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, November 27, 2013

### Computer Day

It is an early release day and 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.

Short.... sweet!

Have a HAPPY THANKSGIVING!

## Tuesday, November 26, 2013

### Hands-On Equations Day 7 (Pictorial Representations, cont)

Today we worked independently on solving equations using only a pictorial model based on Hands-On Equations.  To begin, I did an example problem with the class, which you can view:  Hands-On Equations Day 7 (Pictorial Representations cont).  Then, the students solved four problems on their own...without the use of the pawns and cubes.... they did a great job!!!

Then I asked them to answer a prompt on an exit ticket.

Do you think that working with concrete models (pawns and cubes) and then moving to pictorial models (pictures) was an effective way to learn algebra?  Why or why not?

HOMEWORK:

## Monday, November 25, 2013

### Hands-On Equations Day 7 (Pictorial Representations)

Concrete Model

Pictorial Model

Moving from concrete models to pictorial representations was the focus of our Hands-On Equations lesson.  We began by taking a few notes about algebra.

I wanted the students to have a way to remember the parts of an algebraic equations, so I made up the equation:

A = V + C

Then wrote the equation out in words:

Algebra is solving equations that have Variables (letter/ unknown value) and Constants (number/known value).

Then we labeled the parts of an equation.  Finally, we got to representing an equation pictorially.

To see the explanation of working with algebra equations pictorially, please watch the video:  Hands-On Equations Day 7 (Pictorial Representations).

The student exit ticket today was:

Use a pictorial model to solve:

5x + 2 = 2x + 14

Explain, in words, how the pictorial model works.

HOMEWORK:

## Friday, November 22, 2013

### Hands-On Equations (Day 6)

Today, our lesson with Hands-on Equations had the "Students use concrete models to represent the multiplication of a binomial (two terms) by a positive integer (whole number) constant (a fixed value), such as 2(x+1)." Ok, lots of large words....basically, the students multiplied a binomial (x+1) by a positive whole number that is fixed (2) !  By the end of the class not one child was afraid of any of the words anymore!  It was a very good day!

For example,  students were given the equation:

2(x + 3) = x + 8

To set this up on their scale, they needed to put x+3 TWICE on the left side of the scale and x+ 8 on the right:

x + 3
x + 3 = x + 8

I then told them to take a shortcut by asking them what 3 + 3 was.  We took off the two 3 cubes and replaced it with a six:

x + x + 6 = x + 8

Now, we removed an "x" from each side leaving:

x + 6 = 8

Now we removed 6 from the left, and subtracted 6 from 8 leaving:

x = 2

Finally, we worked the problem knowing that x=2:

2(x + 3) = x + 8
2(2+3) = 2 + 8
2(5) = 2+ 8
10 = 10

To see Hands-On Equations Day 6 in action, please watch the video!

Have a great weekend!

## Thursday, November 21, 2013

### Hand-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.

HOMEWORK:

## Wednesday, November 20, 2013

### Computer Day

Wednesday is spent in the computer lab.  We began with xtramath.org and then worked on khanacademy.org.  I am still attempting to have all of my students complete xtramath.... it is slow going....

We have a khanacademy.org competition going.  The benchmarks of the competition are:

KHAN CLUB

• 30 mastered skills - join the club
• 45 mastered skills - Khan t-shirt
• 60 mastered skills - Invitation to Khan Banquet
• 75 mastered skills - sit at the head table
• 90 mastered skills - medals awarded
• HIGHEST Khan mastered skills - "TOP Khan" award

## Tuesday, November 19, 2013

### 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.

HOMEWORK:

## Monday, November 18, 2013

### Hands-On Equations (Day 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!
HOMEWORK:

•  xtramath.org
• Countdown to STAAR, Series 1, page 1
• Draw a picture that incorporates the concepts learned today (could include:  Subtraction Property of Equality, variables, equivalent, algebraic equations).

## Friday, November 15, 2013

### Autumn Trees

Today is the end of the 2nd 6 weeks and I wanted to give the kids a little break.  They have been working hard in math and I wanted us to just take a moment and reflect on what we like about Autumn.

So, on Wednesday, 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.

It was a great way to end the six weeks!

## Thursday, November 14, 2013

### 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!  Now, to be honest I did have a few that struggled and ended up in tears.... but only 2.  Unbelieveable!  I am very excited about our next lesson!  We won't be able to get to it until Monday because tomorrow is the last day of the six weeks and we are going to be doing a small craft!

HOMEWORK:  xtramath.org and Word Problems

## Wednesday, November 13, 2013

### Computer Lab and KHAN CLUB

Wednesday is not only HUMP DAY, it is also the day we go to the computer lab.  There isn't really much to tell you about the class.... the kids do xtramath.orgto master multiplication facts and then work on khanacademy.org to master math skills.

