the powerpoint is here

(download for the animations to work)

it's a good way to introduce expressions, with some conventions for writing a sequence of operations as an expression and then manipulating such algebraic expressions

initially students input a range of numbers and work out the outputs

"try some simple numbers then some harder ones - maybe big numbers, fractions, decimals, negative numbers"

for integer inputs, by looking at the output numbers, students can find a 'short cut' rule

this is helped by the output numbers all being even

"what happens?"

rather than needing 3 operations you can use a 'shortcut', of two operations

or (deliberately designed to have an alternative)

+ 1, x 2

students can then explore a shortcut rule using 'm' for a million, 'b' for a billion etc. as an input number

here's the script:

"let's check out the rule (shortcut of x 2, + 2) for a really big number"

"what's a really big number?"

"no, 3425 is too small"

"OK, a million is good - how many noughts in a million?"

"oh, that's too big, I think I'll just write 'm' for a million"

"a million (m) add 3 is?"

[m + 3] sometimes they say m3 to which you appeal to worldly conventions

"then multiply by 2 is?"

[2m + 6]

"subtract 4 is?"

[2m + 2]

"does this fit with the rule?"

"why is this the same as + 1 then x 2?"

this encourages writing expressions in an appropriate manner

later work can involve using an expression as an input e.g. 3m + 2

other sets of three (or more) operations can be introduced:

and shortcuts established:

x 5 then + 10

or

+ 2 then x 5

all expressions can be written in two ways

to practice a use of brackets

simple factorisation

this encourages a use of brackets

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