Fact fluency is a critical component of success in the math classroom. But students need to be able to do more than just recall the answer to multiplication facts quickly. A key part of fact fluency is flexibility. That is, can students develop and apply strategies that help them solve a wide range of problems?
Dot talks are a tool that can help build such flexibility. In this routine, the teacher presents students with an image of dots. These dots are often arranged in a certain pattern like the one below. The teacher presents a simple question, “How many?”
Students silently attempt to find an answer. When they find it, they can discreetly signal to the teacher using a thumbs up against their chest. While they wait, they attempt to find their answer in a new way. Each additional strategy they develop can be signalled by raising an additional finger.
At first, the teacher may choose to leave the dot image on the screen for the entire length of the dot talk. However, this may invite students to count the dots one by one. Remember, the goal is to develop efficient and flexible strategies for counting the dots. Many teachers choose to flash the image for a certain amount of time (also called a Quick Look), for example, two seconds. This encourages students to look for patterns that can speed up their counting.
When students are ready to share their answers, model each strategy using a different colored pen. For example, Student A saw four groups of three dots. They used a skip counting strategy to find that four groups of three make twelve.
Student B saw two groups of four, and then two groups of two. They knew that four plus four equals eight, and four more makes twelve.
Student C decided to make two groups of six. They added six plus six to make twelve.
Each of these strategies is unique, but is a valid way of seeing this visual. As dot talks increase in complexity, they can be used to teach multiplication strategies like doubling, doubling and halving, or multiplying by ten!
If your students are in need of flexible multiplication strategies, consider dot talks as one of your computational fluency routines!