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.1 - Demonstrate the ability Establish De Morgan's laws of set theory and use it to solve related problems. to use sets properties and theories to solve real Pedagogy and Learning Experience life problems and apply Collaborative Learning: Learners work in convenient groups (ability, mixed-ability, mixed gender, or binomial theorem to approximate numbers to a given index. 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 - pairs etc.) and use analytic and graphic illustrations to verify De Morgan's laws and other laws of set algebra. Level 3 Strategic

Suggested placement

Semester 1, Week 1 (Week 1 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.276: 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. 276

Exemplars (from the NaCCA curriculum)

Talk for Learning Approaches: Learners brainstorm using strategies such as think-pair-share/square, debates and discussions to explain why a proof of a set property or laws of set algebra is true or false.
Experiential Learning: Learners collaboratively (pair and group work) verify and use graphic illustrations and algebraic manipulations to establish properties of sets and laws of set algebra.
Activity 1: Use graphical representations (e.g., Venn diagrams) and algebraic methods (reasoning) to establish De Morgan's Laws and other laws of set algebra focusing on the complement, union, and intersection of sets.
Using Talk for Learning Approaches in collaborative groups, learners investigate and establish the laws of set algebra, including De Morgan's Laws, using Venn diagrams and by algebraic analysis.
Example
- Show by graphical and algebraic analysis that for any non-empty sets A, B and C, (i)(𝐴 ∪ 𝐵) - =𝐴 - ∩ 𝐵 -

Algebraically ⇔ Let, then thus or
and x ∈
and so
Again, let x . Then and x ∈, thus and
,
Hence =

 (ii)(𝐴 ∩ 𝐵) - = 𝐴 - ∪ 𝐵 - Algebraically
Let x . Then or x ∈, thus and ⇔ ,
Hence =
Let, and x ∈, then thus or and so
- Using a venn diagram, shade the regions represented by:
- (𝐴 ∪ 𝐵) ∩ 𝐶 -
- (𝐴 ∪ 𝐵)' ∩ 𝐶 -
- (𝐴 ∩ 𝐵)' ∪ 𝐶 -
- Rewrite the following:
- (A' ∪ B')'
- (A' ∩ B ' )'
Teaching and Learning Resources:
- ICT tools and resources
- Worksheets
- Scientific calculator
- Technological tools, apps, etc.
- SHS Additional Mathematics Curriculum
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.
reasoning