SHS3 Mathematics · Semester 2, Week 14

Statistical Reasoning and Its Application in Real Life

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Curriculum details

Strand: Making Sense of and Using Data (Strand 4)
Sub-strand: Statistical Reasoning and Its Application in Real Life (4.1)
Content standard: 3.4.1.CS.2 - Demonstrate the ability to compare different data sets and use appropriate vocabulary to contribute to mathematical and everyday discussions and make inferences about the information gathered. 3.4.1.LO.2 Compare different datasets and use mathematical vocabulary and language (concretely, pictorially, symbolically, spoken or written, etc.) to contribute to mathematical and everyday discussions using valid and reliable data to explain and justify the information produced from the data.
Indicator: 3.4.1.LI.1 - Compare the quality of different datasets using knowledge and skills acquired from data analysis techniques you learned in earlier statistics work.
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.373: 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. 373

Exemplars (from the NaCCA curriculum)

Experiential Learning: In convenient groups, tasks learners to compare the quality of given data sets and draw conclusions on the appropriateness of the data in relation to the purpose of the data and its analysis techniques.
Example: Data was taken on the heights of twelve SHS 3 learners in Joaboso Senior High School. The tables below show how two researchers recorded the same data (heights of the students in centimetres and in metres rounded to the nearest tenth).

Two tables of eleven students' heights, one in centimetres to one decimal place and one in metres. — Two tables side by side, A and B, each headed Student and a height column. In A the heights are in centimetres: 170.1, 173.4, 174.1, 175.1, 175.9, 173.2, 175.0, 175.2, 175.6, 173.0 and 175.7. In B the same eleven students' heights are in metres, rounded to one decimal place: 1.7, 1.7, 1.7, 1.8, 1.8, 1.7, 1.8, 1.8, 1.8, 1.7 and 1.8.

 A B Student Student Height Height (cm) (m) 1 1 170.1 1.7 2 2 173.4 1.7 3 3 174.1 1.7 4 4 175.1 1.8 5 5 175.9 1.8 6 6 173.2 1.7 7 7 175.0 1.8 8 8 175.2 1.8 9 9 175.6 1.8 10 10 173.0 1.7 11 11 175.7 1.8

Two small tables pairing 12 with 175.2 and 12 with 1.8. — Two small two-cell tables side by side. The first pairs 12 with 175.2 and the second pairs 12 with 1.8.

 12 12 175.2 1.8
i. Which of the two data sets gives a better representation of the heights of the students? ii. Which of the data sets will aid easy analysis and interpretations, and why? Using think-pair-share activities, task learners to make inferences from a given data and give reasons for their choices. Offer other learners the opportunity to make their own inferences as long as they are referring to the data.
Example: The chart below shows the number of hungry people in the world by year from 2000 to 2018.

3-D bar chart of hungry people worldwide by year: 900m in 2000, 945m in 2005, 821m in 2010, 784m in 2015, 822m in 2018. — A three-dimensional bar chart titled "Number of Hungry People Worldwide by Year", the vertical scale running from 800,000,000 to 1,000,000,000. The bars are 2000 at 900,000,000, 2005 at 945,000,000, 2010 at 821,000,000, 2015 at 784,000,000 and 2018 at 822,000,000, with a colour key beneath.

From the chart, what is your opinion on the trend of hunger across the world? i. ii. What will be your recommendations to world leaders on the strategies they can adopt to combat the menace?
Using Talk for Learning strategy, engage learners in a class debate where they support their argument with data and the use of appropriate mathematics terminology.
Example: As a speaker in a school debate on the topic: "The rise of HIV/AIDs cases in Ghana, a course for worry or a mere public scare", obtain data on HIV/AIDs cases from the Ghana AIDs Commission or from any reputable source (radio, TV, Newspaper, etc.), analyse the data (including using any appropriate technological tool) using charts/tables to support your arguments for or against the motion.
Project-based Learning: Assign project works to learners (individually or in groups) to obtain current data about contemporary issues of interest, then make conclusions, give criticisms and make useful recommendations. As they embark on the project, encourage them to be tolerant, friendly, openminded, patient, hardworking, etc., as they interact with their peers in their assigned project.
Example: Using a mind map such as the one below, learners must think critically, design a mini-project, and execute it to its successful conclusion.

Five-step illustrated flow for planning a data project, ending in a YES or NO branch. — A five-step flow illustration of planning a data project. Boxes ask "1. What is my goal?", "2. What is my area of interest or expertise?", "3. How can I find inspiration?", "4. Where can I find relevant data?" and "5. Can I execute my idea?", the last branching to a green YES and a red NO, each step drawn with small icons.

Teaching and Learning Resources:
- * Samples of bivariate data. * Computer application software such as MS Excel, MS Word, Wordpad, etc. * Mathematical sets. * Technology tools such as computers, mobile phones, etc. * Graph sheets * A computer with data-managment software like MS Excel, MS PowerPoint, etc., * A4 and A3 papers, manila cards, flip charts, markers, colour pens, etc.
Assessment (3.4.1.AS.1). The document marks these depth-of-knowledge levels for this indicator: Level 3 Strategic reasoning; Level 4 Extended critical thinking and reasoning.

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