## The problem

This post contains an excerpt from a conversation between two of my students. This is Mohammed's second lesson on geometric series; the previous lesson we explored what a geometric sequence was through a few basic problems. Daria missed the previous lesson and is trying to catch up.

Mohammed and Daria are working together to solve this problem:

Mohammed and Daria are working together to solve this problem:

## The clips

Now play each clip as you read the summary:

**how is learning taking place?**

What is significant about each clip for you? What are your thoughts after listening to all the clips?

They have just started the problem.

Mohammed:

Mohammed:

*"Mmm, this is weird... we are not given anything in-between [the 2nd and 5th terms]."*In this clip, Mohammed compares this to something he has done in a previous module, and proposes a method of solution.

Mohammed and Daria are looking through the textbook to find more information (Mohammed: "

As they flick through the book, Mohammed is surprised to find logs in the chapter on series:

Mohammed: "

Mohammed then finds what he was looking for, but it appears that his method might not work for this problem.

Mohammed: "

Daria: "

Mohammed: "

*It should be here.*")As they flick through the book, Mohammed is surprised to find logs in the chapter on series:

Mohammed: "

*What is this? This log... Look, there's log...*"Mohammed then finds what he was looking for, but it appears that his method might not work for this problem.

Mohammed: "

*It wouldn't work, we need two values.*"Daria: "

*But we do have two numbers, don't we?*"Mohammed: "

*Yes, but they're not close to each other... Wait a minute...*"In this clip, Mohammed proposes that the common ratio is "

Daria: "

She tries a common ratio of 1/2 to see if it works (it doesn't), at which point Mohammed notices that the common ratio must also be negative, and explains why.

*a fraction*" as the "*numbers are going down.*"Daria: "

*Do you want me to try a half?*"She tries a common ratio of 1/2 to see if it works (it doesn't), at which point Mohammed notices that the common ratio must also be negative, and explains why.

Mohammed turns to another group for help.

Mohammed: "

Mohammed: "

*Have you guys done part 2... it's weird...*"Mohammed: "

Daria: "

Mohammed guides Daria through the method: "

*There has to be some way of working it out, let me just look in the textbook... This is very weird... Wait**a minute, what if we do simultaneous equations, we could just do simultaneous equations!*"Daria: "

*Oh yeah!*"Mohammed guides Daria through the method: "

*It will be better to put the other one on top... the ar^4... it will cancel easier.*"After solving the problem, Mohammed and Daria discuss how they might have solved the problem more efficiently.

Mohammed: "

Daria: "

Mohammed: "

Mohammed: "

*I don't know why I didn't do that at the beginning... it's weird... I don't know why I didn't see it!*"Daria: "

*It's kind of interesting that we used so many different things to find... I'm pretty sure there's one, sort of, formula to find this.*"Mohammed: "

*I really like this chapter because you can check all your answers... if it doesn't make sense, if you don't get the next term, then you're wrong.*"