Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Calculate the probability of a single event.
• Represent data using bar graphs and pie charts.
• Interpret data from tables, bar graphs, and pie charts.
• Determine the sample space for simple experiments.
• Express probability as a fraction, decimal, and percentage.

Lesson summary

Data handling and probability are crucial skills that help us make sense of the world around us. In South Africa, understanding data allows us to analyse trends like crime rates, population demographics, and economic indicators. Probability helps us assess risks and make informed decisions, such as when deciding whether to take an umbrella based on the weather forecast or understanding the odds in the Lotto. This week, we will focus on calculating probability and understanding how to present data effectively.

Lesson notes

2. 1. Probability Probability is the measure of how likely an event is to occur. It is always a number between 0 and 1, where: 0 means the event is impossible. 1 means the event is certain. We can express probability as a fraction, decimal, or percentage.

Formula for Probability: Probability of an event = (Number of favourable outcomes) / (Total number of possible outcomes)

Sample Space: The sample space is the set of all possible outcomes of an experiment.

Example 1: Rolling a Die What is the probability of rolling a 4 on a standard six-sided die?

Sample Space: {1, 2, 3, 4, 5, 6} (Total 6 possible outcomes)

Favourable outcome: Rolling a 4 (1 favourable outcome)

Probability: 1/6 As a decimal: 1/6 = 0.1667 (approximately)

As a percentage: 0.1667 * 100% = 16.67% (approximately)

Example 2: Drawing a Card What is the probability of drawing a heart from a standard deck of 52 cards?

Sample Space: 52 cards (Total 52 possible outcomes)

Favourable outcome: Drawing a heart (13 hearts in the deck)

Probability: 13/52 = 1/4 As a decimal: 1/4 = 0.25 As a percentage: 0.25 * 100% = 25% Example 3: Probability of Rain The weather forecast predicts a 70% chance of rain tomorrow. What is the probability that it will NOT rain? The total probability of all possible outcomes (rain or no rain) is 100%. Probability of no rain = 100% - Probability of rain Probability of no rain = 100% - 70% = 30% As a decimal: 30/100 = 0.3 2.

2. Data Representation: Bar Graphs and Pie Charts Data representation is the way we display collected data in a visual format, making it easier to understand and interpret. Two common methods are bar graphs and pie charts.

Bar Graphs: Bar graphs use bars of different lengths to represent different quantities. They are useful for comparing different categories. The x-axis typically shows the categories, and the y-axis shows the frequency or quantity.

Example: Favourite Sports of Grade 7 Learners | Sport | Number of Learners | | ----------- | ------------------ | | Soccer | 25 | | Netball | 15 | | Rugby | 10 | | Cricket | 5 | We can represent this data on a bar graph with "Sport" on the x-axis and "Number of Learners" on the y-axis. Each sport will have a bar, and the height of the bar will correspond to the number of learners who prefer that sport.

Pie Charts: Pie charts use sectors of a circle to represent proportions of a whole. They are useful for showing how different parts contribute to a total. The size of each sector is proportional to the quantity it represents.

Calculating Angles for a Pie Chart: To create a pie chart, we need to calculate the angle for each sector. The total angle in a circle is 360 degrees. Angle of sector = (Value of category / Total value) * 360 degrees

Example: Favourite Sports of Grade 7 Learners (Continued) Total number of learners = 25 + 15 + 10 + 5 = 55 Soccer: (25/55) 360 = 163.64 degrees (approximately)

Netball: (15/55) 360 = 98.18 degrees (approximately)

Rugby: (10/55) 360 = 65.45 degrees (approximately)

Cricket: (5/55) 360 = 32.73 degrees (approximately) These angles can then be used to draw the pie chart, with each sector representing the proportion of learners who prefer each sport. 2.

3. Interpreting Data Interpreting data involves drawing meaningful conclusions from the information presented in tables, bar graphs, and pie charts. This often involves identifying trends, comparing values, and making predictions.

Example: Analyzing a Bar Graph of Crime Rates Imagine a bar graph shows the number of reported burglaries in different neighbourhoods of Johannesburg over the past year. By analyzing the graph, you could identify which neighbourhoods have the highest burglary rates, compare the rates between different areas, and potentially identify trends (e.g., an increase in burglaries during a specific time of year).

Example: Analyzing a Pie Chart of Household Expenses A pie chart showing how a family spends their monthly income can reveal valuable insights. You could see what percentage of their income goes towards rent, food, transportation, and other expenses. This information could help the family identify areas where they could potentially save money. Guided Practice (With Solutions)

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

Solution: Total number of marbles: 5 + 3 + 2 = 10 Number of blue marbles: 3 Probability of picking a blue marble: 3/10 As a decimal: 3/10 = 0.3 As a percentage: 0.3 * 100% = 30% Question 2: The following data shows the number of learners who walk, take the bus, or get a lift to school: | Mode of Transport | Number of Learners | | ----------------- | ------------------ | | Walk | 20 | | Bus | 30 | | Lift | 10 | Represent this data on a bar graph.

Solution: Draw a bar graph with "Mode of Transport" on the x-axis and "Number of Learners" on the y-axis.