SHS3 Mathematics · Semester 1, Week 9
Patterns and Relations
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Curriculum details
- Strand
- Algebraic Reasoning (Strand 2)
- Sub-strand
- Patterns and Relations (2.2)
- Content standard
- 3.2.2.CS.1 - Demonstrate understanding of the concept of quadratic functions and equations and solve real-life problems with them. 3.2.2.LO.1 Solve problems on quadratic functions and equations, including real-life problems.
- Indicator
- 3.2.2.LI.1 - Identify and solve quadratic equations.
- Suggested placement
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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
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The official curriculum document has a fault in this entry, so the curriculum text above is transcribed exactly as printed:
- exemplars - p.312: the equation text on this page is set in a CambriaMath subset whose /ToUnicode map doubles every letter and gets many of them wrong, and the glyph ids could not be lined up with the extraction to repair it, so any italic variable here may be doubled or be the wrong letter; read the page
- Curriculum reference
- NaCCA curriculum document, p. 312
Exemplars (from the NaCCA curriculum)
Using group Work/Collaborative Learning strategy: review learners' knowledge of quadratic expressions, deal with their misconceptions about such concepts, and extend the ideas to quadratic equations and functions using GeoGebra. Example: A quadratic expression contains only a quadratic term, and it is in the form 𝑎𝑥 2 + 𝑏𝑥 + 𝑐. Where 𝑎. , 𝑏. , 𝑐 are constants and 𝑎 ≠ 0 example 2𝑥 2 + 2𝑥 − 6 while a quadratic equation contains a quadratic expression that is equal to any other expression. It is also in the form 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0. Example 2𝑥 2 + 2𝑥 − 6 = 6. Using group Work/Collaborative learning strategy: review learners' knowledge on how to solve quadratic expressions using the factorization method. Example: Factorise 𝑥 2 − 2𝑥 − 3 completely. Solution: Find two numbers that, if you multiply, will give you -3, but if you add, will give you −2. 𝑥 2 − 3𝑥 + 𝑥 − 3 (𝑥 2 − 3𝑥)(𝑥 − 3) Factor the common factors out. 𝑥(𝑥 − 3) + 1(𝑥 − 3) Add the terms outside and multiply by one of the common terms to give the final result. (𝑥 + 1)(𝑥 − 3) Collaborative Learning: In convenient groups, engage learners to explore why 𝑎 ≠ 0 in a quadratic equation. Example: Learners should be encouraged to put the value of 𝑎 = 0 into the standard form of a quadratic equation. Think-pair-share activities: In pairs, task learners to solve a contextual problem that involves quadratic equations using the factorisation method. Example: Solve the following equations. 1. 𝑥𝑥 2 − 9𝑥𝑥 = 14 2. 2𝑥𝑥 2 − 5𝑥𝑥 = 3 3. (𝑥𝑥 − 2)(𝑥𝑥 + 6) = 0 4. 𝑥𝑥 2 − 16 Example: Madam Alamisi has a rectangular board of area 14𝑚𝑚 2 and perimeter of 18 metres. Find the dimensions of her rectangular board. Solution: Let w = width, and l = length
Think: 2𝑙𝑙 + 2𝑤𝑤 = 18 ... ... ... 1 ⇒ 𝑤𝑤 = 9 − 𝑙𝑙 ... ... ... 2 𝑙𝑙 × 𝑤𝑤 = 14 ... ... ... 3 𝑙𝑙(9 − 𝑙𝑙) = 14 9𝑙𝑙 − 𝑙𝑙 2 = 14 𝑙𝑙 2 − 9𝑙𝑙 + 14 = 0 (𝑙𝑙 − 2)(𝑙𝑙 − 7) = 0 ∴ 𝑙𝑙 = 2 𝑎𝑎𝑎𝑎𝑎𝑎7 𝑤𝑤 = 7, 𝑤𝑤ℎ𝑒𝑒𝑒𝑒 𝑙𝑙 𝑖𝑖𝑖𝑖 2 𝑤𝑤 = 2, 𝑤𝑤ℎ𝑒𝑒𝑒𝑒 𝑙𝑙 𝑖𝑖𝑖𝑖 7 ∴ 2 × 7 = 14 and 2(2) + 2(7) = 18 Teaching and Learning Resources: - Teaching and Learning Resources - Manipulative (dice, coins, spinners, playing cards, counters, digit cards), - Simple Probability Mazes (Printable & Digital), - Worksheets - Task Cards Assessment (3.2.2.AS.1). The document marks these depth-of-knowledge levels for this indicator: Level 3 Strategic reasoning.