Multiplying Fractions with Paper Squares

Multiplying Fractions with Paper Squares

In the last decade or so there has been quite a push back regarding discovery math. I have always found this to be very perplexing.  How can it be denied that we are not born knowing mathematical concepts other than a very base form of quantity (Dehaene, 2011)? At some point, we all need to discover these mathematical ideas for ourselves. The question is really what is the best method for discovering these mathematical ideas. We could discover them through someone showing us (direct instruction), or it could be us figuring them out for ourselves through an experience, or it could be some combination of the two, but regardless at some point, we all need to discover these concepts and begin growing our own personal conceptual images for these ideas.

I am most interested in what types of activities contribute to the richest conceptual understanding and what are the most engaging and interesting. It is this combination that will cause students to excel and

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The Mathematical Fusion Machine

The Mathematical Fusion Machine

In kindergarten, when students are shown 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and THEN    the crowd of students should all looked shocked and say things like “WHOA, what just happened there!!!!”  BUT instead this HUGE mathematical idea goes unnoticed.  So, this activity will make students ooh and ahhh as they should, as well as deepen their understanding of our base 10 system which is foundational to understanding our number code, addition, subtraction, decimals and more.

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Fractal Multiplication

Fractal Multiplication

A drawing/image based activity to help students understand the relationship between number multiples, prime numbers, prime factors, and division. The image-based puzzles reduce the barrier for those who struggle to memorize while helping them to continue to connect to the meaning of multiplication (whereas using a calculator does not connect to meaning). The idea is that over-time these images are meant to aid the student in memorizing their times tables in a non-stressful way.

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