SHS1 Additional Mathematics · Semester 1 Week 6: Number and Algebraic Patterns

Lesson notes

Learning Objectives

Indicator: 1.1.1.LI.5 - Pose and solve simple equations involving indices.

By the end of the lesson, learners can:

Express both sides of a simple indicial equation as powers of the same base to solve for the unknown.
Solve equations of the form a^x = b by converting b to a power of a, where a and b are positive integers.
Solve simultaneous equations involving indices by expressing both equations in index form and equating exponents.
Create their own simple indicial equations and swap them with peers for solving, applying the laws of indices correctly.
Verify solutions to indicial equations by substituting the answers back into the original equation.

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Curriculum details

Strand: Modelling with Algebra (Strand 1)
Sub-strand: Number and Algebraic Patterns (1.1)
Content standard: 1.1.1.CS.2 - Demonstrate knowledge and understanding of numbers in relation to Surds, Indices and Logarithms. 1.1.1.LO.1 Solve problems involving properties of binary operations. 1.1.1.LO.2 Model and solve real life problems on sets. 1.1.1.LO.3 Expand binomials with positive integral indices and simplify coefficients of the terms. 1.1.1.LO.4 Perform basic operations on surds as well as solve simple indicial and logarithmic equations.
Indicator: 1.1.1.LI.5 - Pose and solve simple equations involving indices.
Suggested placement: Semester 1, Week 6 (Week 6 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:

content standard text - p.53: the source prints the content-standard code as 1.1.1.CS2 without the separator before 2; the CSV key uses 1.1.1.CS.2 so the otherwise unambiguous second standard can be imported
exemplars - p.60: adjacent duplicated CambriaMath characters were collapsed, but this PDF also maps some equation glyphs to the wrong letter or operator; verify every mathematical expression in this row against the rendered page
exemplars - p.61: a stacked fraction, matrix, vector or other two-dimensional construct is flattened by the text layer; all visible parts require comparison with the rendered page
Curriculum reference: NaCCA curriculum document, p. 60

Exemplars (from the NaCCA curriculum)

Collaborative Learning, Talk for Learning, Building on what others say.
Learning Experience: Learners in groups solve simple equations involving indices.
Activity 1: Solving simple indicial equations. Learners in their groups apply their knowledge in solving linear equations and indices to solve problems.
Example: Given that 𝑦 − 2𝑥 and 3 0$A = 27, Find 𝑥
Solution 3 0$A = 27 3 0$)0 = 3 " 𝑥 + 2𝑥 = 3 ∴ 𝑥 = 1
Activity 2: Learners in groups create similar problems on the application of linear equations and indices to solve problems.
Activity 3: Learners in groups apply their knowledge in solving simultaneous equations and indices to solve problems.
Example: Solve the simultaneous equations 1 9 )&$' = 729 3 & l9 ' n = 27 Expected Solution: 𝑎 = −3 and 𝑏 = 3
Teaching and Learning Resources:
- Textbooks
- Curriculum
- Cardboards
- Reading resource
- Colour pens
- Notebook
- Technological tools
Assessment (1.1.1.AS.5). The document marks these depth-of-knowledge levels for this indicator: Level 3 Strategic reasoning; Level 4 Extended critical thinking and reasoning.
Solve the simultaneous equations 9 )&$' = 2187 and 3 & × 9 ' = 27