I’ve yet to read a math educator’s blog that endorses Khan Academy materials. Well, this blog does. Yes, you read it right. This blog endorses Mr. Khan’s materials for teaching mathematics. No, not by simply viewing the video but using the Mr Khan’s lecture as the object of investigation. Let’s take the video on direct variation. In the video, Mr Khan started with “varies directly” like it’s the simplest thing in the world to understand. Mr Khan then gave the sample problem and solved it as shown in the image below. Mr. Khan’s method is deductive and he uses lecture method. Click here to view the video in YouTube then read on below to see how the same video can be used to develop the concept of direct variation with conceptual understanding by linking it to students previously learned knowledge about proportion and then as context to introduce or review the concept of function.

###### How to use Mr Khan’s videos in teaching math

- Show the video. It’s a short one so it will be over before your class will realise it’s math.
- Ask the class if they can solve the same problem without using Mr Khan’s solution. The problem is elementary school level so students can solve it using arithmetic. Since a gallon of gas costs 2.25 so all they need to do is to find how many 2.25 in 18. They can continue to add 2.25 until they get to 18; continue taking away 2.25 from 18; or just divide 18 by 2.25.
- Ask for another solution. Didn’t they do ratio and proportion in 5th/6th grade? So, with a little scaffolding, students can set up 1:2.25 = n:18. I’m not a fan of product of the means is equal to the product of the extremes since it has nothing to do with proportional reasoning but I’ll allow it this time.
- Ask for another solution. Again with a little scaffolding questions like “If 1 gallon costs 2.25, how much would 2 gallons cost? 3 gallons? Can you organise those data in tables? It’s important that at 4 gallons you asked the students to solve the problem. There’s no need to continue all the way to 18$. Asking students to predict will make them consider the relationship between pairs of values. This is an important habit of thinking and it is crucial to appreciating and understanding algebra.
- Ask for another solution. With a little scaffolding again like “What do you notice about the values in the table? Can you imagine the arrangement of the points if you plot the values on the Cartesian plane? How will you use the graph to solve the problem?” Again there’s no need to plot the points all the way to 18. Students should think of extending the line to make the prediction.
- Now, go back to Mr Khan. “Study Mr Khan’s solution. What are those x and y that he’s talking about? What does y = kx mean in relation to your graph? Where is it in your table? Anyone can explain what Mr Khan mean by varies directly?”
- Assessment/ Assignment/ Further discussion: “The following are questions other students posted in Mr. Khan’s direct variation video in YouTube. How would you answer them?”

*Sorry if this question seems basic, but I don’t understand how this example relates to functions…could someone please explain? Thanks!**What is K in general?**Why do we always have to set x?**The practice for this video includes inverse variations, which are not yet covered. It would be great if there was practice specifically for direct variation only. Thanks!*

This style of teaching is called teaching math through problem solving. If you enjoyed Teaching Math with Mr Khan, don’t forget to subscribe to this site. I will try to develop more lessons where I will be co-teaching math with Mr Khan’s videos.

I’m with you in endorsing the use of Kahn Academy videos. It’s all in HOW they are used and your explanation above gets at developing conceptual understanding. I’d extend the discussion to include graphing the direct variations which would help in answering the questions in #7.

Using $2.25 for the cost of a gallon of gasoline is fine for the video BUT I suggest that the current price of the different grades of gasoline be used for student work. Also, integrate the use of metrics by using the price per liter in various countries around the world in their specific currency. This brings in some cross curricular information.

The lesson can then be extended of comparing the costs in the US to the cost in the selected countries.

Thank you, Wally. Those are great ideas for making the learning experience richer. I should think of those expansions next time I teach with Mr. Khan.