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

• Construct and interpret frequency tables.
• Calculate the probability of a single event.
• Compare probabilities of different events.
• Identify bias in data collection.
• Represent data using graphs and charts.

Lesson summary

Data handling and probability are essential skills in mathematics, crucial for understanding the world around us. In our daily lives as South Africans, we encounter data and probabilities constantly: from reading news articles about unemployment rates and crime statistics to predicting the chances of rain for a weekend braai. This week, we'll focus on using frequency tables, calculating probabilities, and interpreting data presented in various formats, enabling you to make informed decisions based on evidence. We’ll examine how data handling helps us understand societal trends and make informed choices about resource allocation, health, and safety.

Lesson notes

2.1 Frequency Tables A frequency table organizes data by showing how many times each value (or range of values) occurs in a dataset.

Ungrouped Data: Used when data values are distinct and not clustered. Each unique value gets its own row in the table.

Grouped Data: Used when data values are continuous or have a large range. The data is divided into intervals (groups), and the frequency represents the number of data points falling within each interval. It's crucial to ensure the intervals don't overlap (e.g., 1-5, 6-10, not 1-5, 5-10) and that every data point fits within one of the intervals.

Example 1 (Ungrouped Data): The shoe sizes of 20 Grade 7 learners are: 4, 5, 6, 4, 7, 5, 4, 8, 5, 6, 5, 4, 5, 6, 7, 8, 5, 4, 6, 5. | Shoe Size | Frequency | |-----------|-----------| | 4 | 5 | | 5 | 7 | | 6 | 4 | | 7 | 2 | | 8 | 2 | Example 2 (Grouped Data): The ages of 30 people attending a community meeting are recorded as follows: 12, 15, 18, 22, 25, 28, 31, 35, 38, 42, 45, 48, 51, 55, 58, 62, 65, 68, 71, 75, 14, 17, 20, 23, 26, 29, 32, 36, 39, 43. | Age Group | Frequency | |-----------|-----------| | 10-19 | 4 | | 20-29 | 6 | | 30-39 | 6 | | 40-49 | 4 | | 50-59 | 4 | | 60-69 | 4 | | 70-79 | 2 | 2.2 Probability 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 = (Number of favorable outcomes) / (Total number of possible outcomes)

Scale: Probability ranges from 0 (impossible) to 1 (certain).

Representations: Fraction: e.g., 1/2 Decimal: e.g., 0.5 Percentage: e.g., 50% Example 3: A bag contains 5 red balls, 3 blue balls, and 2 green balls. What is the probability of picking a blue ball at random? Number of favorable outcomes (blue balls) = 3 Total number of possible outcomes (total balls) = 5 + 3 + 2 = 10 Probability (Blue) = 3/10 = 0.3 = 30% Example 4: What is the probability of rolling a 4 on a standard six-sided die? Number of favorable outcomes (rolling a 4) = 1 Total number of possible outcomes (sides on the die) = 6 Probability (rolling a 4) = 1/6 = 0.1666... ≈ 16.7% 2.3 Comparing Probabilities We can compare the probabilities of different events to determine which event is more likely to occur. The higher the probability, the more likely the event.

Example 5: Event A: Drawing a red card from a standard deck of 52 cards.

Event B: Rolling an even number on a standard six-sided die. Probability (Event A) = 26/52 = 1/2 = 50% Probability (Event B) = 3/6 = 1/2 = 50% In this case, both events have equal probabilities. 2.4 Bias in Data Collection Bias occurs when the data collection or representation methods systematically favor certain outcomes or viewpoints over others. It's crucial to be aware of potential sources of bias to ensure data is interpreted fairly and accurately.

Example 6: A survey asking "Do you agree that the government is doing a terrible job?" is biased because it uses leading language ("terrible job") that encourages a negative response.

A less biased question would be: "What is your opinion of the government's performance?" 2.5 Data Representation: Bar Graphs, Histograms, and Pie Charts Bar Graphs: Used to compare categorical data (e.g., favorite sports, types of cars). The height of each bar represents the frequency of the category.

Histograms: Used to represent continuous data grouped into intervals (e.g., ages, heights). The area of each bar represents the frequency of the interval.

Note: No gaps between bars.

Pie Charts: Used to show the proportion of each category relative to the whole. Each slice of the pie represents a category, and the size of the slice is proportional to the percentage of the total. The entire pie represents 100%. Guided Practice (With Solutions)

Question 1: A survey of 40 learners asked about their favorite fruit.

The results are: Apple (12), Banana (10), Orange (8), Mango (6), Other (4). Construct a frequency table for this data.

Solution: | Fruit | Frequency | |---------|-----------| | Apple | 12 | | Banana | 10 | | Orange | 8 | | Mango | 6 | | Other | 4 | Explanation: The frequency table simply lists each fruit type and the number of learners who chose it as their favorite.

Question 2: A spinner is divided into 4 equal sections, colored red, blue, green, and yellow. What is the probability of landing on the red section?

Solution: Number of favorable outcomes (red) = 1 Total number of possible outcomes (sections) = 4 Probability (Red) = 1/4 = 0.25 = 25% Explanation: Since each section is equal, the probability of landing on any one section is 1/

4. Question 3: A bag contains 20 sweets: 8 are lemon flavored, 7 are orange flavored, and 5 are grape flavored. What is the probability of picking an orange or grape flavored sweet?