Lesson Notes By Weeks and Term v5 - Grade 7

Lesson Video

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Performance objectives

• Choose the best graph for a data set.
• Calculate probability as a fraction, decimal, and percentage.
• Interpret probability to predict events.
• Understand dual and compound bar graphs.

Lesson summary

Data handling and probability are essential life skills. In South Africa, understanding data helps us interpret information presented in the news about topics like crime statistics, employment rates, and healthcare access. Probability helps us make informed decisions based on understanding the likelihood of events, such as the chances of winning a competition or experiencing load shedding. This week we will focus on comparing data sets using different types of graphs, and calculating and interpreting probability.

Lesson notes

2.1 Types of Graphs and Their Uses Bar Graphs: Used to compare categorical data. Each bar represents a category, and the height of the bar represents the frequency (count) or amount in that category. Bar graphs are useful for comparing quantities across different groups.

Example:* A bar graph showing the number of learners in each Grade 7 class at a school.

Pie Charts: Used to show proportions of a whole. Each slice represents a category, and the size of the slice represents the percentage or fraction of the whole that the category makes up. Pie charts are useful for seeing the relative size of different parts of a whole.

Example:* A pie chart showing the percentage of learners who travel to school by bus, car, walking, or bicycle.

Histograms: Used to show the distribution of numerical data. The data is grouped into intervals (bins), and the height of each bar represents the frequency of data within that interval. Histograms are useful for seeing the shape of a data distribution.

Example:* A histogram showing the distribution of learners' heights in Grade

7. Line Graphs: Used to show trends over time. The horizontal axis represents time, and the vertical axis represents the value being measured. Line graphs are useful for seeing how something changes over time.

Example:* A line graph showing the daily temperature in Johannesburg over a week.

Dual Bar Graphs (or Grouped Bar Graphs): Shows two or more sets of bars next to each other, grouped by category. This is used to compare related data within each category.

Example:* A dual bar graph showing the number of boys and girls who prefer different sports. Compound Bar Graphs (or Stacked Bar Graphs): Shows different parts of a total amount stacked on top of each other within a single bar for each category. It displays the individual amounts of each segment relative to the total amount.

Example:* A compound bar graph showing the different types of crops planted by farmers in a specific region, with each part of the bar representing a different crop.

Choosing the Right Graph: Comparing categories:* Use bar graphs or pie charts.

Showing proportions of a whole:* Use pie charts. Showing the distribution of numerical data:* Use histograms.

Showing trends over time:* Use line graphs. Comparing multiple sets of categorical data:* Use dual or compound bar graphs. 2.2 Probability Probability is a measure of how likely an event is to occur. It is expressed as a number between 0 and 1 (inclusive), where 0 means the event is impossible and 1 means the event is certain. Probability can also be expressed as a fraction, decimal, or percentage.

Formula for Probability: Probability of an event = (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?

Solution:* Number of favourable outcomes (rolling a 4): 1 Total number of possible outcomes (rolling any number from 1 to 6): 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 at random?

Solution:* Number of favourable outcomes (picking a red ball): 3 Total number of possible outcomes (picking any ball): 3 + 5 = 8 Probability = 3/8 Converting Probability: Fraction to Decimal: Divide the numerator by the denominator. (3/8 = 0.375)

Decimal to Percentage: Multiply by 100. (0.375 = 37.5%)

Percentage to Fraction: Divide by 100 and simplify. (37.5% = 37.5/100 = 3/8) 2.3 Interpreting Probability Probability values can be used to make predictions about future events. A higher probability indicates a higher likelihood of the event occurring.

Example:* If the probability of rain tomorrow is 80%, we can say that it is very likely to rain tomorrow. If the probability of rain tomorrow is 20%, we can say that it is unlikely to rain tomorrow.

Example of Dual/Compound Bar Graph: Let's say a survey was conducted in two schools, School A and School B, asking learners about their favourite subject.

Here is the data: | Subject | School A | School B | |-------------|----------|----------| | Mathematics | 50 | 60 | | Science | 40 | 30 | | English | 30 | 40 | A dual bar graph would have three sets of bars, one for each subject. Within each set, there would be two bars, one for School A and one for School B. The height of each bar would correspond to the number of learners who chose that subject in that school. This allows for easy comparison of subject preferences between the two schools. A compound bar graph would have three bars, one for each subject. Each bar would be divided into two sections, one representing School A and one representing School B. The height of each section would correspond to the number of learners who chose that subject in that school. The total height of the bar would represent the total number of learners who chose that subject across both schools.