Page 64 - 新思维数学学生用书8 样章

Project 1 Algebra chains

Project 1

Algebra chains

An algebra chain is a sequence of expressions where an input number is
substituted as the value of x in the first expression, and then the output of each

expression is substituted as the value of x in the following expression.
So, in the algebra chain below:
3 is substituted for x in the expression 4x − 10, giving the output 2.

Then 2 is substituted for x in the expression 8x + 4, giving the output 20.
3 4x − 10 8x + 4 20

Can you find a way to arrange the eight cards below into four algebra chains
that take the inputs 1, 2, 3 and 4 and give the outputs 40, 30, 20 and 10?

2x + 3 2(x + 1) 5x − 7 12 − 2x

3x − 4 7x + 5 3(x − 4) 8x − 2

1 40

2 30

3 20

4 10

Now choose any two cards and an input number.
Work out what the output of your algebra chain would be.
Tell a partner the input you chose and the output you got.

Can your partner work out which cards you used?
Can they still work it out when you make an algebra
chain with three cards?

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