Lesson Notes By Weeks and Term v3 - Senior Secondary 1
Fundamentals and Derived Quantities and Units
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Fundamentals and Derived Quantities and Units
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Subject: Physics
Class: Senior Secondary 1
Term: 3rd Term
Week: 1
Theme: Interaction Of Matter, Space And Time
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This topic introduces students to the fundamental concepts of physical quantities and their classification, which is crucial for all subsequent studies in Physics. Understanding the distinction between fundamental and derived quantities and their corresponding units provides a foundational framework for accurate measurement, calculation, and scientific communication. This knowledge is essential for Nigerian learners as it underpins various practical applications in daily life, such as accurate measurements in tailoring, construction, trade in markets (e.g., measuring garri, rice, or yam), and understanding technical specifications in engineering and technology.
Interaction Of Matter, Space And Time / Charge) from fundamental units.
Dimensional Analysis: Introduce the concept of dimensional analysis and ask them to use it to check the consistency of equations or derive relationships between quantities. For example, verifying if an equation like Energy = Mass × (Speed)2 is dimensionally consistent.
Research Non-SI Units: Task them to research common non-SI units still used in specific fields or regions in Nigeria (e.g., acres, pounds, gallons, feet) and explain how these relate to or differ from SI units. * Practical Design Challenge: Ask them to design a simple experiment that requires measuring both fundamental and derived quantities (e.g., measure the dimensions of a locally available block of wood to calculate its volume, then measure its mass to calculate its density). according to the mathematical relationships that define the derived quantities. Examples of Derived Units and their Derivation:
1. Area: Unit is (metre × metre) = m2
2. Volume: Unit is (metre × metre × metre) = m3
3. Speed: Unit is (metre / second) = m/s
4. Density: Unit is (kilogram / cubic metre) = kg/m3
5. Force: Unit is (kilogram × metre / second2) = kg m/s
2. This unit is given a special name: Newton (N).
6. Work/Energy: Unit is (Newton × metre) = N m.
This unit is given a special name: Joule (J). (kg m2/s2)
7. Power: Unit is (Joule / second) = J/s.
This unit is given a special name: Watt (W).
8. Pressure: Unit is (Newton / square metre) = N/m
2. This unit is given a special name: Pascal (Pa). Worked
Examples: Example 1: Differentiating Quantities Is 'length' a fundamental or derived quantity? What about 'velocity'?
Reasoning: Length is a basic, independent property of space. Velocity is the rate of change of displacement (a form of length) with respect to time, involving two fundamental quantities (length and time).
Answer: Length is a fundamental quantity. Velocity is a derived quantity.
Example 2: Differentiating Units Is the 'kilogram' a fundamental unit or a derived unit? What about the 'Newton'?
Reasoning: Kilogram is the standard unit for mass, a fundamental quantity. Newton is the unit for force, which is derived from mass, length, and time (kg m/s2).
Answer: Kilogram is a fundamental unit. Newton is a derived unit.
Example 3: Deriving a Unit Show how the unit for 'Acceleration' is derived from fundamental units.
Explanation: Acceleration is defined as the rate of change of velocity with respect to time. Velocity itself is length per unit time (m/s). Acceleration = Velocity / Time Unit of Velocity = m/s (from fundamental units metre and second) Unit of Time = s (fundamental unit second) Unit of Acceleration = (m/s) / s = m/s2 Conclusion: The unit for acceleration (m/s2) is a derived unit, obtained by combining the fundamental units of length (metre) and time (second).
Example 4: Identifying from a list (Nigerian context) A farmer measures the mass of yams in kilograms (kg) and calculates the volume of water in a tank in cubic metres (m3). Classify the bolded items as fundamental or derived.
Reasoning: Mass is one of the seven independent basic quantities. Kilogram is its corresponding basic unit. Volume is the product of three lengths, making it dependent on length. Cubic metre is the product of three metres.
Answer: Mass: Fundamental quantity.
Kilograms (kg): Fundamental unit.
Volume: Derived quantity.
Cubic metres (m3): Derived unit.
3. Teaching and Learning Activities Introduction (10 minutes): Teacher Activity: Begin by engaging students in a discussion about measurements they encounter daily.
For example: "How do we describe the size of a classroom?", "How do we measure the ingredients for Egusi soup?", "How do we know how long it takes to travel from Lagos to Ibadan?".
Student Activity: Students share their experiences and ideas on how various things are measured, mentioning quantities like length, time, mass, etc.
Teacher Activity: Introduce the concept of "physical quantities" and explain that some are basic, while others are combinations.
