Measurement and conversions: Interactive Math Notebooks

Again, I'm behind on posting this! Where does the time go?  We did measurement back in March, and while we did a lot with it, I'm just going to outline what we did with our notebooks in this post.  We began by discussing the two systems of measurement.  We decided the best way to organize this information was in a T chart (we REALLY like those around here!) and we wanted to keep all the types of measurement (length, capacity, weight) together as well.  Here is the list we came up with:

Next, we brainstormed some of the basic conversions we remembered for length for each system and wrote them down.  Lastly, we took notes on an easy way to convert between units of measurement.   A BIG "thank you" to my coworker Adrienne, the 4th grade math teacher, for sharing her mnemonic device!  Some of my students remembered it from last year!  She taught us that there are two ways to change units: to multiply or divide.  When converting from a Big unit to a Small unit, you Multiply, so we think "Best Soccer Mom."  When converting from a Small unit to a Big unit, you Divide, so we think "Silly Babies Dancing."  We always giggle at "Silly Babies Dancing!"

Below is the anchor chart hanging in our room to serve as a reminder.  Another "thank you" to Adrienne!  I got this straight from her!  Thank goodness for kind coworkers willing to share and kick around ideas with!

An Exploration of Volume

Ok ok....So it's April and I taught volume almost a month ago.  Things can get pretty hectic this time of year, what with preparing for the OAA and making sure my kids are in tip top shape to show what they know!  Now that we're on Spring Break, I can finally sit back and reflect on what we've been learning and where we need to go after this.

I truly feel that math should be a hands-on experience for kids of all ages.  It shouldn't stop in 3rd grade.  All too often, we get caught up in making sure they know how to do it on paper and apply formulas, but kids need to be able to touch and feel what they are learning to really grasp it and understand it.  I always try to give them thorough hands-on experiences before teaching them the "math" part: formulas and equations.  So far, I think we've been pretty successful.  But, as in most cases, time is always an issue.  We just have to keep moving, moving, moving!

As will area and perimeter, we did an exploration of volume.  Many of my students had remembered the formula for finding the volume of a rectangular prism from 4th grade, but I wasn't really sure they understood or remembered WHY you multiplied LxWxH.  Thanks to Everyday Math, each student had the net of two different open rectangular prisms in the back of their math journals.  We made predictions for how many cubes we thought would fit into each.  These predictions actually gave me pretty good insight as to where each student was in their understanding of volume.  Then, of course, we began filling!

 We started by just filling the base of the prism and finding out many cubes that was.  I wanted them to see this as the area of the base: of course, some did, some didn't.  We will keep working on this idea of area! (Too often, their idea of area is just a rectangle on a page....must change that thinking!!).  Then we added another layer, and finally a third.  This allowed them to see that we were adding the area of the base however many times tall it was.  For the second prism, we only filled the base and predicted what the volume would be based on the results of the first prism.  From this, we developed the formula for finding the volume of a rectangular prism!

As an extension, and because we had a couple extra minutes at the end of class, I had each student build a rectangular prism on their desk with a volume of 24 cubic centimeters.  I didn't give them any more specifications than that.  After a minute or two of building, I began recording different lengths, widths, and heights that I saw around the room.  Once they saw all the possibilities, hands flew in the air.  They remembered what we had learned about multiplication being part of the commutative property and knew they could use the factors of 24 to build many many different prisms, all with the same volume.  Ah ha moments are the best :)

Lastly, here is the anchor chart we came up with.  They wanted me to point out that volume is "all about the threes":

Volume!  

Measurement: Perimeter and Area

Teaching perimeter and area is one of my favorites because it can be so hands on (oh but just you wait until volume, surface area, and circumference!) Because our 4th grade teachers did such an excellent job in this area (pun completely intended!) I didn't feel the need to dwell on perimeter and area of rectangles for long.  Thanks to Pinterest, I found an easy, hands-on way to review area and perimeter of rectangles that wasn't just a worksheet to complete.  After watching a couple StudyJams videos, we went straight to work with some grid paper, two dice, and our pencils.  Students were to roll the dice and create an array to display the numbers on the dice.  Then, they were to find the area and perimeter of the array.  We discussed either counting the squares, or using the formula they used in 4th grade for area.  I worked with a couple struggling students.  I had them highlight the outside of the array in one color to find perimeter, then color the inside of the array with another color to find the area.  This really seemed to jog their memory!  Below is a picture of Aaliyah's arrays (although, I'll have to remind her that area is measured in square units....or squAREA!)

