Diagrams in Mathematics

Brilliant - Balances Warmup

Brilliant – Balances Warmup

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:

Brilliant Balances solution

select for larger image

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.

Sybilla Beckmann paper

Sybilla Beckmann paper

I have recently referred to Colleen King’s wonderful Thinking Blocks on Math Playground. (See these two posts, Ratio and Fractions Resources)

One of the options on Thinking Blocks is the Modeling Tool. I used this to create a very simple diagram to illustrate this problem. This tool can be used easily to create the strip diagrams discussed in Sylvia Beckman’s paper.

Thinking Blocks Modeling Tool - Math Playground

Thinking Blocks Modeling Tool – Math Playground

Using this tool one can easily create models; note the many instructional videos to help you learn to use the tool.

Another option I found useful is use the extensive library of problems; these all come with models already prepared which you can choose to show or not. The slideshow has images to illustrate:

Master Level

Mobile Puzzles

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 Factorisation

NCTM Illuminations – Algebra Tiles

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

Complete the square

Complete the square – use algebra tiles

For a very easy to use activity, try Jonathan Hall’s Algebra Tiles on his wonderful Mathsbot.com site.
Algebra Tiles mathsbot

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.

Visual Patterns

See also:
Here’s the diagram, what’s the question?

Here's the diagram, what's the question?

Here’s the diagram, what’s the question?

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