SHS3 Mathematics · Semester 1, Week 4
Proportional Reasoning
Full lesson notes coming
Notes for this lesson are being prepared. The curriculum details below are complete and ready to use for your planning.
Curriculum details
- Strand
- Numbers for Everyday Life (Strand 1)
- Sub-strand
- Proportional Reasoning (1.2)
- Content standard
- 3.1.2.CS.2 - Demonstrate a conceptual understanding of proportionality in relation to variation and use it to solve real-life problems. 3.1.2.LO.2 Analyse the impact of variations and conduct simple investigations in solving date-to-day problems.
- Indicator
- 3.1.2.LI.1 - Use proportional reasoning to investigate the various types of variation (direct and inverse) and extend this to make generalisations.
- Suggested placement
-
Semester 1, Week 4
(Week 4 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. 306
Exemplars (from the NaCCA curriculum)
Using group/collaborative strategies, engage learners to establish the concepts of variation (direct, inverse variations), relate them to scientific concepts and use them to solve real life problems. Be aware of instilling leadership, respect for others' opinions, commitment to excellence achievement, discipline and self-confidence and with supportive differentiated instruction to make appropriate generalisations through critical thinking and problem-solving strategies. Examples 1. Direct Variation: The growth of a variable results in the growth of another variable. Eg.1 The area of a given circle is directly proportional to the square of its radius. A ∝ r 2 ⇒ A = π r 2 Eg.2 The more kilometres you travel, the more petrol you will have to use (direct variation). 2. Inverse Variation: The growth of a variable results in the degeneration of another variable. E.g. 3 The longer the term of your subscription, the less you will have to pay per year. E.g. 4 varies inversely as if there exists a real number such that. 1 k t ∝ ⇒ t = v v Teaching and Learning Resources: - * Teaching and Learning Resources * Manipulative (dice, coins, spinners, playing cards, counters, * Task Cards digit cards), * Simple Probability Mazes (Printable & Digital), - * Worksheets Assessment (3.1.2.AS.1). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding.