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Math lesson plan · 10th grade (Year 11 in England) · 45 minutes

Linear and quadratic systems

Algebra

CCSS HSA.REI.C.7England: GCSE Higher Algebra

Objective and success criteria

Students will: Linear and quadratic systems.

  • 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); Solve quadratics by factorising

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); Solve quadratics by factorising). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Solve the system: y = 4x and 3x + 3y = −15. Find x. → x = -1Prompt: Substitute the first equation into the second.
  2. Solve: x² + 2x − 24 = 0. Give both solutions, separated by a comma. → x = -6 or x = 4Prompt: Factorise: find two numbers that multiply to −24 and add to 2.
  3. Solve: 4x + 3y = −26 and 2x − 3y = −4. Find y. → -2Prompt: 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: Linear and quadratic systems. 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: 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-10.

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

eurekami

Linear and quadratic systems

Name

Date

Score/ 8

  1. Question 1

    Solve the system y = x² − 2x + 5 and y = 3x + 1. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = 3x + 1

    x =

  2. Question 2

    Solve the system y = x² + 8x + 13 and y = 2x + 5. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = 2x + 5

    x =

  3. Question 3

    Solve the system y = x² − x − 13 and y = 2x − 3. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = 2x − 3

    x =

  4. Question 4

    Solve the system y = x² + 4x − 2 and y = x + 2. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = x + 2

    x =

  5. Question 5

    Solve the system y = x² − 9x + 15 and y = −2x + 3. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = −2x + 3

    x =

  6. Question 6

    Solve the system y = x² + 3x − 16 and y = 2x + 4. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = 2x + 4

    x =

  7. Question 7

    Solve the system y = x² − 5x + 10 and y = 2x − 2. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = 2x − 2

    x =

  8. Question 8

    Solve the system y = x² − x + 2 and y = 2x. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = 2x

    x =

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Answer key: Linear and quadratic systems

  1. 1. x = 1 or x = 4

  2. 2. x = -4 or x = -2

  3. 3. x = -2 or x = 5

  4. 4. x = -4 or x = 1

  5. 5. x = 3 or x = 4

  6. 6. x = -5 or x = 4

  7. 7. x = 3 or x = 4

  8. 8. x = 1 or x = 2