Equal Sign Explorations

Last spring when I attended the NCTM conference in D.C. I went to a workshop on Number of the Day for Algebra. The leaders of the workshop shared some research done with elementary math students. Students were given the open number sentence 8 + 4 = ☐ + 5. They were asked what number should go in the box. Not only did a majority of younger elementary students provide a wrong answer (usually answering either 12 or 17), but a majority of students through sixth grade did. Fascinated by the workshop, I sought out the book they referred to in their presentation, Thinking Mathematically: Integrating Arithmetic & Algebra in Elementary School.

So how can we help students develop a more accurate understanding of what the equal sign means? The book suggests in part a framework of using true and false number sentences and “open number sentences” (such as in the research above) to get children thinking and talking together about this topic. For children who “get” what the sign means and what that means in terms of the relationships between the numbers involved, it provides a chance to solidify their thinking as they work to explain it. For children who do not fully understand what the equal sign means, it provides a chance for them to hear their classmates explanations, which can help their developing understanding.

I have begun exploring true and false number sentences with my math group. Over time I will also introduce open number sentences in which they need to provide a missing number. It will be interesting to see how these activities and the math talk that they generate will affect the student’s thinking about numbers and equality.

Smathing Pumpkins

In Sky we do math in different ways at different times of day. It doesn't just happen in Math Group. It is a big part of what we call "S'math," science and math together. We draw a lot of our activities from AIMS Education Foundation (http://www.aimsedu.org/). AIMS stands for Activities Integrating Math & Science. We also draw on other sources, and we like to draw in any themes we are pursuing as well as student interests.

Last year we did an AIMS activity about apples. This year I thought I'd put a twist on it and do it with mini-pumpkins. After dividing into groups of 3 (at least one boy, at least one girl, at least one old-timer, at least one new-timer) we worked with the mini-pumpkins. First we looked at them with our "scientist's eye," observing closely and noticing details. Each student drew the group's pumpkin, using observation skills. Then they came up with estimates for how many teddy bear counters they thought it would take to balance the pumpkin in a scale. Once estimates were done, each group worked together to weigh the pumpkin and record how many teddy bear counters it took.

The last part of the activity was to think about the distance around the pumpkin, the circumference. Students estimated how many teddy bear counters would make a train as long as a string that went around the pumpkin in its fattest part. They also estimated how many unifix cubes would make a train that long. Then they worked together to cut a string that went around the pumpkin and to do the actual measurements and recording.