Back to the lesson plan builder
Lesson length30 min45 min60 min
Questions🔀 New questions

Print the plan for yourself; the student sheet prints on its own page after it.

Math lesson plan · 10th grade (Year 11 in England) · 30 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 · 4 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 = 3x and 4x + y = 56. Find x. → x = 8Prompt: Substitute the first equation into the second.
  2. Solve: x² + 11x + 30 = 0. Give both solutions, separated by a comma. → x = -6 or x = -5Prompt: Factorise: find two numbers that multiply to 30 and add to 11.
  3. Solve: 2x + y = 10 and 5x − y = 39. Find y. → -4Prompt: The y terms have opposite coefficients: add the equations to eliminate y.

Hook · 3 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 · 7 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 · 6 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 · 7 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 6 questions are on the student sheet below, with answers in the key.

Exit ticket · 3 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/ 6

  1. Question 1

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

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

    x =

  2. Question 2

    Solve the system y = x² − x − 5 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 + 4x − 5 and y = 0. Give the x-values, separated by a comma.

    xy−8−448−20−16−12−8−4481216200y = 0

    x =

  4. Question 4

    Solve the system y = x² − 7x + 8 and y = −2x + 4. Give the x-values, separated by a comma.

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

    x =

  5. Question 5

    Solve the system y = x² − 18 and y = −2. Give the x-values, separated by a comma.

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

    x =

  6. Question 6

    Solve the system y = x² − 4x − 8 and y = −2x − 5. Give the x-values, separated by a comma.

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

    x =

Free from eurekami.com

for the adult only

Answer key: Linear and quadratic systems

  1. 1. x = -3 or x = 1

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

  3. 3. x = -5 or x = 1

  4. 4. x = 1 or x = 4

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

  6. 6. x = -1 or x = 3