Free Grade 3 Introduction to Introducing Plotting Points Essentials Lesson Plans
Free Grade 3 lesson plans for Introduction to Introducing Plotting Points Essentials: 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 introduction to introducing plotting points essentials
Explain introduction to introducing plotting points essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introduction to introducing plotting points essentials
Calculate introduction to introducing plotting points essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introduction to introducing plotting points essentials
Compare introduction to introducing plotting points essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introduction to introducing plotting points essentials
Justify introduction to introducing plotting points essentials 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 Introduction to Introducing Plotting Points Essentials 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 (2, -5) in?[1]
- 2.Which quadrant is the point (-3, -2) in?[1]
- 3.Which quadrant is the point (4, 4) in?[1]
- 4.Which quadrant is the point (-5, -6) in?[1]
- 5.Find the midpoint of (-1, -6) and (1, -8).[2]
- 6.Find the midpoint of (-5, 0) and (-3, -6).[2]
- 7.Find the midpoint of (-2, -6) and (0, -8).[2]
- 8.Find the midpoint of (1, 6) and (5, 0).[2]
- 9.Find the equation of the line through (3, -2) and (11, 6).[3]
- 10.Find the equation of the line through (-1, -3) and (3, -11).[3]
- 11.Find the equation of the line through (5, 4) and (7, 4).[3]
- 12.Find the equation of the line through (5, 6) and (15, -2).[3]
Show answers and working
1. Fourth quadrant
x is positive, y is negative. Quadrants go anticlockwise from top-right.
2. Third quadrant
x is negative, y is negative. Quadrants go anticlockwise from top-right.
3. First quadrant
x is positive, y is positive. Quadrants go anticlockwise from top-right.
4. Third quadrant
x is negative, y is negative. Quadrants go anticlockwise from top-right.
5. (0, -7)
Average the x values: (-1 + 1) ÷ 2 = 0. Average the y values: (-6 + -8) ÷ 2 = -7.
6. (-4, -3)
Average the x values: (-5 + -3) ÷ 2 = -4. Average the y values: (0 + -6) ÷ 2 = -3.
7. (-1, -7)
Average the x values: (-2 + 0) ÷ 2 = -1. Average the y values: (-6 + -8) ÷ 2 = -7.
8. (3, 3)
Average the x values: (1 + 5) ÷ 2 = 3. Average the y values: (6 + 0) ÷ 2 = 3.
9. y = 1x − 5
Gradient m = (6 − -2) / (11 − 3) = 1. Substitute (3, -2): c = -2 − 1 × 3 = -5.
10. y = -2x − 5
Gradient m = (-11 − -3) / (3 − -1) = -2. Substitute (-1, -3): c = -3 − -2 × (-1) = -5.
11. y = 0x + 4
Gradient m = (4 − 4) / (7 − 5) = 0. Substitute (5, 4): c = 4 − 0 × 5 = 4.
12. y = -0.8x + 10
Gradient m = (-2 − 6) / (15 − 5) = -0.8. Substitute (5, 6): c = 6 − -0.8 × 5 = 10.
Worked examples
Which quadrant is the point (-6, 5) 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 = 5.
- Average the y values: (-3 + 5) ÷ 2 = 1.
- Answer: (5, 1)
Find the equation of the line through (3, 6) and (11, 0).
- Gradient m = (0 − 6) / (11 − 3) = -0.75.
- Substitute (3, 6): c = 6 − -0.75 × 3 = 8.25.
- Answer: y = -0.75x + 8.25
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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