Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Construct and interpret pie charts and compound bar graphs.
• Identify possible outcomes of a probability experiment.
• Calculate the probability of a single event.
• Compare data sets using mean, median, and mode.
• Use data to make predictions in real-life scenarios.

Lesson summary

Data handling and probability are essential tools for understanding the world around us. In South Africa, we encounter data every day – from crime statistics reported on the news, to sports results, to surveys about social issues, and even when checking the weather forecast. Understanding how data is collected, organised, and interpreted allows us to make informed decisions and critically evaluate information. Probability helps us assess the likelihood of different events happening, from winning the Lotto to the chances of rain. This week, we'll focus on representing data visually and using this to make predictions.

Lesson notes

2.1 Pie Charts (Circle Graphs) Pie charts are circular diagrams used to represent data as proportions of a whole. The entire circle represents 100% of the data, and each slice (sector) represents a category's proportion.

Constructing a Pie Chart: Calculate the angle for each category: (Category Value / Total Value) * 360° Draw a circle. Use a protractor to draw each sector starting from the top (0°) and moving clockwise. Label each sector clearly with the category name and its percentage.

Interpreting a Pie Chart: The size of each slice visually represents its proportion in the whole dataset. Larger slices indicate larger proportions.

Example 1: A Grade 7 class of 40 learners was surveyed about their favourite sport.

The results are: Soccer (20), Netball (10), Rugby (5), Other (5). Draw a pie chart to represent this data.

Solution: Angles: Soccer: (20/40) 360° = 180° Netball: (10/40) 360° = 90° Rugby: (5/40) 360° = 45° Other: (5/40) 360° = 45° Draw a circle and use a protractor to draw the sectors with the calculated angles.

Label each sector: Soccer (50%), Netball (25%), Rugby (12.5%), Other (12.5%). 2.2 Compound Bar Graphs Compound bar graphs (also called stacked bar graphs) display data that is broken down into subcategories. They allow us to compare both the total values and the individual components within each category.

Constructing a Compound Bar Graph: Draw the axes: The horizontal axis represents the categories, and the vertical axis represents the values. Draw a bar for each category. Divide each bar into sections representing the subcategories. The height of each section corresponds to the value of that subcategory. Use different colours or patterns to distinguish between the subcategories. Provide a key to explain which colour/pattern represents each subcategory. Label the axes clearly and give the graph a title.

Interpreting a Compound Bar Graph: Look at the overall height of each bar to compare total values between categories. Examine the different sections within each bar to compare the relative proportions of each subcategory.

Example 2: A school recorded the number of boys and girls participating in different sports: | Sport | Boys | Girls | |-----------|------|-------| | Soccer | 30 | 15 | | Netball | 5 | 25 | | Athletics | 20 | 20 | Draw a compound bar graph to represent this data.

Solution: Draw the axes: Sport on the horizontal axis, Number of Participants on the vertical axis. Draw bars for Soccer, Netball, and Athletics. For Soccer, the bar will have two sections: a section representing 30 boys (e.g., blue) and a section representing 15 girls (e.g., red). Repeat for Netball (5 boys, 25 girls) and Athletics (20 boys, 20 girls).

Create a key: Blue = Boys, Red = Girls. Label the axes and give the graph a title (e.g., "Sports Participation by Gender"). 2.3 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.

Calculating Probability: Probability (Event) = (Number of Favourable Outcomes) / (Total Number of Possible Outcomes)

Understanding Probability: A probability of 0 means the event is impossible, while a probability of 1 (or 100%) means the event is certain.

Example 3: A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of picking a red marble at random?

Solution: Number of Favourable Outcomes (Red marbles): 5 Total Number of Possible Outcomes (Total marbles): 5 + 3 + 2 = 10 Probability (Red) = 5/10 = 1/2 Therefore, the probability of picking a red marble is 1/2 (or 50%). 2.4 Measures of Central Tendency and Comparing Data Sets Measures of central tendency (mean, median, mode) help us understand the "average" or typical value in a dataset. Comparing these measures across different datasets allows us to draw conclusions about the differences between the groups.

Mean: The average of all the values in a dataset. Calculate it by adding up all the values and dividing by the number of values.

Median: The middle value in a dataset when the values are arranged in order from smallest to largest. If there's an even number of values, the median is the average of the two middle values.

Mode: The value that appears most frequently in a dataset. A dataset can have no mode, one mode, or multiple modes.

Example 4: Two Grade 7 classes took a mathematics test.

Here are their scores: Class A: 60, 70, 75, 80, 85 Class B: 50, 70, 80, 80, 90 Calculate the mean, median, and mode for each class and compare the results.

Solution: Class A: Mean: (60 + 70 + 75 + 80 + 85) / 5 = 74 Median: 75 (middle value)

Mode: No mode (all values appear once)

Class B: Mean: (50 + 70 + 80 + 80 + 90) / 5 = 74 Median: 80 Mode: 80 Comparison: Both classes have the same mean (74), indicating a similar average performance.

However, the median for Class B (80) is higher than the median for Class A (75), suggesting that Class B's scores are generally higher.