Spot what repeats, find the rule and balance the scale. Play, solve missions, crack the rule puzzles and beat the clock.
Start here. A pattern is something that repeats in a way you can predict. Red, blue, red, blue is a pattern. The small group that repeats is called the core. In red, blue, blue, red, blue, blue the core is red, blue, blue.
Number patterns. Numbers can follow a pattern too. 2, 5, 8, 11 goes up by 3 every time. 20, 17, 14 goes down by 3. 3, 6, 12, 24 doubles every time. To spot the pattern, look at how each number changes to the next one.
Growing shapes. Some pictures grow in steps. If step 1 has 5 dots, step 2 has 8 and step 3 has 11, you add 3 dots each step. A table of step and dots helps you see the rule.
Function machines. A function machine takes a number in and does the same thing to every input. If 2 goes in and 6 comes out, and 5 goes in and 9 comes out, the machine adds 4. Try more inputs to be sure. A rule has to work for every pair, not just one.
The nth term. The rule "3n + 1" is a short way to say: take the step number n, multiply by 3, then add 1. For n = 1, 2, 3 you get 4, 7, 10. For the 10th term you do 3 × 10 + 1 = 31 without writing all the terms.
Balance. An equation like ? + 7 = 15 is a scale that must stay level. Whatever you do to one side you must do to the other. Take 7 away from both sides and ? = 8.
Try this above. In Play, build red, blue, blue, red, blue, blue and watch the core light up. Then open the Function machine, send in 1, 2 and 3 and guess the rule before you reveal it.
The core is the shortest group of items that repeats again and again. In A B B A B B A B B the core is A B B.
Many rules fit one pair. 3 in and 6 out could be add 3 or multiply by 2. A second pair, like 5 in and 10 out, shows which one is right.
It is a rule for any position n in a number pattern. For 4, 7, 10, 13 the nth term is 3n + 1, so the 20th term is 61.
Pick the level, not the age. "Just starting" uses colour and shape patterns. "I know the basics" uses number patterns, growing dots and simple rules. "Challenge me" uses function machines, the nth term and two-step balance problems.
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