Lesson Notes By Weeks and Term v3 - Primary 4
Bar Graph
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Bar Graph
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Subject: General Mathematics
Class: Primary 4
Term: 2nd Term
Week: 4
Theme: Everyday Statistics
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Watch on YouTubeSee Facebook postdraw bar graphs read bar graphs identify bar graph mode identify the most common events/ data in daily life activities
tallest bar (for vertical graphs) or the longest bar (for horizontal graphs).
Example: In the "Favourite Colours" graph, the bar for 'Blue' is the tallest (frequency of 8).
Therefore, 'Blue' is the mode, meaning it is the favourite colour of most students. Worked Example for Drawing and Interpreting: Data: Number of different types of livestock in Farmer Audu's compound.
Goats: 15 Chickens: 25 Cows: 5 Sheep: 10 Steps to draw a vertical bar graph:
1. Title: "Livestock in Farmer Audu's Compound"
2. Horizontal Axis (Categories): Goats, Chickens, Cows, Sheep.
Label: "Types of Livestock"
3. Vertical Axis (Frequency): Numbers representing quantity. Highest frequency is
2
5. A scale of 1 unit = 5 livestock animals would be good (0, 5, 10, 15, 20, 25).
Label: "Number of Animals"
4. Draw Bars: Goats: Bar up to
1
5. Chickens: Bar up to
2
5. Cows: Bar up to 5. * Sheep: Bar up to 10. (Teacher would draw this on the board step-by-step) Interpretation Questions from the above graph:
1. How many chickens does Farmer Audu have? (Answer: 25)
2. Which type of livestock does he have the fewest of? (Answer: Cows)
3. What is the total number of goats and sheep he has? (Answer: 15 + 10 = 25)
4. What is the mode of livestock in Farmer Audu's compound? (Answer: Chickens, as it has the highest frequency of 25). A. What is a Bar Graph? A bar graph is a chart or graph that uses rectangular bars to show comparisons among categories of data. The bars can be plotted vertically or horizontally. The length or height of each bar represents the quantity or frequency of the category it represents.
B. Components of a Bar Graph:
1. Title: A clear, concise heading that explains what the graph is about. (e.g., "Favourite Fruits of Primary 4 Students").
2. Axes: Horizontal Axis (x-axis): Usually represents the categories being compared (e.g., names of fruits, types of vehicles).
Vertical Axis (y-axis): Usually represents the frequency or quantity of each category (e.g., number of students, number of vehicles).
Note: For horizontal bar graphs, these roles are swapped: categories on the vertical axis and frequency on the horizontal axis.
3. Labels: Each axis must have a label describing what it represents. (e.g., "Types of Fruits" for the horizontal axis, "Number of Students" for the vertical axis).
4. Scale: A set of numbers along the frequency axis that shows how much each unit represents. The scale must be consistent (e.g., counting in 1s, 2s, 5s, 10s). It should start from zero.
5. Bars: Rectangular blocks whose length/height corresponds to the frequency of each category. The bars should be of equal width and have equal spacing between them.
C. Types of Bar Graphs:
1. Vertical Bar Graph: Bars extend upwards from the horizontal axis. Categories are on the horizontal axis. Frequencies are on the vertical axis.
2. Horizontal Bar Graph: Bars extend sideways from the vertical axis. Categories are on the vertical axis. Frequencies are on the horizontal axis.
D. How to Draw a Bar Graph (Step-by-Step for Vertical Bar Graph): Let's use an example: Data: Favourite colours of 20 Primary 4 students.
Red: 6, Blue: 8, Green: 4, Yellow: 2
1. Collect and Organise Data: (Already done in the example above).
2. Draw the Axes: Draw a horizontal line (x-axis) and a vertical line (y-axis) intersecting at a point (the origin, usually 0).
3. Label the Axes: Horizontal Axis: "Colours" (for the categories).
Vertical Axis: "Number of Students" (for the frequency).
4. Choose a Scale: Look at the highest frequency (8 in this case). A scale of 1 unit representing 1 student would be suitable. Mark numbers (0, 1, 2, 3, ... 8) along the vertical axis, ensuring even spacing.
5. Plot the Categories: Mark equally spaced points along the horizontal axis for each colour (Red, Blue, Green, Yellow).
6. Draw the Bars: For each category, draw a rectangular bar extending from the horizontal axis up to the corresponding frequency on the vertical axis.
Red: Bar goes up to
6. Blue: Bar goes up to
8. Green: Bar goes up to
4. Yellow: Bar goes up to
2. Ensure all bars have the same width and equal gaps between them.
7. Add a Title: "Favourite Colours of Primary 4 Students."
E. How to Read a Bar Graph: To read a bar graph, locate the category of interest on the appropriate axis, then move along the bar to determine its corresponding frequency or quantity on the other axis.
Example: In the "Favourite Colours" graph, to find how many students like Blue, locate 'Blue' on the horizontal axis, follow the bar up, then move horizontally to the left to read the value on the vertical axis (which is 8).
F. Identifying the Mode from a Bar Graph: The mode is the category with the highest frequency. In a bar graph, this corresponds to the tallest bar (for vertical graphs) or the longest bar (for horizontal graphs).
Example: In the "Favourite Colours" graph, the bar for 'Blue' is the tallest (frequency of 8).
Therefore, 'Blue' is the mode, meaning it is the favourite colour of most students. Worked Example for Drawing and Interpreting: Data: Number of different types of livestock in Farmer Audu's compound.
