SHS2 Mathematics · Semester 1 Week 4: Real Number and Numeration System

Lesson notes

Learning Objectives

Indicator: 2.1.1.LI.1 - Investigate real life problems using laws and properties of indices and logarithms.

By the end of the lesson, learners can:

Identify the laws and properties of indices and logarithms needed to solve a given real-life problem.
Apply the laws of indices to solve problems involving exponential growth and decay in Ghanaian contexts.
Apply the laws of logarithms to solve problems involving unknown exponents in financial and scientific settings.
Justify their choice of strategy when solving a problem involving indices or logarithms.
Work collaboratively in mixed-ability groups to investigate and present solutions to real-life problems using indices and logarithms.

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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.2 - Demonstrate knowledge and understanding of the laws and properties of indices and logarithms and their applications to solving real-life problems. 2.1.1.LO.2 Apply the laws and properties of indices and logarithms to solve real life problems.
Indicator: 2.1.1.LI.1 - Investigate real life problems using laws and properties of indices and logarithms.
Suggested placement: Semester 1, Week 4 (Week 4 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.169: 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. 169

Exemplars (from the NaCCA curriculum)

- Develop a variety of strategies for solving problems involving indices and logarithms and their properties through interactive activities in mixed-ability groupings.
Hint: Possible strategies include establishing certain clues and properties before solving problems on indices and logarithms and, looking for patterns in the results, finding whether the equations have equal exponents and bases and determining the unknowns.
- Encourage learners to collaborate with team/group members and appreciate the worth of persevering to complete tasks successfully.
Examples: If x a y = = a , then x y and if x a b , then a b = x = Thus, exponents are the same since the bases are the same.
In mixed-ability groups, learners investigate and generalise radicals, discuss observations and use these to determine the range of permissible change of the selected numbers.

Figure from the shs2 mathematics curriculum, printed page 169

 Example: 2 2 = 2 2 , 5 5 5 , etc. = 5 3 3 24 24
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.1). The document marks these depth-of-knowledge levels for this indicator: Level 3 Strategic reasoning.