SHS2 Mathematics · Semester 1 Week 5: Real Number and Numeration System

Lesson notes

Learning Objectives

Indicator: 2.1.1.LI.2 - Use mathematical connections to explore the relevance of surds, indices and logarithms and their applications to scientific concepts.

By the end of the lesson, learners can:

Explain how logarithms connect to scientific concepts such as pH values in chemistry and exponential growth in biology.
Calculate pH values of common substances using the formula pH = -log[H⁺], where [H⁺] is the hydrogen ion concentration.
Solve exponential equations arising from scientific contexts using logarithms, showing all steps clearly.
Use a calculator to find common logarithms and apply them to interpret scientific data from Ghanaian or global examples.
Work collaboratively to investigate and present one real-life scientific application of surds, indices or logarithms, connecting mathematics to another subject.

This lesson builds on the work done in Weeks 1 to 4 on surds, indices, logarithm laws, and their application to real-life problems. It extends that work by making explicit mathematical connections to science subjects. The next week moves to modular arithmetic, so this lesson completes the work on logarithms and scientific applications.

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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.2 - Use mathematical connections to explore the relevance of surds, indices and logarithms and their applications to scientific concepts.
Suggested placement: Semester 1, Week 5 (Week 5 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.
Curriculum reference: NaCCA curriculum document, p. 169

Exemplars (from the NaCCA curriculum)

In collaborative groups:
- Assign tasks to help learners apply the understanding of common logarithms to solve real-life problems (i.e., relating to chemistry) if necessary, in a collaborative teaching with the experts (i.e., chemistry facilitator). For instance, calculating for pH values.
- Relate connecting Math to other subjects as a way of also connecting with other learners that although they are all different, there are some common values we all share.
Through a mini project, investigate the connections of logarithms to concepts such as algebraic equations. i.e., Logarithms can be used to solve algebraic equations where the unknown variable appears as a power
Example: Find the value of x if 200(1.1) = 20000 x Step 1. Simplify by dividing across by 200. Step 2. Take logs of both sides (1.1) x = 100 Step 3. Simplify as x = log(100) log(1.1) Step 4. Conclusion log(100) 2 = x = = 48.32 log(1.1) 0.0414
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 no depth-of-knowledge level for this indicator.