Interactive Math Journal: Fractions of Fractions

I've been promising my kids all year that I was going to teach them how to multiply fractions, and now with only 5 teaching days left, I can finally get to it.  Thursday, I introduced the lesson by giving each student multiple half sheets of paper.  Our first task was to find what 1/2 of 1/2 was.  We folded the paper in half vertically, colored half with one color crayon, then folded it in half horizontally and colored that half with a different color crayon.  The piece that had the two overlapping colors showed us what 1/2 of 1/2 was, or 1/4.  We then did the same activity again, but this time wondering what 1/2 of 1/3 was.  I kept recording our findings on the board.  At one point, I heard a gasp from Abbie.  She looked at me excitedly and kind of started bouncing in her seat.  I knew she had discovered something, but I asked her to hold on to her thoughts just a little longer.  As we kept going with the paper, I heard more and more gasps and "oh!!!!!" coming from the class.  I could tell some kids were getting frustrated that the others were discovering something they were not, so I finally let Abbie tell us what she first discovered.  Of course, she saw that we were making arrays with our papers, and noticed that all we had to do was multiply the denominators.  It was a different student that noticed that in each of our examples, the numerators were also multiplied.  It was an exciting moment for the class!! 

Then, someone raised their hand and asked, "Are we going to put this in our notebooks?"  To be honest, I hadn't thought of that, but they had such a great idea!  They actually wanted to add to their notebooks on their own!  YIPEE!!!  Since this activity took so long, we had to wait a day to enter it into our notebooks, but that gave me a chance to type up some blank rectangles to record our drawings in.  Here is the end result: 

This student chose pink and yellow to color with, so the overlapping piece is orange and shows the end result!

This student showed that 1/2 is shaded in yellow, while 3/4 is in pink.  The orange shows that 1/2 of 3/4 is 3/12!

This time, we included a "What I know" and "What I learned" section.  It should be on the left hand page, but oh well.  We are still learning!

Interactive Math Notebooks: Adding and Subtracting Negative Numbers

With testing over, and the end in sight, we are working working working hard to stay on a routine and make sure we are ready for 6th grade!  We just finished a quick unit on negative numbers.  Manipulatives are great to use here and serve as a constant reminder of what is going on.  

First, we spent a couple days adding positive and negative numbers.  We used green counters for positive numbers, and red for negative.  We use these two colors throughout our unit.  I really putting an emphasis on the fact that adding is PUTTING TOGETHER.  This would later help with differentiating between the rules for adding negative and the rules for subtracting negatives.  After doing a few sample problems, the students were able to come up with their own rules for adding positive and negative numbers.  They quickly caught on and all was well in the world! (Don't worry.....subtracting is next....that's a WHOLE different ball game!)  Here are our notebook entries for adding:

Next, we began working on subtracting.  This time, I used a clear bucket to show what we had in the container, and what we needed to subtract, or take out.  Before giving them any tricks, we practiced many many times with counters.  For example, if the problem read: 8- (-4), I would fill the container with 8 green tiles, or 8 positives.  Then, I would ask if we were able to take out 4 red tiles.  Obviously, there were only green tiles in the container, so I couldn't take any out.  We had discussed earlier how the opposite of every number added together equals zero, so I demonstrated putting in groups of one red and one green tile at a time, until I had 4 reds to take out, all the while emphasizing that I wasn't changing the value of the container since I was just adding zero to it.  Then, I was able to take out the red counters, leaving only green behind.  This was not an easy concept to teach, and there were some frustrating looks around the room, but we kept at it until it slowly started clicking.  That's when I introduced Mr. Minus.  

Who is Mr. Minus, you ask?  It's more of a "what".  Mr. Minus is a poem my mother, Mrs. McHugh, also a 5th grade math teacher, made up years ago.  I owe her A LOT this year!  It goes like this:

Mr. Minus, Mr. Minus

Learn you I must

But I think I’m going to turn you into a plus,

Now change the second number to its opposite sign,

Add them both together and life will be fine!   Yeahhhhh!

