Math lesson plan · 12th grade (Year 13 in England) · 45 minutes
Systems of three equations
Algebra
CCSS HSA.REI.C.6
Objective and success criteria
Students will: Systems of three equations.
- 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: Systems of linear equations (simultaneous equations); Systems of equations: word problems
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 (Systems of linear equations (simultaneous equations); Systems of equations: word problems). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve the system: y = x − 2 and 4x + 2y = 8. Find x. → x = 2Prompt: Substitute the first equation into the second.
- Adult tickets cost 12 and child tickets cost 4. A school sold 46 tickets and took 480 in total. How many adult tickets were sold? → 37Prompt: Let a = adult tickets and c = child tickets. Write two equations.
- Solve: 2x + 3y = 4 and 4x − 3y = −28. Find y. → 4Prompt: The y terms have opposite coefficients: add the equations to eliminate y.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Systems of three equations. 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: Solve: x + y + z = 6, x − y + 2z = −4, 2x + y − z = 14. What is z?
- Step 1: 2x + 3z = 2
- Step 2: 3x + z = 10
- Step 3: x = 4, y = 4, z = −2
- Answer: -2
- 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.
- Solve: x + y + z = 0, x − y + 2z = 9, 2x + y − z = −6. What is z? → 3Prompt: Add the first two equations to eliminate y.
- Solve: x + y + z = −1, x − y + 2z = −1, 2x + y − z = 12. What is x? → 5Prompt: Add the first two equations to eliminate y.
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.
- Solve: x + y + z = −2, x − y + 2z = 5, 2x + y − z = −11. What is x? → -3Prompt: Add the first two equations to eliminate y.
- Solve: x + y + z = 8, x − y + 2z = 7, 2x + y − z = −2. What is x? → 0Prompt: Add the first two equations to eliminate y.
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: Systems of linear equations (simultaneous equations).
- 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-12.
Free lesson plan from eurekami.com/lesson-plan-builder