Lesson Notes By Weeks and Term v5 - Grade 7

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

• Represent data using pie charts, bar graphs, and histograms.
• Interpret data from these graphs.
• Determine the probability of simple events.
• Compare the likelihood of different events.
• Collect and organize data using tally tables.

Lesson summary

Data handling and probability are essential mathematical skills that help us understand the world around us. In South Africa, these skills are crucial for interpreting news reports (e.g., unemployment rates, crime statistics), making informed decisions about finances (e.g., understanding interest rates, budgeting), and participating in community planning (e.g., analyzing census data, resource allocation). Understanding probability helps us assess risks and make informed choices, from participating in lotteries to understanding the spread of diseases. This week, we will focus on representing and interpreting data using different graphical methods and understanding the concept of probability.

Lesson notes

2.1 Data Collection and Organization: Before we can analyze data, we need to collect and organize it. The most basic way to collect data is by using tally marks. Each tally mark represents one observation. We group them in fives to make counting easier. A frequency table summarizes the data by showing how many times each observation occurs.

Example: A Grade 7 class was asked about their favourite sport.

The results are: Soccer, Netball, Soccer, Rugby, Netball, Soccer, Cricket, Soccer, Netball, Netball, Rugby, Soccer, Soccer, Netball, Rugby.

We can use tally marks to organize this: Soccer: |||| || Netball: |||| | Rugby: ||| Cricket: | Then, we can create a frequency table: | Sport | Frequency | | -------- | --------- | | Soccer | 6 | | Netball | 5 | | Rugby | 3 | | Cricket | 1 | 2.2 Data Representation: Bar Graphs, Pie Charts, and Histograms Bar Graphs: Bar graphs are used to compare different categories of data. The length of each bar represents the frequency or quantity of that category. Bars should be of equal width and have spaces between them.

Example: Using the favourite sport data above, we can create a bar graph. The x-axis would represent the sports (Soccer, Netball, Rugby, Cricket), and the y-axis would represent the frequency (number of learners who chose each sport). The height of each bar would correspond to the frequency of each sport.

Pie Charts: Pie charts are used to show how a whole is divided into parts. Each slice of the pie represents a percentage or proportion of the whole. The size of each slice is proportional to the value it represents. The entire pie chart represents 100%.

Example: To create a pie chart from the sport data, we first need to calculate the total number of learners: 6 + 5 + 3 + 1 =

1

5. Then, we calculate the percentage of learners who prefer each sport: Soccer: (6/15) 100% = 40% Netball: (5/15) 100% = 33.33% Rugby: (3/15) 100% = 20% Cricket: (1/15) 100% = 6.67% We would then draw a circle and divide it into slices representing these percentages. A protractor is used to accurately measure the angles of each slice. For example, the angle for Soccer would be 0.4 * 360 degrees = 144 degrees.

Histograms: Histograms are similar to bar graphs, but they are used to represent continuous data that is grouped into intervals or ranges. Unlike bar graphs, there are no gaps between the bars in a histogram.

Example: Suppose we have the heights of learners in a class, grouped into intervals: | Height (cm) | Frequency | | ----------- | --------- | | 140-145 | 5 | | 145-150 | 8 | | 150-155 | 10 | | 155-160 | 7 | We would draw a histogram where the x-axis represents the height intervals (140-145, 145-150, etc.) and the y-axis represents the frequency. Each bar would touch the adjacent bar, showing the continuous nature of the data. 2.3 Probability Probability is the chance that something will happen. We express probability as a fraction, decimal, or percentage. Probability = (Number of favourable outcomes) / (Total number of possible outcomes)

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

Number of favourable outcomes: 1 (rolling a 4)

Total number of possible outcomes: 6 (1, 2, 3, 4, 5, 6) Probability = 1/6 Example 2: A bag contains 3 red balls and 5 blue balls. What is the probability of picking a red ball?

Number of favourable outcomes: 3 (red balls)

Total number of possible outcomes: 8 (3 red + 5 blue) Probability = 3/8 2.4 Likelihood: We use terms like "certain," "likely," "unlikely," and "impossible" to describe the likelihood of an event.

Certain: An event that will definitely happen (Probability = 1 or 100%).

Example: The sun will rise tomorrow.

Likely: An event that has a high chance of happening (Probability close to 1).

Example: You are likely to pass if you study hard.

Unlikely: An event that has a low chance of happening (Probability close to 0).

Example: Winning the lottery.

Impossible: An event that cannot happen (Probability = 0).

Example: Flying without any assistance. Guided Practice (With Solutions)

Question 1: A survey was conducted in a Grade 7 class about their favourite fruit.

The results are: Apples (8), Bananas (12), Oranges (6), Grapes (4). Represent this data using a bar graph.

Solution: Draw the axes: Draw a horizontal x-axis and a vertical y-axis.

Label the axes: Label the x-axis with the fruit names (Apples, Bananas, Oranges, Grapes) and the y-axis with the frequency (number of learners).

Draw the bars: For each fruit, draw a bar with a height corresponding to its frequency.

Apples: Bar height = 8 Bananas: Bar height = 12 Oranges: Bar height = 6 Grapes: Bar height = 4 Ensure equal bar widths and spacing.

Commentary: This question directly assesses the ability to represent data using a bar graph. It requires correctly identifying the variables and representing the frequencies accurately.

Question 2: A spinner has 5 equal sections, numbered 1 to

5. What is the probability of spinning a number greater than 3?