Application of Algebra

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.6 - Use a graphical approach (by hand and technology) to solve simultaneous linear inequalities.

Suggested placement

Semester 1, Week 9 (Week 9 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.298: 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. 298

Exemplars (from the NaCCA curriculum)

Collaborative Learning: Learners to work in convenient groups (ability, mixed-ability, mixed gender, etc.) to model real life problems involving linear inequalities and present answers.
Talk for Learning Approaches -learners engage in brainstorming, think-pair-share, building on what others say, debates and discussions, etc., to explain how they model real life linear inequalities.
Project-based Learning: Learners to come up with graphs and solutions of a system of linear inequalities modelled from real life contexts.
Experiential Learning: Engage learners in hands-on activity (learning by doing) by manipulating symbols, using Microsoft Excel spreadsheets and ICT tools such as GeoGebra to sketch real life linear inequalities and explain their solution process.
Problem-based Learning: Learners investigate and explain real life models of linear inequalities and talk about what happens when specific conditions are varied/imposed
Activity: Solutions of systems of linear inequalities.
Collaborative Learning, Problem-based Learning, Experiential Learning and Talk for Learning Approaches: Learners work together from whole class discussions to small convenient groups, then pair work:
- recognise and classify linear inequality as a mathematical statement containing the inequality signs ( >, <, ≥, 𝑜 ≤) instead of an equal sign (=) and create real life context that models linear inequalities.
Example
- A phone company charges 50 pesewas per minute during the daytime and 10 pesewas per minute at night. How many daytime minutes and night-time minutes could you use in one week if you wanted to pay less than GHC 20? Write a mathematical sentence to model the word problem
- Formulate a word sentence that models the inequalities: (i) 4𝑥 + 3 < 15 (ii) 2𝑥 + 3𝑦 ≥ 12
- Solve systems of linear inequalities by algebraic means and graphical solutions using appropriate technology and manually.
Example Find the integer values of 𝑥 satisfying the inequality: 6 < 2- 3𝑥 < 14
Solution: Write 6 < 2- 3𝑥 < 14 as two separate inequalities and solve them separately. 6 < 2 - 3𝑥 3𝑥 < 2 - 6 3𝑥 <- 4 , 𝑥 < − " ; also 2 - 3𝑥 < 14 - 3𝑥 < 14- 2 - 3𝑥 < 12 3𝑥 > - 12 𝑥 >- 4 , Common values: - 4 < 𝑥 < − " : The integer values of 𝑥 are - 3 and - 2
Teaching and Learning Resources:
- Graph paper
- Ruler
- A scientific calculator
Assessment (2.1.1.AS.6). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning; Level 4 Extended critical thinking and reasoning.