Two weeks ago, we shared how arrays in the real world can develop multiplicative thinking, beginning with skip counting. Skip counting is a powerful bridge between counting by ones and thinking in equal groups. One other entry point to skip counting is dice, like those shown in this week’s image. Take a close look and consider the question, How many do you see?
Some students might choose to focus on the unit of the dice, counting them in the array, much as they might have counted the cacti in the image from two weeks ago. But if students choose to focus on the dots instead, a different dimension of skip counting opens up. Students might:
Notice how many in a part of the image, like:
The group of orange dice
A pair of adjacent dice
A row or column of fives
Focus on skip counting only the twos or the five
Use the color structure of the perimeter to skip count by 8s, or use doubling to find that 4 groups of 8 is 32
Skip count all the twos (32 dots) and all the fives (45 dots) and wonder how to join them
Make groups of ten out of two fives and five twos that they can then skip count by tens
And your students may very well invent other ways of using skip counting to figure out an answer to the question, How many do you see? Remember that all of these ways are pathways to multiplicative reasoning, no matter the age of your students. We do not need to call it multiplication to building the very ideas that will ultimately get students to this operation. Indeed, multiplicative thinking is far more powerful than the operation alone. It is a set of big ideas that work flexible together to answer complex, but structured question, like the one in this week’s image.
Each week we bring you a new image and activity you can do with your students tomorrow, and we spotlight a feature of the mathematical work that we think is important for students’ learning and your teaching.
