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Math lesson plan · 8th grade (Year 9 in England) · 60 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 · 6 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: 1, 5, 7 → y: 7, 35, 49 (Yes, proportional / No, not proportional) → Yes, proportionalPrompt: Find y ÷ x for each pair.
  2. Is this relationship proportional? x: 6, 7, 8 → y: 54, 63, 72 (Yes, proportional / No, not proportional) → Yes, proportionalPrompt: Find y ÷ x for each pair.
  3. Is this relationship proportional? x: 3, 5, 9 → y: 12, 20, 36 (Yes, proportional / No, not proportional) → Yes, proportionalPrompt: Find y ÷ x for each pair.

Hook · 6 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 · 12 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 · 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.

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.

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/ 8

  1. Question 1

    Daniel cycles at a steady speed. The graph of distance (km) against time (hours) passes through (0, 0) and (2, 22). What is the slope, and so the speed in km/h?

    xy12345678910660y = 11x(2, 22)

    Answer

  2. Question 2

    Find the slope (gradient) of the line through (2, −4) and (4, −7). Give a whole number or a fraction in simplest form.

    xy−12−6612−12−66120AB

    Answer(as a fraction)

  3. Question 3

    The line passes through the two marked points (0, −2) and (2, −4). What is its slope?

    xy−66−12−66120y = −x − 2AB

    Answer

  4. Question 4

    Kwame cycles at a steady speed. The graph of distance (km) against time (hours) passes through (0, 0) and (2, 8). What is the slope, and so the speed in km/h?

    xy123456789104812162024283236400y = 4x(2, 8)

    Answer

  5. Question 5

    Find the slope (gradient) of the line through (−1, −1) and (−6, −7). Give a whole number or a fraction in simplest form.

    xy−12−6612−12−66120AB

    Answer(as a fraction)

  6. Question 6

    The line passes through the two marked points (0, 3) and (2, 9). What is its slope?

    xy−66−12−66120y = 3x + 3AB

    Answer

  7. Question 7

    Ines cycles at a steady speed. The graph of distance (km) against time (hours) passes through (0, 0) and (6, 54). What is the slope, and so the speed in km/h?

    xy1234567891045900y = 9x(6, 54)

    Answer

  8. Question 8

    Find the slope (gradient) of the line through (4, 3) and (1, 6). Give a whole number or a fraction in simplest form.

    xy−12−6612−12−66120AB

    Answer(as a fraction)

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Answer key: Slope (gradient) of a line

  1. 1. 11

  2. 2. -3/2

  3. 3. -1

  4. 4. 4

  5. 5. 6/5

  6. 6. 3

  7. 7. 9

  8. 8. -1