Math lesson plan · 4th grade (Year 5 in England) · 60 minutes
Function machines and input–output tables
Algebra
CCSS 4.OA.C.5England: Y6 Algebra
Objective and success criteria
Students will: Function machines and input–output tables.
- I can answer questions on today's skill on my own, without help.
- I can explain each step and say why it works.
- I can check my answer and spot a mistake.
Before and after
Needs first: Number patterns; Times tables to 12 × 12
Leads to: Write algebraic expressions; Two-step function machines: forwards and backwards
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 min
- Quick retrieval from earlier learning (Number patterns; Times tables to 12 × 12). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- What comes next? 32, 39, 46, 53, __ → 60Prompt: How much does the pattern go up each time?
- 8 × 11 = ? → 88Prompt: Is there a fact you already know that is close?
- Find the missing number: 116, __, 100, 92, 84 → 108Prompt: Is the pattern going up or down? By how much?
Hook · 6 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Function machines and input–output tables. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: A function machine does: × 4, then + 13. What comes out when 6 goes in?
- Step 1: 6 × 4 = 24
- Step 2: 24 + 13 = 37
- Answer: 37
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- A function machine does: × 2, then + 7. What comes out when 5 goes in? → 17Prompt: Do the steps in order.
- A function machine does: × 7, then + 1. The output is 36. What was the input? → 5Prompt: Work backwards using the inverse operations.
You do: independent practice · 17 min
- Students work on the student sheet. Circulate and check the first two answers of every student early.
- Students who finish: write a question of their own for a partner, with the answer.
The 8 questions are on the student sheet below, with answers in the key.
Exit ticket · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- A function machine does: × 9, then + 3. What comes out when 9 goes in? → 84Prompt: Do the steps in order.
- In → Out: 2 → 18, 6 → 54, 8 → 72. What is the output for 12? → 108Prompt: Find a rule that works for every pair.
Watch out for
- Doing an operation to one side of an equation but not the other.
- Reading 3x as 3 + x, or thinking x always stands for one particular number.
Support and stretch
Support
- Review first: Number patterns.
- Use concrete materials: balance scales or a balance drawing.
- Give the first step of each question, or a partly worked example to finish.
- Pair with a confident partner for the guided practice.
Stretch
- Move on to: Write algebraic expressions; Two-step function machines: forwards and backwards.
- Explain a common mistake in writing and how to fix it.
- Write a word problem that uses today's skill, then solve a partner's.
Homework and more practice
Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-4.
Free lesson plan from eurekami.com/lesson-plan-builder