Let me think...
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Third graders are problem solvers!  When i was a child, I remember feeling worried about math.  I felt like there are all of these things I simply had to KNOW!  It wasn't until I was much older that I realzed it was all about connections, and that I could figure things out for myself.   I truly learned to love math and realized that I had loved it all along, through my interest in sewing, woodworking and other hands-on activities.  I hope my students develop that love much earlier.

Making connections among learning is what it is all about.  We talk about how understanding that 4 + 6 = 10 helps us think about

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40 + 60, 400 + 600, etc.

Instead of simply stacking numbers, crossing out and regrouping and subtracting "the grown-up way", we try thinking about relationships.  If I know that 60 - 40 = 20, then it can help me think about 60 - 41!  It is just one less!  

I am a firm believer in that old Chinese (I think) proverb: "I hear, I forget.  I see, I remember. I do, I understand."  For learning to be meaningful, we need to be active and involved.  For children, this often means using what I call "good junk" (anything that can be used to model our thinking) or math tools like Base 10 blocks.

Challenges

We have learners of different abilities in our room.  It is a big job keeping up with them!  In our Math Lab, there are a variety of activities for students.  For each unit in our curriculum, there are Choice Cards.  Students who are ready for an extra, more open-ended challenge work on these instead of or in addition to class work.  The cards include a variety of tasks, ranging from problem-solving to creating games, to performing a song about math! 

I also include activities I have gathered over the years.  There are games, practice sheets and tools I have found helpful in independent work.

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