Lesson Notes By Weeks and Term v5 - Grade 4

Lesson Video

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Performance objectives

• Collect data using surveys.
• Organize data with tally marks and frequency tables.
• Show data using pictographs.
• Show data using bar graphs.
• Understand and interpret graphs and tables.

Lesson summary

Data handling is an important skill in mathematics that allows us to collect, organize, and represent information in a meaningful way. It helps us to understand patterns, make informed decisions, and solve problems. In South Africa, we use data handling every day, from understanding weather reports for farming, to analyzing the popularity of different sports teams, and even in understanding health statistics. This week, we'll focus on collecting data and representing it visually using bar graphs and pictographs. Imagine needing to know which fruit is the most popular amongst your classmates so that you can order enough for a party. Data handling gives us the tools to figure that out!

Lesson notes

2.1 What is Data? Data is simply information. It can be about anything!

For example: The favourite colours of Grade 4 learners. The number of cars that pass by a school in an hour. The different types of fruit sold at a local market. The number of people who speak different languages in a community. 2.2 Collecting Data We can collect data in many ways: Surveys: Asking people questions. For example, "What is your favourite sport?" Observation: Watching and recording what happens. For example, counting the number of birds in a park. 2.3 Organizing Data Once we have collected our data, we need to organize it so we can easily understand it.

Two common ways to do this are: Tally Marks: Using vertical lines to represent each piece of data. We group them in fives to make counting easier.

For example: |||| represents 4, and |||| represents

5. Frequency Tables: A table that shows how many times each piece of data appears.

Example: Let's say we asked 20 learners what their favourite fruit is. | Fruit | Tally Marks | Frequency | | --------- | ----------- | --------- | | Apples | |||| || | 7 | | Bananas | |||| | | 6 | | Oranges | |||| ||| | 8 | | Grapes | | | 1 | 2.4 Representing Data Representing data visually helps us to see patterns and understand the information more easily.

We will focus on two types of graphs: Pictographs: Uses pictures or symbols to represent data. Each picture represents a certain number of items. It's important to have a key that tells you what each picture represents.

Example: Let's use a pictograph to show the number of learners who like different animals: | Animal | Number of Learners | | -------- | ------------------ | | Dogs | 10 | | Cats | 8 | | Birds | 6 | | Fish | 4 | Pictograph: | Animal | Representation | | -------- | ------------------------------------ | | Dogs | 🐶 🐶 🐶 🐶 🐶 | | Cats | 🐱 🐱 🐱 🐱 | | Birds | 🐦 🐦 🐦 | | Fish | 🐠 🐠 | Key: 🐶 = 2 Learners Bar Graphs: Uses bars of different heights to represent data. The height of the bar shows the frequency of each item. Bar graphs have axes (horizontal and vertical lines) that are labeled. The axes must have an appropriate scale (e.g., counting by 1s, 2s, 5s, or 10s, depending on the data).

Example: Using the same animal data, let's create a bar graph.

Bar Graph: ``` Number of Learners 10| | * 9| | * 8| * | * 7| * | * 6| | 5| | 4| * | * 3| * | * 2| * | * 1| 0|----------------------- Dogs Cats Birds Fish Animal ``` 2.5 Interpreting Data Interpreting data means looking at the graph or table and understanding what it tells us.

For example: Which item is the most popular? (Look for the tallest bar or the largest number of symbols). Which item is the least popular? (Look for the shortest bar or the smallest number of symbols). How many more learners like apples than bananas? (Subtract the number of learners who like bananas from the number who like apples). Guided Practice (With Solutions)

Question 1: A class of Grade 4 learners were asked about their favourite colour.

Here are the results: Red (8), Blue (12), Green (6), Yellow (4). a) Create a frequency table to show this data. b) Represent this data using a pictograph. Use a circle (⚪) to represent 2 learners.

Solution: a)

Frequency Table: | Colour | Frequency | | -------- | --------- | | Red | 8 | | Blue | 12 | | Green | 6 | | Yellow | 4 | b)

Pictograph: | Colour | Representation | | -------- | ------------------------------ | | Red | ⚪ ⚪ ⚪ ⚪ | | Blue | ⚪ ⚪ ⚪ ⚪ ⚪ ⚪ | | Green | ⚪ ⚪ ⚪ | | Yellow | ⚪ ⚪ | Explanation: We create a table with colours as the rows and the count of each colour (frequency) in the second column. For the pictograph, we use circles where one circle represents 2 learners, making it easier to display larger numbers.

Question 2: Use the following bar graph showing the number of books borrowed from the library each day: ``` Number of Books 10| * | * 9| * | * 8| * | * 7| | 6| * | * 5| | 4| | 3| | 2| | 1| 0|----------------------- Mon Tue Wed Thu Day ``` a) How many books were borrowed on Monday? b) On which day were the most books borrowed? c) How many more books were borrowed on Wednesday than on Tuesday?

Solution: a) 7 books were borrowed on Monday. b) Thursday has the tallest bar, so the most books were borrowed on Thursday (10 books). c) Wednesday had 6 books borrowed and Tuesday had 5, so 6-5=1 more book was borrowed on Wednesday.

Explanation: We read the height of each bar from the graph to answer the questions. To find the difference, we subtract the number of books borrowed on Tuesday from Wednesday.

Question 3: A fruit vendor at the market counted the number of each type of fruit he sold in one day.

Apples: 15, Bananas: 20, Oranges: 25, Mangoes:

1

0. Create a scaled bar graph using intervals of 5 to represent this data.

Solution: ``` Number of Fruits 25| * | * 20| | 15| * | * 10| | 5| 0|----------------------- Apples BananasOrangesMangoes Fruit ``` Explanation: The y-axis represents the number of fruits, and the x-axis represents the type of fruits.