Free Grade 3 Working with Midpoints Flashcards
Free Grade 3 flashcards for Working with Midpoints: 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
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with midpoints
Identify working with midpoints accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with midpoints
Explain working with midpoints accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with midpoints
Calculate working with midpoints accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with midpoints
Compare working with midpoints 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 Midpoints 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, 4) in?[1]
- 2.Which quadrant is the point (1, -3) in?[1]
- 3.Which quadrant is the point (4, 6) in?[1]
- 4.Which quadrant is the point (4, -4) in?[1]
- 5.Find the midpoint of (-3, 3) and (3, -5).[2]
- 6.Find the midpoint of (4, -6) and (12, -10).[2]
- 7.Find the midpoint of (-4, 0) and (-2, -8).[2]
- 8.Find the midpoint of (0, 0) and (6, -8).[2]
- 9.Find the equation of the line through (-1, -1) and (9, 1).[3]
- 10.Find the equation of the line through (4, 1) and (10, -3).[3]
- 11.Find the equation of the line through (0, -1) and (6, 7).[3]
- 12.Find the equation of the line through (3, 3) and (11, 9).[3]
Show answers and working
1. First quadrant
x is positive, y is positive. 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. Fourth quadrant
x is positive, y is negative. Quadrants go anticlockwise from top-right.
5. (0, -1)
Average the x values: (-3 + 3) ÷ 2 = 0. Average the y values: (3 + -5) ÷ 2 = -1.
6. (8, -8)
Average the x values: (4 + 12) ÷ 2 = 8. Average the y values: (-6 + -10) ÷ 2 = -8.
7. (-3, -4)
Average the x values: (-4 + -2) ÷ 2 = -3. Average the y values: (0 + -8) ÷ 2 = -4.
8. (3, -4)
Average the x values: (0 + 6) ÷ 2 = 3. Average the y values: (0 + -8) ÷ 2 = -4.
9. y = 0.2x − 0.8
Gradient m = (1 − -1) / (9 − -1) = 0.2. Substitute (-1, -1): c = -1 − 0.2 × (-1) = -0.8.
10. y = -0.67x + 3.67
Gradient m = (-3 − 1) / (10 − 4) = -0.67. Substitute (4, 1): c = 1 − -0.67 × 4 = 3.67.
11. y = 1.33x − 1
Gradient m = (7 − -1) / (6 − 0) = 1.33. Substitute (0, -1): c = -1 − 1.33 × 0 = -1.
12. y = 0.75x + 0.75
Gradient m = (9 − 3) / (11 − 3) = 0.75. Substitute (3, 3): c = 3 − 0.75 × 3 = 0.75.
Worked examples
Which quadrant is the point (-3, -2) in?
- x is negative, y is negative.
- Quadrants go anticlockwise from top-right.
- Answer: Third quadrant
Find the midpoint of (-2, -1) and (4, 3).
- Average the x values: (-2 + 4) ÷ 2 = 1.
- Average the y values: (-1 + 3) ÷ 2 = 1.
- Answer: (1, 1)
Find the equation of the line through (3, 1) and (13, -7).
- Gradient m = (-7 − 1) / (13 − 3) = -0.8.
- Substitute (3, 1): c = 1 − -0.8 × 3 = 3.4.
- Answer: y = -0.8x + 3.4
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 Working with Midpoints
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Frequently asked
- Is this Grade 3 Working with Midpoints 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 Midpoints, Plotting Points. 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 Working with Midpoints?
- Move on to Midpoints in Context, Plotting Points, Distance Between Points, which build directly on this idea.
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