Math lesson plan · 5th grade (Year 6 in England) · 60 minutes
Two-step function machines: forwards and backwards
Algebra
CCSS 5.OA.B.3England: Y6 Algebra
Objective and success criteria
Students will: Two-step function machines: forwards and backwards.
- 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: Function machines and input–output tables
Leads to: the next skill in this area.
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 (Function machines and input–output tables). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A function machine does: × 6, then + 16. What comes out when 11 goes in? → 82Prompt: Do the steps in order.
- A function machine does: × 2, then + 8. The output is 24. What was the input? → 8Prompt: Work backwards using the inverse operations.
- In → Out: 1 → 4, 2 → 5, 4 → 7. What is the output for 8? → 11Prompt: Find a rule that works for every pair.
Hook · 6 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Two-step function machines: forwards and backwards. 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: × 3, then + 4. What is the output when the input is 15?
- Step 1: 15 × 3 = 45
- Step 2: 45 + 4 = 49
- Answer: 49
- 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: × 4, then + 3. What is the output when the input is 9? → 39Prompt: Do the steps in order.
- A function machine does: × 4, then + 18. The output is 34. What was the input? → 4Prompt: Work backwards, undoing each step.
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.
- Inputs 7, 1, 8 give outputs 49, 13, 55. The machine multiplies by 6 and then adds a number. What number is added? → 7Prompt: Multiply one input by 6.
- A function machine does: × 4, then + 2. What is the output when the input is 4? → 18Prompt: Do the steps in order.
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: Function machines and input–output tables.
- 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
- 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-5.
Free lesson plan from eurekami.com/lesson-plan-builder