Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Interpret data in pie charts.
• Construct a pie chart from a data set.
• Define probability and likelihood.
• Calculate the probability of simple events.
• Express probability as a fraction, decimal, and percentage.

Lesson summary

Data handling and probability are crucial skills in the modern world, and especially relevant in South Africa. From understanding crime statistics in our communities to interpreting weather forecasts that impact agriculture and water resources, the ability to analyze data and understand probability is essential for informed decision-making. This week, we will focus on understanding and interpreting different types of data displays, specifically pie charts, as well as calculating probabilities of simple events. Understanding these concepts empowers you to critically evaluate information and make informed choices in your daily lives.

Lesson notes

2.1 Pie Charts: Visualizing Data Proportions A pie chart (also sometimes called a circle graph) is a circular chart divided into sectors, illustrating numerical proportion. In a pie chart, the arc length of each sector (and consequently its central angle and area), is proportional to the quantity it represents. Pie charts are excellent for showing the relative sizes of different categories within a whole.

Key Components: Sectors: Each slice of the pie represents a category or group.

Central Angle: The angle at the center of the circle for each sector. The central angle is proportional to the percentage of the whole that the sector represents. A full circle is 360°.

Percentage: The percentage of the whole that each sector represents. The percentages of all sectors must add up to 100%.

Labels: Each sector should be clearly labeled with the category name and, ideally, the percentage or quantity it represents.

Interpreting Pie Charts: The largest sector represents the largest category. The smallest sector represents the smallest category. To find the percentage represented by a sector, look for the percentage label or estimate the fraction of the whole circle the sector occupies. To calculate the value represented by a sector, multiply the total value by the percentage represented by the sector.

Constructing Pie Charts: Calculate the fraction or percentage of each category: Divide the value of each category by the total value. Calculate the central angle for each sector: Multiply the fraction (or percentage as a decimal) by 360°.

Draw a circle: Use a compass to draw a circle.

Draw the sectors: Use a protractor to draw the central angles for each sector.

Label each sector: Clearly label each sector with the category name and percentage.

Example 1: Favourite Sport A class of 40 Grade 7 learners were surveyed about their favourite sport.

The results are as follows: Football (16), Netball (10), Rugby (8), Cricket (6). Represent this data in a pie chart.

Solution: Calculate fractions: Football: 16/40 = 0.4 Netball: 10/40 = 0.25 Rugby: 8/40 = 0.2 Cricket: 6/40 = 0.15 Calculate central angles: Football: 0.4 360° = 144° Netball: 0.25 360° = 90° Rugby: 0.2 360° = 72° Cricket: 0.15 360° = 54° Draw the circle and sectors: (This step requires drawing, which cannot be done in Markdown. Imagine a pie chart with the calculated angles. Football would be the largest slice).

Label the sectors: Label each sector with the sport and its percentage: Football (40%), Netball (25%), Rugby (20%), Cricket (15%). 2.2 Probability: Measuring Likelihood Probability is a measure of how likely an event is to occur. It is a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Probability can also be expressed as a percentage between 0% and 100%.

Key Terms: Event: An event is a specific outcome or set of outcomes.

Outcome: A possible result of an experiment or situation.

Favorable Outcome: An outcome that satisfies the conditions of the event.

Sample Space: The set of all possible outcomes.

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

Expressing Probability: Probability can be expressed as a: Fraction: e.g., 1/2 Decimal: e.g., 0.5 Percentage: e.g., 50% Example 2: Rolling a Dice What is the probability of rolling a 4 on a standard six-sided die?

Solution: Number of favorable outcomes (rolling a 4): 1 Total number of possible outcomes (rolling a 1, 2, 3, 4, 5, or 6): 6 P(rolling a 4) = 1/6 The probability of rolling a 4 is 1/6, which is approximately 0.167 or 16.7%.

Example 3: Drawing a Card What is the probability of drawing a heart from a standard deck of 52 playing cards?

Solution: Number of favorable outcomes (drawing a heart): 13 (there are 13 hearts in a deck) Total number of possible outcomes (drawing any card): 52 P(drawing a heart) = 13/52 = 1/4 The probability of drawing a heart is 1/4, which is 0.25 or 25%.

Example 4: Spinners A spinner is divided into 8 equal sections, numbered 1 to

8. What is the probability of spinning an even number?

Solution: Favourable outcomes (spinning an even number): 4 (2, 4, 6, 8)

Total possible outcomes: 8 (1, 2, 3, 4, 5, 6, 7, 8) Probability = 4/8 = 1/2 = 0.5 = 50% Guided Practice (With Solutions)

Question 1: A pie chart shows the percentages of different modes of transport used by learners to get to school.

The chart shows: Bus (40%), Car (30%), Walk (20%), Other (10%). What is the angle of the sector representing learners who walk to school?

Solution: Percentage of learners who walk: 20% Total degrees in a circle: 360° Angle of the sector = (20/100) 360° = 72° Answer: The angle of the sector representing learners who walk to school is 72°.

Question 2: A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of randomly selecting a blue marble?