Well, something like M & Ms.

Each child got a ring of chocolates. The younger students graphed the colors.

Then they measured the length and width of their paper with chocolates. They found the perimeter, or how many chocolates it would take to make a border all the way around the paper. The first-grade math student whose hands are pictured below realized that she could just use her measurements from the length and width to calculate the perimeter without actually making a border around the whole page.

The students were then asked to figure out the border if they folded their papers in half. Some students folded their papers horizontally while others folded theirs vertically. They ended up with different numbers of chocolates required to make the border. At first they thought mistakes had been made. But after confirming that their different answers were in fact right, some of the students realized why. Others didn't, but at least they now have a question in their minds to keep considering. A sixth-grader who was watching was challenged to think about what proportions of rectangles give you the most area for the least perimeter.

After figuring out the border, the children were asked to find out how many chocolates could fit on the page (the area). They didn't have enough chocolates to cover the paper and count, so this required some thinking. Some kids made a few rows, counted the chocolates, then moved the chocolates down the paper and counted them again. They figured the area pretty accurately. One first-grader realized that ten chocolates fit

*across*the page, so she could make a line of chocolates

*down*the page and count each chocolate in that line as ten. She shared her idea with her classmates. As a teacher, it was incredibly fun to watch a first grader discover and teach her friends that the area of a rectangle is its length times its width (even though the she didn't phrase it that way).

Older students were asked to find out how many chocolates could fit on the foil circle that the chocolates had come from. They realized pretty quickly that it was too hard to work on that bumpy surface, so they traced the outline onto paper. A third-grade math student started to cover her shape with chocolates. She ran out and decided just to cover half of the shape and multiply by two. She confirmed her answer later by borrowing chocolates from someone else and covering the whole shape.

A sixth-grade student, who knows how to use pi to calculate the area of a circle, placed chocolates across the large circle to find the diameter and calculated the area that way. He knew that he had to subtract area of the smaller circle, so he started to calculate the area of the smaller circle the same way. After a few moments, he realized it would be easier just to fill the inner circle with chocolates and count them. Sometimes in real life, lower math is more practical than higher math! As a result of watching him figure out the area using pi times the square of the radius, the third-grader was interested in that time-saving formula.

We don't do these kinds of activities every day; our students do have their own grade-appropriate textbooks. However, lessons like these are what make a multi-age class really crackle. Children can work side-by-side on problems that challenge them, and gain new understanding and inspiration that they wouldn't otherwise have. And the students can have the last word on this lesson. "I love yummy math!"

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