Interactive Math Notebook: Factors and Multiples

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We have been busy working on determining whether one number is a factor or multiple of another number.  We started by building arrays both with tiles and on centimeter grid paper to determine a number's factors.  Becoming proficient at building arrays has really helped some of my struggling students feel successful in finding factors even when they aren't proficient in their facts or have many strong strategies to use to determine a fact.  After practicing many many times,  I gave each student a pair of die (some were six sided, some were more for my kids who are proficient in their facts and wanted a challenge!) and grid paper and instructed them to roll the die and create an array with dimensions that match the numbers on the die.  We then added this page to our notebooks.  Below is an example.  

Next, we used our Math Handbooks and its Table of Contents (oh hello, Language Arts skills! See....I'm learning how to incorporate it all!) to find the definition and examples of factor, prime number, composite number, and square number.  We used this information to create a foldable to glue into the right hand side of the page.  An example is below!

We are also learning about multiples.  After many days of discovering, discussing, and applying this knew knowledge, we finally were able to put the information into our notebooks.  I always try to wait until I feel they understand it to put it into the notebooks.  We used a hundreds chart to choose a factor, then highlighted all of its multiples.  We also used this factor to create a basic real world problem to show how to apply it to multiples.  

This student chose the factor two, and wrote the problem: A store has CDs for $2 each.  She then drew a picture to show that one CD would cost $2, two CDs would cost $4, three would cost $6, and so on.  This shows that the price of buying CDs are multiples of 2

This student chose the factor four.  His problem is about video games costing $4 each, so two would cost $8, three would be $12, and so on.  He goes on to begin to write a question associated with it!

Lastly, I really wanted to make sure we understood the difference between factors and multiples, as it can get very confusing.  We used markers to circle all the factors in a list and all the multiples associated with it.  Students were allowed to pick their own factor, or for those who are still not feeling comfortable with multiplication, were permitted to use the factor four as I did in my example.  Then, they showed an example of an array that shows one of their listed factors and multiples, as well as a non array (just to make sure they understood that an array is a rectangle and cannot have any pieces sticking off the end!!).  These last two pages might be my favorite!  

This student wrote all the problems for the number four.  He circled all of the fours to show that is the factor.  He wrote: 4 is a factor of any whole number that it divides evenly.  He also circled all the multiples to show that you can multiply any number by four to get a multiple of four.

This student did an excellent job of showing the difference between an array that four is a factor of one of its multiples, as well as a non example saying "21 is not a multiple of 4" and using his array as proof!

Arrays: The Gateway to Multiplication

Our first unit is all about factors, multiples, and arrays.  I know from teaching 5th grade that if students don't understand what multiplication truly shows, they are missing the foundation to a deeper understanding of numbers, as well as the key to success with many many other parts of math.  That is why I plan on really spending time this year developing a deep understanding of multiplication, how numbers are related, and strategies students can use to help them if they get stuck.

We first began, as always, using manipulatives.  We have these wonderful one inch tiles that are perfect for creating arrays, but connecting cubes work as well.  We discussed what the word "dimensions" mean when looking at the lengths of each side.  We started by practicing arrays with smaller numbers and built our way up.  Once I felt they understood, I put them in pairs and gave them each two numbers to find all the arrays for.  An example of our work is shown below! (Please ignore the fact that the array she has showing shows 4x5 and is not an array for 18!  She was actually building for their next number: 39)

This activity led into a discussion about why certain numbers had only one array, like 17.  It was a "prime" time to talk about prime numbers!  We displayed the posters throughout the room and refer to them often, especially when discussing multiples, factors, and special numbers!


If you have any suggestions for other awesome activities, or ways I can improve, please leave a comment below!  Thank you!

New Beginnings

Is it really that time again?!  SO SOON?  August has truly flown by, and all of a sudden we are starting school.  Except this year is going to be different.  You see, last year, and the three years prior to that, I drove over an hour each day to my school (68 miles!!).  While I loved my job, coworkers, students, and families, I needed to make a change.  I couldn't continue using up two hours of my day (and all my extra cash for gas!) so I accepted a job closer to home.  With this job is a different grade level (a 3-4 split....yowza) AND I get to teach all subjects (not just math as before)!  I haven't figured out yet how this will affect my blog, but I'm sure that will come in due time.  I look forward to doing math notebooks again, this year catering to 4th grade, while making many adjustments and improving it.  I am also learning a new math curriculum, Investigations.  Hopefully there will be lots of new and exciting ways to teach MATH!  And perhaps, if I feel ambitious, I will broaden the blog to include all the wonderful things we will be doing in Language Arts.  We shall see.....  :)

Wrapping up Notebooks: A time for Reflection

Last week was our last full week of school, so when Friday rolled around, we used our last full class together to wrap up our Interactive Math Notebooks.  When I told my students it would be our last entry, some loudly groaned and others said audible "Noooooo!'s"  I'll admit, I was sad too.  We had all grown fond of the days we would add a new entry.  They were all very excited that our last entry fell on page 100, which had been our goal for a while.  "Ms. McHugh!  We wrote a book that is 100 pages long!"  And it's true, we did write a book.  Who says Math and Language Arts don't go together??

Before adding our last page, I had created a word scramble page from SuperTeachers (currently a free feature).  Each of the words were math terms that could be found in their table of contents.  This was just a fun way to sum up our year together.  Next, we all sat on the floor (Kindergarten style, as I call it) and slowly flipped through each page of our Notebook.  This was by far the best part of that entire week.  They couldn't believe all we had learned and how far we had come!  Some mentioned that when we entered certain pages, they still had not understood it completely, but now at the end of the year, they "got it."  This was a great lesson to learn.  It doesn't always "click" for all our students at the same time.  But with a little bit of hard work and a lot of  perseverance, most students understood everything by the end of the year.  Our Notebooks were a great reminder of that.

After we reflected on the year as a class, I let them make their very last foldable.  This was a reflection on what they thought they were good at in math, things that were difficult or easy for them, and times that they had the most fun.  I must admit, most said they had fun when their teacher got distracted or off track.  What?  I have no idea what they are talking about......

Here are some of my favorites from that last day:

This one makes me smile :)

Who...me? No!

Fun is a theme in our room.  When we have fun, we are learning and it sticks!

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!