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Math activity

Mystery Number Machine

Build a mystery number machine from a box! Put a number in and a different number comes out. Can you figure out the secret rule?

Hands OnAbout 20 minutesScreen-freeParent help expected

Materials and setup

How this changes by age

Pre-K (ages 3–4)

Build a mystery number machine from a box! Put a number in and a different number comes out. Can you figure out the secret rule?

Difficulty 1 of 3

Steps

  1. Decorate a box as a 'number machine.' Cut a slot on top and a hole on the side.
  2. Explain: 'When a number goes IN, a different number comes OUT. The machine has a secret rule!'
  3. Start with the rule 'add 1': put in a card with 2, say the machine does its magic, pull out a card with 3.
  4. Try inputs of 1, 2, 3, 4, 5. Outputs are 2, 3, 4, 5, 6. Can your child guess the rule?
  5. Try 'add 2' as the next rule. Put in 1 (out comes 3), put in 3 (out comes 5).
  6. Tell a grown-up one thing that surprised you.

Learning objectives

  • Understand that a rule transforms an input number into an output number
  • Identify the 'add 1' and 'add 2' rules from examples
  • Predict outputs for new inputs once the rule is known

Kindergarten (ages 5–6)

Use the function machine to explore different rules: add, subtract, and double. Record input-output pairs in a table and guess the mystery rule.

Difficulty 2 of 3

Steps

  1. Build or use a function machine box. The parent picks a secret rule (add 3, subtract 1, or double).
  2. Child sends in numbers: 'I put in 4.' Parent announces the output: 'Out comes 7!'
  3. Child records each pair in a table: IN: 4, OUT: 7. IN: 2, OUT: 5. IN: 6, OUT: 9.
  4. After 4-5 inputs, child guesses the rule. 'The machine adds 3!'
  5. Now child picks a secret rule and parent has to guess!
  6. Try the rule 'double': in 3, out 6. In 5, out 10. In 1, out 2.
  7. Tell a grown-up one thing that surprised you.

Learning objectives

  • Record input-output pairs in a table
  • Identify addition, subtraction, and doubling rules from input-output data
  • Create and test their own function rules

Early elementary (ages 6–8)

Explore function machines with multiplication and two-step rules. Write rules using variables and complete input-output tables.

Difficulty 2 of 3

Steps

  1. Play function machine with multiplication rules: 'multiply by 3' turns 4 into 12, 5 into 15.
  2. Try two-step rules: 'multiply by 2, then add 1' turns 3 into 7, 5 into 11.
  3. Complete input-output tables for 5 different rules. Given some pairs, fill in the missing inputs OR outputs.
  4. Write each rule in words AND as an expression: 'multiply by 2 then add 1' = 2n + 1.
  5. Challenge: given ONLY the outputs (3, 5, 7, 9, 11), figure out the inputs if the rule is 2n + 1.
  6. Design 3 function machine challenges for a family member with increasing difficulty.
  7. In one sentence, tell a parent or sibling what surprised you today.

Learning objectives

  • Identify and write two-step function rules
  • Express function rules using variables
  • Work forward (input to output) and backward (output to input)

Upper elementary (ages 8–10)

Use function machines to explore algebraic functions, graph input-output pairs on a coordinate plane, and discover linear and non-linear relationships.

Difficulty 3 of 3

Steps

  1. Write 5 function rules as equations: f(x) = 3x - 2, f(x) = x^2, f(x) = x/2 + 4, etc.
  2. Create input-output tables for each function using inputs from -3 to 5.
  3. Graph each function on a coordinate plane by plotting the ordered pairs (input, output).
  4. Identify which functions create straight lines (linear) and which create curves (non-linear).
  5. Given a graph, write the equation of the function it represents.
  6. Challenge: create a function machine that converts Fahrenheit to Celsius: C = (F - 32) x 5/9. Test with 3 temperatures.
  7. In one sentence, tell a parent or sibling what surprised you today.

Learning objectives

  • Write and evaluate algebraic functions for given inputs
  • Graph functions on a coordinate plane from input-output tables
  • Distinguish between linear and non-linear functions from graphs and tables

Safety and evidence note

Read the full activity before beginning. An adult should supervise tools, heat, food, outdoor work, movement, and experiments as appropriate. Completion records that the activity was done; the child’s explanation, work sample, photo, or demonstration is stronger evidence of learning than a completion check alone.

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