Application of Algebra

Lesson notes

Curriculum details

Strand

Modelling with Algebra (Strand 1)

Sub-strand

Application of Algebra (1.1)

Content standard

2.1.1.CS.2 - Demonstrate the ability to apply algebraic processes and reasoning to model and solve real life situations involving sequences, and linear programming and use appropriate techniques to solve quadratic inequalities, as well as resolve rational functions. 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.3 - Determine the arithmetic and geometric means of linear and exponential sequences and apply linear and exponential sequences to solve real life problems.

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.287: 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

Curriculum reference

NaCCA curriculum document, p. 287

Exemplars (from the NaCCA curriculum)

Collaborative Learning, Experiential Learning, Problem-based Learning and Talk for Learning approaches
Activity: Arithmetic and geometric means of sequences.
Use Collaborative Learning, Experiential Learning, Problem-based Learning and Talk for Learning approaches to support learners in solving problems related to geometric and arithmetic means of sequences: Learners in small mixed-ability/gender groups discuss arithmetic and geometric means outlining their differences and similarities and extending the conversation to include;
- how to insert means between given sequences;
- when to use either means in contexts.
Example
- The three numbers, n − 2, 𝑛 , n + 3, are consecutive terms of a G.P. find n, and the term after n+3.
- Insert three arithmetic means between 25 and 9.
- Insert three geometric means between 243 and 48.)
The geometric mean between 2 and 8 is 4, and two arithmetic means between 2 and 8 are 4 and 6.
Teaching and Learning Resources:
- Worksheets
- Scientific Calculator
- Technological tools, apps, etc.
- SHS Additional Mathematics Curriculum
Assessment (2.1.1.AS.3). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding; Level 4 Extended critical thinking and reasoning.