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Math lesson plan · 8th grade (Year 9 in England) · 45 minutes

Solve a system by reading the intersection of two lines

Algebra

CCSS 8.EE.C.8.ACCSS 8.EE.C.8.BEngland: KS3 AlgebraEngland: GCSE Foundation Algebra

Objective and success criteria

Students will: Solve a system by reading the intersection of two lines.

  • 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: Check whether a point solves a system; Graphs of linear equations y = mx + b

Leads to: Predict the number of solutions of a system

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 (Check whether a point solves a system; Graphs of linear equations y = mx + b). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Is (−2, 0) a solution of the system 2x + 4y = −4 and −3x − y = 8? (Yes / No) → NoPrompt: Substitute x and y into BOTH equations.
  2. Which point solves both x + y = −2 and x − y = −6? ((2, −4) / (−2, −6) / (−3, 1) / (−4, 2)) → (−4, 2)Prompt: Test each point in both equations.
  3. Is (−5, −1) a solution of the system 2x − 2y = −8 and −3x − 2y = 16? (Yes / No) → NoPrompt: Substitute x and y into BOTH equations.

Hook · 5 min

  • Show a "think of a number" puzzle and ask the class to work out the starting number.
  • Share the objective: Solve a system by reading the intersection of two lines. 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.
  • Model one question from the student sheet, thinking aloud.
  • 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.

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.

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: Check whether a point solves a system.
  • 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: Predict the number of solutions of a system.
  • 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-8.

Free lesson plan from eurekami.com/lesson-plan-builder

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Solve a system by reading the intersection of two lines

Name

Date

Score/ 8

  1. Question 1

    The graph shows y = x − 5 and y = 2x − 8. What is the solution of the system? Type it like (2, −3).

    xy−8−6−4−22468−10−8−6−4−22468100y = x − 5y = 2x − 8

    Answer

  2. Question 2

    The graph shows y = 3x − 3 and y = 3x − 4. How many solutions does the system have?

    xy−8−6−4−22468−10−8−6−4−22468100y = 3x − 3y = 3x − 4
    • A. 0
    • B. 1
    • C. Infinitely many

  3. Question 3

    The graph shows y = −3x − 12 and y = x + 4. What is the solution of the system? Type it like (2, −3).

    xy−8−6−4−22468−10−8−6−4−22468100y = −3x − 12y = x + 4

    Answer

  4. Question 4

    The graph shows y = −x − 1 and y = −x + 2. How many solutions does the system have?

    xy−8−6−4−22468−10−8−6−4−22468100y = −x − 1y = −x + 2
    • A. 0
    • B. 1
    • C. Infinitely many

  5. Question 5

    The graph shows y = x + 1 and y = −3x + 13. What is the solution of the system? Type it like (2, −3).

    xy−8−6−4−22468−10−8−6−4−22468100y = x + 1y = −3x + 13

    Answer

  6. Question 6

    The graph shows y = 3x + 4 and y = 3x − 1. How many solutions does the system have?

    xy−8−6−4−22468−10−8−6−4−22468100y = 3x + 4y = 3x − 1
    • A. 0
    • B. 1
    • C. Infinitely many

  7. Question 7

    The graph shows y = x − 1 and y = −2x − 1. What is the solution of the system? Type it like (2, −3).

    xy−8−6−4−22468−10−8−6−4−22468100y = x − 1y = −2x − 1

    Answer

  8. Question 8

    The graph shows y = x + 2 and y = x + 3. How many solutions does the system have?

    xy−8−6−4−22468−10−8−6−4−22468100y = x + 2y = x + 3
    • A. 0
    • B. 1
    • C. Infinitely many

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Answer key: Solve a system by reading the intersection of two lines

  1. 1. (3, −2)

  2. 2. A. 0

  3. 3. (−4, 0)

  4. 4. A. 0

  5. 5. (3, 4)

  6. 6. A. 0

  7. 7. (0, −1)

  8. 8. A. 0