Wednesday, November 21, 2012

Number Talks

As previously mentioned, our district has the fortunate opportunity to train teachers on the CCSS.  In addition to discussing RICH problems and how they can be used in our own classrooms, we conduct Number Talks.  We use the book Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K-5, by Sherry Parrish as a resource.  Number Talks were designed to improve students' mental computation skills and number sense.  Inside Mathematics is another fantastic resource that shows how different teachers in varying grade levels apply Number Talks to their lessons.  In fact, this is a wonderful website that allows you to see teachers in action applying the Common Core Practice Standards! Woo! 

Anyway, we have been doing our best to introduce these talks into our classroom.  In my room, students sit together right in front of the board.  I tell them to summon their inner Kindergartner, which they giggle at.  We have only had time for a couple "formal" Number Talks, but we are beginning to apply it in all aspects of our day when answering questions verbally.  Here is an example of how my students were able to solve a basic addition problem using mental math and their process for doing so: 

Are they stellar?  Probably not.  My students were looking at me like I was a crazy person that day.  They didn't quite understand why understanding how to compose and decompose numbers is so important.  Many said, "I put them on top of each other and added.  I also carried the one." My point was that I wanted them to know what "carrying the one" actually meant.  As we do more, they do improve, and I can see it translating in other areas of math.  They are really starting to think about the VALUE of the numbers.  

I plan on doing more complex problems as we go and seeing how they improve.  I told them I would keep their original posters so we can compare them to how they are doing in a few months.  They have already drastically improved!  If you don't do Number Talks in your classroom, I highly recommend you look into incorporating them every now and then, especially in younger classrooms!

RICH Problems: Thanksgiving Table

I am extremely fortunate to be teaching in a district that is forward thinking in their training of their teachers for the CCSS.  We are able to attend professional development once a month (once a month!!!) in the area of Math and English Language Arts.  Even though I currently only teach math, as schools are constantly changing, so are teaching positions, and there may come a time where I will be teaching L.A., also.  I am so thankful that I will be prepared if that day comes!

Because the meetings are monthly, we are able to apply what we are learning about Common Core to the concepts we are currently teaching.  We have been told to continue to teach the Ohio Academic Content Standards, while slowly implementing Common Core where appropriate.  I, for one, love this approach.  I feel I will be better prepared to fully implement Common Core when the time comes.  

One thing we discuss during our meetings are RICH problems: mathematically rich problems that challenge students to investigate math problems and empower them to use their knowledge to come up with different solutions.  These problems also force students to apply the CCSS Mathematical Practice Standards.  We solve the problems ourselves during our meetings and create posters just as our students would be expected to do.  It's a great way to show that even adults come up with varying solutions to the same problem.  We then implement these problems in our classrooms and report back on our results.  

Here is the most recent problem we did in honor of Thanksgiving.  It is aptly named "The Thanksgiving Table Problem."  

 Because we just learned multiplication, this problem really seemed quite perfect.  It forced students to look at numbers based on place value.  They used base-ten blocks to "build" a table with the dimensions of 13 ft x 7 feet and were asked how many ten ft. boards and one ft. boards were used to construct the table.  Students used longs and cubes to create their table, and in doing so, created an area model for 7 x 13.  We have just begun discussing the distributive property, and this was a great way to apply it!  Students saw that they would need seven 10 ft. boards and 21 one ft. boards: 7 (10 + 3).  

One group building their table using base-ten blocks

The beauty of RICH problems is that there are many parts using many different forms of math.  Students complete what they can and can delve further and further into the problem.  The next part of the problem had the students deciding if they needed to add more square footage to make a 100 sq. foot table (the original was only 91 sq. ft.).  They all concluded they needed 9 more sq. ft., but quickly realized that would make their table odd looking: it was no longer a rectangle.  Most groups decided that they would add a few more square feet to either the length or width to ensure the table was at least 100 sq. feet.  

The next task had them calculating the price of their add on, then figuring out if there was a cheaper way to add on to their table.  Here are some of the finished products:

This group did a fantastic job of displaying their information!  They showed their add-on as well as all the math they did to come up with the price of the add-on. 

Love their organization and clear answers!

This particular problem applies many of the CCSS Mathematical Practice Standards:

1. Making sense of problems and persevere in solving them.
4. Model with mathematics.
5. Use appropriate tools strategically.

At the end, each group was able to present their findings.  They really seem to be getting better at doing group work and including all members (this is something we have REALLY been practicing!).  Overall, I would say the problem was a huge success.  I will choose some projects to take with me to my next CCSS meeting next week to share with the other 5th grade teachers in the district.   

A great website for RICH problems is the Ohio Resource Center.  I will follow up with a post about more of the RICH problems we do from this website called "Stella's Stunners".  They are WONDERFUL!

Discovery Learning: Sum of Angles

Rather than just tell students how to do something, I like them to discover it on their own.  It gives me an opportunity to later point out "Hey, remember that day we figured this out?"  On this particular day, we had been talking about angle measures and were going to be moving on to angle measures in triangles and quadrilaterals.  I decided that our Interactive Notebooks would be perfect for discovering the sums of the angles in these polygons.  Students first received two congruent triangles to cut out.  One was glued into their notebooks and the angles measured.  I casually asked the students what the sum of those angles were: 180 degrees.  "Hey!  That's the same number as the measure of a straight line!" piped up Calli.  So, I told them to go ahead and draw a straight line in their notebooks.  Then, we glued the corners of the triangle together to prove that the angles together form a straight line. 

