Lesson Notes By Weeks and Term v5 - Grade 5

Lesson Video

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Performance objectives

• Construct and interpret bar graphs and pictographs.
• Describe events as certain, likely, unlikely, or impossible.
• Determine the probability of a simple event.
• Collect and organize data using tally marks and frequency tables.

Lesson summary

Data handling is a crucial skill that helps us make sense of the world around us. From understanding the popularity of different sports in our school to analyzing rainfall patterns for farming, data is everywhere! Probability helps us to understand the likelihood of events happening, such as predicting whether it will rain tomorrow or understanding our chances of winning a small prize in a school raffle. In South Africa, being able to interpret data and understand probability is important for informed decision-making in various aspects of life, from understanding election results to making smart financial choices.

Lesson notes

2. 1. Collecting and Organizing Data Before we can represent data, we need to collect it. A common way to collect data is by using tally marks. Each tally mark represents one item. After every four tally marks, the fifth one crosses the previous four, making it easier to count in groups of five. We then organize this data into a frequency table, which shows how many times each item occurs.

Example: Let's say we surveyed 20 learners in our class about their favourite fruits. Here's how we collected the data using tally marks: Apples: |||| ||| Bananas: |||| | Oranges: |||| |||| Mangoes: || Now, we can organize this into a frequency table: | Fruit | Tally Marks | Frequency | | -------- | ----------- | --------- | | Apples | |||| ||| | 8 | | Bananas | |||| | | 6 | | Oranges | |||| |||| | 8 | | Mangoes | || | 2 | 2.

2. Representing Data: Bar Graphs A bar graph uses bars of different lengths to represent data. The length of each bar corresponds to the frequency of that category.

Steps to Create a Bar Graph: Draw the axes: Draw a horizontal axis (x-axis) and a vertical axis (y-axis).

Label the axes: The x-axis will show the categories (e.g., fruits). The y-axis will show the frequency (number of learners).

Choose a scale: Determine a suitable scale for the y-axis based on the highest frequency. For example, if the highest frequency is 10, we can use a scale of 1, 2, 3…

1

0. Draw the bars: Draw bars for each category. The height of the bar should match the frequency for that category.

Give the graph a title: The title should clearly describe what the graph shows.

Example: Using the fruit data from above, we can create a bar graph.

X-axis: Apples, Bananas, Oranges, Mangoes Y-axis: Frequency (0-8) Draw bars with heights corresponding to the frequencies in the table.

Title: "Favourite Fruits of Grade 5 Learners" 2.

3. Representing Data: Pictographs A pictograph uses pictures or symbols to represent data. Each picture represents a certain number of items. A key must be included to show what each picture represents.

Steps to Create a Pictograph: Choose a symbol: Select a picture that relates to the data. For example, for fruit data, you could use a picture of a fruit.

Determine the key: Decide what number each picture will represent. For example, one fruit picture could represent 2 learners.

Draw the pictures: Draw the correct number of pictures for each category, according to the key.

Give the graph a title: The title should clearly describe what the graph shows.

Example: Using the fruit data from above, let's create a pictograph where each fruit picture represents 2 learners.

Symbol: 🍎 (for apples), 🍌 (for bananas), 🍊 (for oranges), 🥭 (for mangoes)

Key: 🍎 = 2 learners, 🍌 = 2 learners, 🍊 = 2 learners, 🥭 = 2 learners Apples: 🍎🍎🍎🍎 Bananas: 🍌🍌🍌 Oranges: 🍊🍊🍊🍊 Mangoes: 🥭 Title: "Favourite Fruits of Grade 5 Learners" 2.

4. Understanding Probability Probability is the chance of something happening. We can describe the probability of an event using words like: Certain: It will definitely happen. (e.g., The sun will rise tomorrow.)

Likely: It will probably happen. (e.g., It is likely to rain in Cape Town in winter.)

Unlikely: It probably won't happen. (e.g., It is unlikely to snow in Durban in summer.)

Impossible: It cannot happen. (e.g., A pig will fly.) We can also express probability as a fraction. For example, if there are 4 marbles in a bag (1 red, 1 blue, 1 green, and 1 yellow), the probability of picking the red marble is 1 out of 4, or 1/

4. Example: In a bag, there are 3 red balls and 1 blue ball. What is the probability of picking a red ball? 3 out of 4, or 3/

4. It is likely. What is the probability of picking a blue ball? 1 out of 4, or 1/

4. It is unlikely. What is the probability of picking a green ball? Impossible. (0/4) Guided Practice (With Solutions)

Question 1: The following data represents the number of rainy days in different South African cities in the month of July: Cape Town: 20 days Durban: 5 days Johannesburg: 2 days Bloemfontein: 1 day Create a bar graph to represent this data.

Solution: Draw the axes. Label the x-axis as "City" and the y-axis as "Number of Rainy Days". Choose a scale for the y-axis from 0 to 20 (or slightly higher, like 22) with increments of

2. Draw bars for each city with heights corresponding to the number of rainy days: Cape Town: Bar height = 20 Durban: Bar height = 5 Johannesburg: Bar height = 2 Bloemfontein: Bar height = 1 Title the graph "Rainy Days in South African Cities (July)".

Question 2: Use the same data from Question 1 to create a pictograph. Let each umbrella symbol represent 2 rainy days.

Solution: Choose Umbrella Symbol: ☔ Key: ☔ = 2 rainy days Represent Rainy Days: Cape Town: ☔☔☔☔☔☔☔☔☔☔ (10 umbrellas)

Durban: ☔☔½ (2 and a half umbrellas - half an umbrella represents 1 day)

Johannesburg: ☔ (1 umbrella)

Bloemfontein: ½ (Half of an umbrella)

Title: "Rainy Days in South African Cities (July)" Question 3: A bag contains 2 green marbles, 3 blue marbles, and 5 yellow marbles.