SHS1 Mathematics · Semester 1 Week 12: Applications of Expressions, Equations and Inequalities

Lesson notes

Learning Objectives

Indicator: 1.2.1.LI.4 - Analyse and apply operations on simple algebraic fractions involving monomial and binomial denominators and determine the conditions under which an algebraic fraction is zero or undefined.

By the end of the lesson, learners can:

State the conditions under which an algebraic fraction is zero or undefined (zero when the numerator is zero and the denominator is not zero; undefined when the denominator is zero).
Multiply and divide algebraic fractions with monomial and binomial denominators, simplifying the results completely.
Add and subtract algebraic fractions with monomial and binomial denominators, finding equivalent fractions with common denominators.
Find the value(s) of the variable that make a given algebraic fraction undefined by solving the equation formed when the denominator is set to zero.
Apply operations on algebraic fractions to solve routine problems and explain their reasoning using strategic thinking.

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Curriculum details

Strand: Algebraic Reasoning (Strand 2)
Sub-strand: Applications of Expressions, Equations and Inequalities (2.1)
Content standard: 1.2.1.CS.1 - Demonstrate knowledge and understanding of algebraic expressions and solve real-life problems on them. 1.2.1.LO.1 Formulate algebraic expressions using patterns to create models and solve real life problems (e.g., linear and quadratic models).
Indicator: 1.2.1.LI.4 - Analyse and apply operations on simple algebraic fractions involving monomial and binomial denominators and determine the conditions under which an algebraic fraction is zero or undefined.
Suggested placement: Semester 1, Week 12 (Week 12 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.60: this exemplar sets a two-dimensional construct - a stacked fraction, an index or a column vector - which the text layer flattens into separate lines, so the parts are present but their vertical arrangement is lost; read the page
Curriculum reference: NaCCA curriculum document, p. 59

Exemplars (from the NaCCA curriculum)

Group discussions, Problem-based Learning and Collaborative Learning.
Using Talk for Learning strategy, the class discuss and explain what an algebraic fraction is and use the idea to solve problems.
Example 1: Explain how operations involving algebraic fractions are applied; that is, when fractions are multiplied, their numerators are multiplied, and denominators are also multiplied, etc. m a ma E.g. × = n b nb When a fraction is divided by another, multiply the first fraction by the reciprocal of the second m a m b mb fraction. Thus ÷ = × = etc. n b n a na
Example 2: Extend the idea to perform operations on algebraic fractions, including monomial and binomial denominators.
E.g.: Multiply and divide algebraic fractions. Simplify the following: 2𝑥 × 2𝑦 i. 1 1 𝑥 2 +3 6𝑥+8 ii. ÷ 5𝑥 2 4
Example 2: Add and subtract algebraic fractions with binomial denominators. Simplify the following. 10 2 i. + 𝑥−4 𝑥+1 −1 − 6 ii. 3𝑥+4 2𝑥−1 𝑥 2𝑥 iii. − 𝑥+1 𝑥+2 𝑥 1 3 iv. + + 𝑥 2 −5𝑥+6 𝑥−2 𝑥−3
Collaborative Learning: Using think-pair-share in mixed-ability groups, learners identify and explain the condition under which an algebraic fraction is zero or undefined.
Example 1: Learners, after discussions, come out with the idea that an algebraic fraction is said to be undefined or have no meaning if the denominator is equal to zero and also zero if the numerator is zero. 3𝑎 E.g., Determine the condition under which is zero or undefined and determine the value of x that 𝑎−4 makes the expression undefined.
Solution 3𝑎 For to be zero, then 3𝑥 = 0 𝑎−4 3𝑎 For to be undefined, 𝑎 − 4 = 0 𝑎−4
To find the value of 𝑎 that makes the expression undefined, we take the denominator and solve for 𝑎 Therefore, the expression is undefined if 𝑎 = 4 .
Example 2: Determine the condition under which an algebraic expression is undefined. Find the value of 𝑥 that makes the expressions undefined. 3 i. 𝑥−1 (2𝑥−1)(𝑥−4) ii. 4𝑥 2 −1
2𝑥 + 5 𝑥 2 + 5𝑥 − 20
Teaching and Learning Resources:
- Algebraic tiles
- Patterns
- calculator
- technology tools such as
- computer
- mobile phone
- YouTube videos, etc.
- Paper grids
- Maths posters
- YouTube videos
- Whiteboard
- Pan balance
- Videos
- mini whiteboards or laminated white paper
- Dry-erase markers and erasers
Assessment (1.2.1.AS.4). The document marks these depth-of-knowledge levels for this indicator: Level 3 Strategic reasoning.