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LMartin - The student has a deep understanding of number sense and an effective strategy for "If I double one number, I can half the other." The student also demonstrates understanding of the relationship between multiplication and division.

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LMartin - The student has a deep understanding of number sense and an effective strategy for "If I double one number, I can half the other." The student also demonstrates understanding of the relationship between multiplication and division.

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We can use the same concept but with easier operations and numbers for our younger students. The student work shown obviously demonstrates that they understand number and operation how they can be broken down and built up in differing relationships. This activity points to the key role that the "=" sign plays in math. Basically you can have a multitude of combinations and permutations of numbers on either side of the "=" sign, but they have to be equal!

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This student knows and understands the connection between multiplication and division. They also understand how numbers are build (place value) due to the fact they knew 7 is half of 14. They know by breaking the larger numbers into smaller parts the problem can be easier to work with. They have a strong foundation of basic math and are able to apply it to new situations.

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The student knows their multiplication facts. They know the relationship between numbers and the relationship between multiplying and dividing. They try to present their knowledge in a logical order.

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The student is able to build on the multiplication facts they understand, and see how larger facts can relate to ideas they already know. The lines dividing the thinking on the work page, shows that the student is organizing their thought process.

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The student obviously has basic multiplication skills, and appears that there is a pattern she /he uses.

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This student understands basic math facts, fact families, and how multiplication and division are related. This student also knows how to use the half and doubling strategy. Other qualities include neatness and legibility. This student also can explain his thinking and how he understands how these numbers form a relationship to one another. His "thinking" is easy to follow and to understand. It is easy to reference back to the problem so apply the thinking.

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This student is able to see the connections between multiplication and division, as well as how the numbers relate to each other (double/half). They are able to go back to what they already know (7x8) and then apply it to the problem.

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This student realizes that numbers can be manipulated... that they are flexible. The student knows that it is easier to use things you know (such as doubles in this case) to solve math problems than working with the one you were given. This student is confident enough to take a risk and try to solve this problem in a new way.

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This individual likes to be organized and neat. Breaking down the 56 into smaller parts which makes it easier solve.

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This individual likes to be organized and neat. Breaking down the 56 into smaller parts which makes it easier solve.

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This student seems to have strong number sense.  The student understands the connection between multiplication and division.  He/she knows some basic multiplication facts (7 x 8), and uses this knowledge to help him find what would be multiplied by 14 to equal 56. He/she applies the double/half strategy to find the solution.

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I like the way that this student drew lines across the page to demonstrate the three different thought process.

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This student has a good idea of how the numbers work and understands how to deconstruct and reconstruct to get the answer