Free Grade 3 Introducing Gradient Lesson Plans
Free Grade 3 lesson plans for Introducing Gradient: 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
Higher
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing gradient
Identify introducing gradient accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing gradient
Explain introducing gradient accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing gradient
Calculate introducing gradient accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing gradient
Compare introducing gradient 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 Gradient 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, 1) in?[1]
- 2.Which quadrant is the point (-6, -3) in?[1]
- 3.Which quadrant is the point (3, -1) in?[1]
- 4.Which quadrant is the point (3, -2) in?[1]
- 5.Find the midpoint of (1, 4) and (9, -2).[2]
- 6.Find the midpoint of (2, 2) and (8, 6).[2]
- 7.Find the midpoint of (-4, -5) and (0, -13).[2]
- 8.Find the midpoint of (-2, 6) and (0, 4).[2]
- 9.Find the equation of the line through (6, 1) and (8, 3).[3]
- 10.Find the equation of the line through (-6, -1) and (-4, -9).[3]
- 11.Find the equation of the line through (-5, -3) and (-3, -1).[3]
- 12.Find the equation of the line through (-2, -2) and (0, -4).[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. Fourth quadrant
x is positive, y is negative. Quadrants go anticlockwise from top-right.
4. Fourth quadrant
x is positive, y is negative. Quadrants go anticlockwise from top-right.
5. (5, 1)
Average the x values: (1 + 9) ÷ 2 = 5. Average the y values: (4 + -2) ÷ 2 = 1.
6. (5, 4)
Average the x values: (2 + 8) ÷ 2 = 5. Average the y values: (2 + 6) ÷ 2 = 4.
7. (-2, -9)
Average the x values: (-4 + 0) ÷ 2 = -2. Average the y values: (-5 + -13) ÷ 2 = -9.
8. (-1, 5)
Average the x values: (-2 + 0) ÷ 2 = -1. Average the y values: (6 + 4) ÷ 2 = 5.
9. y = 1x − 5
Gradient m = (3 − 1) / (8 − 6) = 1. Substitute (6, 1): c = 1 − 1 × 6 = -5.
10. y = -4x − 25
Gradient m = (-9 − -1) / (-4 − -6) = -4. Substitute (-6, -1): c = -1 − -4 × (-6) = -25.
11. y = 1x + 2
Gradient m = (-1 − -3) / (-3 − -5) = 1. Substitute (-5, -3): c = -3 − 1 × (-5) = 2.
12. y = -1x − 4
Gradient m = (-4 − -2) / (0 − -2) = -1. Substitute (-2, -2): c = -2 − -1 × (-2) = -4.
Worked examples
Which quadrant is the point (4, 3) in?
- x is positive, y is positive.
- Quadrants go anticlockwise from top-right.
- Answer: First quadrant
Find the midpoint of (0, 2) and (2, -2).
- Average the x values: (0 + 2) ÷ 2 = 1.
- Average the y values: (2 + -2) ÷ 2 = 0.
- Answer: (1, 0)
Find the equation of the line through (3, 1) and (5, 7).
- Gradient m = (7 − 1) / (5 − 3) = 3.
- Substitute (3, 1): c = 1 − 3 × 3 = -8.
- Answer: y = 3x − 8
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 Gradient 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 The Coordinate Plane. 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 Introducing Gradient?
- Move on to Working with Gradient, Gradient in Context, y = mx + c, Parallel and Perpendicular Lines, which build directly on this idea.
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