Proportional Reasoning

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.2 - Use proportional reasoning to investigate the various types of variation (joint and partial) and extend this to make generalisations.

Suggested placement

Semester 1, Week 5 (Week 5 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 discuss direct and inverse variations to establish joint and partial variations, relate them to scientific concepts and use them to solve real life problems. Take note of introducing leadership, respect for team members' views, commitment to excellence achievement, discipline and self-confidence.
Example 1 1. Joint Variation
E.g. 5 Establish the connection between a variable and other variables that are either directly or inversely related. i.e. F ∝ m 1 m 2 , and , F ∝ d 2 mm ⇒ F = G 1 2 2 d
2. Partial Variation
Establish the equation of a straight line as an example of a variation of this form: = y ax + c
where the value 𝑦 is partly constant and partly varies as the value 𝑥.
Example 2: Investigate the possible areas of applications of variations in real life situations.
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.2). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall.