Free Grade 3 Gradient in Context Techniques Lessons
Free Grade 3 lessons for Gradient in Context Techniques: 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
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify gradient in context techniques
Identify gradient in context techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain gradient in context techniques
Explain gradient in context techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate gradient in context techniques
Calculate gradient in context techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare gradient in context techniques
Compare gradient in context techniques 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 Gradient in Context Techniques 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, 5) in?[1]
- 2.Which quadrant is the point (-1, 6) in?[1]
- 3.Which quadrant is the point (-3, 1) in?[1]
- 4.Which quadrant is the point (2, -5) in?[1]
- 5.Find the midpoint of (0, -4) and (6, -2).[2]
- 6.Find the midpoint of (-6, 2) and (4, 2).[2]
- 7.Find the midpoint of (3, 4) and (9, 2).[2]
- 8.Find the midpoint of (0, -3) and (8, 3).[2]
- 9.Find the equation of the line through (3, -2) and (7, 0).[3]
- 10.Find the equation of the line through (2, 0) and (12, -8).[3]
- 11.Find the equation of the line through (-6, 5) and (4, 11).[3]
- 12.Find the equation of the line through (6, 6) and (16, -2).[3]
Show answers and working
1. Second quadrant
x is negative, y is positive. Quadrants go anticlockwise from top-right.
2. Second quadrant
x is negative, y is positive. Quadrants go anticlockwise from top-right.
3. Second quadrant
x is negative, y is positive. Quadrants go anticlockwise from top-right.
4. Fourth quadrant
x is positive, y is negative. Quadrants go anticlockwise from top-right.
5. (3, -3)
Average the x values: (0 + 6) ÷ 2 = 3. Average the y values: (-4 + -2) ÷ 2 = -3.
6. (-1, 2)
Average the x values: (-6 + 4) ÷ 2 = -1. Average the y values: (2 + 2) ÷ 2 = 2.
7. (6, 3)
Average the x values: (3 + 9) ÷ 2 = 6. Average the y values: (4 + 2) ÷ 2 = 3.
8. (4, 0)
Average the x values: (0 + 8) ÷ 2 = 4. Average the y values: (-3 + 3) ÷ 2 = 0.
9. y = 0.5x − 3.5
Gradient m = (0 − -2) / (7 − 3) = 0.5. Substitute (3, -2): c = -2 − 0.5 × 3 = -3.5.
10. y = -0.8x + 1.6
Gradient m = (-8 − 0) / (12 − 2) = -0.8. Substitute (2, 0): c = 0 − -0.8 × 2 = 1.6.
11. y = 0.6x + 8.6
Gradient m = (11 − 5) / (4 − -6) = 0.6. Substitute (-6, 5): c = 5 − 0.6 × (-6) = 8.6.
12. y = -0.8x + 10.8
Gradient m = (-2 − 6) / (16 − 6) = -0.8. Substitute (6, 6): c = 6 − -0.8 × 6 = 10.8.
Worked examples
Which quadrant is the point (-2, -4) in?
- x is negative, y is negative.
- Quadrants go anticlockwise from top-right.
- Answer: Third quadrant
Find the midpoint of (0, -3) and (10, 5).
- Average the x values: (0 + 10) ÷ 2 = 5.
- Average the y values: (-3 + 5) ÷ 2 = 1.
- Answer: (5, 1)
Find the equation of the line through (4, 0) and (14, 2).
- Gradient m = (2 − 0) / (14 − 4) = 0.2.
- Substitute (4, 0): c = 0 − 0.2 × 4 = -0.8.
- Answer: y = 0.2x − 0.8
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 Gradient in Context Techniques lesson really free?
- Yes. Every lessons 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 Gradient in Context Essentials, Working with Gradient. Each one has its own free lesson, worksheet and quiz.
- How is the lesson 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 Gradient in Context Techniques?
- Move on to Gradient in Context Word Problems, Gradient in Context Common Errors, Introducing Gradient, Working with Gradient, which build directly on this idea.
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