Image of the Week

Give It a Go!

Alongside our amazing Look-Think-Talk activities, we offer another routine, Off You Go, and you should give it a go. In Off You Go, you show students an image that represents a concept that they have seen before but where they can still deepen their understanding. This could be a number, shape, pattern, structure, or relationship. You invite them to notice this concept in the image and then you send them off to find example of that concept in their environment that they can bring back to share and discuss.

What’s truly amazing is what happens when students bring back their examples. They might take photos, bring objects, draw sketches, or make lists, but no matter how they collect their examples, the class creates a museum of the many ways the mathematical concept can look. The collections your class assembles can tell you a lot about how they are understanding the concept, and where their thinking is stretching – or needs to be. In fact, my colleagues Geetha and Thomas and I wrote a paper for NCTM’s journal about all that students can learn – and all that you can learn about students – from Off You Go.

Look at this week’s Off You Go image. Here we are inviting students to think about the many ways they might see even numbers in their world. Even and odd numbers are a topic that has been consistently demoted in prominence over the past three decades, but it is one of the first ways students start to grapple with properties of number. And it is as a property that we want students to understand it, not just that even and odd numbers alternate in sequence. What is an even number? Older students often think of it as a number divisible by 2, but what if you’re a first grader and divisibility is not a concept that can help? We want students to see that even numbers are those that make pairs, just like the shoes in this image. (We also want students to see that odd numbers cannot make pairs of all of their elements, so try our Off You Go on odd numbers, too!)

When students are repeatedly exposed to the same ways of seeing concepts (like only seeing AB patterns or equilateral triangles), they often don’t understand the diversity within that concept. Some students may at first struggle to see even numbers all around them, but this activity can turn on a mathematical lens for examining their own bodies (hands, fingers, eyes), classroom furniture (legs on a chair or table), or window panes. When you gather to discuss the even numbers that students have found, be sure to discuss the central questions, What is an even number? How did you know what to look for? How did you know when you found an even number?

We designed the Off You Go routine so that it can be used in at least two ways. You can use this kind of activity as a scavenger hunt in the classroom or school, or try it as an outside walk around your school building or neighborhood. Launching the focus, taking students on the hunt, and then discussing their findings can be an entire rich lesson. Alternatively, you can send students home to look for examples and then hold your class discussion the following day. This is a rich use of homework and widens the possibilities for examples students might collect from their homes, school buses, and neighborhoods. Off you go!

To multiplicity, cheers!

Jen Munson and the multiplicity lab group