Lesson Notes By Weeks and Term v5 - Grade 5

Lesson Video

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Performance objectives

• Collect and organize data using tally marks and frequency tables.
• Represent data using bar graphs and pictographs.
• Interpret data from graphs to answer questions.
• Describe the likelihood of events as certain, likely, unlikely, or impossible.
• Conduct simple probability experiments.

Lesson summary

Data handling and probability are essential skills in mathematics and everyday life. In South Africa, understanding data helps us interpret information about our communities, such as population statistics, school performance, and even the popularity of different sports. Probability allows us to make informed guesses about events, from predicting the weather to understanding the chances of winning a school raffle. This week, we will delve into collecting, organizing, representing, and interpreting data, as well as explore basic probability concepts. This will equip you with the tools to become critical thinkers and make sense of the world around you.

Lesson notes

2.1 Data Collection and Organisation Data is information.

We can collect data in many ways: through surveys, observations, or experiments. Once we collect data, we need to organise it so that it is easy to understand. Two common methods are using tally marks and frequency tables.

Tally Marks: Tally marks are a quick way to count items. Each item is represented by a stroke (|). After every four strokes, the fifth stroke crosses the previous four, making a group of five (||||).

Frequency Table: A frequency table shows how many times each item appears in a set of data.

It usually has two columns: one for the items and one for the frequency (number of times the item appears).

Example 1: Let's say we asked 20 Grade 5 learners about their favourite fruit.

Here are the results: Apple, Banana, Apple, Orange, Banana, Banana, Apple, Apple, Orange, Grape, Apple, Banana, Orange, Apple, Grape, Banana, Apple, Orange, Apple, Banana Using Tally Marks: Apple: |||| || (7)

Banana: |||| | (6)

Orange: |||| (4)

Grape: || (2)

Frequency Table: | Fruit | Frequency | | -------- | --------- | | Apple | 7 | | Banana | 6 | | Orange | 4 | | Grape | 2 | 2.2 Data Representation: Bar Graphs and Pictographs Once we have organised our data, we can represent it visually using bar graphs and pictographs.

Bar Graph: A bar graph uses bars of different lengths to represent the frequency of each item. The longer the bar, the higher the frequency. Bar graphs have a horizontal axis (x-axis) and a vertical axis (y-axis). One axis shows the categories (e.g., fruit types), and the other axis shows the frequency (number of learners).

Pictograph: A pictograph uses pictures or symbols to represent data. Each picture represents a certain number of items. A key is used to show what each picture represents. Pictographs are a fun and engaging way to represent data, especially for younger learners.

Example 2: Using the fruit data from Example 1, let's create a bar graph and a pictograph.

Bar Graph: (Imagine a bar graph with Fruit types on the x-axis and Frequency on the y-axis.

The bars would be: Apple = 7, Banana = 6, Orange = 4, Grape = 2). Remember to label the axes and give the graph a title (e.g., "Favourite Fruits of Grade 5 Learners").

Pictograph: Key: 🍎 = 1 Learner | Fruit | Representation | | -------- | -------------------------------------------- | | Apple | 🍎🍎🍎🍎🍎🍎🍎 | | Banana | 🍎🍎🍎🍎🍎🍎 | | Orange | 🍎🍎🍎🍎 | | Grape | 🍎🍎 | 2.3 Data Interpretation Data interpretation involves looking at the data representation (bar graph or pictograph) and drawing conclusions or answering questions.

Example 3: Using the bar graph or pictograph from Example 2: Which fruit is the most popular? (Answer: Apple) Which fruit is the least popular? (Answer: Grape) How many learners chose Banana? (Answer: 6) How many more learners chose Apple than Orange? (Answer: 3) 2.4 Probability: Likelihood of Events Probability is the chance of something happening. We use words like "certain," "likely," "unlikely," and "impossible" to describe the likelihood of events.

Certain: Something that will definitely happen. (

Example: The sun will rise tomorrow.)

Likely: Something that has a good chance of happening. (

Example: It is likely to rain in Cape Town in winter.)

Unlikely: Something that has a small chance of happening. (

Example: It is unlikely to snow in Durban in summer.)

Impossible: Something that cannot happen. (

Example: A dog will start speaking English.)

Example 4: Imagine a bag with 5 red balls and 1 blue ball. It is likely that you will pick a red ball. It is unlikely that you will pick a blue ball. It is impossible to pick a green ball from the bag. 2.5 Simple Probability Experiments We can also explore probability through simple experiments, like tossing a coin or rolling a dice. We record the results to see how often each outcome occurs.

Example 5: Tossing a coin 20 times and recording whether it lands on heads or tails. We can then create a frequency table to show the number of heads and tails. Guided Practice (With Solutions)

Question 1: A survey was conducted in a Grade 5 class to find out their favourite South African snack.

The results are: Biltong, Droëwors, Biltong, Koeksisters, Droëwors, Biltong, Biltong, Koeksisters, Droëwors, Droëwors, Biltong, Biltong, Droëwors, Biltong, Biltong, Koeksisters, Biltong, Droëwors, Biltong, Droëwors. Create a frequency table to represent this data.

Solution: | Snack | Frequency | | ----------- | --------- | | Biltong | 10 | | Droëwors | 7 | | Koeksisters | 3 | Explanation: We counted how many times each snack appeared in the list and recorded it in the frequency column.

Question 2: Use the frequency table from Question 1 to create a pictograph.