Free Grade 3 Introducing Gradient Word Problems Flashcards
Free Grade 3 flashcards 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.
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30 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, -6) in?[1]
- 2.Which quadrant is the point (-3, -1) in?[1]
- 3.Which quadrant is the point (1, -5) in?[1]
- 4.Which quadrant is the point (-4, 1) in?[1]
- 5.Find the midpoint of (5, 0) and (9, -2).[2]
- 6.Find the midpoint of (-1, -3) and (5, 3).[2]
- 7.Find the midpoint of (5, -4) and (7, -12).[2]
- 8.Find the midpoint of (3, -4) and (7, -8).[2]
- 9.Find the equation of the line through (-5, -5) and (-3, -7).[3]
- 10.Find the equation of the line through (-1, -2) and (7, 2).[3]
- 11.Find the equation of the line through (4, -1) and (14, 5).[3]
- 12.Find the equation of the line through (3, -4) and (5, 4).[3]
Show answers and working
1. Third quadrant
x is negative, 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. Fourth quadrant
x is positive, y is negative. Quadrants go anticlockwise from top-right.
4. Second quadrant
x is negative, y is positive. Quadrants go anticlockwise from top-right.
5. (7, -1)
Average the x values: (5 + 9) ÷ 2 = 7. Average the y values: (0 + -2) ÷ 2 = -1.
6. (2, 0)
Average the x values: (-1 + 5) ÷ 2 = 2. Average the y values: (-3 + 3) ÷ 2 = 0.
7. (6, -8)
Average the x values: (5 + 7) ÷ 2 = 6. Average the y values: (-4 + -12) ÷ 2 = -8.
8. (5, -6)
Average the x values: (3 + 7) ÷ 2 = 5. Average the y values: (-4 + -8) ÷ 2 = -6.
9. y = -1x − 10
Gradient m = (-7 − -5) / (-3 − -5) = -1. Substitute (-5, -5): c = -5 − -1 × (-5) = -10.
10. y = 0.5x − 1.5
Gradient m = (2 − -2) / (7 − -1) = 0.5. Substitute (-1, -2): c = -2 − 0.5 × (-1) = -1.5.
11. y = 0.6x − 3.4
Gradient m = (5 − -1) / (14 − 4) = 0.6. Substitute (4, -1): c = -1 − 0.6 × 4 = -3.4.
12. y = 4x − 16
Gradient m = (4 − -4) / (5 − 3) = 4. Substitute (3, -4): c = -4 − 4 × 3 = -16.
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 (5, 2) and (9, 4).
- Average the x values: (5 + 9) ÷ 2 = 7.
- Average the y values: (2 + 4) ÷ 2 = 3.
- Answer: (7, 3)
Find the equation of the line through (-2, -5) and (0, -3).
- Gradient m = (-3 − -5) / (0 − -2) = 1.
- Substitute (-2, -5): c = -5 − 1 × (-2) = -3.
- Answer: y = 1x − 3
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 flashcards really free?
- Yes. Every flashcards 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 flashcards 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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