Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Calculate the relative frequency of an event.
• Express relative frequency as a fraction, decimal, and percentage.
• Determine the probability of a simple event.
• Express probability as a fraction.
• Use relative frequency to make predictions.

Lesson summary

Data handling and probability are essential skills that help us understand the world around us. In South Africa, we constantly encounter data in the news (e.g., crime statistics, unemployment rates), and understanding probability helps us make informed decisions about risks and opportunities (e.g., lottery, insurance). This week, we will focus on calculating the relative frequency of events and understanding simple probability calculations. Relative frequency helps us understand how often something actually happens, while probability tells us how likely it is to happen. These concepts are used everywhere, from predicting election outcomes to managing business risks.

Lesson notes

2.1 Relative Frequency Relative frequency is a measure of how often an event occurs within a set of trials or observations. It’s calculated by dividing the number of times an event occurs by the total number of trials.

Formula: Relative Frequency = (Number of times the event occurs) / (Total number of trials)

Example 1: Imagine a survey was conducted in a Grade 7 class of 40 learners to find out their favorite type of music.

The results are shown below: Hip Hop: 15 learners Gqom: 10 learners Amapiano: 8 learners Other: 7 learners What is the relative frequency of learners who like Gqom?

Solution: Number of learners who like Gqom = 10 Total number of learners = 40 Relative Frequency of Gqom = 10 / 40 = 1/4 = 0.25 = 25% This means that 25% of the learners in the class prefer Gqom music.

Example 2: A soccer team, "The Lions," played 20 matches this season. They won 12 matches, lost 5 matches, and drew 3 matches. What is the relative frequency of The Lions winning a match?

Solution: Number of matches won = 12 Total number of matches played = 20 Relative Frequency of winning = 12 / 20 = 3/5 = 0.6 = 60% The Lions won 60% of their matches this season. 2.2 Probability Probability is a measure of how likely an event is to occur. It is expressed as a fraction, decimal, or percentage, with values ranging from 0 to 1 (or 0% to 100%). A probability of 0 means the event is impossible, and a probability of 1 means the event is certain.

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

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

Solution: Number of favorable outcomes (rolling a 4) = 1 Total number of possible outcomes (1, 2, 3, 4, 5, or 6) = 6 Probability of rolling a 4 = 1/6 Example 2: A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of randomly selecting a blue marble?

Solution: Number of favorable outcomes (selecting a blue marble) = 3 Total number of possible outcomes (total number of marbles) = 5 + 3 + 2 = 10 Probability of selecting a blue marble = 3/10 2.3 Relationship Between Relative Frequency and Probability While probability is a theoretical measure based on what should happen, relative frequency is an experimental measure based on what actually happened. If you repeat an experiment many times, the relative frequency of an event should approach the theoretical probability of that event. This is known as the Law of Large Numbers.

Example: If you flip a fair coin (theoretical probability of heads = 1/2) many times, the relative frequency of getting heads should get closer and closer to 1/2 as you increase the number of flips. Guided Practice (With Solutions)

Question 1: A survey was conducted among 50 shoppers at a local Spar to find out their preferred brand of maize meal. 20 shoppers preferred "Iwisa," 15 preferred "Impala," 10 preferred "White Star," and 5 preferred other brands. What is the relative frequency of shoppers who prefer "Iwisa"? Express your answer as a fraction, decimal, and percentage.

Solution: Number of shoppers who prefer "Iwisa" = 20 Total number of shoppers = 50 Relative Frequency = 20 / 50 = 2/5 = 0.4 = 40%

Commentary: We applied the relative frequency formula directly. Remember to simplify the fraction where possible and convert to decimal and percentage forms.

Question 2: A spinner has 8 equal sections, numbered 1 to

8. What is the probability of the spinner landing on an odd number?

Solution: Number of favorable outcomes (odd numbers: 1, 3, 5, 7) = 4 Total number of possible outcomes (numbers 1 to 8) = 8 Probability = 4/8 = 1/2

Commentary: We identified the favorable outcomes (odd numbers) and the total possible outcomes, then applied the probability formula.

Question 3: A bag contains 7 apples, 5 bananas, and 3 oranges. If you randomly select a fruit from the bag, what is the probability that it is an apple?

Solution: Number of favorable outcomes (selecting an apple) = 7 Total number of possible outcomes (total number of fruits) = 7 + 5 + 3 = 15 Probability = 7/15

Commentary: This question reinforced the understanding of calculating probability when presented with different quantities of items.

Question 4: A student, Zola, wrote a test consisting of 30 questions. She answered 24 questions correctly. What is the relative frequency of Zola answering a question correctly? Express this as a percentage.

Solution: Number of correctly answered questions = 24 Total number of questions = 30 Relative Frequency = 24/30 = 4/5 = 0.8 = 80%

Commentary: This reinforces the concept in the context of school assessments. Independent Practice (Questions Only) A survey was conducted in a neighborhood to find out the number of children per household.

The results are as follows: 0 children - 15 households, 1 child - 20 households, 2 children - 30 households, 3 or more children - 10 households. What is the relative frequency of households with 2 children?