Seeing this problem on Brilliant recently reminded me how useful diagrams can be in the study of Algebra. I solved the problem using Algebra (with a little colour for clarity!) as follows:
Sybilla Beckmann’s paper, Solving Algebra and Other Story Problems with Simple Diagrams: a Method Demonstrated in Grade 4–6 Texts Used in Singapore is an interesting read on the subject of the use of diagrams.
A clear diagram can be so helpful in understanding a problem, look what one of my Year 7 students did when asked for the nth term of a sequence having been given a diagram:
For more Algebra with diagrams try Mobile Puzzles a collection of problems varying in difficulty for simple for young students to rather more complex.
Algebra Tiles are such a good way to demonstrate algebraic manipulation, see the online demonstration on MathsBits.com.
Write x2+6x+11 in the form (x+a)2+b
For a very easy to use activity, try Jonathan Hall’s Algebra Tiles on his wonderful Mathsbot.com site.
And from Fawn Nguyen comes the brilliant Visual patterns, note the menu; the Gallery includes blog posts from teachers and students who’ve used visual patterns in their classrooms.
Here’s the diagram, what’s the question?
…and for some lovely visualisations have a look at this post.