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.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.12 - Recall the processes of finding the domain, range, zero of a rational function and state when it is undefined.

Suggested placement

Semester 1, Week 13 (Week 13 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:

• indicator text - p.315: this page prints a complete, self-contained indicator - its own statement, pedagogies, examples and assessment 2.1.1.AS.10 - under the code 2.1.1.LI.10, which printed p.306 already uses under the same content standard 2.1.1.CS.3. The two indicators are unrelated (polynomial factors and zeros against the domain, range and zeros of a rational function), so merging them into one lesson would have lost curriculum and produced a lesson covering two topics. Filed as 2.1.1.LI.12, the next free number under this standard, because the database identifies a row by its content standard and indicator code and has no third discriminator; the printed code is 2.1.1.LI.10

Curriculum reference

NaCCA curriculum document, p. 315

Exemplars (from the NaCCA curriculum)

Collaborative Learning, Experiential Learning, Problem-based Learning, Project-based Learning and Talk for Learning
Activity: Recall basic facts about rational functions.
Collaborative Learning, Experiential Learning, Whole class discussion, Talk for Learning Approaches and Problem-based learning:
Learners work in pairs; one of the pairs decomposes the irrational function into partial terms, whiles the other composes the fractions back into a single function. Learners recall facts using graphs and by algebraic methods, the domains, range and zeros of rational function.
Example
- ! The domain of the function 𝑦 = is the set of all real numbers except 𝑥 = 2 i.e., the Domain 0*) of 𝑦 is {𝑥: 𝑥 ∈ 𝑅, 𝑥 ≠ 2}
- State the largest possible domain of the function defined by 𝑓: 𝑥 → )0 ! *20*. )0*!
- Learners recall processes for adding, subtracting, multiplying, dividing and simplifying rational function.
)0$ /A Example: Simplify 0 ! $,0A$"A !
Teaching and Learning Resources:
- Graph paper
- Ruler
- A scientific calculator
Assessment (2.1.1.AS.10). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding.