Lesson Notes By Weeks and Term v5 - Grade 4

Lesson Video

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Performance objectives

• Collect and organise data using tally marks and frequency tables.
• Represent data using pictographs with a key.
• Draw and interpret bar graphs with a suitable scale.
• Answer questions using your graphs and tables.

Lesson summary

Data handling is a vital skill in mathematics and in everyday life. In South Africa, we encounter data constantly – from election results to sports statistics, weather forecasts, and even the prices of groceries. Understanding how to collect, organise, and represent data helps us to make informed decisions and understand the world around us. For example, knowing the rainfall patterns in your region can help you plan your vegetable garden effectively! This week, we will focus on collecting and representing data using tally marks, pictographs, and bar graphs. We will practice reading and interpreting these representations to answer questions about the data.

Lesson notes

2. 1. Collecting Data with Tally Marks Tally marks are a simple way to count things quickly. Each time you see something, you make a mark. Usually, we use four vertical lines and then a diagonal line across the four to represent five. This makes it easier to count in groups of five.

Example: Let’s say we want to find out the favourite fruits of learners in our class. We can go around and ask each learner to tell us their favourite fruit. We will use tally marks to record the answers. | Fruit | Tally Marks | |----------|-------------| | Apple | |||| || | | Banana | |||| |||| |||| | | Orange | |||| ||| | | Mango | |||| | | Here, we see that 7 learners chose apples, 15 chose bananas, 8 chose oranges, and 5 chose mangoes. 2.

2. Frequency Tables A frequency table shows how often something occurs. It’s just a more organised way of showing the information we collected using tally marks. We simply write the number of tally marks as a number (the frequency).

Example: Using the data from the fruit survey above, we can create a frequency table: | Fruit | Frequency | |----------|-----------| | Apple | 7 | | Banana | 15 | | Orange | 8 | | Mango | 5 | 2.

3. Pictographs A pictograph uses pictures or symbols to represent data. Each picture represents a certain number of items. A key is very important in a pictograph to tell you what each picture stands for.

Example: Let's represent the favourite fruit data using a pictograph. Let's say that each fruit picture represents 2 learners. | Fruit | Pictograph | |----------|---------------------------------------------| | Apple | 🍎🍎🍎 🍎 (Each apple represents 2 learners, last apple is half for 1 learner) | | Banana | 🍌🍌🍌🍌🍌🍌🍌 🍌 (Each banana represents 2 learners, last banana is half for 1 learner) | | Orange | 🍊🍊🍊🍊 | | Mango | 🥭🥭🥭 | Important: Always include a key!

In this case: 🍎 = 2 learners, 🍌 = 2 learners, 🍊 = 2 learners, 🥭 = 2 learners. If the number isn't even, you might need to use half a picture. 2.

4. Bar Graphs A bar graph uses bars of different lengths to represent data. The length of the bar shows how much of something there is.

The graph has two axes: a horizontal axis (usually showing the categories) and a vertical axis (usually showing the frequency or amount).

Example: Let’s create a bar graph to represent the favourite fruit data.

Draw the Axes: Draw a horizontal and a vertical line.

Label the Axes: Label the horizontal axis with the names of the fruits (Apple, Banana, Orange, Mango). Label the vertical axis with "Number of Learners".

Choose a Scale: Look at the highest frequency (15 in this case). Choose a scale that goes up to at least that number. We could choose a scale that goes up to 16, counting in 2s. Mark the scale on the vertical axis (0, 2, 4, 6, 8, 10, 12, 14, 16).

Draw the Bars: Draw a bar for each fruit. The height of the bar should match the frequency. For example, the bar for Apple should go up to

7. Since our scale is in twos, 7 will be halfway between 6 and

8. The bar for Banana should go up to 15, half way between 14 and

1

6. Give the Graph a Title: "Favourite Fruits of Grade 4 Learners" Choosing the Right Scale: Choosing the right scale is important. If the scale is too small, the bars will be very tall and the graph will be difficult to read. If the scale is too big, the bars will be very short and the differences between them will be hard to see. Consider the largest number in your data set when deciding on your scale. Also, consider what intervals to use. Intervals of 1, 2, 5, or 10 are usually easiest to read. Guided Practice (With Solutions)

Question 1: Sipho asked his classmates which pet they own.

He recorded the following information: 5 learners own dogs, 3 learners own cats, 2 learners own birds, and 4 learners own fish. Create a frequency table to show this data.

Solution: | Pet | Frequency | |---------|-----------| | Dog | 5 | | Cat | 3 | | Bird | 2 | | Fish | 4 |

Commentary: We simply list the categories (the pets) and the corresponding number of learners (frequency). This is a direct application of the definition of a frequency table.

Question 2: Use the data from Question 1 to create a pictograph. Let one picture of a paw print (🐾) represent 1 pet owner.

Solution: | Pet | Pictograph | |---------|----------------| | Dog | 🐾🐾🐾🐾🐾 | | Cat | 🐾🐾🐾 | | Bird | 🐾🐾 | | Fish | 🐾🐾🐾🐾 | Key: 🐾 = 1 pet owner

Commentary: Since each picture represents 1 pet owner, we simply draw the corresponding number of paw prints for each pet.

Question 3: Use the data from Question 1 to create a bar graph.

Solution: Draw and label the axes (Pets on the horizontal axis, Number of Learners on the vertical axis). Choose a scale. The highest frequency is 5, so we can choose a scale that goes up to 6 (counting in 1s). Draw the bars for each pet, making sure the height of the bar matches the frequency. Title the graph "Pet Ownership in Sipho's Class".

Commentary: The scale is crucial here.