Here is our finished product.  We tested our theory that the sum of a triangle's angles is always 180 degrees.  I found a fantastic interactive website that allows you to adjust the angles in a triangle to show they always add up to 180 degrees, no matter how you do it.  

We then followed the same process for a quadrilateral.  

The kids loved it!  The information stuck with them and they know that a triangle's angles add up to 180 degrees, while a quadrilateral adds up to 360.  One inquisitive student asked if this works for all polygons.  I challenged him to test a pentagon, hexagon, and so on to see if there is any sort of pattern relating to the number of sides in a polygon.  Of course, many students took on this challenge with protractors out and pencils writing.  It was only a matter of time when they excitedly yelled, "There IS a pattern!  You add 180 degrees every time you add a side!"  And my work here is done :)

CCSS Mathematical Practice Standards applied:

2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning

Interactive Notebooks: Algebra

Because both the Ohio Academic Standards and the Common Core State Standards rely heavily on algebraic thinking in 5th grade, Jamie and I knew we really needed to find an effective, yet simple way to get our students thinking algebraically.  We searched for ways that other teachers were teaching variables and stumbled upon another teacher's blog that we found to be extremely useful!  I Speak Math is a wonderful blog written by a 6th/7th grade math teacher in North Carolina.  She created a graphic organizer specifically for writing linear equations from word problems.  We copied the graphic organizer and glued two into our Interactive Notebooks.  Then, we did a whole page of word problems using it!  We quickly saw the relationship between addition and subtraction and multiplication and division and are now able to write two equations using different operations: a fantastic skill!  

This forces students to really think about the unknown: what they are trying to solve for.  They were able to write two equations: 35 + g = 64 and 64 - g = 35 using two operations.  Bring it on, OAA!
My students loved it so much that they still follow all four steps when solving ALL word problems, whether I tell them to or not (and we did this over a month ago!).  They are getting really great at solving for the unknown.  Once we get into Order of Operations, they will be able to deal with more complex equations.  I can't wait to see what the future holds for us! 

Magic Number

One thing we started in our room is our Magic Number.  We brainstormed ideas on different ways to make a number: tally marks, addition problems, base-ten blocks, number sentences, etc.  Every couple days, I put a new number on our extra side board.  We started with lower numbers.  Since we had already learned about square numbers, I used a couple of those.  I also used a couple prime numbers since we had been talking about them as well.  When the students finish their work, they may add different ways to name that number.  When we started learning about decimals, our magic number was a decimal.  It was great to see what they came up with!  I can't wait to see what they can do once we get to fractions!  Here is an example of our Magic Number board.  After a few days, the kids decided they wanted to call it our graffiti board: love that idea!

Magic Number 27: I used this because so many kids kept mistakenly  thinking 27 was prime.  Many decided to list 27's factors and realized: nope! Not prime!

It is great to see how much they have improved in their accuracy since we began our graffiti board back in October.  Many are even coming up with their own word problems using the number, and some are even using variables to display the number!  This is one activity that gets them thinking about numbers as soon as they walk in our classroom.  They all can't wait for a chance to show off their ideas! 

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!

Interactive Notebooks

I am fortunate to have an amazing co-worker to plan and plot alongside.  Her name is Jamie, and just being able to collaborate with her this first few months of school has been awesome!  She only teaches one 90 period of math and the rest science, but it's enough to get us talking to each other every day about lessons and how they went.  She showed me some interactive math and science notebooks she found on blogs, and we both agreed that this would be the perfect year to start them.  We have been given the go-ahead from our district heads that we can now use EDM as a general framework and supplement where necessary so as to cover the Ohio Standards and the Common Core...all at once!  An interactive notebook would be the perfect place to combine all of our accumulative notes and materials. 
Rules page and Table of Contents

After setting up the foundation of our notebooks, we began our first activity and first entry with a game we so creatively call "The Barrier Game."

Barrier Game game boards.  This was a great way to see how my  new students reacted to a challenge!

For this activity, I paired students up (remember, this was the first week of school. I didn't know personalities!) and gave them two different grids: one student received a blank 3x3 grid, while the second received a grid with simple math terms and symbols on it.  We then placed a folder between them so they couldn't see each other's board.  It was the second student's responsibility to communicate what his or her grid looked like while the first student drew it.  Some quickly discovered they weren't communicating efficiently.  They realized they needed to be more specific in their directions to their partner.  One student, Aaliyah, said to me "Ms. McHugh, Cale and I just aren't good partners.  He isn't drawing what I want him to!"  I asked if I could listen in on their conversation.  It turned out that Aaliyah was just telling him things like "Draw a square at the top."  Poor Cale didn't know where to draw his square!  When reflecting on the activity at the end, Aaliyah raised her hand and admitted "It wasn't that we were bad partners, I just need to be more specific when I communicate.  I wasn't giving him enough details!"  That was a wonderful "ah-ha" moment for the class.  Of course, I had some students get extremely frustrated with their partner.  I would like to do this activity again later in the year and see how they do.  They will be doing a LOT of partner/group work in my class, so they need to know how to communicate well!  After we reflected on the activity, we wrote down our thoughts in our notebooks.  Below is an example of an entry regarding the "Barrier Game."

Cale's reflection on his experience with Aaliyah

We also brainstormed ideas on how good mathematicians communicate.  I was really impressed with their ideas!