Goats: 15 Chickens: 25 Cows: 5 Sheep: 10 Steps to draw a vertical bar graph:
1. Title: "Livestock in Farmer Audu's Compound"
2. Horizontal Axis (Categories): Goats, Chickens, Teacher Activity: Divide the class into small groups. Provide each group with a simple data collection task (e.g., "Ask 5 classmates their favourite Nigerian fruit: Mango, Orange, Pineapple, Watermelon").
2. Student Activity: Each group collects data, then works together to draw a bar graph (either vertical or horizontal) representing their collected data on a small chart paper or in their books. They should also identify the mode of their data.
3. Teacher Activity: Circulate among groups, providing guidance and checking for understanding of drawing and interpretation.
F. Lesson Conclusion (5 minutes)
1. Teacher Activity: Briefly summarise the key points: what a bar graph is, its components, how to draw it, how to read it, and how to find the mode.
2. Student Activity: Learners share one new thing they learned or one way they can use bar graphs in their daily lives.
Materials: Whiteboard/Blackboard, markers/chalk, rulers, exercise books, pencils, chart papers, pre-drawn bar graphs (optional), actual data sets relevant to the local environment.
A. Introduction (10 minutes)
1. Teacher Activity: Begin by asking learners about data they encounter daily (e.g., number of classmates present, types of food eaten, vehicles seen on the road). Ask how they might show this information clearly.
2. Teacher Activity: Briefly review pictograms as a prior knowledge link. Explain that bar graphs are another way to show data, often clearer and more precise than pictograms, especially for larger numbers.
3. Student Activity: Learners share examples of daily data and discuss how it could be counted.
B. Development Phase 1: Drawing Bar Graphs (20 minutes)
Performance Objective Covered: 1. draw bar graphs
1. Teacher Activity: Present a simple data set collected from the class, e.g., "Favourite Local Snacks of Primary 4 Students". (e.g., Puff-puff: 7, Akara: 5, Chin Chin: 9, Kuli-kuli: 4).
2. Teacher Activity: Guide learners through the step-by-step process of drawing a vertical bar graph on the board, explaining each component (title, axes, labels, scale, bars, equal width/spacing). Emphasise the importance of a consistent scale.
Step 1: Draw the L-shaped axes.
Step 2: Label horizontal axis (Snack Types) and vertical axis (Number of Students).
Step 3: Determine a suitable scale for the vertical axis (e.g., 1 unit = 1 student). Mark the scale.
Step 4: Mark equal spacing for categories on the horizontal axis.
Step 5: Draw the bars according to the frequencies.
Step 6: Add a title.
3. Student Activity: Learners draw the same bar graph in their exercise books as the teacher demonstrates, ensuring they follow all steps. Teacher moves around to assist and check for understanding.
4. Teacher Activity: Briefly demonstrate how the same data could be represented as a horizontal bar graph, highlighting the swapping of axes for categories and frequencies. (No need for detailed drawing, just a sketch).
5. Student Activity: Learners discuss in pairs the differences between vertical and horizontal bar graphs.
C. Development Phase 2: Reading Bar Graphs (15 minutes)
Performance Objective Covered: 2. read bar graphs
1. Teacher Activity: Display a pre-drawn bar graph (chart paper or projected) on a different topic, e.g., "Number of Students who took various transportation to school today" (e.g., Walk: 12, Keke Napep: 8, Bicycle: 5, Car: 3).
2. Teacher Activity: Ask questions that require learners to extract specific information from the graph. "How many students came by Keke Napep?" "Which mode of transport did the fewest students use?" "How many more students walked than rode bicycles?" "What is the total number of students represented in this graph?"
3. Student Activity: Learners raise their hands to answer the questions based on the displayed bar graph. Encourage them to explain how they found the answers.
D. Development Phase 3: Identifying Bar Graph Mode (10 minutes) * Performance Objective Covered: 3. identify bar graph mode, 4. identify the most common events/ data in daily life activities
1. Teacher Activity: Revisit the "Transportation to school" bar graph. Introduce the concept of "mode" as the item or category that appears most frequently (has the highest number).
2. Teacher Activity: Ask learners to identify the mode from the graph (e.g., "Walk", as it has the tallest bar/highest frequency of 12). Explain that this tells us the most common way students travel to school.
3. Student Activity: Learners identify the mode from the graph and explain why it is the mode. They can also provide other real-life examples of "most common" events.
E. Collaborative Activity (10 minutes)
1. Teacher Activity: Divide the class into small groups. Provide each group with a simple data collection task (e.g., "Ask 5 classmates their favourite Nigerian fruit: Mango, Orange, Pineapple, Watermelon").
2. Student Activity: Each group collects data, then works together to draw a bar graph (either vertical or horizontal) representing their collected data on a small chart paper or in their books. They should also identify the mode of their data.
3. Teacher Activity: Circulate among groups, providing guidance and checking for understanding of drawing and interpretation. F. Lesson Conclusion (5 minutes) 1.
Community Health and Environment: Bar graphs can be used to represent the number of people who fall ill from different diseases in a community over a month, or the amount of waste collected from different parts of a village. This helps health workers and community leaders identify the most prevalent issues and allocate resources effectively (e.g., focusing on malaria prevention if it's the mode, or setting up more waste bins in areas with high waste).
Market Surveys and Business: Local market vendors can use bar graphs to track the sales of different food items (e.g., tomatoes, peppers, onions, rice) over a week. This helps them understand which items are most popular (the mode) and need to be stocked more, and which are less popular, guiding their purchasing decisions and reducing waste.
School Administration and Planning: Schools can use bar graphs to represent data such as student attendance per class, enrollment numbers for different extra-curricular activities, or the number of books borrowed from the library per month. This aids school management in identifying trends, allocating resources (e.g., more teachers for a large class), and planning activities. For instance, if 'football' is the mode for sports club enrollment, more football equipment might be needed.