Free Grade 3 Working with Angles on a Straight Line Techniques Worksheets
Free Grade 3 worksheets for Working with Angles on a Straight Line 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
Foundation
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with angles on a straight line techniques
Identify working with angles on a straight line techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with angles on a straight line techniques
Explain working with angles on a straight line techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with angles on a straight line techniques
Calculate working with angles on a straight line techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with angles on a straight line techniques
Compare working with angles on a straight line 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 Working with Angles on a Straight Line 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, 2) in?[1]
- 2.Which quadrant is the point (-4, -1) in?[1]
- 3.Which quadrant is the point (-5, 4) in?[1]
- 4.Which quadrant is the point (4, -6) in?[1]
- 5.Find the midpoint of (-2, 6) and (4, 10).[2]
- 6.Find the midpoint of (-2, 2) and (6, 2).[2]
- 7.Find the midpoint of (-5, 0) and (5, -4).[2]
- 8.Find the midpoint of (0, 1) and (6, 3).[2]
- 9.Find the equation of the line through (-6, 5) and (0, -1).[3]
- 10.Find the equation of the line through (3, 6) and (13, 0).[3]
- 11.Find the equation of the line through (5, -1) and (7, -7).[3]
- 12.Find the equation of the line through (-4, -2) and (4, -8).[3]
Show answers and working
1. Second quadrant
x is negative, 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. 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. (1, 8)
Average the x values: (-2 + 4) ÷ 2 = 1. Average the y values: (6 + 10) ÷ 2 = 8.
6. (2, 2)
Average the x values: (-2 + 6) ÷ 2 = 2. Average the y values: (2 + 2) ÷ 2 = 2.
7. (0, -2)
Average the x values: (-5 + 5) ÷ 2 = 0. Average the y values: (0 + -4) ÷ 2 = -2.
8. (3, 2)
Average the x values: (0 + 6) ÷ 2 = 3. Average the y values: (1 + 3) ÷ 2 = 2.
9. y = -1x − 1
Gradient m = (-1 − 5) / (0 − -6) = -1. Substitute (-6, 5): c = 5 − -1 × (-6) = -1.
10. y = -0.6x + 7.8
Gradient m = (0 − 6) / (13 − 3) = -0.6. Substitute (3, 6): c = 6 − -0.6 × 3 = 7.8.
11. y = -3x + 14
Gradient m = (-7 − -1) / (7 − 5) = -3. Substitute (5, -1): c = -1 − -3 × 5 = 14.
12. y = -0.75x − 5
Gradient m = (-8 − -2) / (4 − -4) = -0.75. Substitute (-4, -2): c = -2 − -0.75 × (-4) = -5.
Worked examples
Which quadrant is the point (5, -5) in?
- x is positive, y is negative.
- Quadrants go anticlockwise from top-right.
- Answer: Fourth quadrant
Find the midpoint of (-1, 1) and (7, -5).
- Average the x values: (-1 + 7) ÷ 2 = 3.
- Average the y values: (1 + -5) ÷ 2 = -2.
- Answer: (3, -2)
Find the equation of the line through (2, 0) and (10, -8).
- Gradient m = (-8 − 0) / (10 − 2) = -1.
- Substitute (2, 0): c = 0 − -1 × 2 = 2.
- Answer: y = -1x + 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 Working with Angles on a Straight Line Essentials, Introducing Angles on a Straight Line. 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 Angles on a Straight Line Techniques?
- Move on to Working with Angles on a Straight Line Word Problems, Working with Angles on a Straight Line Common Errors, Introducing Angles on a Straight Line, Angles on a Straight Line in Context, which build directly on this idea.
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