Free Grade 3 Plotting Points in Context Lessons
Free Grade 3 lessons for Plotting Points in Context: 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
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain plotting points in context
Explain plotting points in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate plotting points in context
Calculate plotting points in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare plotting points in context
Compare plotting points in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify plotting points in context
Justify plotting points in context 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 Plotting Points in Context 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 (-4, -4) in?[1]
- 2.Which quadrant is the point (-4, 3) in?[1]
- 3.Which quadrant is the point (-6, -1) in?[1]
- 4.Which quadrant is the point (-5, -6) in?[1]
- 5.Find the midpoint of (6, 6) and (16, 10).[2]
- 6.Find the midpoint of (3, -1) and (7, 5).[2]
- 7.Find the midpoint of (5, -2) and (7, 2).[2]
- 8.Find the midpoint of (-4, -5) and (-2, -7).[2]
- 9.Find the equation of the line through (-6, -6) and (-4, -6).[3]
- 10.Find the equation of the line through (2, -1) and (12, -9).[3]
- 11.Find the equation of the line through (5, -4) and (15, -8).[3]
- 12.Find the equation of the line through (1, -5) and (9, -5).[3]
Show answers and working
1. Third quadrant
x is negative, y is negative. Quadrants go anticlockwise from top-right.
2. Second quadrant
x is negative, y is positive. Quadrants go anticlockwise from top-right.
3. Third quadrant
x is negative, y is negative. Quadrants go anticlockwise from top-right.
4. Third quadrant
x is negative, y is negative. Quadrants go anticlockwise from top-right.
5. (11, 8)
Average the x values: (6 + 16) ÷ 2 = 11. Average the y values: (6 + 10) ÷ 2 = 8.
6. (5, 2)
Average the x values: (3 + 7) ÷ 2 = 5. Average the y values: (-1 + 5) ÷ 2 = 2.
7. (6, 0)
Average the x values: (5 + 7) ÷ 2 = 6. Average the y values: (-2 + 2) ÷ 2 = 0.
8. (-3, -6)
Average the x values: (-4 + -2) ÷ 2 = -3. Average the y values: (-5 + -7) ÷ 2 = -6.
9. y = 0x − 6
Gradient m = (-6 − -6) / (-4 − -6) = 0. Substitute (-6, -6): c = -6 − 0 × (-6) = -6.
10. y = -0.8x + 0.6
Gradient m = (-9 − -1) / (12 − 2) = -0.8. Substitute (2, -1): c = -1 − -0.8 × 2 = 0.6.
11. y = -0.4x − 2
Gradient m = (-8 − -4) / (15 − 5) = -0.4. Substitute (5, -4): c = -4 − -0.4 × 5 = -2.
12. y = 0x − 5
Gradient m = (-5 − -5) / (9 − 1) = 0. Substitute (1, -5): c = -5 − 0 × 1 = -5.
Worked examples
Which quadrant is the point (5, 1) in?
- x is positive, y is positive.
- Quadrants go anticlockwise from top-right.
- Answer: First quadrant
Find the midpoint of (4, 2) and (6, -2).
- Average the x values: (4 + 6) ÷ 2 = 5.
- Average the y values: (2 + -2) ÷ 2 = 0.
- Answer: (5, 0)
Find the equation of the line through (2, -2) and (12, 0).
- Gradient m = (0 − -2) / (12 − 2) = 0.2.
- Substitute (2, -2): c = -2 − 0.2 × 2 = -2.4.
- Answer: y = 0.2x − 2.4
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.
Every free resource for Plotting Points in Context
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Frequently asked
- Is this Grade 3 Plotting Points in Context lesson really free?
- Yes. Every lessons 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, Introducing Plotting Points, Probability. Each one has its own free lesson, worksheet and quiz.
- How is the lesson 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 Plotting Points in Context?
- Move on to Midpoints, Distance Between Points, which build directly on this idea.
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