Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Construct and interpret bar graphs, pie charts, and line graphs.
• Determine the probability of a single event.
• Compare different data displays.
• Predict the likelihood of events.
• Extract information from existing graphs.

Lesson summary

Data handling and probability are essential skills for navigating the world around us. In South Africa, understanding these concepts helps us interpret news reports on unemployment rates, analyze crime statistics, make informed decisions about voting, and even understand the odds in the National Lottery! Data handling teaches us how to collect, organize, and represent information meaningfully, while probability helps us to understand the likelihood of different events occurring. This week, we'll focus on representing data using various graphs and understanding basic probability concepts.

Lesson notes

2.1 Representing Data: Data can be presented in many ways, including: Bar Graphs: Use rectangular bars to represent the frequency of different categories. The height of each bar corresponds to the number of items in that category. Bar graphs are excellent for comparing quantities across different groups.

Pie Charts: Represent data as sections of a circle. The size of each section corresponds to the proportion of the whole represented by that category. Pie charts are useful for showing how a whole is divided into parts.

Line Graphs: Use lines to connect data points over time. They are perfect for showing trends and changes in data over a period. 2.2 Bar Graphs (Detailed Explanation): Bar graphs consist of two axes: a horizontal axis (x-axis) showing the categories and a vertical axis (y-axis) showing the frequency or quantity. The bars are drawn for each category, with their height corresponding to the frequency/quantity. Always label your axes and include a title.

Example: A survey was conducted in a Grade 7 class to find out their favourite South African sport.

The results are: Soccer (15 students), Rugby (10 students), Cricket (8 students), Netball (7 students).

To create a bar graph: Draw your axes.

The x-axis will be the sports: Soccer, Rugby, Cricket, Netball. The y-axis will represent the number of students. Choose a suitable scale for the y-axis. Since the highest number is 15, we can go up to 16, counting in 2s (0, 2, 4, 6, 8, 10, 12, 14, 16). Draw a bar for each sport, making sure its height matches the number of students who chose it. Label the axes and give the graph a title, e.g., "Favourite Sport of Grade 7 Students". 2.3 Pie Charts (Detailed Explanation): Pie charts show parts of a whole. To create a pie chart, you need to calculate the angle for each category. The total angle in a circle is 360 degrees. Example (continuing from the above example): Find the total number of students: 15 + 10 + 8 + 7 = 40 Calculate the fraction of students for each sport: Soccer: 15/40 Rugby: 10/40 Cricket: 8/40 Netball: 7/40 Calculate the angle for each sport: Soccer: (15/40) 360° = 135° Rugby: (10/40) 360° = 90° Cricket: (8/40) 360° = 72° Netball: (7/40) 360° = 63° Draw a circle and use a protractor to draw the angles for each sport. Label each section with the sport and its percentage. Give the chart a title. 2.4 Line Graphs (Detailed Explanation): Line graphs show how data changes over time. The x-axis represents time, and the y-axis represents the data being measured.

Example: The average monthly rainfall in Durban (in mm) for the first 6 months of the year is: January (120), February (140), March (100), April (70), May (50), June (30). Draw the axes. The x-axis will be the months (January to June), and the y-axis will be the rainfall in mm. Choose a suitable scale for the y-axis. We can go up to 150, counting in 10s. Plot each data point (e.g., January (120), February (140)). Connect the points with a straight line. Label the axes and give the graph a title. 2.5 Probability: Probability is the chance of an event happening.

It is calculated as: Probability = (Number of favourable outcomes) / (Total number of possible outcomes) Probability can be expressed as a fraction, decimal, or percentage.

Example: What is the probability of rolling a 4 on a standard six-sided die? Number of favourable outcomes (rolling a 4): 1 Total number of possible outcomes (1, 2, 3, 4, 5, 6): 6 Probability = 1/6 (as a fraction) Probability = 0.1667 (as a decimal) Probability = 16.67% (as a percentage) 2.6 Certain, Likely, Unlikely, Impossible: We can describe the likelihood of an event using these terms: Certain: The event will definitely happen (Probability = 1 or 100%).

Example: The sun will rise tomorrow.

Likely: The event is more likely to happen than not (Probability is greater than 0.5 or 50%).

Example: South Africa will have a public holiday next year.

Unlikely: The event is less likely to happen than not (Probability is less than 0.5 or 50%).

Example: It will snow in Durban in July.

Impossible: The event cannot happen (Probability = 0 or 0%).

Example: A pig will fly. Guided Practice (With Solutions)

Question 1: A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of randomly selecting a blue marble from the bag? Express your answer as a fraction, a decimal, and a percentage.

Solution: Total number of marbles: 5 + 3 + 2 = 10 Number of blue marbles: 3 Probability of selecting a blue marble: 3/10 As a decimal: 3/10 = 0.3 As a percentage: 0.3 * 100% = 30%

Commentary: We first find the total possible outcomes (total number of marbles) and then determine the number of favorable outcomes (number of blue marbles). The probability is then calculated as the ratio of favorable to total outcomes.

Question 2: The following data represents the number of learners absent each day during a week at a school: Monday: 5, Tuesday: 2, Wednesday: 3, Thursday: 1, Friday: 4.