Image of the Week: What do we mean by "more"?
May 15, 2022
What do we mean by “more”?
Take a look at this week’s image: Which is more, the yellow potatoes or the pink potatoes? Before you try to answer that question, consider all the things that question could actually be asking – and that your students might hear in the question:
- Which is more, the quantity of yellow potatoes or the quantity of pink potatoes?
- Which is more, the weight of yellow potatoes or the weight of pink potatoes?
- Which is more, the volume of yellow potatoes or the volume of pink potatoes?
- Which is more, the area of yellow potatoes in the image or the area of pink potatoes in the image?
“More” here could be asking us to compare any number of attributes, some of which are easier to see in the image than others. All of these interpretations are worthy of mathematical consideration, but they may not point to the same answer. That is, a student focused on comparing quantity might leap to their being more yellow potatoes, but a student thinking about volume or weight might argue that the yellow and pink are about equal. It makes little mathematical sense to debate who of these two is “right” since they are both sensible, but different, comparisons. Instead, it is important to clarify what students are comparing so they can debate quantity comparisons separate from weight, as they are not the same question.
If your students only focus on quantity, consider opening up debate about what this question means by asking, Are there other ways to thinking about which is more? Is counting or estimating number the only way? What else might matter? Encourage this complex thinking, where they can hold two or more different ideas simultaneously by acknowledging that these potatoes have different attributes that can be compared.
And we invite you to follow us on Twitter! Tweet us the fascinating ideas you students have about our activities or how you’re trying these activities in your space. We can’t wait to hear from you!
To multiplicity, cheers!
Jen Munson and the multiplicity lab group