Free Grade 3 Introducing Gradient Word Problems Worksheets
Free Grade 3 worksheets for Introducing Gradient Word Problems: 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing gradient word problems
Identify introducing gradient word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing gradient word problems
Explain introducing gradient word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing gradient word problems
Calculate introducing gradient word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing gradient word problems
Compare introducing gradient word problems 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 Word Problems 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, -3) in?[1]
- 2.Which quadrant is the point (6, -3) in?[1]
- 3.Which quadrant is the point (4, 1) in?[1]
- 4.Which quadrant is the point (-3, 2) in?[1]
- 5.Find the midpoint of (6, 1) and (12, -1).[2]
- 6.Find the midpoint of (-5, 0) and (1, 0).[2]
- 7.Find the midpoint of (3, 6) and (13, 6).[2]
- 8.Find the midpoint of (-3, 0) and (7, 6).[2]
- 9.Find the equation of the line through (-6, -6) and (0, -6).[3]
- 10.Find the equation of the line through (-2, -6) and (8, 0).[3]
- 11.Find the equation of the line through (3, 5) and (7, 7).[3]
- 12.Find the equation of the line through (5, 5) and (15, 1).[3]
Show answers and working
1. Fourth quadrant
x is positive, y is negative. Quadrants go anticlockwise from top-right.
2. Fourth quadrant
x is positive, 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. Second quadrant
x is negative, y is positive. Quadrants go anticlockwise from top-right.
5. (9, 0)
Average the x values: (6 + 12) ÷ 2 = 9. Average the y values: (1 + -1) ÷ 2 = 0.
6. (-2, 0)
Average the x values: (-5 + 1) ÷ 2 = -2. Average the y values: (0 + 0) ÷ 2 = 0.
7. (8, 6)
Average the x values: (3 + 13) ÷ 2 = 8. Average the y values: (6 + 6) ÷ 2 = 6.
8. (2, 3)
Average the x values: (-3 + 7) ÷ 2 = 2. Average the y values: (0 + 6) ÷ 2 = 3.
9. y = 0x − 6
Gradient m = (-6 − -6) / (0 − -6) = 0. Substitute (-6, -6): c = -6 − 0 × (-6) = -6.
10. y = 0.6x − 4.8
Gradient m = (0 − -6) / (8 − -2) = 0.6. Substitute (-2, -6): c = -6 − 0.6 × (-2) = -4.8.
11. y = 0.5x + 3.5
Gradient m = (7 − 5) / (7 − 3) = 0.5. Substitute (3, 5): c = 5 − 0.5 × 3 = 3.5.
12. y = -0.4x + 7
Gradient m = (1 − 5) / (15 − 5) = -0.4. Substitute (5, 5): c = 5 − -0.4 × 5 = 7.
Worked examples
Which quadrant is the point (1, -4) in?
- x is positive, y is negative.
- Quadrants go anticlockwise from top-right.
- Answer: Fourth quadrant
Find the midpoint of (4, 3) and (6, 9).
- Average the x values: (4 + 6) ÷ 2 = 5.
- Average the y values: (3 + 9) ÷ 2 = 6.
- Answer: (5, 6)
Find the equation of the line through (-5, 1) and (-1, 5).
- Gradient m = (5 − 1) / (-1 − -5) = 1.
- Substitute (-5, 1): c = 1 − 1 × (-5) = 6.
- Answer: y = 1x + 6
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 Word Problems worksheet really free?
- Yes. Every worksheets 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 Introducing Gradient Techniques, Introducing Gradient Essentials, The Coordinate Plane. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet 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 Word Problems?
- Move on to Introducing Gradient Common Errors, Working with Gradient, Gradient in Context, which build directly on this idea.
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