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

• Analyze and interpret data in tables and graphs.
• Calculate mean, median, and mode.
• Determine the probability of a single event.
• Compare experimental and theoretical probability.
• Solve real-life problems using data and probability.

Lesson summary

Data handling and probability are crucial skills for Grade 7 learners as they develop their ability to interpret the world around them. In South Africa, understanding data is vital for making informed decisions about everything from household budgeting to understanding news reports about crime statistics or election results. Probability helps us assess risks and chances in everyday life, such as the likelihood of winning a school raffle or the chance of rain affecting weekend plans. This week's focus is on consolidating data handling techniques, particularly analyzing data presented in different formats, and applying probability concepts to solve practical problems.

Lesson notes

2.1 Data Handling: Analyzing Tables and Graphs Data is often presented in tables and graphs to make it easier to understand and interpret. We will focus on three common types of graphs: bar graphs, pie charts, and line graphs.

Bar Graphs: Bar graphs use bars of different lengths to represent different quantities. They are useful for comparing discrete categories.

Example: A survey of favorite fruits among Grade 7 learners resulted in the following data: Apples (20 learners), Bananas (30 learners), Oranges (15 learners), Pears (10 learners), Mangoes (25 learners). This data can be represented using a bar graph with fruit types on the x-axis and the number of learners on the y-axis.

Pie Charts: Pie charts (or circle graphs) show how a whole is divided into parts. Each slice of the pie represents a proportion of the whole.

Example: A school's budget is allocated as follows: Salaries (60%), Resources (20%), Maintenance (10%), Extracurricular Activities (10%). This can be represented in a pie chart, where each sector's angle is proportional to its percentage. For instance, the Salaries sector will occupy 60/100 360° = 216° of the circle.

Line Graphs: Line graphs show how data changes over time. They are useful for identifying trends and patterns.

Example: The daily maximum temperature in Johannesburg during the first week of July was recorded as follows: Monday (15°C), Tuesday (17°C), Wednesday (18°C), Thursday (16°C), Friday (20°C), Saturday (22°C), Sunday (21°C). A line graph can be used to visualize the temperature trend over the week.

Interpreting Graphs: When interpreting graphs, pay attention to the labels on the axes, the scale used, and any trends or patterns that are visible.

Ask yourself questions like: "What is the highest value?", "What is the lowest value?", "Is there an increasing or decreasing trend?". 2.2 Measures of Central Tendency: Mean, Median, and Mode Measures of central tendency are used to describe the "typical" value in a set of data.

Mean: The mean (or average) is calculated by adding up all the values in a data set and dividing by the number of values.

Formula: Mean = (Sum of all values) / (Number of values)

Example: The heights of 5 learners are 140cm, 145cm, 150cm, 155cm, and 160cm. The mean height is (140 + 145 + 150 + 155 + 160) / 5 = 750 / 5 = 150cm.

Median: The median is the middle value in a data set when the values are arranged in order from smallest to largest. If there is an even number of values, the median is the average of the two middle values.

Example 1 (Odd number of values): The ages of 7 siblings are 3, 5, 7, 9, 11, 13,

1

5. The median age is 9 (the middle value).

Example 2 (Even number of values): The test scores of 6 learners are 60, 70, 75, 80, 85,

9

0. The median score is (75 + 80) / 2 = 77.

5. Mode: The mode is the value that appears most frequently in a data set. A data set can have one mode, more than one mode (bimodal, trimodal, etc.), or no mode at all.

Example: The number of siblings among 10 learners are: 1, 2, 1, 3, 2, 1, 0, 2, 1,

4. The mode is 1 (appears 4 times). 2.3 Probability: Understanding Chance Probability is the measure of how likely an event is to occur. It is expressed as a fraction, decimal, or percentage.

Theoretical Probability: This is the probability calculated based on what should happen in theory.

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

Example: The probability of rolling a 4 on a fair six-sided die is 1/6, since there is one favorable outcome (rolling a 4) and six possible outcomes (1, 2, 3, 4, 5, 6). This can also be expressed as approximately 0.167 or 16.7%.

Experimental Probability: This is the probability calculated based on the results of an experiment. It is the ratio of the number of times an event occurs to the total number of trials.

Formula: Experimental Probability = (Number of times the event occurs) / (Total number of trials)

Example: A coin is flipped 50 times, and heads comes up 28 times. The experimental probability of getting heads is 28/50 = 0.56 or 56%. Comparing Theoretical and Experimental Probability: Theoretical and experimental probability are not always the same. Experimental probability becomes closer to theoretical probability as the number of trials increases (Law of Large Numbers). Guided Practice (With Solutions)

Question 1: The table below shows the number of rainy days in Durban for each month of the year. | Month | Rainy Days | |-----------|------------| | January | 12 | | February | 10 | | March | 11 | | April | 9 | | May | 7 | | June | 5 | | July | 4 | | August | 5 | | September | 7 | | October | 9 | | November | 11 | | December | 12 | What is the mean number of rainy days per month in Durban?

Solution: Mean = (12 + 10 + 11 + 9 + 7 + 5 + 4 + 5 + 7 + 9 + 11 + 12) / 12 = 102 / 12 = 8.5 Therefore, the mean number of rainy days per month in Durban is 8.5 days.

Question 2: A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles.