mr barton maths

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Function Machines

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Foundational Skills
Identify parts of a function machine
\[ 5 \rightarrow [+3] \rightarrow 8 \]
Identify input, operation, or output.
State the inverse operation
\[ +5 \rightarrow -5 \]
State the inverse (opposite) operation.
One-Step Forwards
One-step forward: Addition
\[ 7 \rightarrow [+4] \rightarrow ? \]
Find the output after adding.
One-step forward: Subtraction
\[ 12 \rightarrow [-5] \rightarrow ? \]
Find the output after subtracting.
One-step forward: Multiplication
\[ 6 \rightarrow [\times 3] \rightarrow ? \]
Find the output after multiplying.
One-step forward: Division
\[ 24 \rightarrow [\div 4] \rightarrow ? \]
Find the output after dividing.
One-Step Backwards
One-step backward: Addition
\[ ? \rightarrow [+4] \rightarrow 11 \]
Find the input when adding.
One-step backward: Subtraction
\[ ? \rightarrow [-5] \rightarrow 7 \]
Find the input when subtracting.
One-step backward: Multiplication
\[ ? \rightarrow [\times 3] \rightarrow 18 \]
Find the input when multiplying.
One-step backward: Division
\[ ? \rightarrow [\div 4] \rightarrow 5 \]
Find the input when dividing.
Two-Step Forwards
Two-step forward: Add/subtract only
\[ 5 \rightarrow [+3] \rightarrow [-2] \rightarrow ? \]
Two steps using + and −.
Two-step forward: Multiply/divide only
\[ 6 \rightarrow [\times 2] \rightarrow [\div 3] \rightarrow ? \]
Two steps using × and ÷.
Two-step forward: Mixed (×/÷ first)
\[ 4 \rightarrow [\times 3] \rightarrow [+5] \rightarrow ? \]
× or ÷ first, then + or −.
Two-step forward: Mixed (+/− first)
\[ 5 \rightarrow [+3] \rightarrow [\times 2] \rightarrow ? \]
+ or − first, then × or ÷.
Two-Step Backwards
Two-step backward: Add/subtract only
\[ ? \rightarrow [+3] \rightarrow [-2] \rightarrow 8 \]
Find input for +/− chain.
Two-step backward: Multiply/divide only
\[ ? \rightarrow [\times 2] \rightarrow [\div 4] \rightarrow 3 \]
Find input for ×/÷ chain.
Two-step backward: Mixed (×/÷ first)
\[ ? \rightarrow [\times 3] \rightarrow [+5] \rightarrow 17 \]
Find input for × or ÷ then +/−.
Two-step backward: Mixed (+/− first)
\[ ? \rightarrow [+3] \rightarrow [\times 2] \rightarrow 16 \]
Find input for + or − then ×/÷.
Three-Step Forwards
Three-step forward: Add/subtract only
\[ 5 \rightarrow [+3] \rightarrow [-2] \rightarrow [+4] \rightarrow ? \]
Three steps with + and −.
Three-step forward: Multiply/divide only
\[ 6 \rightarrow [\times 2] \rightarrow [\div 3] \rightarrow [\times 4] \rightarrow ? \]
Three steps with × and ÷.
Three-step forward: Mixed operations
\[ 4 \rightarrow [\times 2] \rightarrow [+5] \rightarrow [\div 3] \rightarrow ? \]
Three steps with all operations.
Three-Step Backwards
Three-step backward: Add/subtract only
\[ ? \rightarrow [+3] \rightarrow [-2] \rightarrow [+4] \rightarrow 12 \]
Find input for +/− chain.
Three-step backward: Multiply/divide only
\[ ? \rightarrow [\times 2] \rightarrow [\div 4] \rightarrow [\times 3] \rightarrow 12 \]
Find input for ×/÷ chain.
Three-step backward: Mixed operations
\[ ? \rightarrow [+2] \rightarrow [\times 3] \rightarrow [-4] \rightarrow 14 \]
Find input with all operations.
Finding Missing Operations
One-step: Find missing operation
\[ 5 \rightarrow [?] \rightarrow 15 \]
Find the missing operation.
One-step: Find missing value
\[ 6 \rightarrow [\times ?] \rightarrow 24 \]
Find the missing number.
Two-step: Find one missing operation
\[ 4 \rightarrow [?] \rightarrow [+3] \rightarrow 15 \]
Find one missing operation.
Two-step: Find one missing value
\[ 5 \rightarrow [\times ?] \rightarrow [+3] \rightarrow 18 \]
Find the missing number.
Special Cases
Same input with different machines
\[ \text{Compare A and B outputs} \]
Compare outputs from different machines.
Multiple inputs through same machine
\[ 2, 5, 8 \rightarrow [\times 3][+2] \rightarrow ?, ?, ? \]
Find outputs for multiple inputs.
Find input that gives specific output
\[ ? \rightarrow [\times 3][+2] \rightarrow 17 \]
Find input for a target output.
Same input and output
\[ 7 \rightarrow [?] \rightarrow 7 \]
Identify identity operations.
Timer (Optional)
Question