Everyday Statistics and probability : Pictograms, histogram, bar chat etc Primary 4 Third Term Lesson Notes Mathematics Week 11

Subject: Mathematics
Class: Primary 4
Term: Third Term
Week: 11
Topic: Everyday Statistics and Probability: Pictograms, Histograms, Bar Charts, etc.

Sub-topic: Introduction to Data Representation

Duration: 45 minutes

Behavioural Objectives:

• Students will identify different methods of representing data.
• Students will understand the purpose of using pictograms, histograms, and bar charts.
• Students will be able to interpret information presented in pictograms, histograms, and bar charts.

Key words: Statistics, Probability, Pictograms, Histograms, Bar Charts

Entry Behaviour: Students are familiar with basic shapes and can count and identify objects.

Learning Resources and Materials:

• Whiteboard and markers
• Pictures or symbols for pictograms
• Sample data for histograms and bar charts
• Worksheets with pictograms, histograms, and bar charts

Building Background/Connection to Prior Knowledge:

• Review basic shapes and counting skills.
• Discuss how we use charts and graphs to understand information in everyday life.

Embedded Core Skills:

• Data interpretation
• Critical thinking
• Numeracy

Learning Materials: Worksheets, visual aids, examples of pictograms, histograms, and bar charts

Reference Books: Lagos State Scheme of Work for Primary 4 Mathematics

Instructional Materials: Whiteboard, markers, pictures or symbols for pictograms, sample data for histograms and bar charts

Content:

Everyday Statistics and Probability

1. Pictograms: 📊
   • Represent data using pictures or symbols.
   • Example: Using smiley faces to show how many students like different fruits.
2. Histograms: 📈
   • Show frequency of data in intervals or ranges.
   • Example: Representing the number of books read by students in a month.
3. Bar Charts: 📊
   • Display data using rectangular bars of different lengths.
   • Example: Showing the favorite colors of students in a class.
4. Probability: 🎲
   • The chance or likelihood of an event happening.
   • Example: Tossing a coin has a probability of landing heads or tails.
5. Data Collection: 📝
   • Gathering information or observations to analyze.
   • Example: Surveying classmates about their favorite animals.
6. Data Interpretation: 🤔
   • Understanding and making sense of collected data.
   • Example: Explaining what the pictogram or bar chart represents.
7. Mean: ➕➖➗✖️
   • Average of a set of numbers.
   • Example: Finding the mean score of a class test.
8. Mode: 📊
   • The value that appears most frequently in a data set.
   • Example: Identifying the most common shoe size among students.
9. Range: 🔢
   • The difference between the highest and lowest values in a data set.
   • Example: Determining the range of temperatures recorded in a week.
10. Probability Experiment: 🎲
    • A planned activity to observe outcomes and calculate probabilities.
    • Example: Rolling a dice to see which number comes up most often.

Worked examples covering pictograms, histograms, bar charts, and probability:

1. Pictogram Example:
   • Question: Use smiley faces to represent the number of students who like different colors: 5 like red, 3 like blue, and 6 like green.
   • Solution: Draw 5 smiley faces for red, 3 for blue, and 6 for green.
2. Histogram Example:
   • Question: Create a histogram showing the number of books read by students in a month: 2 students read 0-5 books, 4 read 6-10 books, and 3 read 11-15 books.
   • Solution: Draw bars for each interval: 0-5, 6-10, and 11-15, with heights representing the frequency.
3. Bar Chart Example:
   • Question: Make a bar chart displaying the favorite fruits of students: 8 like apples, 5 like bananas, and 7 like oranges.
   • Solution: Draw three bars with lengths corresponding to the number of students who like each fruit.
4. Probability Example:
   • Question: What is the probability of rolling a 4 on a fair six-sided dice?
   • Solution: There is 1 favorable outcome (rolling a 4) out of 6 possible outcomes, so the probability is 1/6.
5. Data Collection Example:
   • Question: Conduct a survey to find out the favorite subjects of students in your class.
   • Solution: Give each student a survey form and record their responses.
6. Data Interpretation Example:
   • Question: Interpret the pictogram showing the number of pets owned by students: 3 have dogs, 2 have cats, and 5 have fish.
   • Solution: Explain that each picture represents a certain number of pets, with the key indicating how many.
7. Mean Calculation Example:
   • Question: Calculate the mean score of 5 students in a test: 75, 80, 85, 90, and 95.
   • Solution: Add up the scores (75+80+85+90+95) and divide by the number of students (5) to get the mean.
8. Mode Identification Example:
   • Question: Identify the mode from the following data set: 5, 6, 7, 7, 8, 9, 9, 9.
   • Solution: The mode is the number that appears most frequently, which is 9 in this case.
9. Range Calculation Example:
   • Question: Find the range of temperatures recorded in a week: 20°C, 22°C, 18°C, 25°C, and 28°C.
   • Solution: Subtract the lowest temperature (18°C) from the highest temperature (28°C) to get the range.
10. Probability Experiment Example:
    • Question: Conduct an experiment to determine the probability of getting heads when tossing a fair coin.
    • Solution: Toss the coin multiple times and record the outcomes, then calculate the ratio of heads to total tosses to find the probability.