We are implementing a new incentive program called:

KHAN CLUB

30 Mastered Skills - Get in the club
45 Mastered Skills - Awarded a Khan Club t-shirt
60 Mastered Skills - Invitation to Khan Banquet
75 Mastered Skills - Sit at the head table at the banquet
90 Mastered Skills - Medals Awarded

Highest number of Khan Mastered Skills -
"TOP Khan Award"

This Club is just one type of incentive.  In 5th grade, I award a bead for our Outdoor School necklaces for every 5 skills mastered.

HOMEWORK:  word problem corrections

## Tuesday, November 12, 2013

### 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!

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

HOMEWORK:  xtramath.org and Word Problems

## Monday, November 11, 2013

### Order of Operations: Independent Work

Today we put our knowledge of the Order of Operations to the test!

I had the students solve the problems on this "leaf".  I had them write the equation they were working with and writing PEMDAS beside it. As they worked through the problem, they were to mark out the letter they just solved for.  Using this acronym helped students to remember the order. Working with PEMDAS was especially confusing with a problem like:

45 - 2 x (15 - 3)

My classes had no problem doing the parentheses operation first, however, then they wanted to jump to the beginning to complete the problem instead of multiplying by 2 THEN going to the beginning.  It really opened their eyes as to what the Order of Operations really meant.

Another problem that changed their thinking was:

81 divided by 27 x 6 -2

Since there was no parentheses, they jumped to multiplication (it is the next letter in PEMDAS).  What they were having difficulty with was the fact that multiplication and division are EQUAL in the order of operations.  You do the one that appears first (in order left to right).  This seemed to open some eyes as well!

HOMEWORK:  xtramath.org and finish your "leaf"

## Friday, November 8, 2013

### Order of Operations: The Power of the Parentheses

Our objective today was the same.  I wanted my classes to understand the impact that changing the order has when performing a series of operations.

So, we continued working with the Order of Operations using PEMDAS.  First, we finished up the worksheet "A Skeleton of My Former Self."  We worked the problems on our desk using dry erase markers.  The kids will do a hundred math equations if they can write on their desk!  :-)
Then I posed new problems.  These problems were equations that were missing the needed parenthesis.  Our first problem was:

57 - 15 + 17 = 25

1. I asked the classes to solve this problem based on PEMDAS.  Once we discovered that we just needed to add/subtract from left to right, I asked them if the answer they found equaled 25.  The answer was "no" and they were shocked!
2. Next, I placed the parentheses on the equation:
57 - (15 + 17) = 25

When performing the operation within the parentheses FIRST.... the equation worked!

We spent the remainder of class working with groups of equations that were missing the parentheses and determining exactly where the parenthesis needed to placed.  The kids loved it (it may have just been the markers, but I like to think they actually liked the math)!

To finish the class, the students had to fill out an exit ticket.  Today's prompt was:

If math parentheses could talk, how would they explain their work in mathematical equations?

Have a great weekend!

## Thursday, November 7, 2013

### Order of Operations: PEMDAS

To introduce our new topic, I asked the kids to write the following math problem on their desk (using dry erase markers):

3 + 3 x 4 + 2 x 3 + 3

Most students solved from left to right getting an answer of 81.  Other students are in UIL Number sense and had a better idea.  They grouped the multiplication problems together and got an answer of 24.  However, when I added in the parenthesis in the correct position:

3 + (3 x 4) + 2 x (3 + 3)

We found that the answer was 27.  This lead into my lesson objective:

We will understand the need for a standard order of operations by investigating the impact that changing the order has when performing a series of operations.

I explained to the kids that there is an agreed upon order of operations:  parenthesis, exponents, multiply/divide, then add/subtract.  Knowing that just telling them one time would have little to no effect on their long term memory, I employed a tactic I had seen on one of my favorite blogs, Runde's Room.  The link will take you to the day she chose to teach the order of operations using the game of hopscotch!

I decided to try this myself!  I planned to take the kids outside and make hopscotch boards using sidewalk chalk and then doing all kinds of equations.....but then the cold front came through.... 38 degrees may not be cold to many people, but to Texans, you would think it just snowed!  So, instead, I made hopscotch boards on the floor of my classroom with masking tape.

Then we played some hopscotch calling out the order of operations as we proceeded.  To make it more entertaining (for me especially), we kept increasing the speed at which we played the game!

After playing hopscotch, we recorded our new learning in our journal.  I found another blog whose teacher used the hopscotch method in her classroom and then created the PEMDAS graphic organizer that we used in class today.  The video with information is at:  Order of Operations: PEMDAS

I discussed that they need many different ways to help them remember the Order of Operations.  My kids told me that they would never forget hopscotch, but I explained that they needed something that would not allow them to mix up the order of the multiplication/division, and addition/subtraction.  At this point, I mentioned the acronym PEMDAS.  I also encouraged them to use a mnemonic device to remember the steps such as:

To complete the day, we worked with a page from Mailbox Magazine called "A Skeleton of My Former Self."  This page allowed us to work with the order of operations while finding answers to interesting facts about the body!

We did not quite finish all of the facts today, so we will do that tomorrow.

