Lesson Notes By Weeks and Term v5 - Grade 8

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Construct and interpret bar graphs, pie charts, and histograms.
• Calculate relative frequency to estimate probability.
• Determine the probability of a single event.
• Choose the best way to represent different types of data.
• Solve real-life probability problems.

Lesson summary

Data handling and probability are essential skills that help us make sense of the world around us. In South Africa, understanding data is crucial for interpreting statistics related to everything from employment rates and crime statistics to public health data and election results. Probability helps us assess risks and make informed decisions in situations involving uncertainty, such as understanding the chances of winning the Lotto or the likelihood of rain affecting outdoor events. This week, we will focus on representing data effectively using various graphs and understanding basic probability concepts.

Lesson notes

2.1 Data Representation: Bar Graphs: These graphs use rectangular bars of different heights to represent the frequency or quantity of different categories. They are useful for comparing discrete categories.

Example:* A bar graph showing the number of learners in each Grade 8 class (8A, 8B, 8C, 8D).

Key Features:* Clear labels on both axes, appropriate scale, bars should be of equal width, spaces between bars.

Pie Charts: These circular charts divide a circle into sectors, where each sector represents a proportion of the whole. Pie charts are excellent for showing how different parts contribute to a whole.

Example:* A pie chart showing the percentage of learners in a school who prefer different sports (soccer, netball, rugby, cricket).

Key Features: Each sector represents a category, the size of the sector is proportional to the frequency of the category, the entire chart represents 100%. To calculate the angle of each sector, use the formula: (Frequency of category / Total frequency) 360°.

Histograms: Similar to bar graphs, but used for continuous data grouped into intervals (called bins). The bars in a histogram touch each other, indicating the continuous nature of the data.

Example:* A histogram showing the distribution of heights of Grade 8 learners. The height is grouped in classes of width 5cm (e.g. 140-145 cm, 145-150cm, etc.).

Key Features:* The bars touch each other, x-axis represents intervals of the continuous variable, y-axis represents the frequency. Why Histograms?: Histograms are great when you have lots of data and want to get a sense of how it is distributed. The data is 'continuous', meaning it can take on any value within a range (unlike shoe sizes which only come in specific values). 2.2 Probability: Probability: The chance or likelihood of an event occurring. It is a number between 0 and 1 (inclusive), where 0 means the event is impossible and 1 means the event is certain. Probability can also be expressed as a percentage (0% to 100%).

Event: A specific outcome or set of outcomes.

Sample Space: The set of all possible outcomes.

Calculating Probability: The probability of an event (P(event)) is calculated as: P(event) = (Number of favorable outcomes) / (Total number of possible outcomes)

Example: What is the probability of rolling a "4" on a fair six-sided die? The number of favorable outcomes is 1 (rolling a "4"). The total number of possible outcomes is 6 (1, 2, 3, 4, 5, 6).

Therefore, P(rolling a 4) = 1/

6. Relative Frequency: The number of times an event occurs in an experiment, divided by the total number of trials. It can be used as an estimate of the probability of the event.

Example: If you flip a coin 100 times and get heads 55 times, the relative frequency of getting heads is 55/100 = 0.55 or 55%. This suggests that the probability of getting heads is approximately 0.55.

Worked example

Data Representation (Bar Graph): A survey was conducted in a Grade 8 class to find out their favourite flavor of Mageu.

The results are: Strawberry (12 learners), Banana (8 learners), Cream (10 learners), and Pineapple (5 learners). Draw a bar graph to represent this data.

Solution:*

Draw two axes: The horizontal axis represents the flavors of Mageu (Strawberry, Banana, Cream, Pineapple). The vertical axis represents the number of learners.

Choose a suitable scale for the vertical axis (e.g., 1 unit represents 1 learner).

Draw bars for each flavor, with the height of the bar corresponding to the number of learners who prefer that flavor. Ensure bars are equal width and spaces between them are equal.

Label the axes and give the graph a title (e.g., "Favourite Mageu Flavors in Grade 8").

Data Representation (Pie Chart): A fruit vendor sold 200 apples, 150 oranges, 100 bananas, and 50 pears in a day. Represent this data using a pie chart.

Solution:*

Calculate the total number of fruits sold: 200 + 150 + 100 + 50 = 500

Calculate the proportion of each fruit sold:

Apples: 200/500 = 0.4

Oranges: 150/500 = 0.3

Bananas: 100/500 = 0.2

Pears: 50/500 = 0.1

Calculate the angle for each sector:

Apples: 0.4 360° = 144°

Oranges: 0.3 360° = 108°

Bananas: 0.2 360° = 72°

Pears: 0.1 360° = 36°

Draw a circle and divide it into sectors corresponding to the calculated angles. Label each sector with the fruit and its percentage (e.g., Apples: 40%).

Probability: 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?

Solution:*

Find the total number of marbles: 5 + 3 + 2 = 10

Find the number of blue marbles: 3

Calculate the probability: P(blue marble) = (Number of blue marbles) / (Total number of marbles) = 3/

1

0. Data Representation (Histogram): The following data represents the test scores of 25 students on a test graded out of

5

0. The scores are: 25, 32, 48, 19, 35, 42, 29, 38, 45, 22, 30, 37, 40, 27, 33, 49, 20, 36, 43, 31, 39, 46, 23, 34,

4

1. Represent this data as a histogram with class intervals of width 5.