©2021 Compass Learning Technologies → Live Mathematics on the Web → GXWeb Showcase → GXWeb Jigsaws and Quizzes

## GXWeb Jigsaws and Quizzes

Symbolic computations on these pages useNerdamer Symbolic JavaScriptto complement the in-built CAS of GXWeb

Saltire Software, home of Geometry Expressions and GXWeb

YouTube Introduction to GXWeb Jigsaws (6:46)

Fancy some mathematical fun?

UsejigsawsandGXWebto explore some mathematical gems drawn from geometry, number theory and elementary algebra - and then follow the links provided to see some of their many and varied applications!

## Create Your Own GXWeb SpiroGraph

The spirograph is a geometric drawing device that has been a source of interest and fun for young and old for some two hundred years!

But have you ever thought of designing your own spirograph?The amazing free GXWeb software makes creating all manner of beautiful geometry easy, and the spirograph is no exception!

## GXWeb Polygon Playground

Two teams (A and B) of \(n\) players each are seated around a \(2\cdot n\)-gon polygonal table. Team A are allocated the odd-numbered seats, and team B, the even numbers.

How do we set up the draw so that each member of team A competes against each member of team B exactly once?

How many times must they meet?

How many such variants do you think exist for a hexagon? For an octagon, decagon - or the standard clock dodecagon?

Why stop there?Play! Try your own! Browse the examples - and then try the

Polygon Quiz!

Try the

GXWeb Polygon Playground!⇒Then explore the

GXWeb Polygon Angles Theorem GeneratorFinally, try out two different

GXWeb Polygon Constructions.

## TakTiles Jigsaw

Tak Tiles were designed by Geoff Giles for the DIME (Developments in Mathematics Education) Project. This live web version supports three levels of interaction for students:

Explore the

Meaningful Algebra Collection

## Algebra Tiles Jigsaw

What does\(2x + 1\)mean to you? What about\(4-3x\)or even\(x^2=x+1\)?What dominant image springs to mind?

Do you see an object or a process?

Do you think of a graph? A table of values?

Students who are successful in algebra tend to have a richer repertoire of images compared to those less proficient. As teachers, we need to

build these images deliberately and with care.

Algebra tilescan be a powerful tool for building deep understanding, and the virtual variety actually offer some major advantages: they explicitly link the shapes to the symbolic form, and they establish that variables are dynamic rather than static things.

Play morewith Algebra TilesExplore the

Meaningful Algebra Collection

Explore GXWeb TakTiles

## Fractured Fractions Jigsaw

(Never heard of continued fractions? Tap here.)

Every real number, rational and irrational, can be represented by a continued fraction - the rational ones are finite, of course, but both finite and infinite offer some wonderful patterns and opportunities to explore!

Play morewith continued fractionsExplore the

Fractured Fractions Collection

## The Kiss Precise: Kissing Circles Jigsaw

Given the sequence \([-1,2,2]\), what do you predict to be the next number?

And what might follow \([-1,2,3]\) - or \([2,2,3]\)?

What about \([-2,3,6]\)? Or \([-6,7,42]\)?

Each number refers to the

curvature- orbend- of the circle it describes - which is the reciprocal of theradius. Anegative benddescribes the circle surrounding the others!Here we imagine a shape (circle, rectangle, triangle(-ish)... even a Golden (Pappus) chain!) completely filled with bubbles - kissing circles!

Rene Descartes found the rule for such patterns, and it lay in a

quadratic equation!

Play morewith Kissing Circles and mathematical bubbles!Explore the

Kissing Circles Collection

## Fraction Trees, Farey Numbers and Continued Fractions

## Did You Know that Fractions Grow on Trees?

## Or that (Fraction) Trees Can Grow from (Continued) Fractions?

Suppose you wanted to make a list of all the rationals... How might you start?Can you see how the fractions at each level of our

fraction treesare calculated from their parents?

How do thepathsto each term lead tocontinued fractions?And how can a special

continued fractionlead to ourfraction trees?\[0+\cfrac{1}{3-\cfrac{1}{1-\cfrac{1}{3-\cfrac{1}{1}}}}\]

Explore fraction trees, farey numbers and kissing circles further ⇒

Explore the Stern-Brocot Continued Fraction ⇒

Stern-Brocot Continued Fraction YouTube demonstration (7:34)

Construct your own Model with GXWeb

Behind the Scenes

©2021 Compass Learning Technologies ← Live Mathematics on the Web ← GXWeb Showcase ← GXWeb Jigsaws and Quizzes