students think that because an estimation is not "close" to the actual answer, the estimation must be wrong.  On the exit ticket students were asked:

Explain why it is "ok" for your estimate to be greater than or less than the actual answer.

While she worked with compatible numbers, my groups completed their Estimation Kahoots that will be presented to their classes tomorrow.  These students not only created the problems, they imported the images/pictures used, and had to find the answers to their problems.  Fun!

### Front-end Estimation

The focus today was Front-end Estimation.  Basically, instead of rounding to a given place value, we round the digit that is in the front.

Ms. Colson led class again today.  She began with a 101 Questions to get brains moving, then she moved into Estimation180.  As she introduced the lesson, she reminded students that there are three types of estimation:  rounding, front-end, and compatible numbers.  Estimation is a strategy used to achieve a reasonable guess.

Before she began teaching the lesson, we broke the class into two groups.  There was a small group of students in each homeroom who pretested "out" of this lesson, so I moved that group to work with me.

To teach front-end estimation, Ms. Colson used a Kahoot!  The students solved a problem, were shown if the had chosen the correct answer, and then Ms. Colson asked a student to come and show how they had solved the front-end estimation problem to the class.  The students worked through six different problems with varying operations.  Once they understood the process, she handed out their assignment.  It was called "What's for Homework".  The students were asked to, first, solve the problem using front-end estimation and, second, solve the original problem for the actual answer.  They were given ample time to complete the assignment in class, however, some students may have needed to complete a problem or two for homework.  To end the class, she asked the students to complete and "Exit Ticket".  They had to "explain the difference between using front-end estimation and rounding."

In the meantime, I was working with my small group.  We began with the assignment "What's for Homework."  This allowed to me to monitor for understanding.  While all of the students understood front-end estimation completely, a few had difficulty remembering the steps to larger multiplication problems.  No big deal, I just need to be sure to review this with all kids soon!

After completing the assignment, I asked the group to help me create another estimation assignment.  They were given the choice of creating stations for their class to work through, or they could create a Kahoot for their class to play.  Hands down, every group chose a Kahoot.  We spent the remainder of our time creating the questions and looking for images and/or taking photographs to go with each question.  These groups also ended their day by completing the "Exit Ticket".  Tomorrow we will begin making the actual Kahoot.