Free Grade 3 Working with Introducing Plotting Points Essentials Lesson Plans
Free Grade 3 lesson plans for Working with 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
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with introducing plotting points essentials
Explain working with introducing plotting points essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with introducing plotting points essentials
Calculate working with introducing plotting points essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with introducing plotting points essentials
Compare working with introducing plotting points essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with introducing plotting points essentials
Justify working with 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 Working with 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 (6, 1) in?[1]
- 2.Which quadrant is the point (-6, -2) in?[1]
- 3.Which quadrant is the point (1, 4) in?[1]
- 4.Which quadrant is the point (1, 1) in?[1]
- 5.Find the midpoint of (5, -5) and (11, -3).[2]
- 6.Find the midpoint of (6, -3) and (14, 1).[2]
- 7.Find the midpoint of (1, -1) and (3, 5).[2]
- 8.Find the midpoint of (2, 6) and (6, 0).[2]
- 9.Find the equation of the line through (6, 0) and (12, -4).[3]
- 10.Find the equation of the line through (1, -4) and (3, -8).[3]
- 11.Find the equation of the line through (-3, -6) and (5, -4).[3]
- 12.Find the equation of the line through (-1, -1) and (7, -3).[3]
Show answers and working
1. First quadrant
x is positive, y is positive. 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. First quadrant
x is positive, y is positive. Quadrants go anticlockwise from top-right.
5. (8, -4)
Average the x values: (5 + 11) ÷ 2 = 8. Average the y values: (-5 + -3) ÷ 2 = -4.
6. (10, -1)
Average the x values: (6 + 14) ÷ 2 = 10. Average the y values: (-3 + 1) ÷ 2 = -1.
7. (2, 2)
Average the x values: (1 + 3) ÷ 2 = 2. Average the y values: (-1 + 5) ÷ 2 = 2.
8. (4, 3)
Average the x values: (2 + 6) ÷ 2 = 4. Average the y values: (6 + 0) ÷ 2 = 3.
9. y = -0.67x + 4
Gradient m = (-4 − 0) / (12 − 6) = -0.67. Substitute (6, 0): c = 0 − -0.67 × 6 = 4.
10. y = -2x − 2
Gradient m = (-8 − -4) / (3 − 1) = -2. Substitute (1, -4): c = -4 − -2 × 1 = -2.
11. y = 0.25x − 5.25
Gradient m = (-4 − -6) / (5 − -3) = 0.25. Substitute (-3, -6): c = -6 − 0.25 × (-3) = -5.25.
12. y = -0.25x − 1.25
Gradient m = (-3 − -1) / (7 − -1) = -0.25. Substitute (-1, -1): c = -1 − -0.25 × (-1) = -1.25.
Worked examples
Which quadrant is the point (3, 1) in?
- x is positive, y is positive.
- Quadrants go anticlockwise from top-right.
- Answer: First quadrant
Find the midpoint of (6, 1) and (16, 5).
- Average the x values: (6 + 16) ÷ 2 = 11.
- Average the y values: (1 + 5) ÷ 2 = 3.
- Answer: (11, 3)
Find the equation of the line through (3, -3) and (13, 1).
- Gradient m = (1 − -3) / (13 − 3) = 0.4.
- Substitute (3, -3): c = -3 − 0.4 × 3 = -4.2.
- Answer: y = 0.4x − 4.2
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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- What should a learner already know before this?
- Start with Rules and Methods in Introducing Plotting Points Essentials, Key Vocabulary of Introducing Plotting Points Essentials, Probability. Each one has its own free lesson, worksheet and quiz.
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- 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 Introducing Plotting Points Essentials?
- Move on to Introducing Plotting Points Essentials in Examinations, Introducing Plotting Points Techniques, Introducing Plotting Points Word Problems, Introducing Plotting Points Common Errors, which build directly on this idea.
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