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.
• Interpret data from bar graphs.
• Use probability words like certain, likely, unlikely, and impossible.
• List all possible outcomes of simple events.

Lesson summary

Data handling and probability are essential skills that help us understand and interpret information in our everyday lives. In South Africa, we encounter data everywhere, from weather forecasts on the news to statistics about our favourite sports teams, and even when voting in elections. Understanding probability helps us make informed decisions, like judging the likelihood of rain or understanding the chances of winning a raffle. This week, we will learn how to collect, organize, represent, and interpret data using bar graphs, and we will also explore the concept of probability and how to describe the likelihood of events happening.

Lesson notes

2.1 Data Collection and Organisation Data is information. We can collect data by counting, measuring, asking questions (surveys), or observing. To organise data, we can use tally marks and frequency tables.

Tally Marks: Tally marks are a quick way to count things. We make a mark for each item, and every fifth mark crosses the previous four, making it easy to count groups of five.

For example: |||| represents 4 |||| represents 5 Frequency Table: A frequency table shows how often something occurs.

It has two columns: one for the item and one for the frequency (how many times it appears).

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

Here are the responses: Apple, Banana, Banana, Orange, Apple, Strawberry, Banana, Apple, Orange, Apple, Strawberry, Apple, Banana, Orange, Banana, Apple, Apple, Strawberry, Orange, Banana To organize this data, we use tally marks and a frequency table: | Fruit | Tally Marks | Frequency | |------------|-------------|-----------| | Apple | |||| || | 7 | | Banana | |||| | | 6 | | Orange | |||| | 4 | | Strawberry | ||| | 3 | 2.2 Representing Data: Bar Graphs A bar graph uses bars to show data. The height of each bar represents the frequency of that item.

Key features of a bar graph are: Title: Tells us what the graph is about.

Axes: The horizontal (x-axis) and vertical (y-axis) lines.

Labels: Words or numbers that describe what each axis represents (e.g., Fruit, Number of Learners).

Scale: The numbers on the y-axis that show the frequency. Choosing an appropriate scale is very important.

How to choose a scale: Look at the largest frequency in your data. Your scale must go up to at least that number. Choose an interval (the amount between each number on the scale) that is easy to read (e.g., 1, 2, 5, 10).

Example 2: Creating a Bar Graph from the Fruit Data Using the frequency table above, we can create a bar graph: Draw the axes: Draw a horizontal (x) and vertical (y) axis.

Label the x-axis: Write the names of the fruits (Apple, Banana, Orange, Strawberry) along the x-axis.

Choose a scale for the y-axis: The highest frequency is

7. We can use a scale from 0 to 8, with an interval of

1. Label the y-axis: Write "Number of Learners".

Draw the bars: Draw a bar for each fruit, with the height of the bar corresponding to the frequency.

Title the graph: "Favourite Fruits of Grade 5 Learners" (Imagine a bar graph here, with bars of heights 7, 6, 4, and 3 for Apple, Banana, Orange, and Strawberry, respectively) 2.3 Interpreting Data: Answering Questions from a Bar Graph Once we have a bar graph, we can use it to answer questions about the data.

Example 3: Interpreting the Fruit Bar Graph Which fruit is the most popular? Apple (because it has the highest bar). Which fruit is the least popular? Strawberry (because it has the lowest bar). How many learners like bananas? 6 (read the height of the bar for bananas). How many more learners like apples than oranges? 7 - 4 = 3 (subtract the height of the orange bar from the height of the apple bar). 2.4 Probability: Describing the Chance of Events Probability is the chance of something happening.

We can use words like: Certain: It will definitely happen (100% chance).

Example: The sun will rise tomorrow.

Likely: It has a good chance of happening.

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

Unlikely: It has a small chance of happening.

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

Impossible: It cannot happen (0% chance).

Example: A dog will speak Afrikaans.

Example 4: Probability in Everyday Life Rolling a standard six-sided die: It is impossible to roll a

7. It is likely to roll a number less than

5. Drawing a ball from a bag containing only red balls: It is certain that you will draw a red ball. 2.5 Listing Possible Outcomes The outcomes of an event are the possible things that can happen.

Example 5: Possible Outcomes Flipping a coin: The possible outcomes are Heads or Tails.

Rolling a six-sided die: The possible outcomes are 1, 2, 3, 4, 5, or

6. Drawing a card from a deck with 10 cards numbered 1 to 10: The possible outcomes are 1, 2, 3, 4, 5, 6, 7, 8, 9,

1

0. Guided Practice (With Solutions)

Question 1: Thandi surveyed her classmates about their favourite South African animals.

Here are the results: Elephant (5), Lion (8), Springbok (10), Zebra (7). Create a frequency table to organize this data.

Solution: | Animal | Frequency | |------------|-----------| | Elephant | 5 | | Lion | 8 | | Springbok | 10 | | Zebra | 7 | Explanation: We simply counted how many times each animal was mentioned and recorded it in the frequency column.

Question 2: Use the frequency table from Question 1 to draw a bar graph representing the favourite South African animals. Choose an appropriate scale and label your axes clearly.

Solution: (Imagine a bar graph here, with bars of heights 5, 8, 10, and 7 for Elephant, Lion, Springbok, and Zebra, respectively.