Math lesson plan · 9th grade (Year 10 in England) · 60 minutes
Tell how many solutions a linear system has
Algebra
CCSS 8.EE.C.8.BCCSS HSA.REI.C.6
Objective and success criteria
Students will: Tell how many solutions a linear system has.
- 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); Classify pairs of lines as parallel, perpendicular or neither
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 (Systems of linear equations (simultaneous equations); Classify pairs of lines as parallel, perpendicular or neither). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve the system: y = −2x + 3 and x + y = 2. Find x. → x = 1Prompt: Substitute the first equation into the second.
- Line 1: y = −x − 1 Line 2: y = −2x + 2 Are the lines parallel, perpendicular or neither? (Parallel / Perpendicular / Neither) → NeitherPrompt: Compare the two slopes.
- Solve: 2x + y = −2 and 5x − y = −19. Find y. → 4Prompt: The y terms have opposite coefficients: add the equations to eliminate y.
Hook · 6 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Tell how many solutions a linear system has. 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: How many solutions does this system have? y = x + 4 y = x + 7
- Step 1: y = x + 7
- Step 2: None
- Answer: None
- 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.
- How many solutions does this system have? y = −3x − 1 2y = −6x − 2 (Exactly one / None / Infinitely many) → Infinitely manyPrompt: Write both in y = mx + b form and compare.
- How many solutions does this system have? 2x + 2y = 6 4x + 4y = 12 (Exactly one / None / Infinitely many) → Infinitely manyPrompt: Multiply the first equation by 2 and compare.
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.
- How many solutions does this system have? −3x − 5y = −5 6x + 10y = 12 (Exactly one / None / Infinitely many) → NonePrompt: Multiply the first equation by −2 and compare.
- How many solutions does this system have? y = 2x − 3 y = 3x − 5 (Exactly one / None / Infinitely many) → Exactly onePrompt: Write both in y = mx + b form and compare.
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-9.
Free lesson plan from eurekami.com/lesson-plan-builder