In the previous activity, you had a chance to try a Connect with Color activity with your PLC. In this section, we will show you a video from the face-to-face workshops that elaborates on the purpose of a Connect with Color activity, and also discuss the ways students might use the 3 C's to look for and make use of structure as they complete activities like this.

Watch the video

As you watch the video, take note of the different ways that a Connect with Color activity might provide you insight into the ways in which your students are thinking about and using the 3 C's as they work to make connections between a visual and related symbolic expressions. Take note of how a Connect with Color activity is both similar to and different from a dot talk, and why it might provide a different form of insight into student understanding.

Discuss with your PLC

In dot talks, students are encouraged to think flexibly about how to determine the total number of "dots" in a given figure. The teacher plays an important role in supporting the student in describing their way of calculating using mathematical symbols. In a Connect with Color activity, students instead need to start with given symbolic expression and figure out how that expression might describe a way of calculating the number of dots in the figure. This is an example of what Terry means when he says in the video, "Everything I teach forward, I also want to teach backwards." Discuss with your PLC the similarities and differences between dot talks and Connect with Color activities. How might you use both in your classroom?

What Understandings Do These Methods Reveal?

In the second half of the video, Christy discusses how different ways of "chunking" can make a difference in student understanding as students move from arithmetic to algebra. Consider the three different ways of showing that there are "4 + 5 + 4" hexagons in the hexagon figure shown in figure 1. With your PLC, discuss these three different methods. What understanding does each method reveal? Imagine that these three solutions came up in your classroom. What questions would you ask to help students make connections between these strategies? What mathematical understandings would you want the students to be able to communicate to their peers?

Figure 1: Three different ways of showing that there are "4 + 5 + 4" hexagons in the figure

How Might Students Describe the Figures?

Each of the methods shown in figure 1 is an accurate way to show that there are "4 + 5 + 4" hexagons in the figure. However, Methods 2 and 3 capture regularity in a way that Method 1 does not. Noticing regularity is an important aspect of algebraic thinking. Consider the pattern made up of hexagons (shown in figure 2). With your PLC, discusshow a student using "Method 1" might describe the fifth figure in this pattern. The 100th figure? How might a student using "Method 2" describe the fifth figure? The 100th figure? How might a student using "Method 3" describe the fifth figure? The 100th figure? Note that you will explore the ways you can use patterns to support students in connecting their number sense and "algebra sense" in more depth in later activities in this module. For now, just discuss how the different ways students look for "chunks" in figure 4 of this pattern might impact the ways they see and describe the pattern in later steps.

Figure 2: The first 4 steps of a hexagon pattern

Are Your students Ready for a Connect with Color Activity?

We recommend doing dot talks (or number talks) more frequently than Connect with Color activities, in part because dot talks should be a quick, 5-10 minute whole-class discussion (once the routine is established), whereas Connect with Color activities will take more time. Dot talks also help students learn how to make connections between mathematical symbols and ways of decomposing a dot figure, and students (even in advanced classes) often need multiple opportunities to see their way of calculating the total number of "dots" in different figures described using symbolic expressions before they are ready for a Connect with Color activity. In the previous activity in this module, you tried a dot talk in your classroom. Discuss with your PLC whether you think your students are ready for a Connect with Color activity or if you think they would benefit from doing more dot talks first. If necessary, do more dot talks before moving onto the next section in this module in which you will try a Connect with Color activity in your classroom.