SHS2 Mathematics · Semester 1, Week 3
Real Number and Numeration System
Lesson notes
Learning Objectives
Indicator: 2.1.1.LI.3 - Compose and decompose logarithm laws and properties with exponents and apply the concepts to solve real-life problems.
By the end of the lesson, learners can:
- State the three basic laws of logarithms (addition-product, subtraction-quotient, and exponent law) using correct mathematical vocabulary.
- Compose logarithm expressions into single logarithms using the addition-product and subtraction-quotient laws.
- Decompose single logarithms into sums, differences, or multiples using the logarithm laws.
- Apply logarithm laws to evaluate numerical expressions without a calculator.
- Solve at least one real-life problem involving logarithms in base ten, such as comparing magnitudes or sound intensity levels.
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Sign in with phone numberCurriculum 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.3 - Compose and decompose logarithm laws and properties with exponents and apply the concepts to solve real-life problems.
- Suggested placement
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Semester 1, Week 3
(Week 3 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
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The official curriculum document has a fault in this entry, so the curriculum text above is transcribed exactly as printed:
- exemplars - p.167: 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. 166
Exemplars (from the NaCCA curriculum)
Using group work and think-pair-share activities, extend the idea of exponents to logarithms in base ten. Then, review and investigate the concept of logarithm as an exponent to which a base is raised to produce a given number or power. Encourage Talk for Learning and draw learners' attention to the importance of listening to one another and respecting each other's views. In collaborative and gender-responsive groups, investigate to discover the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. In doing so, ensure diversity and offer equal opportunities for learners to interact with the lesson and learning materials. Examples: i.e. log 𝑏 𝑥 = 𝑦 , E.g., for 𝑥 = 𝑏 𝑦 , 𝑦 is the index or exponent, and 𝑏 is the base. The logarithm y is the exponent to which b is to be raised to get . In other words, the log of a number "x" to a given base "b" is equal to the exponent "y". log 10 2 = 0.30102999566398119521373889472449 ⇒ 10 0.30102999566398119521373889472449 = 2 No. 0 1 2 3 4 2 1 2 3 2 4 Powers 2 0 2 2 Base 2 1 2 4 8 16 ... ... ... ... ... ... Base 1 10 100 1000 10000 10 Figure 2.3 Using Project-based Learning, task learners to establish the laws and properties of indices for any real number 𝑎 and natural numbers 𝑚 and 𝑛. The laws and properties are applicable: Examples a. Addition Product Law, The Subtraction-Quotient Law, The Index (Power) Law, The product-index law, the Product - index law Quotient - index law, Fractional Power (or Root) Law, The Zero Exponent or Index, Negative Integer Exponents, etc. b. The Addition-Product Law log a k +log b k = log ab k . The Addition-Product Law log k a + log k b = log k a b a The Subtraction-Quotient Law log k a −log k b = log k b The exponent law: log a b m = m log a b Same base law: log b a = 1 log b Change of base law: log a b = log k a k The characteristic is 0 and the mantissa is 0.5441. Discuss the logarithms of numbers less than 1. 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.3). The document marks these depth-of-knowledge levels for this indicator: Level 4 Extended critical thinking and reasoning.