The next day, we moved on to finding the area of parallelograms and triangles.  This proved to be much more difficult, they concluded.  The triangles and parallelograms were drawn on centimeter grid paper, and at first, some students were trying to shade whole squares, then put together pieces to create more wholes.  When we shared answers and found that we all had something slightly different, we need we needed a better solution.  I asked them why finding the area of a rectangle was so easy for them, but these polygons were so much more difficult.  The conversation went something like this:

Student 1: Because with rectangles you just count the squares and that's the area!
Me: Ok.....so why are triangles and parallelograms so much harder?
Student 2: There are sometimes all these little pieces of squares that you have to put together.  Sometimes they are easy, like if it's just a half of a square.  But other times they are harder.
Me: What is it about rectangles that make it have just whole squares or half squares then? <silence in the room>
Student 3: It....has....right angles?
Me: And....?
Student 3: Right angles are squared off....so they are easier to count!
Me: So what if we made our parallelograms into rectangles so that they are easier to count?

We went on to change each polygon into rectangles and go from there.  I let them struggle with this method for homework: not all of the polygons were easy to change accurately.  On day 3, we went at it again.  Many students came in frustrated and unsure if their answers were correct.  And this is how we led into the discovery of the formula for finding the area of triangles and parallelograms!

We began class by looking at a scalene triangle and trying to find its area.  I had them do what they did before.....divide it into 2 rectangles and find the area of each, then add them together.  This time, however, they had to add up a bunch of half squares and quarter squares.  It took them forever and they were frustrated (yet again).  After all that, they knew they still had to divide it in half because it was only a triangle.  That's when they saw that they were really just finding the area of a rectangle and dividing it in half!  We tried this method, which was much simpler to multiply the length by the width, then divide in half, rather then count up all these pieces of squares.  I actually had one student's face light up as she yelled out "OhMyGosh! That is SO much easier!  Can we ALWAYS do it like that?!" To which I happily replied, "Yes, Ivy, because you just figured out the formula for finding the area of a triangle!"  They were so relieved, and shocked, that it was THAT easy.  We did a similar discovery lesson with parallelograms, cutting them in half and making them rectangles.

The last 15 minutes of class were spent updating our notebooks and reflecting.  We used the right side so show sample problems and made sure to highlight the base and height of each polygon in separate colors to help out our brains.  Then, on the left side, I allowed them to write whatever they wanted on area of parallelograms and triangles.  They were told they could use words, pictures, examples, formulas, or a combination to reflect on what they had learned.  I think they did a great job! They even asked for more time! Here are some examples on the work we've done in our notebooks for area and perimeter:

Each student received two random arrays.  They were asked to find the perimeter of one, use it to define perimeter, and think of examples.  Then, we did the same with area of the other.  Great visual! 

Here is the right side of Allison's notebook.  They used one color highlighter for base, and one for height to help them see that they come together to form a right angle.

Here are a couple of the left side thinking from my students.  Again, they were able to write their own notes on area.  Each are a little different, but reflect how each student prefers to receive their information.

And lastly, as usual, we always make an anchor chart after we have learned something.  Perhaps, if they glance at it enough, the information will stick!!

Area of Triangles and Parallelograms Anchor Chart

Anchor Charts and We Can!

I am a huge fan of using anchor charts in my classroom.  I let the kids help me decide what information to include, then hang them up where they are easily seen.  I remind them to refer to them during tests.  I think of them as a resource and love when I look around and see the kids referring to them.  To me, it's their way of telling me they care and want to do well.  After a while of referring to the charts, the information is just committed to memory!  I don't know what I am going to do in January when we move into our brand new buildings (!!!!!!)  and we aren't allowed to hang things on the walls!  I'll come up with a solution I'm sure!  Here are a couple examples of some of the anchor charts currently hanging in the room:

Using models such as base-ten blocks and number lines to display decimals

Rounding Decimals: CCSS 5.NBT.4

Additionally, I like to really make sure my students know what our goals and objectives are each day.  I want them to be able to say, "Yeah, I did learn that today!"  Each time we learn a new concept, I let them know how it is connected not only to the Ohio Academic Standards, but also to Common Core.   This way, we are all working toward a common goal.  I never want them to be in the dark about what they are learning and what they should be able to understand after a lesson.  Here are two examples of our "We Can" posters:

We Can do so much!

I am really thankful to have so much wall space in our room!