Learning intention LI
- Understand that substitution means replacing a variable with a given value.
- Use a function machine to connect an input, an algebra rule, and an output.
- Evaluate simple algebraic expressions by following the order of operations.
- Explain what the expression means before calculating.
Success criteria SC
- I can describe substitution as “putting a number in place of a letter”.
- I can predict the output of a function machine for a given input.
- I can evaluate expressions such as x + 1, 3x, 2x + 5 and (x + 4) ÷ 2.
- I can use Polypad or written working to check my answer.
Core idea Experience first
A function machine gives students a physical-feeling version of substitution: the number goes in, the rule acts on it, and the result comes out. The letter x is a placeholder for the input value.
Teacher setup Prep
- Open Polypad function machines.
- Have mini-whiteboards ready for prediction and notice/wonder routines.
- Prepare a simple first rule, such as x + 1, 2x or x + 4.
- Have the Student Quiz and Worksheet Creator ready for practice.
Visual anchor Function machine
Example teacher language: “The input is 3. The rule is x + 1. So we substitute 3 in for x: 3 + 1 = 4.”
ELPSA lesson sequence Overview
1
E Number talk to prime the operation
Begin with a short number talk using an additive or multiplicative strategy that matches the first function rule. For example, before x + 7, ask students to solve 36 + 7 in multiple ways. Before 3x, ask students to solve 3 × 8 or 6 × 12 using doubling, partitioning or known facts.
2
L Elicit the meaning of “substitution”
Ask: “What do you think the word substitution means? Where have you heard it?” Collect ideas such as sport substitutions, swapping ingredients, replacing a person, or using a substitute teacher. Build the class definition: substitution means replacing one thing with another.
3
E Explore function machines on Polypad
Load Polypad’s function machines. Show the function or algebra rule. Drop a number into the machine and ask students to record a notice and a wonder on mini-whiteboards. Keep the early focus on input, rule and output rather than formal written notation.
4
P Predict the output
Prepare another value to drop into the machine. Before dropping it, ask students to predict the output on mini-whiteboards. Reveal the output and ask: “Who used the rule? Who used a pattern? Who changed their mind?” Repeat with several different values.
5
S Name the mathematics: substituting for x
Bring the class together and explain that the input value is substituting in for the x term. Write the connection beside the machine: if the rule is x + 1 and the input is 3, then x is replaced by 3, so 3 + 1 = 4.
6
A Guided and independent practice: Student Quiz
Students practise on the Substitution in Algebra Student Quiz. Allow Polypad support at first, especially for students who still need the input-rule-output model. Encourage students to move from using the machine to mentally replacing the variable with the value.
7
A Consolidation: Worksheet Creator
Use the Worksheet Creator for printed fluency. Choose a level that matches the class: Sweet for one-step single-variable expressions, Mild for two-step expressions, Medium for two variables, and Spicy for negative values.
Number talk options Prime
- Additive: 47 + 8, 36 + 19, 102 − 7. Ask students to share compensation, bridging to ten, or partitioning strategies.
- Multiplicative: 4 × 7, 6 × 12, 3 × 15. Ask students to share doubling, halving, arrays or distributive thinking.
- Match the number talk to the first machine rule so the arithmetic is already active before algebra appears.
Mini-whiteboard prompts Predict
- “What do you think will come out? Write your prediction.”
- “What did the machine do to the input?”
- “How could we write the rule using x?”
- “If x = 5, what does this expression become?”
- “Which part changed? Which part stayed the same?”
Teacher talk moves Language
Revoice
“So you’re saying the machine takes the input and applies the same rule each time.”
Press for structure
“Where do you see the input value in the written expression?”
Connect to notation
“When we write x = 3, every x in the rule is replaced by 3.”
Common misconceptions Watch for
- Students add the input and output instead of applying the rule.
- Students treat 3x as 3 + x rather than 3 × x.
- Students substitute only once when the variable appears more than once.
- Students lose the negative sign when substituting negative values.
Exit ticket AFL
- Explain what substitution means in your own words.
- If x = 6, evaluate x + 4.
- If a = 3, evaluate 5a.
- If x = 8, evaluate (x + 4) ÷ 2.
