Free Grade 3 Adding Vectors in Context Word Problems Lessons
Free Grade 3 lessons for Adding Vectors in Context Word Problems: 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
Core
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain adding vectors in context word problems
Explain adding vectors in context word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate adding vectors in context word problems
Calculate adding vectors in context word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare adding vectors in context word problems
Compare adding vectors in context word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify adding vectors in context word problems
Justify adding vectors in context word problems 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 Adding Vectors in Context Word Problems 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 = (4, 6), b = (-3, -1). Find a + 3b.[1]
- 2.a = (-6, 6), b = (-6, 5). Find a + 4b.[1]
- 3.a = (6, -2), b = (-4, -6). Find a + 3b.[1]
- 4.a = (-3, -1), b = (-1, 2). Find a + 3b.[1]
- 5.a = (5, 1), b = (1, -1). Find a + 4b.[2]
- 6.a = (2, 3), b = (-4, 3). Find a + 4b.[2]
- 7.a = (1, 3), b = (4, 5). Find a + 2b.[2]
- 8.a = (1, 3), b = (6, 1). Find a + 4b.[2]
- 9.Find the magnitude of (-3, 0) to 2 d.p.[3]
- 10.Find the magnitude of (5, -4) to 2 d.p.[3]
- 11.Find the magnitude of (3, 6) to 2 d.p.[3]
- 12.Find the magnitude of (-5, -3) to 2 d.p.[3]
Show answers and working
1. (-5, 3)
3b = (-9, -3). Add components: (4 + -9, 6 + -3).
2. (-30, 26)
4b = (-24, 20). Add components: (-6 + -24, 6 + 20).
3. (-6, -20)
3b = (-12, -18). Add components: (6 + -12, -2 + -18).
4. (-6, 5)
3b = (-3, 6). Add components: (-3 + -3, -1 + 6).
5. (9, -3)
4b = (4, -4). Add components: (5 + 4, 1 + -4).
6. (-14, 15)
4b = (-16, 12). Add components: (2 + -16, 3 + 12).
7. (9, 13)
2b = (8, 10). Add components: (1 + 8, 3 + 10).
8. (25, 7)
4b = (24, 4). Add components: (1 + 24, 3 + 4).
9. 3
|v| = √(x² + y²) = √(9 + 0). = 3.
10. 6.4
|v| = √(x² + y²) = √(25 + 16). = 6.4.
11. 6.71
|v| = √(x² + y²) = √(9 + 36). = 6.71.
12. 5.83
|v| = √(x² + y²) = √(25 + 9). = 5.83.
Worked examples
a = (-1, 1), b = (-2, -5). Find a + 3b.
- 3b = (-6, -15).
- Add components: (-1 + -6, 1 + -15).
- Answer: (-7, -14)
a = (-1, -1), b = (5, 4). Find a + 4b.
- 4b = (20, 16).
- Add components: (-1 + 20, -1 + 16).
- Answer: (19, 15)
Find the magnitude of (-5, -2) to 2 d.p.
- |v| = √(x² + y²) = √(25 + 4).
- = 5.39.
- Answer: 5.39
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.
Every free resource for Adding Vectors in Context Word Problems
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Adding Vectors in Context Word Problems lesson really free?
- Yes. Every lessons 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 Adding Vectors in Context Techniques, Adding Vectors in Context Essentials, Working with Adding Vectors. Each one has its own free lesson, worksheet and quiz.
- How is the lesson 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 Adding Vectors in Context Word Problems?
- Move on to Adding Vectors in Context Common Errors, Introducing Adding Vectors, Working with Adding Vectors, which build directly on this idea.
Related resources
Stuck on Adding Vectors in Context Word Problems? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor