©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!

## 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!

Unlike irrational decimals, however, even irrational continued fractions can be predictable and are an ideal way to calculate approximate values - as accurately as you like!

See from the model that \(\frac{10}{7}\) becomes \([1,2,3] = 1 + \cfrac{1}{2 + \cfrac{1}{3}} \).

So what number gives the continued fraction \([1,2,3,4]\)?

Can you find some values whose continued fractions are composed entirely of the number 1?

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 few numbers?

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

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

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