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

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:
Seqences

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?

…and for some lovely visualisations have a look at this post.

data-pointed

Stephen Von Worley

 

 

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