Free Grade 3 Working with Position Vectors Lesson Plans
Free Grade 3 lesson plans for Working with Position Vectors: 12 real questions with a full answer key and worked solutions. A vector has size and direction. Add vectors component by component; multiply by a number to scale. Magnitude = √(x² + y²).
Free
Foundation
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with position vectors
Identify working with position vectors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with position vectors
Explain working with position vectors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with position vectors
Calculate working with position vectors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with position vectors
Compare working with position vectors 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 Position Vectors works
A vector has size and direction. Add vectors component by component; multiply by a number to scale. Magnitude = √(x² + y²).
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.a = (-5, -3), b = (6, 6). Find a + 2b.[1]
- 2.a = (1, -2), b = (-1, 3). Find a + 4b.[1]
- 3.a = (-4, -1), b = (-6, 5). Find a + 3b.[1]
- 4.a = (1, -1), b = (-1, 1). Find a + 3b.[1]
- 5.a = (5, 5), b = (3, -5). Find a + 4b.[2]
- 6.a = (-1, 6), b = (3, 5). Find a + 2b.[2]
- 7.a = (3, -5), b = (3, -2). Find a + 3b.[2]
- 8.a = (6, 5), b = (-5, 6). Find a + 4b.[2]
- 9.Find the magnitude of (-1, 2) to 2 d.p.[3]
- 10.Find the magnitude of (5, 1) to 2 d.p.[3]
- 11.Find the magnitude of (4, 4) to 2 d.p.[3]
- 12.Find the magnitude of (-5, 6) to 2 d.p.[3]
Show answers and working
1. (7, 9)
2b = (12, 12). Add components: (-5 + 12, -3 + 12).
2. (-3, 10)
4b = (-4, 12). Add components: (1 + -4, -2 + 12).
3. (-22, 14)
3b = (-18, 15). Add components: (-4 + -18, -1 + 15).
4. (-2, 2)
3b = (-3, 3). Add components: (1 + -3, -1 + 3).
5. (17, -15)
4b = (12, -20). Add components: (5 + 12, 5 + -20).
6. (5, 16)
2b = (6, 10). Add components: (-1 + 6, 6 + 10).
7. (12, -11)
3b = (9, -6). Add components: (3 + 9, -5 + -6).
8. (-14, 29)
4b = (-20, 24). Add components: (6 + -20, 5 + 24).
9. 2.24
|v| = √(x² + y²) = √(1 + 4). = 2.24.
10. 5.1
|v| = √(x² + y²) = √(25 + 1). = 5.1.
11. 5.66
|v| = √(x² + y²) = √(16 + 16). = 5.66.
12. 7.81
|v| = √(x² + y²) = √(25 + 36). = 7.81.
Worked examples
a = (-1, -3), b = (-4, -5). Find a + 3b.
- 3b = (-12, -15).
- Add components: (-1 + -12, -3 + -15).
- Answer: (-13, -18)
a = (-1, -1), b = (1, 3). Find a + 4b.
- 4b = (4, 12).
- Add components: (-1 + 4, -1 + 12).
- Answer: (3, 11)
Find the magnitude of (1, 6) to 2 d.p.
- |v| = √(x² + y²) = √(1 + 36).
- = 6.08.
- Answer: 6.08
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Adds x of one vector to y of the other.
Correction: Add x with x, y with y.
Forgets that a negative component means the opposite direction.
Correction: Draw the vector to check.
Teacher tips
- · Draw vectors on squared paper end to end.
Parent tips
- · Give directions as '3 steps right, 2 steps up'.
Real-life applications
- · Navigation, forces in physics, game movement.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Working with Position Vectors lesson plan really free?
- Yes. Every lesson plans 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 Position Vectors, Vector Basics. Each one has its own free lesson, worksheet and quiz.
- How is the lesson plan 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 Position Vectors?
- Move on to Position Vectors in Context, Collinearity, Vector Proof, which build directly on this idea.
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