Lesson Notes By Weeks and Term v5 - Grade 5

Lesson Video

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Performance objectives

• Collect data using tally marks and questionnaires.
• Organize data using frequency tables.
• Represent data using pictographs, bar graphs, and pie charts.
• Describe the likelihood of events as certain, likely, unlikely, or impossible.
• Interpret data from graphs to answer questions.

Lesson summary

Data handling and probability are essential skills for understanding the world around us. In South Africa, we see data everywhere, from weather forecasts on SABC to statistics about school performance and even voting results. Understanding how data is collected, organised, and interpreted helps us make informed decisions. Probability helps us understand the chances of something happening, which is useful in games, sports, and even predicting traffic patterns. This week, we will focus on collecting, organizing, and representing data. We will also touch on the basic idea of probability as the chance of an event occurring.

Lesson notes

Data Collection Data is information. We collect data by asking questions, observing, or measuring. The first step in data handling is collecting data in a systematic way. One common way to collect data is using tally marks.

Example: Imagine we want to find out what the favourite fruits are of the children in Grade 5 at Mzansi Primary School. We could ask each learner and record their answer using tally marks. | Fruit | Tally Marks | Frequency | | --------- | ----------- | --------- | | Apples | IIII | 4 | | Bananas | IIIII II | 7 | | Oranges | IIIII | 5 | | Mangoes | III | 3 | Each tally mark represents one person's answer. The "Frequency" column is just the number of tally marks written as a numeral. Another way to collect data is through simple questionnaires.

For example: Questionnaire: What is your favourite sport? (Rugby, Soccer, Cricket, Netball, Other) How do you get to school? (Walk, Car, Bus, Bicycle) Frequency Tables A frequency table organizes data into categories and shows how often each category appears. The table above showing favourite fruits is an example of a frequency table. The categories are the different fruits (Apples, Bananas, Oranges, Mangoes), and the frequency shows how many learners chose each fruit. Representing Data Graphically Once we have our data organized in a frequency table, we can represent it visually using different types of graphs: Pictograph: Uses pictures to represent data. Each picture represents a certain number of items.

Example: Using the favourite fruits data. Let each fruit picture represent 1 learner. | Fruit | Pictograph | | --------- | ----------------------------------------- | | Apples | 🍎🍎🍎🍎 | | Bananas | 🍌🍌🍌🍌🍌🍌🍌 | | Oranges | 🍊🍊🍊🍊🍊 | | Mangoes | 🥭🥭🥭 | Key: 🍎= 1 learner, 🍌= 1 learner, 🍊 = 1 learner, 🥭 = 1 learner Bar Graph: Uses bars of different lengths to represent data. The length of each bar represents the frequency of that category.

Example: Using the favourite fruits data. (Imagine a bar graph here, with fruits on the x-axis and frequency on the y-axis. The bar for Apples would reach a height of 4, Bananas to a height of 7, Oranges to a height of 5, and Mangoes to a height of 3.)

Important elements of a bar graph: Title: Favourite Fruits of Grade 5 Learners X-axis label: Fruit Y-axis label: Number of Learners Scale: (e.g., 1 unit = 1 learner)

Pie Chart: A circular chart divided into slices. Each slice represents a proportion of the whole. The size of each slice corresponds to the frequency of that category. Pie charts are best used when you want to show how each category contributes to the overall total. For now, learners just need a general understanding of its use. Calculating the angles for a pie chart is beyond the scope of Grade 5, but teachers may use resources to create them for demonstration.

Example: (Imagine a pie chart divided into four sections representing Apples, Bananas, Oranges, and Mangoes. The Banana section would be the largest, followed by Oranges, Apples, and then Mangoes.) Probability Probability is the chance of something happening. We can describe the likelihood of events using words like: Certain: It will definitely happen.

Likely: It has a good chance of happening.

Unlikely: It probably won't happen.

Impossible: It cannot happen.

Example: It is certain that the sun will rise tomorrow. It is likely that you will eat supper tonight. It is unlikely that it will snow in Durban in summer. It is impossible to fly without wings. Guided Practice (With Solutions)

Question 1: A class of Grade 5 learners were asked what their favourite colour is.

The results are shown below: Red: IIIII Blue: IIIII IIIII Green: IIII Yellow: II a) Create a frequency table to represent this data. b) Draw a bar graph to represent the data.

Solution: a)

Frequency Table: | Colour | Tally Marks | Frequency | | ------- | ----------- | --------- | | Red | IIIII | 5 | | Blue | IIIII IIIII | 10 | | Green | IIII | 4 | | Yellow | II | 2 |

Commentary: We simply counted the tally marks for each colour to determine the frequency. b)

Bar Graph: (Imagine a bar graph here, with colours on the x-axis and frequency on the y-axis. Red bar up to 5, Blue bar up to 10, Green bar up to 4, Yellow bar up to

2. Include title and axis labels as described above.)

Commentary: We made sure the bars' heights match the frequencies in the table. Remember to add a title and labels to your graph.

Question 2: Here is a pictograph showing the number of cars sold by a dealership in one week: | Day | Number of Cars | | -------- | -------------- | | Monday | 🚗🚗🚗 | | Tuesday | 🚗🚗 | | Wednesday| 🚗🚗🚗🚗 | | Thursday | 🚗 | | Friday | 🚗🚗🚗🚗🚗 | Key: 🚗 = 2 cars a) How many cars were sold on Wednesday? b) On which day were the fewest cars sold? c) How many cars were sold in total during the week?