Free Grade 3 Rules and Methods in Introducing Plotting Points Techniques: Worked Examples Worksheets
Free Grade 3 worksheets for Rules and Methods in Introducing Plotting Points Techniques: Worked Examples: 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
Foundation
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify rules and methods in introducing plotting points techniques: worked examples
Identify rules and methods in introducing plotting points techniques: worked examples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain rules and methods in introducing plotting points techniques: worked examples
Explain rules and methods in introducing plotting points techniques: worked examples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate rules and methods in introducing plotting points techniques: worked examples
Calculate rules and methods in introducing plotting points techniques: worked examples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare rules and methods in introducing plotting points techniques: worked examples
Compare rules and methods in introducing plotting points techniques: worked examples 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 Rules and Methods in Introducing Plotting Points Techniques: Worked Examples 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 (-5, -3) in?[1]
- 2.Which quadrant is the point (3, 6) in?[1]
- 3.Which quadrant is the point (6, -5) in?[1]
- 4.Which quadrant is the point (6, 4) in?[1]
- 5.Find the midpoint of (3, 2) and (13, 4).[2]
- 6.Find the midpoint of (-4, -5) and (0, 3).[2]
- 7.Find the midpoint of (1, 6) and (3, 8).[2]
- 8.Find the midpoint of (-4, 1) and (4, 3).[2]
- 9.Find the equation of the line through (-5, -1) and (3, 3).[3]
- 10.Find the equation of the line through (1, 1) and (11, 9).[3]
- 11.Find the equation of the line through (3, -3) and (13, -9).[3]
- 12.Find the equation of the line through (0, 6) and (6, 10).[3]
Show answers and working
1. Third quadrant
x is negative, 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. First quadrant
x is positive, y is positive. Quadrants go anticlockwise from top-right.
5. (8, 3)
Average the x values: (3 + 13) ÷ 2 = 8. Average the y values: (2 + 4) ÷ 2 = 3.
6. (-2, -1)
Average the x values: (-4 + 0) ÷ 2 = -2. Average the y values: (-5 + 3) ÷ 2 = -1.
7. (2, 7)
Average the x values: (1 + 3) ÷ 2 = 2. Average the y values: (6 + 8) ÷ 2 = 7.
8. (0, 2)
Average the x values: (-4 + 4) ÷ 2 = 0. Average the y values: (1 + 3) ÷ 2 = 2.
9. y = 0.5x + 1.5
Gradient m = (3 − -1) / (3 − -5) = 0.5. Substitute (-5, -1): c = -1 − 0.5 × (-5) = 1.5.
10. y = 0.8x + 0.2
Gradient m = (9 − 1) / (11 − 1) = 0.8. Substitute (1, 1): c = 1 − 0.8 × 1 = 0.2.
11. y = -0.6x − 1.2
Gradient m = (-9 − -3) / (13 − 3) = -0.6. Substitute (3, -3): c = -3 − -0.6 × 3 = -1.2.
12. y = 0.67x + 6
Gradient m = (10 − 6) / (6 − 0) = 0.67. Substitute (0, 6): c = 6 − 0.67 × 0 = 6.
Worked examples
Which quadrant is the point (-2, 1) in?
- x is negative, y is positive.
- Quadrants go anticlockwise from top-right.
- Answer: Second quadrant
Find the midpoint of (5, -6) and (11, -14).
- Average the x values: (5 + 11) ÷ 2 = 8.
- Average the y values: (-6 + -14) ÷ 2 = -10.
- Answer: (8, -10)
Find the equation of the line through (1, 5) and (5, 11).
- Gradient m = (11 − 5) / (5 − 1) = 1.5.
- Substitute (1, 5): c = 5 − 1.5 × 1 = 3.5.
- Answer: y = 1.5x + 3.5
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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