Algebraic Expressions Lesson 1 Episode 1 (Teachers)

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ET and Haleemah make sense of a swimming pool context and create a method for finding the number of tiles in the border of the pool.

Students’ Conceptual Challenges

The students think there are 40 tiles in the border [1:22]. Haleemah offers as evidence that there are 10 tiles on each side and 4 sides, to give her 10 × 4 = 40. ET agrees. Both students are double counting the corners.
Haleemah initially struggles to connect the symbolic representation “10” with the visual representation of 10 tiles on each side the border of the pool. She first circles blue tiles in the pool rather than the white tiles on the border. She quickly realizes her mistake after ET explains where he saw the 10 tiles and circles 10 white tiles on the border of the pool [7:40].

Focus Questions

For use in a classroom, pause the video and ask these questions:

[Pause video at 0:35] Without counting one-by-one, how many tiles do you think are in the border of this pool? Once you have an idea, turn and tell your partner your thoughts.
[Pause the video at 1:30] Haleemah and ET both think the border has 40 tiles. Do you agree or disagree with them? Why? How might your thinking be different from their thinking?
[Pause the video at 4:31] ET and Haleemah saw the 36 tiles in the border by focusing on ten tiles on the left and right sides and then eight tiles on the top and bottom. Did you see 36 tiles differently? Show your neighbor how you counted 36 tiles and compare your thinking with theirs.

Supporting Dialogue

Focus students’ attention on conjecturing and providing evidence for their conjectures:

As you support your students in this task, encourage them to explicitly link the symbols in their expressions and equations to the picture of the pool. For example, if a student has written 4 × 9, ask them to circle where they see the 9 in the pool diagram and ask them what the 4 means in the context of the diagram.
If students have written multiple arithmetic expressions or equations to find the total number of tiles in the border (e.g., 4 × 8 = 32 and 32 + 4 = 36), ask if they can write a single equation that expresses their method (e.g., (4 × 8) + 4 = 36).