It's catchy and the kids love it!  Here is our notebook page on subtracting.  Again, the pictures are of containers holding what we need to take out and the step by step change it goes through.  

Mother's Day Crafts

Let's take a break from math for just a moment to honor those amazing women in our lives: our mothers!  We took a moment after testing was over to create these wonderful plates.  Most students decorated the plate for their mother, but some included their dads and still others included their entire family.  I left it entirely up to them.  I purchased the plates from the Dollar Tree (a teacher's best friend!) after each student donated a dollar (one boy, Ben, donated $4 "in case someone else can't bring you the money."  Who said kids aren't compassionate?! I melted!).  I had them create a rough draft first, but once they realized baby wipes would wipe away mistakes, they lost all fear of messing up and got really creative!  This is an easy, awesome project and is all over Pinterest.  Just color your plate with Sharpies, and bake for 30 minutes at 350....and viola! A personalized gift :)  Check them out!

Allison chose to include her entire family with a descriptive word about each starting with the same letter as the first letter in their name; I love majestic mom! :)

They had so much fun displaying their love for their mothers!

Numerical Expressions: Common Core

Now that the OAA is over with and testing season is behind us, we are going to start focusing on some of the things that are included in the new CCSS that were not on the Ohio Standards, as well as touch on some things that I  think they need more exposure to to make sure they are ready for 6th grade.  

We have two great activities for numerical expressions today!  We learned about numerical expressions already, but I didn't feel like I covered it deep enough.  The Common Core is all about going deep with the concepts and really applying them to their lives.  We began by practicing oral expressions and displaying them numerically on their slates.  Here are some examples:

Twice a number, decreased by twenty-nine

Five times a number y increased by 3

Multiply three by two, then subtract one

Once we did enough practice and most of the kids had caught on consistently, we moved toward some independent work.  They didn't have a lot of problems, just ten, and most were asking the kids to analyze the expressions without evaluating them.  As they finished, there was an assignment on the projector waiting for them: our performance assessment.  I always find that if I ask them to write their own problem, I can really see if they understand what's going on.  

The CCSS is: 5.OA2: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. 

The performance assessment asked them to create their own real world problem that could use an expression, write the expression, and draw a picture to match.  Being able to see math in REAL LIFE situations AND create their own problems is a HUGE skill that is SO important!  Here were some of the final products: 

A basketball game ticket cost $17.  Hot dogs are $5.00.  If Molly and 6 friends go and all get hot dogs, how much money will they spend?  --Submitted by Molly K.

A ticket to the school dance costs 15 dollars.  A picture costs 10 dollars.  El and three friends each buy a ticket and each get a picture taken.  How much did they spend? --submitted by Shante J.

Ms. McHugh's class bought her 3 bags of chocolates.  Each bag has 10 pieces of chocolate.  Then, Mrs. Haught bought her 7 bags of hard candy.  Ms. McHugh ate 20 pieces of chocolate and hard candy all together.  How many pieces does she have left? --Submitted by Ashley M. (can you tell I LOVE candy??

Next, I had a challenge for them.  I found this idea on K-5 Math Teaching Resources, except I modified it for our purposes.  The task was to use only the digit 4 (the original says only four 4's, but we just stuck to 4s) to create problems equaling the numbers 1-12 so that you could place those numbers on a blank clock face.  Once they figured out a couple (4/4=1, and so on), they were unstoppable!  It was one of those classes where kids asked "can I finish this over the weekend??" even when it wasn't a required assignment!  Check out some of their clocks!! 

Truly, they learned the most from having to write their own problems.  We did a similar activity with division back in December, and I will definitely incorporate this task more next year!  It's just a great way to really see how they look at and see problems! Hope you enjoyed! 

Technology: Finally!

We have Technoooooolllloooogy!!!! (Said in my best "Oprah's Favorite Things" voice).  Because we were able to build all new schools, we also received all new interactive whiteboards, as well as speakers in our ceilings and MICROPHONES!  If you know me at all, you know I love to sing, so my poor students always catch me singing into the microphone.  It always lightens the mood, especially during testing prep when things can get a little tense.

