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Math lesson plan · 8th grade (Year 9 in England) · 30 minutes

Slope (gradient) of a line

Algebra

CCSS 8.EE.B.5CCSS 8.EE.B.6CCSS 8.F.B.4England: KS3 AlgebraEngland: GCSE Foundation Algebra

Objective and success criteria

Students will: Slope (gradient) of a line.

  • 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: Coordinates in all four quadrants; Proportional relationships; Equivalent fractions

Leads to: Scatter graphs and correlation; Graphs of linear equations y = mx + b; Find the slope from a graph using rise over run

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 (Coordinates in all four quadrants; Proportional relationships; Equivalent fractions). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. Is this relationship proportional? x: 3, 6, 8 → y: 6, 12, 16 (Yes, proportional / No, not proportional) → Yes, proportionalPrompt: Find y ÷ x for each pair.
  2. Is this relationship proportional? x: 4, 5, 6 → y: 20, 25, 30 (Yes, proportional / No, not proportional) → Yes, proportionalPrompt: Find y ÷ x for each pair.
  3. Is this relationship proportional? x: 5, 9, 10 → y: 45, 82, 90 (Yes, proportional / No, not proportional) → No, not proportionalPrompt: Find y ÷ x for each pair.

Hook · 3 min

  • Show a "think of a number" puzzle and ask the class to work out the starting number.
  • Share the objective: Slope (gradient) of a line. 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: Coordinates in all four quadrants.
  • 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: Scatter graphs and correlation; Graphs of linear equations y = mx + b; Find the slope from a graph using rise over run.
  • 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

eurekami

Slope (gradient) of a line

Name

Date

Score/ 6

  1. Question 1

    The line passes through the two marked points (0, 2) and (2, 10). What is its slope?

    xy−66−12−66120y = 4x + 2AB

    Answer

  2. Question 2

    Find the slope (gradient) of the line through (−3, −3) and (−1, −4). Give a whole number or a fraction in simplest form.

    xy−12−6612−12−66120AB

    Answer(as a fraction)

  3. Question 3

    Kwame cycles at a steady speed. The graph of distance (km) against time (hours) passes through (0, 0) and (2, 14). What is the slope, and so the speed in km/h?

    xy1234567891028560y = 7x(2, 14)

    Answer

  4. Question 4

    The line passes through the two marked points (0, 3) and (2, −1). What is its slope?

    xy−66−12−66120y = −2x + 3AB

    Answer

  5. Question 5

    Find the slope (gradient) of the line through (0, 1) and (−3, 3). Give a whole number or a fraction in simplest form.

    xy−12−6612−12−66120AB

    Answer(as a fraction)

  6. Question 6

    Liam cycles at a steady speed. The graph of distance (km) against time (hours) passes through (0, 0) and (4, 48). What is the slope, and so the speed in km/h?

    xy1234567891012243648607284961081200y = 12x(4, 48)

    Answer

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Answer key: Slope (gradient) of a line

  1. 1. 4

  2. 2. -1/2

  3. 3. 7

  4. 4. -2

  5. 5. -2/3

  6. 6. 12