Application of Algebra · SHS2 Additional…

Lesson notes

Learning Objectives

Indicator: 2.1.1.LI.1 - Review indices and apply the idea to create and solve real life problems involving indices.

By the end of the lesson, learners can:

State the laws of indices (multiplication, division, power of a power, zero, negative, and fractional indices) from memory and apply them to simplify algebraic expressions.
Simplify expressions involving indices by applying the correct law at each step and justifying the choice of law.
Solve exponential equations of the form aˣ = b by expressing both sides in the same base where possible.
Solve simultaneous equations involving indices by converting to linear equations and solving the resulting system.
Create and solve a real life problem involving indices drawn from a context such as population growth, cell division, or financial calculations.

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Curriculum details

Strand: Modelling with Algebra (Strand 1)
Sub-strand: Application of Algebra (1.1)
Content standard: 2.1.1.CS.3 - Demonstrate understanding of the laws and properties of indices and apply the ideas to solve problems. 2.1.1.LO.1 Investigate De Morgan's law on sets algebraically and graphically, formulate and solve real life problems up to three sets. 2.1.1.LO.2 Model sequence recursively and explicitly, and establish the relationship between the two forms, as well as solve real life problems involving linear and exponential sequences and series. 2.1.1.LO.3 Apply indices and logarithms to solve real life problems, including logarithms with different bases, and sketch and interpret logarithmic functions. 2.1.1.LO.4 Formulate and derive appropriate strategies to solve quadratic inequalities. 2.1.1.LO.5 Graph systems of given inequality and identify the region that provides the feasible solution and apply it to real life situations. 2.1.1.LO.6 Determine the set of values for which a rational function is defined and resolve rational functions into partial fractions. 2.1.1.LO.7 Multiply matrices, determine the inverse of a 2 x 2 matrix, find the determinant up to a 3 x 3 matrix and represent matrices in linear transformations.
Indicator: 2.1.1.LI.1 - Review indices and apply the idea to create and solve real life problems involving indices.
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. 289

Exemplars (from the NaCCA curriculum)

Collaborative Learning: Learners work in convenient groups (ability, mixed-ability, mixed gender, etc.) to model real life problems involving indices and logarithms and present answers.
Talk for Learning Approaches: Learners engage in brainstorming, think-pair-share, building on what others say, debates and discussions to explain how to solve problems involving indices and logarithms and the relationship between the two concepts.
Project-based Learning: Engage learners to come up with graphs and solutions of logarithmic functions modelled from real life contexts.
Experiential Learning: Learners practice hands-on activities (learning by doing) by manipulating symbols, using any spreadsheet programme such as Microsoft Excel and ICT tools such as GeoGebra to draw graphs of logarithmic functions and explain their solution process.
Problem-based earning: Learners to investigate and explain real life models of logarithmic functions and talk about what happens when specific conditions are varied/imposed.
Activity: Application of the Laws of indices Use Talk for Learning Approaches, Problem-based, Experiential and Collaborative Learning Approaches to solve problems related to the application of the laws of indices. Learners working with a partner or in small groups recall and investigate properties of indices and make deductions from the laws.
Example $ 2 * !
- Simplify i ). j $ $ (!$0) ! *)0(!$0) . !
- Simplify $ (!$0) !
Learners working with a partner or in small groups apply the laws of indices to solve problems.
Example !
- Solve 3 )% = 1! $ "
- 16 × 2 = 8 ' 0 (
- Solve the simultaneous equations: ! )0 ! A$) 3 0*! = 27 A*! and i " j = i 2 j
Teaching and Learning Resources:
- Graph paper
- Ruler
- A scientific calculator
Assessment (2.1.1.AS.1). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall; Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning; Level 4 Extended critical thinking and reasoning.