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 compound bar graphs and pie charts.
• Calculate probabilities of simple events.
• Compare data sets and draw conclusions.
• Differentiate between experimental and theoretical probability.
• Use tree diagrams for multi-stage events.

Lesson summary

Data handling and probability are essential life skills. Understanding how data is collected, organized, and interpreted helps us make informed decisions every day, from understanding news reports about crime statistics in our communities to predicting the likelihood of winning the Lotto. Probability, in particular, allows us to assess risk and make calculated choices, such as deciding whether to invest in a small business or understanding the chances of drought affecting our crops. This week, we will focus on using and interpreting different types of data displays and applying probability concepts.

Lesson notes

2.1 Data Displays: Compound Bar Graphs A compound bar graph (also known as a stacked bar graph) is used to represent data that can be divided into different categories within each group. It allows us to compare the total size of each group as well as the proportion of each category within that group.

Example: A survey was conducted in a Grade 8 class to find out the favourite sports of boys and girls.

The results are shown below: | Sport | Boys | Girls | | ----------- | ---- | ----- | | Soccer | 20 | 5 | | Netball | 2 | 18 | | Rugby | 15 | 1 | | Athletics | 8 | 10 | To create a compound bar graph: Draw the axes: The horizontal axis represents the sports, and the vertical axis represents the number of students.

Draw the bars: For each sport, draw a bar representing the total number of students who like that sport.

Divide the bars: Divide each bar into two sections representing the number of boys and girls who like that sport. Use different colours or patterns to distinguish the sections.

Label the axes and provide a key: Clearly label the axes and provide a key to indicate which colour represents boys and which colour represents girls.

Add a title: Give the graph a title that describes the data being represented (e.g., "Favourite Sports of Grade 8 Students").

Interpreting the graph: From the compound bar graph, we can easily see which sport is the most popular overall and the breakdown of boys and girls for each sport. For example, we can quickly see that soccer is much more popular among boys than girls, while netball is more popular among girls. 2.2 Data Displays: Pie Charts A pie chart (or circle graph) is a circular chart divided into sectors, where each sector represents a proportion of the whole. Pie charts are useful for showing how a total amount is divided into different parts.

Example: A family spends their monthly income as follows: Rent: R5000 Food: R3000 Transport: R1500 Education: R2500 Entertainment: R1000 Total Income = R5000 + R3000 + R1500 + R2500 + R1000 = R13000 To create a pie chart: Calculate the fraction for each category: Divide the amount for each category by the total income.

Rent: 5000/13000 = 5/13 Food: 3000/13000 = 3/13 Transport: 1500/13000 = 3/26 Education: 2500/13000 = 5/26 Entertainment: 1000/13000 = 1/13 Calculate the angle for each sector: Multiply each fraction by 360° (the total degrees in a circle).

Rent: (5/13) 360° ≈ 138.5° Food: (3/13) 360° ≈ 83.1° Transport: (3/26) 360° ≈ 41.5° Education: (5/26) 360° ≈ 69.2° Entertainment: (1/13) 360° ≈ 27.7° Draw the pie chart: Use a compass to draw a circle. Use a protractor to draw each sector with the calculated angle.

Label the sectors: Label each sector with the category name and its percentage.

Rent: (5/13)100% = 38.5% Food: (3/13)100% = 23.1% Transport: (3/26)100% = 11.5% Education: (5/26)100% = 19.2% Entertainment: (1/13)100% = 7.7% Add a title: Give the chart a title (e.g., "Family's Monthly Spending").

Interpreting the graph: The pie chart shows the proportion of the family's income spent on each category. We can quickly see that rent takes up the largest portion of the income, followed by food. 2.3 Probability: Basic Concepts Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain. We can also express probability as a percentage (between 0% and 100%).

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

Example: A bag contains 5 red marbles and 3 blue marbles. What is the probability of picking a red marble? Number of favourable outcomes (red marbles) = 5 Total number of possible outcomes (total marbles) = 5 + 3 = 8 Probability of picking a red marble = 5/8 = 0.625 = 62.5% 2.4 Experimental vs. Theoretical Probability Theoretical Probability: This is what we expect to happen based on mathematical calculations, assuming all outcomes are equally likely.

Experimental Probability: This is what actually happens when we conduct an experiment multiple times. It is calculated by dividing the number of times an event occurs by the total number of trials.

Example: Theoretical: The theoretical probability of flipping a fair coin and getting heads is 1/2 (or 50%).

Experimental: You flip a coin 20 times and get heads 12 times. The experimental probability of getting heads is 12/20 = 3/5 (or 60%). As the number of trials increases, the experimental probability usually gets closer to the theoretical probability. 2.5 Tree Diagrams Tree diagrams are useful for calculating probabilities in multi-stage events (events with more than one step). Each branch of the tree represents a possible outcome, and the probabilities are written along the branches.

Example: A coin is flipped twice. What is the probability of getting two heads?

First flip: The first flip can result in heads (H) or tails (T), each with a probability of 1/2.