Making Sense
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ET and Haleemah make sense of a cobblestone pattern and look for relationships between the Size Number and the number of gray stones in the figure.
Episode Supports
Students’ Conceptual Challenges
In mathematics, language is important, especially if the goal is to have productive mathematical conversations with students. Notice how ET isn’t quite sure which words to use as he initially describes what he sees in the pictures [2:27]. He says “I noticed there are three rows, like in each gray tile. There are three gray sets, and in a gray set there’s three rows, three tiles in a row.” As he says this, he circles the bottom row of stones in a picture. This could present a challenge for other students engaged in this conversation. Thus, it’s important to support students in using precise language, as the teacher does later in this video by asking clarifying questions [e.g.,3:55] and using such terminology herself [e.g., 4:10, when she introduces the word “column”].
Focus Questions
For use in a classroom, pause the video and ask these questions:
- [Pause the video at 2:15] Ask your students to discuss with a partner or their group where they see a relationship between the Size Number and the number of gray stones in the figures.
- [Pause the video at 6:37] Have students repeat in their own words what they heard ET say regarding the second section of gray stones. Ask them how else they might talk about or represent the relationship between the Size Number and the number of gray stones.
Supporting Dialogue
- Pause the video at 0:35 and/or 1:10 so that the images of the cobblestone patterns are displayed. Tell your students to take 30 seconds to look at the cobblestone patterns. When they’re finished, ask them to turn and talk with a partner to talk about what they noticed and wondered as they viewed the cobblestone patterns. Have students share out.
- At 5:44, ET has just finished explaining what he circled and labeled in the diagrams. He said that for the second section of gray stones, the number of stones in a row is actually “1 size or one number above the size.” He is close to generalizing a relationship he has noticed. Ask your students to talk about ET’s idea and explain to one another what they think his explanation means.