Find the hidden rule of a number machine by testing your guess on every row, then use it on the missing row.
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A step-by-step way to guess and test a hidden rule.
A pattern machine takes 3 numbers, , and , does some operations on them, and gives out one result.
The rule a + b − c, tested on every row.
Problem. Find the rule of Machine 1 and the result of the last row. (Textbook pp. 41–42)
Find Machine 2's rule and fill the last result.
Textbook p. 42: Find the operations being done by Machine 2 and fill in the blank. Use the table above.
Stuck? Look at for the row 5, 3, 7.
Pick an easy row.
Write it using a, b and c.
Show the working for each row.
Use your rule.
Find the rule of the machine from the exercises.
Figure it Out, Textbook p. 43, Q7. Find the operations done by this machine.
| a | b | c | Result | |---|---|---|---| | 4 | 8 | −3 | 28 | | 6 | 9 | 6 | −48 | | 2 | 3 | −2 | 8 | | −9 | 5 | −8 | 31 | | 7 | −4 | −6 | −17 | | −16 | −6 | −9 | ? |
Then make your own machine and challenge a friend to crack it (Math Talk, p. 42).
Write it using a, b and c.
Show each row.
Use the rule.
Give 4 rows and keep the rule secret.