Algebraic Expressions Lesson 4 Episode 3 (Teachers)

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ET and Haleemah fall into a common trap of proceduralizing methods based on non-mathematical features. In previous episodes, the pair multiplied the trip time and the velocity to get the distance traveled, but those numbers were the first and third numbers to be entered in the applet (for example, see Episode 1, 3:02). In this episode, the problem is stated in words, and the starting location is the first number encountered in the reading of the problem, while the trip time is the third number encountered. Consequently, Haleemah and ET incorrectly multiply Hector’s starting location by the trip time [1:36 and 1:48], rather than multiplying trip time by velocity. By allowing them to test their incorrect conjecture, the teacher provides Haleemah and ET with an opportunity to reorganize their understanding of the context to one that is more productive [3:50]. 

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

1. [Pause the video at 1:24] Ask your students to determine where Hector’s end location will be when his starting location is 4, he rides at a velocity of 5 meters per second, and he rides for 3 seconds. After some time, ask them for their answers and note any points of disagreement.
2. [Pause the video at 3:30] If you posed Focus Question 1, ask students to compare their work and answers with that of Haleemah and ET. If you did not pose Focus Question 1, ask your students to consider Haleemah and ET’s work. Do they agree with what the pair has written? If not, how would they change it?

1. After watching Haleemah and ET make a prediction and then check it using the applet [through 3:53], ask your students to anticipate what ET will say. Why did Haleemah and ET’s prediction not match up with the applet? Ask students what they might say to help ET and Haleemah fix their mistake and be better prepared for the next example.
2. Pose the following scenario featuring a fictional student to your class: “Suppose another student, Raul, joined ET and Haleemah. Raul tells Haleemah and ET that the key is if you’re given the applet, you multiply the first and third numbers to find the distance, but if you’re given a word problem, you have to multiply the last two numbers to find the distance. How would you respond to Raul?”