Free Grade 3 Angles on a Straight Line in Context Techniques Flashcards
Free Grade 3 flashcards for Angles on a Straight Line 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
Core
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify angles on a straight line in context techniques
Identify angles on a straight line in context techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain angles on a straight line in context techniques
Explain angles on a straight line in context techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate angles on a straight line in context techniques
Calculate angles on a straight line in context techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare angles on a straight line in context techniques
Compare angles on a straight line 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 Angles on a Straight Line 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 (-4, 1) in?[1]
- 2.Which quadrant is the point (1, 2) in?[1]
- 3.Which quadrant is the point (2, -3) in?[1]
- 4.Which quadrant is the point (-1, 5) in?[1]
- 5.Find the midpoint of (1, -2) and (11, -10).[2]
- 6.Find the midpoint of (2, -6) and (12, -4).[2]
- 7.Find the midpoint of (-1, 0) and (9, 4).[2]
- 8.Find the midpoint of (5, 4) and (11, 12).[2]
- 9.Find the equation of the line through (3, 2) and (5, 0).[3]
- 10.Find the equation of the line through (5, 5) and (13, -3).[3]
- 11.Find the equation of the line through (5, -3) and (15, -7).[3]
- 12.Find the equation of the line through (2, -1) and (10, -9).[3]
Show answers and working
1. Second quadrant
x is negative, y is positive. Quadrants go anticlockwise from top-right.
2. First quadrant
x is positive, y is positive. 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. (6, -6)
Average the x values: (1 + 11) ÷ 2 = 6. Average the y values: (-2 + -10) ÷ 2 = -6.
6. (7, -5)
Average the x values: (2 + 12) ÷ 2 = 7. Average the y values: (-6 + -4) ÷ 2 = -5.
7. (4, 2)
Average the x values: (-1 + 9) ÷ 2 = 4. Average the y values: (0 + 4) ÷ 2 = 2.
8. (8, 8)
Average the x values: (5 + 11) ÷ 2 = 8. Average the y values: (4 + 12) ÷ 2 = 8.
9. y = -1x + 5
Gradient m = (0 − 2) / (5 − 3) = -1. Substitute (3, 2): c = 2 − -1 × 3 = 5.
10. y = -1x + 10
Gradient m = (-3 − 5) / (13 − 5) = -1. Substitute (5, 5): c = 5 − -1 × 5 = 10.
11. y = -0.4x − 1
Gradient m = (-7 − -3) / (15 − 5) = -0.4. Substitute (5, -3): c = -3 − -0.4 × 5 = -1.
12. y = -1x + 1
Gradient m = (-9 − -1) / (10 − 2) = -1. Substitute (2, -1): c = -1 − -1 × 2 = 1.
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 (6, -4) and (12, -2).
- Average the x values: (6 + 12) ÷ 2 = 9.
- Average the y values: (-4 + -2) ÷ 2 = -3.
- Answer: (9, -3)
Find the equation of the line through (-2, 6) and (4, 10).
- Gradient m = (10 − 6) / (4 − -2) = 0.67.
- Substitute (-2, 6): c = 6 − 0.67 × (-2) = 7.33.
- Answer: y = 0.67x + 7.33
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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- Start with Angles on a Straight Line in Context Essentials, Working with Angles on a Straight Line. Each one has its own free lesson, worksheet and quiz.
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- Move on to Angles on a Straight Line in Context Word Problems, Angles on a Straight Line in Context Common Errors, Introducing Angles on a Straight Line, Working with Angles on a Straight Line, which build directly on this idea.
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