Since there was new learning today and I wanted the kids to showcase their understanding the knowledge gained today, I assigned an Order Of Operations Math Concepts Poster.  This poster was created by Jen Runde, the author of the blog Runde's Room (I have attached the link for any interested in purchasing).

It was a busy class, but fun!

## Wednesday, November 6, 2013

### Computer Lab

Wednesday's are our math day in the computer lab.  When we get into the lab, the first item on the agenda is completing an xtramath.org exercise.  We have a reason to celebrate!  Two of my students finished the multiplication portion of xtramath today!

These two students will receive a bead for their Outdoor School necklace, a Bullpup brag, AND a token for a free ice cream cone from Dairy Queen!  OH, not to mention.... they do not have xtramath for homework ANYMORE!

Our next order of business, is to work on khanacademy.org.  I am trying to build incentives into this, so I have told the kids that for every 5 skills that are mastered, they will receive a bead for their Outdoor School necklace.  The student with the most mastered skills, so far, has 65!  He will be receiving at least 13 beads for his necklace!

Remember, your child can work on khanacademy at home and from 7:00 - 8:00 in our computer lab Monday - Friday!

HOMEWORK:  None

## Tuesday, November 5, 2013

### Interpreting Remainders

Whoa.... interpreting remainders.... working with word problems....!

Lots of THINKING was happening in my classes today!  First, we had to read the word problem to determine the division problem we needed to solve for A.

A.  93 divided by 5

Once we had the quotient to the division problem, we had to determine what the quotient meant.

A.  93 divided by 5 = 18 r3

18 = the number of students per group
3 =  the number of students left over

Now that we know the labels to our quotient parts, we are able to answer the question.

The least number of players at each station is 18.

What happened to our remainder?

Ignore It!

Next, we needed to answer question B.  This meant that our division problem changed:

B.  93 divided by 8

We had a new quotient to work with:

93 divided by 8 = 11 r5

11 = the number of stations with 8 players
5 = the number of players not at a station

12 stations

What happened to the remainder?

Since 11 stations was not enough for
everyone to be included
(our remainder shows 5 kids left out),
we needed to ADD ONE station!

After working this problem together, I asked the classes to work in table groups to complete the remaining problems.  I wanted them to have small group, purposeful talk about the problem:  how to solve it, what the quotient meant, and what to do with the remainder, etc.

During this time, groups were to ask me clarifying questions as needed.  After solving each problem, the entire group would come to me to have it checked for immediate feedback and reinforcement about their problem solving and answer!

To complete the lesson I had the kids write me an exit ticket in an effort to get them to write critically about their learning.  Today's ticket was:

How do you think you could make the concept of
interpreting remainders easier to learn?

HOMEWORK:  xtramath.org

## Monday, November 4, 2013

### Intervention: Don't Get Vexed By This Hex!

I have subscribed to The University of Waterloo CEMC Problem of the Week (follow this link to view their page and subscribe).  One of the problems was called "Don't Get Vexed By this Hex!" and I presented the problem to my students during our Intervention time.

Suppose you had 11 green triangles, 5 rhombuses, and 5 trapezoids.

1. How many hexagons congruent to the pattern block hexagon can you create?
2. How many shapes are left over?

Once I posed the problem, I asked the students to make a prediction to the number of hexagons that would be created and the number of pattern blocks that would be left over.  Next, I gave each student di-cut pattern blocks to manipulate to discover the answer (6 hexagons, no remainders).  We glued or taped these to a piece of construction paper.  Then,   to explain why we did not have left over pieces mathematically, I used the "Something to Think About" portion of the answer given by CEMC.

With the remaining time, we explored what would happen if we changed the value of each shape.  We began by making the value of the triangle = 1 whole, then we made the value of the rhombus = 1 whole, then we worked with the trapezoid = 1 whole, and finally the hexagon became our whole.  With each change, we found the value of the other shapes (triangle, rhombus, trapezoid, and hexagon).

We were even able to create a figure with pattern blocks and used this as our whole and found the value of the other pattern blocks!

### Open Number Lines and Interpreting Remainders

I introduced the concept of open number lines today.  Basically, an open number line is a completely blank number line.  Our focus was to "navigate" on a number line.  To begin, I gave the students two numbers, an "I have" and "I wish I had".  Using any strategy they wanted, they were to begin with what they had and move to what they wished they had.

For example, I gave the students the following:

• I have 17
• I wish I had 24
I asked them to place the 17 on the number line and show me how they would get to 24.  Invariably, they would start with 17 and use seven tick marks to get to 24 (see below).

I asked them to think about this in a different way.  What if we "jumped" to friendly numbers (the nearest 5 or 10) to keep us from having to make all those tick marks (see above).

From there we experimented with a variety of "I have" but "I wish I had" statements in an effort to become more comfortable working with open number lines.  I also wanted them to understand the strategy of "jumping to friendly numbers."

To finish our day, we created a foldable about interpreting remainders called "What do I do with a remainder?".  We ran out of time before we could put our notes to any use!

HOMEWORK:  xtramath.org