One of the most important parts about working in math is being able to explain one's thinking to others. Whether you're convincing colleagues of a budget line item, or working with your partner to buy enough food for the week, we need to be able to share our strategy.

Today's homework, the problem of the week, is designed to hone students' skills in this area. We write about our math thinking often during math workshop but it is a skill that demands a lot of practice. The problems are not necessarily meant to push a child's computational abilities, but to challenge them to explain their problem solving and math thinking.

For example, today's problem states: Today I found 6 coffee cups in the Elms (true story!). If I found the same amount for a week, how many would I find all together?

Now, you might find yourself asking right away, "Wait a second, does she mean a 7 day week, a 5 day week or just the remainder of this week?" Any of those assumptions is "correct" as long as you explain what you chose in your solution.

We talked about using a rubric to help us categorize the detail in explanations. Using a scale of 1 to 5, students could see very concretely what a "complete" solution was. Here is what we came up with:

Level 1 - Simply the answer, or an attempt that shows no understanding of the math situation.

e.g. (for this week's prooblem) "30"

Level 2 - A label or two. Numbers that show computation. An attempt that shows a weak understanding of the math situation.

e.g. "6x5=30"

Level 3 - Labels. Computation for multiple steps. Answer is labled clearly.

e.g. "6x7days=42 You'd find 42 cups"

Level 4 - Complete explanation but a computational error. Solid computation and labels but more limited explanation.

e.g. "6 cups x 5 days in a school week = 30 cups Anwer: 30 cups by Friday."

Level 5 - Complete explanation and correct computation. Pictures often add to explanation.

e.g. "Step 1: I decided to think about a school week, Monday to Friday that has 5 days.

Step 2: Each day had 6 cups. That's 5 groups of 6. I used multiplication (6 cups x 5 days) and found there were 30 cups total

Answer: There were 30 cups at the end of the week (and one empty cover.)

Some students had great questions about the rubric, including asking if it was a grade. We explained how using a rubric can help show how they can grow in an area. They can find out in a very specific way how they can deepen their skills as a math thinker and communicator.

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