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