Math lesson plan · 6th grade (Year 7 in England) · 45 minutes
Find the equation linking two variables in a table
Algebra
CCSS 6.EE.C.9England: KS3 Algebra
Objective and success criteria
Students will: Find the equation linking two variables in a table.
- 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: Dependent and independent variables
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 · 5 min
- Quick retrieval from earlier learning (Dependent and independent variables). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Fatima earns 7 for each hour of dog walking: e = 7h. How much does Fatima earn for 9 hours? → 63Prompt: Substitute the number of hours for h.
- Which equation matches the table? x: 1, 2, 3, 4 → y: 4, 5, 6, 7 (y = 3x / y = x − 3 / y = x + 3 / y = 4x) → y = x + 3Prompt: Test each equation with the first pair, then with another pair.
- Grace earns 8 for each hour of dog walking: e = 8h. How much does Grace earn for 4 hours? → 32Prompt: Substitute the number of hours for h.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Find the equation linking two variables in a table. 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: x: 4, 6, 7, 10. y: 44, 66, 77, 110. Write an equation for y in terms of x. Type the right-hand side only.
- Step 1: 44 ÷ 4 = 11
- Step 2: y = 11x
- Answer: 11x
- 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.
- x: 3, 5, 6, 9. y: 33, 55, 66, 99. Write an equation for y in terms of x. Type the right-hand side only. → 11xPrompt: Divide each y by its x. Is it always the same?
- Age of Ana (x): 3, 4, 11, 12. Age of her brother (y): 17, 18, 25, 26. Write an equation for y in terms of x. Type the right-hand side only. → x+14Prompt: Find y − x for each 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.
- x: 1, 2, 6, 7. y: 11, 22, 66, 77. Write an equation for y in terms of x. Type the right-hand side only. → 11xPrompt: Divide each y by its x. Is it always the same?
- Number of tables pushed together (x): 1, 2, 3, 4. Seats (y): 12, 17, 22, 27. Write y in terms of x. Type the right-hand side only. → 5x+7Prompt: By how much does y go up each time x goes up by 1?
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: Dependent and independent variables.
- 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-6.
Free lesson plan from eurekami.com/lesson-plan-builder