Real Number and Numeration… · SHS2 Mathematics

Lesson notes

Learning Objectives

Indicator: 2.1.1.LI.2 - Explain the concepts of indices and logarithms with examples.

By the end of the lesson, learners can:

Define an index (exponent) as a shorthand for repeated multiplication of a base, and identify the base and index in expressions such as 5³ and 2⁴.
State and apply at least four laws of indices (product law, quotient law, power law, and zero exponent law) to simplify numerical expressions.
Define a logarithm as the inverse operation of index (if aⁿ = b, then logₐ b = n) and convert between index form and logarithmic form.
Evaluate simple logarithms such as log₂ 8, log₃ 81, and log₁₀ 1000 without a calculator.
Explain, with at least one real-life example, how indices and logarithms are used in everyday activities such as population growth, sound measurement, or mobile money calculations.

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Curriculum details

Strand: Numbers for Everyday Life (Strand 1)
Sub-strand: Real Number and Numeration System (1.1)
Content standard: 2.1.1.CS.1 - Demonstrate knowledge and understanding of surds, indices and logarithms and establish their laws and properties. 2.1.1.LO.1 Evaluate the relationships between the laws and properties of surds, indices and logarithms and apply them to solve problems with radicands.
Indicator: 2.1.1.LI.2 - Explain the concepts of indices and logarithms with examples.
Suggested placement: Semester 1, Week 2 (Week 2 of the year)
Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.
Source document note: The official curriculum document has a fault in this entry, so the curriculum text above is transcribed exactly as printed:

exemplars - p.166: this exemplar sets a two-dimensional construct - a stacked fraction, an index or a column vector - which the text layer flattens into separate lines, so the parts are present but their vertical arrangement is lost; read the page
Curriculum reference: NaCCA curriculum document, p. 165

Exemplars (from the NaCCA curriculum)

Talk for Learning: In interactive, collaborative and gender-responsive groupings, describe the concept of indices through repeated multiplication of a given base. Learners carry out these activities to understanding promote the use of appropriate technology (calculators, computers, and other tools), leading to the development of learners' technology Literacy Skills for everyday life, further studies and/or the world of reasoning work.
Examples
a 1 = a
a 2 = a × a
a 3 = a × a × a 4 a = a × a × a × a

The definition a to the power n = a times a times a times ... times a. — A displayed definition of an index: a to the power n equals a times a times a times, and so on, times a.

a n = a × a × a × × a
3 3 × 3 4 = ( 3 × 3 × 3 ) × ( 3 × 3 × 3 × 3 ) =2 7
Compose the various indicial laws such as 1. Addition Product Law 2. Subtraction-Quotient Law 3. Index (Power) Law 4. product-index law 5. Quotient - index law 6. Fractional Power (or Root) Law 7. Zero Exponent or Index 8. Negative Integer Exponents and use them to solve real life problems.
Teaching and Learning Resources:
- * Geodot * Rubber bands * Computer
- * GeoGebra * Google search * Mobile phone
- Calculator
- YouTube videos, etc.
- Geodot,
- Rubber bands
- Cardboards
- Measuring instruments
Assessment (2.1.1.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 4 Extended critical thinking and reasoning.
Skills of conceptual Strategic