Statistical Reasoning and Its… · SHS1 Mathematics

Lesson notes

Learning Objectives

Indicator: 1.4.1.LI.2 - Organise and present data (grouped/ungrouped) using frequency tables, line graphs, pie charts, multiple bar graphs, infographics, etc., including generating 3D graphs/charts with appropriate digital technology (where available) and solving problems on them.

By the end of the lesson, learners can:

Organise ungrouped raw data (discrete data like colours, counts) into a frequency distribution table with tally marks, frequency, and percentage columns.
Organise grouped raw data (continuous data like tree counts) into a grouped frequency distribution table using appropriate class intervals, and compute the total frequency accurately.
Solve problems by reading and interpreting a multiple bar graph, including calculating percentage differences between two categories.
Construct and interpret a pie chart from a frequency table by converting frequencies into angles.
Use digital tools (MS Excel or equivalent, where available) to generate a basic 3D chart or graph from a frequency table.

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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: 1.4.1.CS.2 - Demonstrate conceptual understanding of data organisation and presentation for grouped and ungrouped data, including 3D graphs/charts with appropriate digital technology. 1.4.1.LO.2 Organise and present data (grouped/ungrouped) using frequency tables, line graphs, pie charts, multiple bar graphs, infographics, etc.; generate 3D graphs/charts with appropriate digital technology (where available) and solve problems on them.
Indicator: 1.4.1.LI.2 - Organise and present data (grouped/ungrouped) using frequency tables, line graphs, pie charts, multiple bar graphs, infographics, etc., including generating 3D graphs/charts with appropriate digital technology (where available) and solving problems on them.
Suggested placement: Semester 2, Week 13 (Week 33 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. 136

Exemplars (from the NaCCA curriculum)

Using think-pair-share activities, learners are tasked to Organise a given/chosen raw data into a frequency distribution table.
Example 1: Ungrouped data A jar containing beads of different colours- red, green, blue, black, red, green, blue, yellow, red, red, green, green, green, yellow, red, green, yellow. Organise the data in a frequency table.

Tally table: Red 5, Green 6, Blue 2, Black 1, Yellow 3. — A small tally table headed Categories, Tally Marks and Frequency, with the rows Red 5, Green 6, Blue 2, Black 1 and Yellow 3, each frequency matched by its tally strokes.

Example 2: Grouped data One hundred schools decided to plant 100 tree saplings in their gardens on World Environment Day. Represent the given data in the form of frequency distribution and find the number of schools that are able to plant 50% of the plants or more. 95, 67, 28, 32, 65, 65, 69, 33, 98, 96, 76, 42, 32, 38, 42, 40, 40, 69, 95, 92, 75, 83, 76, 83, 85, 62, 37, 65, 63, 42, 89, 65, 73, 81, 49, 52, 64, 76, 83, 92, 93, 68, 52, 79, 81, 83, 59, 82, 75, 82, 86, 90, 44, 62, 31, 36, 38, 42, 39, 83, 87, 56, 58, 23, 35, 76, 83, 85, 30, 68, 69, 83, 86, 43, 45, 39, 83, 75, 66, 83, 92, 75, 89, 66, 91, 27, 88, 89, 93, 42, 53, 69, 90, 55, 66, 49, 52, 83, 34, 36.

Grouped frequency table, classes 20-29 to 90-99, frequencies 3, 14, 12, 8, 18, 10, 23 and 12, total 100. — A grouped frequency table on a blue ground, headed "Number of plants survived", "Tally Marks" and "Number of schools (frequency)". The classes 20-29, 30-39, 40-49, 50-59, 60-69, 70-79, 80-89 and 90-99 have frequencies 3, 14, 12, 8, 18, 10, 23 and 12, totalling 100.

Example 3: Line Graphs The temperature of a city from 5 a.m. to 8 p.m. on a day was recorded in the form of a line graph, as shown below. Study the graph and answer the following questions. a) At which time of the day was the temperature 40° F? b) What was the maximum recorded temperature?

Line graph of temperature in degrees Fahrenheit against time, rising from 40 to 60 by midday and back to 40. — A line graph titled "TEMPERATURE CHANGE", with Temperature in degrees Fahrenheit up the side from 0 to 60 and Time along the foot at 5:00 A.M., 6:00 A.M., 11:00 A.M., 2:00 P.M., 5:00 P.M. and 8:00 P.M. The orange line rises from 40 to 50 then to 60, stays at 60, and falls back to 40.

Example 4: Multiple Bar Graphs The chart below is the summary of cases and recoveries of the coronavirus pandemic recorded in various regions in Ghana from March 2020 to 11th August 2022.

Bar chart of cases by Ghanaian region, scale to 180,000, with tall bars at Greater Accra and international travellers. — A bar chart of recorded cases by region, the vertical scale running to 180,000 in steps of 20,000 and the regions named along the foot: Ahafo, Bono east, Central, Greater accra, Northern, Savannah, Upper west, Western and International travelers. Two tall bars stand at Greater accra and at International travelers and the rest are short. Two questions follow, asking which region recorded the least cases and the percentage difference between Greater Accra and the total.

From the graph: 1. Which region recorded the least cases over the period? 2. What is the percentage difference between cases recorded in Greater Accra and the total cases?
Teaching and Learning Resources:
- * Graph sheets * mathematical sets * computer with data organising software like MS Excel, MS
- PowerPoint, etc. * A4, A3 papers * flip charts
- * markers * colour pens, etc. * Reports from analysed data * manila cards
- * worksheets * posters * teaching presentations * enquiry project-template
Assessment (1.4.1.AS.2). The document marks these depth-of-knowledge levels for this indicator: Level 1 Recall; Level 2 Skills of conceptual understanding; Level 3 Strategic reasoning; Level 4 Extended critical thinking and reasoning.