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##### Wednesday, July 22, 2015

Good Morning!  I am Terri Izatt from KinderKapers, and I am excited to be blogging here today.  I am the kind of person who loves to see all my students merrily and actively moving about my classroom learning in very hands on and creative ways.
Today I want to talk about math and developing number sense in students of all ages.  I recently attended a class where we learned ways to cognitively guide our math instruction.  I was so excited to learn that many of the things I was already doing, were just that.

We were taught (or reminded) that students come to school with a great deal of informal or intuitive knowledge of mathematics and we can use that to build mathematical understandings.  Given the opportunity students can work their way through a given task or problem and gain understandings as a result.  This requires both time to work on solving the problem and the chance to discuss the thinking behind their solutions.  As students listen to each other they can even increase their own understandings as they first, explain their own thinking, and second, listen to someone's different thought process.
Number Talks
This can begin with a task as simple as dot cards or ten frame quick match.

When you ask a student how they knew there were 7 or 8 or 12 dots on a card, they have to think about their thought process.  What did they do?  Did they see any patterns?  Did they do anything to stay organized or count quicker?  When you ask, "Did anyone do something different?", or "...see something different?", students begin to realize that there is more than one way to approach a problem.

Being able to see ten frames in your mind is a skill that will be so helpful as students need to compose and decompose larger numbers.  One thing I like to do is a game of 10 Frame Quick Draw.  I will hold up one (or mask one on my smartboard) for just a few seconds and then the students need to draw dots that match the 10 frame I showed.  As time goes on, I show it for shorter amounts of time and let them play with partners.  My favorite question to ask is, "Which did you count....the circles or the spaces".  Once again, students have to slow down and think about what they did, and they get to see that not everyone thinks the same.

We should have students solve problems not to apply mathematics, but to learn new mathematics.  Tasks or problems can and should be posed that engage students in thinking about, and developing the important mathematics they need to learn.  When designing a task we should begin where the students are, be sure the engaging aspect of the problem relates to the mathematics the students are to learn, and it must require a chance to talk about and justify their answer and methods.

Try this task:  If we start with ____ (you pick the number) ______ (cubes, dinosaurs, shark teeth) and I hide some, how many did I hide?  Have the students tell you how they plan to solve the problem without actually telling you the answer.  Give them time to think about about what they need to know and what they want to do, and then justify their methods.  Then they can check their methods and see if they can get the correct answer.

Now this math task, becomes a game, a game you can play in any season (just change up the manipulative), a game you can differentiate on many levels (just change the number of manipulatives you use).  I love it and it is one of my favorites.  I could call it Missing Addends,  but I usually try to find a name that matches the manipulative I am using.   This time of year, it seems that shark teeth would be fun.  I created these recording sheets to go with some shark teeth I picked up at Amazon.com and I called the game Shark Attack.
 Using a recording sheet can help students to keep track of their thinking, especially as they play multiple times.

 Giving the students sentence stems and a math talk work mat will also help them to be able to explain their thinking.

You can pick this up along with other versions in my TpT store.  Your students will have fun with this all year long.