In the following video Mr. Khan’s gave an excellent task and solution on finding the equation of a sequence of blocks. I suggest you stop the video after the presentation of the problem. Let the students solve it first before you let Mr. Khan do the talking.

Mr Khan did give an excellent explanation especially the one  about x – 1.  The last solution involving the slope and equation of lines was not as clear. This is the part where your students need you. So I suggest that after viewing the video ask the students what part of the video made sense to them and which part was not very clear.

I think it would be best to ask students first about the rate at which the number of blocks is increasing rather than use the term slope. If you want to relate this to slope ask the students to plot the values in the table on a grid. You make then ask what the slope is of the line containing the points.

Here are two more solutions to the problem. The first solution involve dividing then adding. This leads to a a different expression but will still simplify to 4x-3.

Dividing and putting together

The second solution involve completing the figure into rectangles for easy counting then taking away what was added. This leads directly to the simplified equation. Don’t you love it:-) I do. So please share this post to FB and Google. Thanks.