Lesson Notes By Weeks and Term v5 - Grade 5

Lesson Video

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Performance objectives

• Collect and organise data using tally marks and tables.
• Represent data using pictographs.
• Interpret data from tables and pictographs.
• Use 'certain', 'possible', and 'impossible' for probability.
• Order events from most likely to least likely.

Lesson summary

Data handling and probability are essential skills that help us make sense of the world around us. In South Africa, we encounter data and probability every day, from reading news about weather patterns affecting our farms to understanding statistics about our favorite sports teams. Being able to collect, organise, and interpret data allows us to make informed decisions. Probability helps us understand the chances of different events happening, which is useful in games, weather forecasting, and even planning events.

Lesson notes

2.1 Data Collection and Organisation Data is information. We collect data by observing, counting, or asking questions. One common way to collect data is by using tally marks. A tally mark is a simple vertical line, and we group them in sets of five to make counting easier. (|||| represents 4, and |||| represents 5). We then organize this data into a table, which has rows and columns.

Example 1: Let's say we want to find out which fruit is the most popular among Grade 5 learners in Ms. Dlamini's class. We ask each learner to choose their favorite fruit from the following options: Apples, Bananas, Oranges, and Mangoes. Here's how we collect the data using tally marks: | Fruit | Tally Marks | |-----------|-------------| | Apples | |||| || | | Bananas | |||| |||| | | Oranges | |||| | | Mangoes | |||| | | Now, we can organize this data into a table showing the number of learners who chose each fruit: | Fruit | Number of Learners | |-----------|--------------------| | Apples | 7 | | Bananas | 9 | | Oranges | 5 | | Mangoes | 6 | 2.2 Pictographs A pictograph is a way to represent data using pictures or symbols. Each picture or symbol represents a certain number of items. It is important to have a key that specifies the number of items represented by each picture.

Example 2: Let's use the fruit data from Example 1 to create a pictograph. We'll use an apple icon 🍎 to represent two learners. | Fruit | Pictograph | |-----------|----------------------| | Apples | 🍎🍎🍎 🍎/2 | | Bananas | 🍎🍎🍎🍎 🍎/2 | | Oranges | 🍎🍎 🍎/2 | | Mangoes | 🍎🍎🍎 | Key: 🍎 = 2 Learners; 🍎/2 = 1 learner Explanation: For Apples, we have 7 learners. Since each apple represents 2 learners, we draw three whole apples (3 x 2 = 6 learners) and one half apple (1 learner). 2.3 Interpreting Data Interpreting data means understanding what the data tells us. We can answer questions about the data, compare different categories, and draw conclusions.

Example 3: Using the fruit data from Examples 1 and 2, we can answer the following questions: Which fruit is the most popular? (Bananas) Which fruit is the least popular? (Oranges) How many more learners chose Bananas than Mangoes? (9 - 6 = 3) How many learners participated in the survey in total? (7 + 9 + 5 + 6 = 27) 2.4 Probability Probability is the chance of something happening. We use words like "certain," "possible," and "impossible" to describe the probability of events.

Certain: The event will definitely happen. For example, "The sun will rise tomorrow" is certain.

Possible: The event might happen. For example, "It might rain tomorrow" is possible.

Impossible: The event will definitely not happen. For example, "A cow will fly" is impossible. We can also order events from most likely to least likely.

Example 4: Consider a bag containing 5 red balls and 2 blue balls. Let's consider the probability of picking a ball from the bag. It is possible to pick a red ball. It is possible to pick a blue ball. It is impossible to pick a green ball (since there are no green balls in the bag). Picking a red ball is more likely than picking a blue ball because there are more red balls in the bag. Guided Practice (With Solutions)

Question 1: The following data was collected about the number of cars passing by a school in one hour: | Colour | Tally Marks | |---------|-------------| | Red | |||| |||| | | Blue | |||| || | | White | |||| |||| |||| | | Black | |||| | | a) Create a table to show the number of cars of each colour. b) Which colour of car was most common? c) Which colour of car was least common?

Solution: a) | Colour | Number of Cars | |---------|----------------| | Red | 8 | | Blue | 7 | | White | 15 | | Black | 6 | b) White car was most common. c) Black car was least common.

Commentary: This question reinforces the ability to transfer data from tally marks to a table. It also encourages interpreting the data to identify the most and least frequent occurrences.

Question 2: Represent the following data using a pictograph, where one picture represents 5 items.

Data: Learners who like different sports.

Soccer: 20, Netball: 15, Rugby: 10, Cricket:

5. Use a ball ⚽ as the symbol.

Solution: | Sport | Pictograph | |----------|-------------------| | Soccer | ⚽⚽⚽⚽ | | Netball | ⚽⚽⚽ | | Rugby | ⚽⚽ | | Cricket | ⚽ | Key: ⚽ = 5 Learners

Commentary: This question checks the understanding of pictographs and the ability to choose an appropriate scale.

Question 3: Consider a standard six-sided die (with numbers 1 to 6). Describe the probability of the following events using "certain," "possible," or "impossible." a) Rolling a number less than 7. b) Rolling a 7. c) Rolling an even number.

Solution: a) Certain b) Impossible c) Possible

Commentary: This problem introduces probability concepts using a familiar tool (a die). It requires the student to understand the possible outcomes and use the correct vocabulary to describe the probability.