Applications of Algebra · SHS1 Additional…

Lesson notes

Learning Objectives

Indicator: 1.1.2.LI.17 - Carry out the basic arithmetic operations on rational functions.

By the end of the lesson, learners can:

Identify a rational function as a ratio of two polynomials and state the condition under which it is undefined.
Factorise the numerators and denominators of rational functions to simplify them fully.
Add and subtract rational functions by finding a common denominator.
Multiply and divide rational functions, stating any restrictions on the variable.
Apply the four basic arithmetic operations on rational functions to solve problems set in practical contexts.

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Curriculum details

Strand: Modelling with Algebra (Strand 1)
Sub-strand: Applications of Algebra (1.2)
Content standard: 1.1.2.CS.1 - Demonstrate knowledge and understanding of applying algebraic processes and reasoning involving sequence, functions, and linear programming. 1.1.2.LO.1 Examine, analyse, determine and predict other terms in a pattern/sequence. 1.1.2.LO.2 Distinguish among various types of relations, find the domain and range of, and evaluate functions. 1.1.2.LO.3 Show that a function is injective (into) and/or surjective (onto). Find the inverse, describe the relationship between two variables and establish composite functions. 1.1.2.LO.4 Graph linear and quadratic functions and determine the intercepts. 1.1.2.LO.5 Find graphical and algebraic solutions to a system of three linear equations in three variables and apply them to solve real life problems. 1.1.2.LO.6 Perform algebraic manipulations on polynomial functions and graph polynomial functions. 1.1.2.LO.7 Find the domain, range, and zero of a rational function and state when it is undefined. 1.1.2.LO.8 Identify and describe the order of a matrix, the identity matrix and the zero matrix; find the determinant and perform basic arithmetic operations on 2 by 2 matrices (addition and subtraction).
Indicator: 1.1.2.LI.17 - Carry out the basic arithmetic operations on rational functions.
Suggested placement: Semester 1, Week 17 (Week 17 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. 119

Exemplars (from the NaCCA curriculum)

Activity 1: Basic arithmetic operations on rational numbers.
Collaborative Learning, Experiential Learning, Whole class discussion, Talk for Learning Approaches and Problem-based Learning:
- Learners work in groups/pairs to perform basic operations on rational functions.
- Learners explore factorisation and expansion of denominators and numerators to simplify rational functions.
)0$ /A Example: Simplify 0 ! $,0A$"A ! Learners express rational functions into the same denominator to add and subtract.
)0*! 0*" Example: Simplify − 0$" 0*)
Teaching and Learning Resources:
- Cut out shapes of different colours and orientation
- Maths Technology learning apps, tools and devices
- Chalkboard illustrations
- Worksheets
- Cut-out geometrical shapes of different colours and orientation
Assessment (1.1.2.AS.17). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall; Level 2 Skills of conceptual understanding.