Free Grade 3 Midpoints in Context Worksheets
Free Grade 3 worksheets for Midpoints in Context: 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
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain midpoints in context
Explain midpoints in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate midpoints in context
Calculate midpoints in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare midpoints in context
Compare midpoints in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify midpoints in context
Justify midpoints in context 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 Midpoints in Context 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 (-3, -3) in?[1]
- 3.Which quadrant is the point (1, 1) in?[1]
- 4.Which quadrant is the point (4, 1) in?[1]
- 5.Find the midpoint of (4, 0) and (10, -2).[2]
- 6.Find the midpoint of (4, 5) and (12, 9).[2]
- 7.Find the midpoint of (2, 4) and (12, 10).[2]
- 8.Find the midpoint of (-4, -5) and (4, -5).[2]
- 9.Find the equation of the line through (6, 6) and (10, 12).[3]
- 10.Find the equation of the line through (-5, 2) and (-1, 4).[3]
- 11.Find the equation of the line through (3, -2) and (9, 0).[3]
- 12.Find the equation of the line through (-6, -6) and (-2, -4).[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. First quadrant
x is positive, y is positive. Quadrants go anticlockwise from top-right.
4. First quadrant
x is positive, y is positive. Quadrants go anticlockwise from top-right.
5. (7, -1)
Average the x values: (4 + 10) ÷ 2 = 7. Average the y values: (0 + -2) ÷ 2 = -1.
6. (8, 7)
Average the x values: (4 + 12) ÷ 2 = 8. Average the y values: (5 + 9) ÷ 2 = 7.
7. (7, 7)
Average the x values: (2 + 12) ÷ 2 = 7. Average the y values: (4 + 10) ÷ 2 = 7.
8. (0, -5)
Average the x values: (-4 + 4) ÷ 2 = 0. Average the y values: (-5 + -5) ÷ 2 = -5.
9. y = 1.5x − 3
Gradient m = (12 − 6) / (10 − 6) = 1.5. Substitute (6, 6): c = 6 − 1.5 × 6 = -3.
10. y = 0.5x + 4.5
Gradient m = (4 − 2) / (-1 − -5) = 0.5. Substitute (-5, 2): c = 2 − 0.5 × (-5) = 4.5.
11. y = 0.33x − 3
Gradient m = (0 − -2) / (9 − 3) = 0.33. Substitute (3, -2): c = -2 − 0.33 × 3 = -3.
12. y = 0.5x − 3
Gradient m = (-4 − -6) / (-2 − -6) = 0.5. Substitute (-6, -6): c = -6 − 0.5 × (-6) = -3.
Worked examples
Which quadrant is the point (2, -1) in?
- x is positive, y is negative.
- Quadrants go anticlockwise from top-right.
- Answer: Fourth quadrant
Find the midpoint of (5, -6) and (15, -10).
- Average the x values: (5 + 15) ÷ 2 = 10.
- Average the y values: (-6 + -10) ÷ 2 = -8.
- Answer: (10, -8)
Find the equation of the line through (-2, -2) and (0, 2).
- Gradient m = (2 − -2) / (0 − -2) = 2.
- Substitute (-2, -2): c = -2 − 2 × (-2) = 2.
- Answer: y = 2x + 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.
Every free resource for Midpoints in Context
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Frequently asked
- Is this Grade 3 Midpoints in Context 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 Working with Midpoints, Introducing Midpoints, Plotting Points. 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 Midpoints in Context?
- Move on to Plotting Points, Distance Between Points, which build directly on this idea.
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