Reflecting
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Captions
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The students work to explain what each symbol in their equation means in the pool context.
Episode Supports
Students’ Conceptual Challenges
Haleemah and ET seem to have slightly different ideas of what multiplication means. For example, when asked what 10 times 4 means, Haleemah says “ten groups of four” and then “or four groups of ten,” [3:37], but ET says he thinks it’s the latter. At [5:04] Haleemah says that 40 (the result of 10 • 4) is “the number of tiles on the border and the corners being multiplied twice” while ET says he doesn’t think they are multiplying them, instead they “are just adding or counting them one more time than we need to be.” In both instances, both students are correct, but seem unsure of the other’s ideas about multiplication.
Focus Questions
For use in a classroom, pause the video and ask these questions:
- [Pause the video at 0:58] Before Haleemah and ET connect their equation to the diagram, ask students to do the same. Prompt students to visualize where they see (a) the 10, (b) the 10 • 4, and (c) the –4. Ask for volunteers to circle or point out each of these on a pool diagram and ask the class if they agree or disagree and why.
- [Pause the video at 3:36] Pose the same questions from the video to your students: What does multiplication means here in the pool context? What is 10 times 4? Press students to be explicit about this, and notice when both 10 groups of 4 and 4 groups of 10 are mentioned. You can have a discussion about if those are equal and if one or both are appropriate or not for this given context.
- [Pause the video at 9:30] Ask your students to consider the general case, in which there are x tiles on one side of the pool. Prompt them to discuss connections between the equation and the diagram, including where they see x, 4x, and the minus 4 from ET and Haleemah’s equation.
Supporting Dialogue
If you pose Focus Question 2, when students provide an explanation for what multiplication means, first ask “Why do you think that?” Afterwards, ask for other students to restate what they heard in their own words.