Today, I decided to slow things down a bit and let the students use the interactive whiteboard to show their answers on their homework.  Normally, I would just slide their paper under our document camera, but he's been feeling a little under the weather lately, so we've had to do without (I feel LOST without it, but we make do!).  We have been doing a lot of reviewing lately, as well as making connections between all the different areas of math, so last night's homework involved circle graphs, fractions, and percents.  We can ALWAYS review that!  They were given four frequency charts with information that they had to put into circle graphs using the fractions given.  Here are some pictures of a few of the students recreating their graphs;

Ben was the first brave soul to give it a try!  Pretty good!

Paige and TeShon hard at work!

The last class of the day seemed to have a hard time deciding which fraction was larger; 3/8 or 1/4, so we decided to use the highlight feature on the interactive whiteboard to give us a better visual.  As we were highlighting, I heard lots of  "ohhhhh!!!!!!"  The visual really helped, and it was so much easier with the interactive feature.  Check out the picture below!

 I can't wait to start  utilizing our new technology in the future!  Woo!

Probability: Math Notebooks

Today's Math Notebook was inspired by the WONDERFUL Mrs. Runde over at Runde's Room, although, I catered it to our needs.  I really liked how she had her students write out the learning goals and task before starting, so I decided to try it.  I always let the kids know what our goals for the day are, as well as have our "I Can" statements posted clearly in the room, but this is the first time we really put it in writing as a class.  We have been working with probability, so I decided to make a spinner as well. I also liked how she had the kids figure out a way to divide their circle in ten equal pieces as a nice review on dividing as well as remembering how many degrees are in a circle!  We also love working with protractors, so it was a nice review.   (We also had the chance to review equivalent fractions AND percents!  All in one activity! YAY!) Below is our page:

Because our goal was to compare theoretical results with actual results, and to make predictions, our notebooks ends up steering away from Runde's a little bit.  We have been having trouble creating frequency tables lately, so here was a great opportunity to do so.  I was going to have them do their experiment 20 times instead of just ten, so we based our theoretical results off of 20 (and reviewed equivalent fractions at the same time!)  I also had them come up with a prediction of what they thought would happen, based on their theoretical results.  Then, it was spin time!  They recorded their results in their frequency table and wrote out their conclusions based on their actual results.

Lastly, we met to talk about the reasonableness of certain results.  We used our theoretical results to determine if the actual result was reasonable or not.  Before this lesson, only 50% of my students answered a "reasonable or not reasonable" question correctly.  After this lesson, we were up to 87%!  I would say we succeeded!  :)

Algebraic Expressions and Math Notebooks

We covered Algebra way back in October and did a really great foldable for the four steps to follow when solving a problem with unknowns.  We came back to it today, both as a review, and to extend our thinking to expressions and patterns.  Our learning target for today was to introduce the use of algebraic expressions to represent situations and describe rules.  First, we watched this StudyJam on Function Tables, as well as one on Addition and Subtraction Equations and Multiplication and Division Equations.  We also did a sample problem in our notebooks, as shown below.  The problem reads:

Joe and Maria are 5th graders.  Joe is two inches taller than Maria.  

I asked the students to put this information into a function table and give me some measurements for Joe and Maria.  I reminded them to make them reasonable measurements for 5th grade students.  Of course, everyone had different answers, and all were acceptable as long as Joe was two inches taller.  Next, I recorded some of their measurements on the board and asked them to explain how they came up with Joe's height.  We also noticed that our function table was similar to the In and Out boxes they have become so familiar with using Everyday Math.  I asked them what the rule was for this table.  Of course, they all said "add 2!"  Then, I encouraged them to tell me the rule for finding Joe's height based on Maria's if we use m for Maria.  This was a little tricker, but with a little prompting, they said "m+2!" Now we're talking!

Next, we wrote some sample problems in our notebooks and came up with expressions to describe the problems (EDM 10.3):

After some more practice independently, I gave the students an opportunity to write their own problem situations that would require the use of a variable.  I forgot to capture this in a photo, but they did a really great job!  Being able to write their own, and accurately, made me feel confident in their understanding of expressions.