Free Grade 3 Working with Plotting Points Lessons
Free Grade 3 lessons for Working with Plotting Points: 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
Higher
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with plotting points
Identify working with plotting points accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with plotting points
Explain working with plotting points accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with plotting points
Calculate working with plotting points accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with plotting points
Compare working with plotting points 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 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 (-3, -6) in?[1]
- 2.Which quadrant is the point (-2, 1) in?[1]
- 3.Which quadrant is the point (3, -3) in?[1]
- 4.Which quadrant is the point (5, -1) in?[1]
- 5.Find the midpoint of (-4, 6) and (4, 2).[2]
- 6.Find the midpoint of (-3, -4) and (5, 2).[2]
- 7.Find the midpoint of (6, 4) and (8, 6).[2]
- 8.Find the midpoint of (-5, 5) and (3, 1).[2]
- 9.Find the equation of the line through (6, 1) and (16, 7).[3]
- 10.Find the equation of the line through (4, -5) and (12, -11).[3]
- 11.Find the equation of the line through (3, -4) and (5, 4).[3]
- 12.Find the equation of the line through (5, 0) and (15, -4).[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. Fourth quadrant
x is positive, y is negative. Quadrants go anticlockwise from top-right.
4. Fourth quadrant
x is positive, y is negative. Quadrants go anticlockwise from top-right.
5. (0, 4)
Average the x values: (-4 + 4) ÷ 2 = 0. Average the y values: (6 + 2) ÷ 2 = 4.
6. (1, -1)
Average the x values: (-3 + 5) ÷ 2 = 1. Average the y values: (-4 + 2) ÷ 2 = -1.
7. (7, 5)
Average the x values: (6 + 8) ÷ 2 = 7. Average the y values: (4 + 6) ÷ 2 = 5.
8. (-1, 3)
Average the x values: (-5 + 3) ÷ 2 = -1. Average the y values: (5 + 1) ÷ 2 = 3.
9. y = 0.6x − 2.6
Gradient m = (7 − 1) / (16 − 6) = 0.6. Substitute (6, 1): c = 1 − 0.6 × 6 = -2.6.
10. y = -0.75x − 2
Gradient m = (-11 − -5) / (12 − 4) = -0.75. Substitute (4, -5): c = -5 − -0.75 × 4 = -2.
11. y = 4x − 16
Gradient m = (4 − -4) / (5 − 3) = 4. Substitute (3, -4): c = -4 − 4 × 3 = -16.
12. y = -0.4x + 2
Gradient m = (-4 − 0) / (15 − 5) = -0.4. Substitute (5, 0): c = 0 − -0.4 × 5 = 2.
Worked examples
Which quadrant is the point (-5, 3) in?
- x is negative, y is positive.
- Quadrants go anticlockwise from top-right.
- Answer: Second quadrant
Find the midpoint of (2, 3) and (6, 11).
- Average the x values: (2 + 6) ÷ 2 = 4.
- Average the y values: (3 + 11) ÷ 2 = 7.
- Answer: (4, 7)
Find the equation of the line through (-5, -1) and (1, -3).
- Gradient m = (-3 − -1) / (1 − -5) = -0.33.
- Substitute (-5, -1): c = -1 − -0.33 × (-5) = -2.67.
- Answer: y = -0.33x − 2.67
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 Working with Plotting Points
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Frequently asked
- Is this Grade 3 Working with Plotting Points 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 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 Working with Plotting Points?
- Move on to Plotting Points in Context, Midpoints, Distance Between Points, which build directly on this idea.
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