Free Grade 3 Working with Plotting Points Techniques Lesson Plans
Free Grade 3 lesson plans for Working with Plotting Points Techniques: 12 real questions with a full answer key and worked solutions. A coordinate (x, y) gives a position: across first, then up. The gradient of a line is rise over run, and y = mx + c describes a straight line.
Free
Core
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with plotting points techniques
Explain working with plotting points techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with plotting points techniques
Calculate working with plotting points techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with plotting points techniques
Compare working with plotting points techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with plotting points techniques
Justify working with plotting points techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Working with Plotting Points Techniques works
A coordinate (x, y) gives a position: across first, then up. The gradient of a line is rise over run, and y = mx + c describes a straight line.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Which quadrant is the point (-6, -5) in?[1]
- 2.Which quadrant is the point (5, -5) in?[1]
- 3.Which quadrant is the point (-6, 6) in?[1]
- 4.Which quadrant is the point (1, -3) in?[1]
- 5.Find the midpoint of (6, -2) and (12, -2).[2]
- 6.Find the midpoint of (-2, -2) and (2, 2).[2]
- 7.Find the midpoint of (2, -6) and (4, -2).[2]
- 8.Find the midpoint of (2, 4) and (4, 8).[2]
- 9.Find the equation of the line through (1, -6) and (5, 0).[3]
- 10.Find the equation of the line through (1, 6) and (9, 14).[3]
- 11.Find the equation of the line through (-1, -5) and (9, -9).[3]
- 12.Find the equation of the line through (0, -4) and (4, 0).[3]
Show answers and working
1. Third quadrant
x is negative, y is negative. Quadrants go anticlockwise from top-right.
2. Fourth quadrant
x is positive, y is negative. Quadrants go anticlockwise from top-right.
3. Second quadrant
x is negative, y is positive. Quadrants go anticlockwise from top-right.
4. Fourth quadrant
x is positive, y is negative. Quadrants go anticlockwise from top-right.
5. (9, -2)
Average the x values: (6 + 12) ÷ 2 = 9. Average the y values: (-2 + -2) ÷ 2 = -2.
6. (0, 0)
Average the x values: (-2 + 2) ÷ 2 = 0. Average the y values: (-2 + 2) ÷ 2 = 0.
7. (3, -4)
Average the x values: (2 + 4) ÷ 2 = 3. Average the y values: (-6 + -2) ÷ 2 = -4.
8. (3, 6)
Average the x values: (2 + 4) ÷ 2 = 3. Average the y values: (4 + 8) ÷ 2 = 6.
9. y = 1.5x − 7.5
Gradient m = (0 − -6) / (5 − 1) = 1.5. Substitute (1, -6): c = -6 − 1.5 × 1 = -7.5.
10. y = 1x + 5
Gradient m = (14 − 6) / (9 − 1) = 1. Substitute (1, 6): c = 6 − 1 × 1 = 5.
11. y = -0.4x − 5.4
Gradient m = (-9 − -5) / (9 − -1) = -0.4. Substitute (-1, -5): c = -5 − -0.4 × (-1) = -5.4.
12. y = 1x − 4
Gradient m = (0 − -4) / (4 − 0) = 1. Substitute (0, -4): c = -4 − 1 × 0 = -4.
Worked examples
Which quadrant is the point (-4, 1) in?
- x is negative, y is positive.
- Quadrants go anticlockwise from top-right.
- Answer: Second quadrant
Find the midpoint of (-5, -6) and (1, -6).
- Average the x values: (-5 + 1) ÷ 2 = -2.
- Average the y values: (-6 + -6) ÷ 2 = -6.
- Answer: (-2, -6)
Find the equation of the line through (-5, -4) and (5, 2).
- Gradient m = (2 − -4) / (5 − -5) = 0.6.
- Substitute (-5, -4): c = -4 − 0.6 × (-5) = -1.
- Answer: y = 0.6x − 1
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Plots (y, x) instead of (x, y).
Correction: Along the corridor, then up the stairs.
Calculates gradient as run over rise.
Correction: Gradient = change in y ÷ change in x.
Teacher tips
- · Play coordinate battleships.
Parent tips
- · Find places on a map using grid references.
Real-life applications
- · Maps, game boards, GPS.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Working with Plotting Points Techniques lesson plan really free?
- Yes. Every lesson plans on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Working with Plotting Points Essentials, Introducing Plotting Points. Each one has its own free lesson, worksheet and quiz.
- How is the lesson plan sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Working with Plotting Points Techniques?
- Move on to Working with Plotting Points Word Problems, Working with Plotting Points Common Errors, Introducing Plotting Points, Plotting Points in Context, which build directly on this idea.
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