Activity 1: Exploring Quantities (15 minutes)
Teacher Activity: Write a diverse list of physical properties on the board (e.g., "length of this table", "weight of a bag of rice", "time for break", "speed of a bicycle", "amount of water in a bucket", "temperature of the room", "area of the blackboard").
Student Activity: In pairs or small groups, students discuss and classify these properties into two tentative categories: those that seem "basic" or "independent" and those that seem "complex" or "made up of other properties." They should attempt to justify their classifications.
Teacher Activity: Facilitate a brief class discussion where groups share their classifications. Do not yet introduce the terms "fundamental" or "derived." Guide students to see the inherent simplicity of some quantities versus the composite nature of others. *Activity 2: Formalizing Concepts of the room", "area of the blackboard").
Student Activity: In pairs or small groups, students discuss and classify these properties into two tentative categories: those that seem "basic" or "independent" and those that seem "complex" or "made up of other properties." They should attempt to justify their classifications.
Teacher Activity: Facilitate a brief class discussion where groups share their classifications. Do not yet introduce the terms "fundamental" or "derived." Guide students to see the inherent simplicity of some quantities versus the composite nature of others.
Activity 2: Formalizing Concepts (25 minutes)
Teacher Activity: Formally introduce and define Fundamental Quantities, listing the seven SI fundamental quantities and their corresponding Fundamental Units (metre, kilogram, second, ampere, kelvin, mole, candela). Provide clear examples for each, connecting them to real-life observations (e.g., "length of a road in metres," "mass of a person in kilograms," "time for a class period in seconds").
Teacher Activity: Formally define Derived Quantities and Derived Units. Use concrete examples to demonstrate how derived quantities and their units are formed by combining fundamental ones.
Example 1: Area. Explain Area = Length × Width. Show that if Length is 'm' and Width is 'm', then Area unit is 'm × m = m2'.
Example 2: Speed. Explain Speed = Distance / Time. Show that if Distance is 'm' and Time is 's', then Speed unit is 'm/s'.
Example 3: Density. Explain Density = Mass / Volume. Show that if Mass is 'kg' and Volume is 'm3', then Density unit is 'kg/m3'.
Student Activity: Students actively listen, ask clarifying questions, and take comprehensive notes in their notebooks. They should practice writing down the SI units and their symbols.
Activity 3: Application and Classification (20 minutes)
Teacher Activity: Write a mixed list of quantities and units on the board.
For example: "Mass," "Force," "Temperature," "Volume," "Joule," "Kilogram," "Metre per second," "Ampere," "Pascal," "Time," "Energy." Student Activity: Students, individually or in pairs, classify each item as either a fundamental quantity, derived quantity, fundamental unit, or derived unit. They should be prepared to justify their answers.
Teacher Activity: Go through the list item by item, asking students to share their classifications and justifications. Provide immediate feedback and correct any misconceptions. This reinforces the distinctions.
4. Guided Practice (With Solutions)
1. Question: Classify the following quantities as either Fundamental or Derived: (a) Length of a school compound (b) Volume of water in a borehole (c) Time taken to cook Jollof rice (d) Speed of a Keke Napep (e) Mass of a bag of cement (f) Force exerted by a person lifting a load Solution: (a)
Length of a school compound: Fundamental Quantity (b)
Volume of water in a borehole: Derived Quantity (c)
Time taken to cook Jollof rice: Fundamental Quantity (d)
Speed of a Keke Napep: Derived Quantity (e)
Mass of a bag of cement: Fundamental Quantity (f)
Force exerted by a person lifting a load: Derived Quantity
Commentary: This question directly targets the ability to distinguish between fundamental and derived quantities by providing common, relatable examples.
2. Question: Identify the following units as either Fundamental or Derived: (a) Kilogram (kg) (b) Metre per second (m/s) (c) Second (s) (d) Newton (N) (e)
Cubic metre (m3) (f)
Ampere (A)
Solution: (a)
Kilogram (kg): Fundamental Unit (b)
Metre per second (m/s): Derived Unit (c)
Second (s): Fundamental Unit (d)
Newton (N): Derived Unit (e)
Cubic metre (m3): Derived Unit (f)
Ampere (A): Fundamental Unit
Commentary: This question focuses on the units, ensuring students can apply the same classification logic to units as they do to quantities.
3. Question: Explain how the unit for Pressure (Pascal, Pa) is derived from fundamental SI units.
Solution: Pressure is defined as Force per unit Area (Pressure = Force / Area). Force is a derived quantity, and its unit (Newton, N) is derived from fundamental units as N = kg m/s
2. Area is a derived quantity, and its unit is m2 (metre × metre).
Therefore, the unit of Pressure = (Unit of Force) / (Unit of Area) = (kg m/s2) / m2 = kg / (m s2) = *kg