Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Interpret and compare different data displays like bar graphs and pie charts.
• Calculate the probability of a single event.
• Use data to predict the likelihood of future events.
• Explain the difference between theoretical and experimental probability.

Lesson summary

This week, we delve deeper into data handling and probability, building on the foundational concepts introduced last week. Understanding data handling and probability is crucial in today's world. From interpreting election results in South Africa to understanding weather forecasts or making informed decisions about budgeting and spending money, these skills are essential for active and responsible citizenship. Knowing how to collect, organize, and interpret data allows us to make sense of the world around us and make informed choices. Probability helps us understand the likelihood of events, allowing us to assess risks and make better predictions.

Lesson notes

2.1 Interpreting Data Displays Data displays are visual representations of information. The most common types you'll encounter are: Bar Graphs: Use bars of different lengths to represent data. They're good for comparing quantities.

Example:* A bar graph showing the number of learners who prefer different sports: soccer, rugby, netball, and cricket. The taller the bar, the more learners prefer that sport.

Pie Charts (Circle Graphs): Divide a circle into sectors, where each sector represents a proportion of the whole. They're good for showing how different parts contribute to a whole.

Example:* A pie chart showing the percentage of households in a town with access to electricity, running water, and internet. Each slice represents the percentage of households with each type of access. The entire pie represents 100% of the households.

Pictograms: Use pictures or symbols to represent data. Each picture represents a certain number of items. They are simple and visually appealing.

Example:* A pictogram showing the number of cars sold by a dealership each month. Each car picture might represent 10 cars sold.

Line graphs: Display data that changes over time as a line. They show trends over a period of time.

Example:* A line graph displays the average monthly rainfall recorded in Durban over the past year.

Important Considerations: Scale: Pay close attention to the scale used on the axes of graphs. A misleading scale can distort the data.

Labels: Ensure all axes and sections are clearly labeled to understand what the data represents.

Key/Legend: Pictograms and some pie charts need a key to explain what each symbol or color represents.

Choosing the right display: Bar graphs and line graphs are suited for displaying distinct or continuous changes, respectively. Pie charts are great for visualizing proportions of a whole. Pictograms, being more visual, are useful for capturing attention but are usually less precise. 2.2 Probability of a Single Event Probability is the measure of how likely an event is to occur. It is expressed as a fraction, decimal, or percentage.

Formula: Probability of an event (P(event)) = (Number of favorable outcomes) / (Total number of possible outcomes)

Favorable Outcome: The outcome you're interested in.

Possible Outcomes: All the possible results of an event.

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

Favorable outcome: rolling a 4 (1 outcome)

Possible outcomes: 1, 2, 3, 4, 5, 6 (6 outcomes) P(rolling a 4) = 1/6 ≈ 0.167 = 16.7% Example 2: Picking a Marble: A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. What is the probability of picking a blue marble?

Favorable outcome: picking a blue marble (5 outcomes)

Possible outcomes: red, blue, or green marbles (3 + 5 + 2 = 10 outcomes) P(picking a blue marble) = 5/10 = 1/2 = 0.5 = 50% Example 3: Tossing a Coin: What is the probability of getting tails when tossing a fair coin?

Favorable outcome: getting tails (1 outcome)

Possible outcomes: heads or tails (2 outcomes) P(getting tails) = 1/2 = 0.5 = 50% 2.3 Making Predictions from Data Data can be used to make predictions about future events. This is done by analyzing trends and patterns in the data.

Example 1: A survey shows that 60% of Grade 7 learners prefer soccer over other sports. If there are 200 Grade 7 learners in the school, we can predict that approximately 60% of 200 = 0.6 200 = 120 learners prefer soccer.

Example 2:* A weather report states that there is an 80% chance of rain tomorrow. This means that based on historical weather data and current conditions, there is a high likelihood of rain. 2.4 Theoretical vs. Experimental Probability Theoretical Probability: What should happen based on mathematical calculations. This is what we calculated in Section 2.

2. It assumes all outcomes are equally likely.

Example:* The theoretical probability of flipping heads on a fair coin is 1/

2. Experimental Probability: What actually happens when you conduct an experiment. It is based on observed data.

Example:* If you flip a coin 10 times and get heads 6 times, the experimental probability of getting heads is 6/10 = 3/

5. Important Notes: The more trials you conduct in an experiment, the closer the experimental probability will likely be to the theoretical probability (Law of Large Numbers). Sometimes, experimental probability can differ significantly from theoretical probability, especially with a small number of trials. Guided Practice (With Solutions)

Question 1: A pie chart shows the percentage of students who walk, cycle, take the bus, or are driven to school. 40% walk, 25% cycle, 20% take the bus and the rest are driven to school. What percentage of students are driven to school?

Solution: Since the entire pie chart represents 100%, the percentage of students driven to school is 100% - (40% + 25% + 20%) = 100% - 85% = 15%.

Commentary: This question reinforces understanding of pie charts and how to interpret percentages.