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Grade 10 · Core Mathematics · Lesson 1 of 21

Explaining Vector and Scalar Quantities

A Grade 10 Core Mathematics CBE lesson from the sub-strand Vectors I. In it, learners define scalar and vector quantities accurately with appropriate units and physical examples.

Strand Measurements and GeometrySub-strand Vectors ILesson code 10CM-28-L140 minutes · 2 slides

KICD learning outcome (a)

Explain vector and scalar quantities with illustrations.

By the end of this lesson, learners should be able to

  1. Define scalar and vector quantities accurately with appropriate units and physical examples.
  2. Classify physical quantities and real-world scenarios as representing either vectors or scalars.
  3. Illustrate vector quantities using directed line segments indicating magnitude and direction.

Key vocabulary

Scalar quantity
A physical quantity that is specified entirely by magnitude alone without direction.
Mass is a scalar quantity because fifty kilograms has no associated direction.
Vector quantity
A physical quantity that possesses both magnitude and a specific direction.
Displacement of ten metres East is a vector quantity with magnitude and direction.
Magnitude
The numerical value or numerical size of a physical quantity including units.
The magnitude of a force vector measuring twenty Newtons is twenty.

Lesson preview

Slide 1 · Understanding Scalar and Vector QuantitiesModel · 18 min
A visual comparison showing a scalar distance of 12 km and a vector displacement of 12 km pointing North.
Figure 1: A visual comparison showing a scalar distance of 12 km and a vector displacement of 12 km pointing North.

Physical quantities are measurements used to describe nature and movement. A scalar quantity is defined completely by its numerical size, called magnitude, alongside appropriate units, such as a temperature of 24∘C or a mass of 55 kg. In contrast, a vector quantity requires both magnitude and a specific direction to be fully described. For instance, moving 12 km due North describes a displacement vector, whereas walking 12 km without specifying direction is simply a scalar distance. Look at Figure 1 to see how a vector includes direction while a scalar only shows size.

  • Scalar quantities are completely described by magnitude alone, such as mass, temperature, and speed.
  • Vector quantities require both magnitude and a specified direction, such as weight, velocity, and force.
  • Displacement specifies distance in a given direction, distinguishing it from scalar distance.
  • Diagrams illustrate vectors using directed arrows where length shows magnitude and arrowheads show direction.
Worked example. Identify quantities having magnitude only: temperature (37∘C), speed (60 km/h), and mass (12 kg). Identify quantities requiring magnitude and direction: displacement (5 km South) and acceleration (3 m/s2 downward). Group them accordingly into scalar and vector lists. Answer: Scalar quantities: temperature, speed, mass. Vector quantities: displacement, acceleration..

Check question: A matatu drives at 80 km/h along the highway, while a second matatu drives at 80 km/h due West. Which of the following correctly classifies these quantities?

  1. The first is a scalar quantity (speed) and the second is a vector quantity (velocity).
  2. The first is a vector quantity (velocity) and the second is a scalar quantity (speed).
  3. Both are scalar quantities because they have the same numerical value of 80 km/h.
  4. Both are vector quantities because they both describe the motion of a vehicle.
Show answer

The first is a scalar quantity (speed) and the second is a vector quantity (velocity). The first statement gives magnitude only (80 km/h), making it a scalar quantity (speed). The second statement specifies both magnitude (80 km/h) and direction (due West), which defines a vector quantity (velocity).

Slide 2 · Classifying Real-World Scenarios and Physical QuantitiesCheck · 22 min
An aeroplane dropping a relief package illustrates a downward displacement vector of 150 m compared to a scalar volume.
Figure 2: An aeroplane dropping a relief package illustrates a downward displacement vector of 150 m compared to a scalar volume.

Teach the full lesson on the projector

This lesson, and every other Grade 1–10 CBE lesson, comes ready to project with the EAP ClassKit. It runs without electricity or internet.

  • Both slides with diagrams and class activities
  • Teacher notes, SNE adaptations and assessment checks
  • Homework and the other 20 lessons in this sub-strand
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All 21 lessons in Vectors I

  1. 1Explaining Vector and Scalar QuantitiesExplain vector and scalar quantities with illustrations
  2. 2Using Vector Notations in Different WaysUse vector notations in different ways
  3. 3Representing Vectors GeometricallyRepresent vectors geometrically in different situations
  4. 4Representing Vectors Geometrically in Different SituationsRepresent vectors geometrically in different situations
  5. 5Identifying Equivalent VectorsIdentify equivalent vectors in different situations
  6. 6Equivalent VectorsIdentify equivalent vectors in different situations
  7. 7Adding Vectors GeometricallyAdd vectors in different situations
  8. 8Adding Vectors Geometrically in Different SituationsAdd vectors in different situations
  9. 9Multiplying Vectors by ScalarsMultiply vectors by scalars
  10. 10Multiplying Vectors by Scalars: Graphical Construction and Scalar RatiosMultiply vectors by scalars
  11. 11Determining Column Vectors from Coordinates and DiagramsDetermine column vectors in different situations
  12. 12Determining Column Vectors and Vector ArithmeticDetermine column vectors in different situations
  13. 13Determining Position Vectors from the OriginDetermine position vectors in different situations
  14. 14Determining Position Vectors and Calculating Vector DisplacementsDetermine position vectors in different situations
  15. 15Calculating the Magnitude of a VectorWork out magnitude of a vector in different situations
  16. 16Working Out Vector Magnitudes in Different SituationsWork out magnitude of a vector in different situations
  17. 17Determining the Midpoint of a VectorDetermine the midpoint of a vector in different situations
  18. 18Determining Vector Midpoints and Endpoint CoordinatesDetermine the midpoint of a vector in different situations
  19. 19Determining Translation Vector as a TransformationDetermine translation vector as a transformation
  20. 20Determining Translation Vectors as TransformationsDetermine translation vector as a transformation
  21. 21Appreciating Vectors in Real-Life SituationsAppreciate the use of vectors in real-life situations