Math lesson plan · 9th grade (Year 10 in England) · 30 minutes
Write the equation of a parallel line through a point
Algebra
CCSS HSG.GPE.B.5England: GCSE Higher Algebra
Objective and success criteria
Students will: Write the equation of a parallel line through a point.
- 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: Write the equation of a line from two points
Leads to: Write the equation of a perpendicular line through a point
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 (Write the equation of a line from two points). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Find the equation of the line through (0, −4) and (−3, −2). Type the right-hand side of y = … (fractions are fine). → -(2/3)x-4Prompt: The slope will be a fraction this time.
- A line passes through (−1, 2) and (−2, 3). The point (1, k) is also on the line. Find k. → 0Prompt: Find the equation of the line first.
- Find the equation of the line through (0, −1) and (4, −3). Type the right-hand side of y = … (fractions are fine). → -(1/2)x-1Prompt: The slope will be a fraction this time.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Write the equation of a parallel line through a point. 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.
- Example: Find the line parallel to −3x − y = −1 through (−1, 6). Type the right-hand side of y = … .
- Step 1: m = −3
- Step 2: b = 6 − −3 × (−1) = 3
- Step 3: y = −3x + 3
- Answer: -3x+3
- 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.
- Find the line parallel to −3x − y = −1 through (3, −2). Type the right-hand side of y = … . → -3x+7Prompt: Rearrange the given line into y = mx + b to read its slope.
- Find the line parallel to −3x − 3y = 0 through (4, 2). Type the right-hand side of y = … . → -x+6Prompt: Rearrange the given line into y = mx + b to read its slope.
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.
- Find the line parallel to −x − y = 0 through (3, −4). Type the right-hand side of y = … . → -x-1Prompt: Rearrange the given line into y = mx + b to read its slope.
- Find the line parallel to 9x − 3y = −6 through (1, −3). Type the right-hand side of y = … . → 3x-6Prompt: Rearrange the given line into y = mx + b to read its slope.
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: Write the equation of a line from two points.
- 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: Write the equation of a perpendicular line through a point.
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder