#1676. GOfigure - patterning exercise

Mathematics, level: Elementary
Posted Tue Apr 18 17:43:59 PDT 2000 by Rick Newell (r.newell@home.com).
GOfigure email numbers game
Clik-fx Inc., Markham, Ontario, Canada
Materials Required: none
Activity Time: 10 minutes
Concepts Taught: Basics - addition, subtraction, multiplication, division

GOfigure, a classroom activity

Here is the challenge. Take these eight digits 1, 2, 2, 9, 3, 6, 8, and 5

Now find a pattern by using as many as you can.

Rules: the pattern must have one rule that is used at least twice. for example

the pattern 1, 2, 3

the pattern 1, 3, 9

There are over 300 patterns and 54 of them use all eight digits, put the above
numbers on the board and see how many the class can find. Watch the CRUNCHING
begin as they look for the eight digit patterns.

You may want to do a lesson patterning before they start searching. Following
is an outline of patterns used in this exercise.

What is a pattern?

The aim of the game is to create numeric patterns from the digits students
have available to them.

Ask the question Is "2,4" a pattern?

Asking this question beforehand could serve as an effective introduction to
the game, especially for younger students. If everyone agrees that two numbers
are not enough to show a pattern, they're probably all ready to begin.

If, however, someone says that "2 , 4" is a pattern, ask that person what number
comes next and why. The answer often given is 6, because you're adding 2 each
time. But, depending on their math experience and abilities, other students
may be quick to point out, for example, that "8" or "16" are two other possibilities,
and will be able to explain why.

e.g. 2, 4, 6 (add 2 to the previous number each time)

2, 4, 8 (multiply the previous number by 2 each time)

2, 4, 16 (square the previous number each time)

Each pattern is formed by using a different rule, but it's not until the third
number in the sequence that the rule being used repeatedly becomes clear. Only
then can the pattern be identified. Discussions around a few examples will help
students see why they need to use at least three digits to form a recognizable
pattern and how the rule is applied at least twice.

A note about graphic or visual patterns:

Some students, especially younger ones, may want to use numbers that create
a visual pattern such as 1,1,9,9,3,3. Since no one rule is being followed consistently
to create this pattern, it is not a mathematical pattern and therefore does
not qualify for this exercise. In the example shown first, you multiply the
first number by 1, then add 8 to the second; then multiply the third by 1 and
subtract 6 from the fourth then multiply times 1 again (*1, +8, *1, -6, *1).
Who knows what number might come next?

For answers, more information on this activity, and additional activities see
www.clik-fx.com