Organising and Representing and Interpreting Data

Curriculum details

Strand

Handling Data (Strand 4)

Sub-strand

Organising and Representing and Interpreting Data (4.1)

Content standard

3.4.1.CS.2 - Demonstrate an understanding of relationship arising from cause and effect or contribution of one or more variables to another. 3.4.1.LO.1 Describe the nature and strength of relationship between two given variables using scatter diagram and correlation coefficient. 3.4.1.LO.2 Model and solve problems using regression analysis.

Indicator

3.4.1.LI.2 - Fit a linear function to a given data and use the line of best fit to solve problems in the context of the data.

Suggested placement

Semester 2, Week 14 (Week 34 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.546: adjacent duplicated CambriaMath characters were collapsed, but this PDF also maps some equation glyphs to the wrong letter or operator; verify every mathematical expression in this row against the rendered page
• exemplars - p.547: a stacked fraction, matrix, vector or other two-dimensional construct is flattened by the text layer; all visible parts require comparison with the rendered page

Curriculum reference

NaCCA curriculum document, p. 546

Exemplars (from the NaCCA curriculum)

Talk for Learning, Think-pair-share, Experiential Learning; and Group Work/Collaborative Learning.
Learning Experience: Learners in groups brainstorm to find the line of best fit for better accuracy using least square method.
Activity 1: Line of best fit Learners in groups draw a tabular representation for a given data set. Learners in groups use the formula ∑ # =0 6 *0>dA 6 *Ae 67$ 𝑚 = to estimate slope the line of best fit and use these to construct a table with the ! ∑ # =0 6 *0> 67$ details in the formula. Learners work to obtain the 𝑦 − 𝑖 using the formula of equation of a line.
Example 1: Use the least square method to determine the equation of best fit of the line for the given data and plot the graph. 𝑥 8 2 11 6 5 4 12 9 6 1 𝑦 3 10 3 6 8 12 1 4 9 14
Solution NB: 𝑥 = 6.4 and 𝑦 = 7
𝑥 𝑦 l𝑥 L − 𝑥n i𝑦 L ) l𝑥 L − 𝑥n i𝑦 L l𝑥 L − 𝑥n
− 𝑦j − 𝑦j
8 3 1.6 -4 -6.4 2.56 2 10 -4.4 3 -13.2 19.36 11 3 4.6 -4 -18.4 21.16 6 6 -0.4 -1 -0.4 0.16 5 8 -1.4 1 -1.4 1.97 4 12 -2.4 5 -12 5.76 12 1 5.6 -6 -33.6 31.36 9 4 2.6 -3 -7.8 6.76 6 9 -0.4 2 -0.8 0.16 1 14 -5.4 7 -37.8 29.16 𝛴 = -131 118.4
∑ %L4! l𝑥 L − 𝑥n i𝑦 L − 𝑦j 131 ∴ 𝑚 = = ) ∑ %L4! l𝑥 L − 𝑥n 118.4
= −1.1 To find the 𝑦 − 𝑖, the equation of the line is given as 𝑦 = 𝑚𝑥 + 𝑏 ∴ 7 = (−1.1 × 6) + 𝑏 𝑏 ≈ 14 Therefore, the equation of the best-fit line is 𝑦 = −1.1𝑥 + 14
Activity 4: Learners work in groups sketch of 𝑦 = −1.1 + 14 in graph sheets.
Activity 5: Learners work in groups to solve given examples and use the equation of best fit to estimate values within the domain and the range of the data. Learners to model their own data and use the idea of line of best fit to arrive at estimated values.
Teaching and Learning Resources:
- ICT tools
- Calculators
- SHS curriculum
Assessment (3.4.1.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning.