Using function machines with a single operation to find outputs from inputs, and working backwards to find inputs.
Where your child meets this in real life: Understanding processes with inputs and outputs, like vending machines or recipes
SEAGReady breaks one-step function machines into 2 steps, taught in order so each skill builds on the last.
Find the output when given an input and a single operation in a function machine
Find the input when given an output and a single operation by working backwards using inverse operations
Three free sample questions from our one-step function machines course. Every question comes with a full explanation, and hints that guide without giving the answer away.
Ciara is using a function machine. The machine takes a number, multiplies it by 4, and gives the output. If she puts in 8, what number comes out?
Answer: A. 32
The input is 8. The operation is x4 (multiply by 4). Apply the operation: 8 x 4 = 32 The output is 32.
Stuck? Start here: What is the input number? What operation does the machine do?
Aoife is using a function machine that multiplies by 5. The output is 35. What number did she put in?
Answer: A. 7
The output is 35 and the operation is x5. To find the input, use the inverse operation. The inverse of x5 is /5. 35 / 5 = 7 Aoife put in 7.
Stuck? Start here: The machine multiplies by 5, and the output is 35. You need to work backwards.
Sean has a function machine that multiplies by 5. He puts in 6. What number comes out?
Answer: C. 30
The input is 6. The operation is x5 (multiply by 5). Apply the operation: 6 x 5 = 30 The output is 30.
Stuck? Start here: The input is 6 and the operation is multiply by 5.
This is the exact interactive worked example your child sees in SEAGReady. Step through it and watch the method build up.
Aoife is using a function machine. The machine takes a number, multiplies it by 4, and gives the output.
If she puts in 7, what number comes out?
7 → ×4 → ?
Step 1 of 3
Aoife is using a function machine. The machine takes a number, multiplies it by 4, and gives the output.
If she puts in 7, what number comes out?
When Aoife puts in 7, the machine gives 28.
The key insight: A function machine always does the same thing to any number you put in!
Watch out: 7 + 4 = 11. The operation is multiply (×4), not add (+4). Read the operation symbol carefully.
These are the misconceptions we see most often in one-step function machines, including the ones our practice questions are specifically designed to catch.
Struggling with one-step function machines? The real gap is often in one of these earlier topics.
SEAGReady finds the exact step where your child gets stuck, teaches it with worked examples like the one above, and brings it back for review so it sticks.