Free Grade 3 Working with Plotting Points Word Problems Lesson Plans
Free Grade 3 lesson plans for Working with Plotting Points Word Problems: 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
Stretch
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with plotting points word problems
Explain working with plotting points word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with plotting points word problems
Calculate working with plotting points word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with plotting points word problems
Compare working with plotting points word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with plotting points word problems
Justify working with plotting points word problems 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 Word Problems 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, 4) in?[1]
- 2.Which quadrant is the point (-3, 3) in?[1]
- 3.Which quadrant is the point (-4, -3) in?[1]
- 4.Which quadrant is the point (-6, 3) in?[1]
- 5.Find the midpoint of (4, 1) and (6, -1).[2]
- 6.Find the midpoint of (-2, 5) and (8, 3).[2]
- 7.Find the midpoint of (-5, 0) and (-1, 8).[2]
- 8.Find the midpoint of (-6, 4) and (4, 4).[2]
- 9.Find the equation of the line through (-6, -4) and (-2, 0).[3]
- 10.Find the equation of the line through (-6, 2) and (0, 2).[3]
- 11.Find the equation of the line through (3, 3) and (11, -5).[3]
- 12.Find the equation of the line through (3, 1) and (13, 3).[3]
Show answers and working
1. Second quadrant
x is negative, y is positive. 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. Second quadrant
x is negative, y is positive. Quadrants go anticlockwise from top-right.
5. (5, 0)
Average the x values: (4 + 6) ÷ 2 = 5. Average the y values: (1 + -1) ÷ 2 = 0.
6. (3, 4)
Average the x values: (-2 + 8) ÷ 2 = 3. Average the y values: (5 + 3) ÷ 2 = 4.
7. (-3, 4)
Average the x values: (-5 + -1) ÷ 2 = -3. Average the y values: (0 + 8) ÷ 2 = 4.
8. (-1, 4)
Average the x values: (-6 + 4) ÷ 2 = -1. Average the y values: (4 + 4) ÷ 2 = 4.
9. y = 1x + 2
Gradient m = (0 − -4) / (-2 − -6) = 1. Substitute (-6, -4): c = -4 − 1 × (-6) = 2.
10. y = 0x + 2
Gradient m = (2 − 2) / (0 − -6) = 0. Substitute (-6, 2): c = 2 − 0 × (-6) = 2.
11. y = -1x + 6
Gradient m = (-5 − 3) / (11 − 3) = -1. Substitute (3, 3): c = 3 − -1 × 3 = 6.
12. y = 0.2x + 0.4
Gradient m = (3 − 1) / (13 − 3) = 0.2. Substitute (3, 1): c = 1 − 0.2 × 3 = 0.4.
Worked examples
Which quadrant is the point (-5, 4) in?
- x is negative, y is positive.
- Quadrants go anticlockwise from top-right.
- Answer: Second quadrant
Find the midpoint of (-3, -3) and (7, 5).
- Average the x values: (-3 + 7) ÷ 2 = 2.
- Average the y values: (-3 + 5) ÷ 2 = 1.
- Answer: (2, 1)
Find the equation of the line through (2, -2) and (8, -10).
- Gradient m = (-10 − -2) / (8 − 2) = -1.33.
- Substitute (2, -2): c = -2 − -1.33 × 2 = 0.67.
- Answer: y = -1.33x + 0.67
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.
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Frequently asked
- Is this Grade 3 Working with Plotting Points Word Problems 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 Techniques, 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 Word Problems?
- Move on to Working with Plotting Points Common Errors, Introducing Plotting Points, Plotting Points in Context, which build directly on this idea.
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