Math lesson plan · 6th grade (Year 7 in England) · 45 minutes
Dependent and independent variables
Algebra
CCSS 6.EE.C.9England: KS3 Algebra
Objective and success criteria
Students will: Dependent and independent variables.
- 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: Evaluate expressions; Ratio tables and double number lines
Leads to: Functions: definition and comparison; Find the equation linking two variables in a table
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Evaluate expressions; Ratio tables and double number lines). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Find the value of 9x + 9 when x = 1. → 18Prompt: Replace x with 1.
- A recipe uses 5 eggs for every 3 pancakes. Complete the table: eggs 5, 10, 35; pancakes 3, 6, __ → 21Prompt: How many times 5 is 35?
- Evaluate x² + y when x = 4 and y = 2. → 18Prompt: Substitute each letter, using brackets around negative numbers.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Dependent and independent variables. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Felix earns 5 for each hour of dog walking: e = 5h. How much does Felix earn for 7 hours?
- Step 1: 5 × 7 = 35
- Answer: 35
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Lucia earns 11 for each hour of dog walking: e = 11h. How much does Lucia earn for 15 hours? → 165Prompt: Substitute the number of hours for h.
- Which equation matches the table? x: 1, 2, 3, 4 → y: 7, 8, 9, 10 (y = 7x / y = x + 6 / y = 6x / y = x − 6) → y = x + 6Prompt: Test each equation with the first pair, then with another pair.
You do: independent practice · 10 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 · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Aisha earns 6 for each hour of dog walking: e = 6h. How much does Aisha earn for 14 hours? → 84Prompt: Substitute the number of hours for h.
- Which equation matches the table? x: 1, 2, 3, 4 → y: 6, 12, 18, 24 (y = x + 11 / y = 7x / y = x + 6 / y = 6x) → y = 6xPrompt: Test each equation with the first pair, then with another 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: Evaluate expressions.
- 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: Functions: definition and comparison; Find the equation linking two variables in a table.
- 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-6.
Free lesson plan from eurekami.com/lesson-plan-builder