Feed numbers into function machines, swap letters for numbers and sort algebra tiles. Play, solve missions, crack puzzles and beat the clock.
Start here. Algebra uses letters to stand for numbers. Imagine a machine: you put a number in, the machine does something to it, and a new number comes out. If the machine multiplies by 2 and then adds 3, the number 4 becomes 11. We can write the rule for any number n that goes in: 2n + 3.
Letters next to numbers. In algebra, 2n means 2 × n. We leave out the times sign. A letter on its own, like n, means 1 × n. A plain number such as 3 is just 3.
Substitution. To substitute means to swap a letter for a number. If x = 4, then 3x + 2 is 3 × 4 + 2 = 14. Be careful: 3x does not mean 34. It means 3 times x. Do any brackets first, then multiply, then add or subtract.
Like terms. Algebra tiles help you see this. An x-tile is a long tile worth x. A 1-tile is a small tile worth 1. Tiles of the same kind are like terms, and you can combine them: 3x + 2x = 5x. An x-tile and a 1-tile are different, so 5x + 7 cannot be made any shorter.
Two letters. Expressions can have more than one letter, like 2a + 3b. You can only combine the a-terms with each other, and the b-terms with each other. The expression 3a + 2b + a + 4b simplifies to 4a + 6b.
Brackets. 2(n + 3) means 2 groups of (n + 3). Each part inside the brackets is multiplied by 2, so it equals 2n + 6.
Try this above. In Play, set the machine to times 3 and add 1, then check the outputs for 0, 1, 2 and 3. At the next level fill two bags and press "Put the tiles together". At the top level, change what a and b are worth and watch the value change while the expression stays the same.
It means 2 × n. In algebra we do not write the times sign between a number and a letter. If n is 5, then 2n is 10.
To substitute is to replace a letter with a number. If you know that x = 3, you can work out the value of 4x + 1 by putting 3 where the x is: 4 × 3 + 1 = 13.
Like terms have the same letter part. 3x and 5x are like terms, so 3x + 5x = 8x. A number and an x-term, such as 3x and 5, are different, so you cannot add them into one term.
Because 3x means 3 times x, not the digits 3 and 4 side by side. So 3x = 3 × 4 = 12.
Just starting: function machines and writing rules. I know the basics: substituting numbers, brackets and collecting like terms. Challenge me: two letters, words into expressions and simplifying.
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