Evaluation questions on everyday statistics and probability for Primary 4 pupils:

1. Pictograms are used to represent data using __________. a) numbers
   b) pictures
   c) letters
   d) shapes
2. Histograms show the __________ of data in intervals. a) length
   b) frequency
   c) width
   d) color
3. Bar charts display data using __________ bars. a) round
   b) rectangular
   c) triangular
   d) oval
4. Probability is the chance or likelihood of an __________ happening. a) event
   b) animal
   c) object
   d) place
5. Data collection involves gathering __________ or observations. a) shapes
   b) information
   c) colors
   d) toys
6. Mean is the __________ of a set of numbers. a) biggest
   b) smallest
   c) average
   d) longest
7. Mode is the value that appears __________ frequently in a data set. a) least
   b) most
   c) randomly
   d) quickly
8. Range is the difference between the __________ and lowest values in a data set. a) highest
   b) smallest
   c) biggest
   d) longest
9. A histogram is similar to a bar chart but uses __________. a) circles
   b) rectangles
   c) triangles
   d) squares
10. Probability experiments are planned activities to observe __________. a) animals
    b) shapes
    c) outcomes
    d) colors
11. Pictograms represent data using __________ or symbols. a) numbers
    b) pictures
    c) letters
    d) shapes
12. In a bar chart, the height of the bars represents the __________. a) length
    b) frequency
    c) width
    d) color
13. Probability is the likelihood of an event __________. a) happening
    b) ending
    c) starting
    d) changing
14. Mean is calculated by __________ all the numbers and dividing by the total. a) adding
    b) subtracting
    c) multiplying
    d) dividing
15. Range is found by subtracting the __________ value from the highest value. a) biggest
    b) smallest
    c) largest
    d) longest

Class Activity Discussion with answers on everyday statistics and probability:

1. Q: What is a pictogram?
   • A: A pictogram is a way to show data using pictures or symbols.
2. Q: What does a histogram show?
   • A: A histogram shows the frequency of data in intervals or ranges.
3. Q: How are bar charts different from histograms?
   • A: Bar charts use rectangular bars, while histograms use bars to show intervals.
4. Q: What does probability mean?
   • A: Probability is the chance or likelihood of an event happening.
5. Q: What is data collection?
   • A: Data collection is gathering information or observations to analyze.
6. Q: How do you find the mean?
   • A: Add up all the numbers and divide by the total.
7. Q: What does mode mean in statistics?
   • A: Mode is the value that appears most frequently in a data set.
8. Q: What is the range of data?
   • A: The range is the difference between the highest and lowest values in a data set.
9. Q: How do histograms differ from bar charts?
   • A: Histograms show intervals, while bar charts display individual categories.
10. Q: What is a probability experiment?
    • A: A probability experiment is a planned activity to observe outcomes and calculate probabilities.
11. Q: How do pictograms represent data?
    • A: Pictograms use pictures or symbols to represent data instead of numbers.
12. Q: What does the height of a bar in a bar chart represent?
    • A: The height of a bar represents the frequency or number of observations.
13. Q: What is the purpose of probability in everyday life?
    • A: Probability helps us understand the likelihood of events occurring and make decisions.
14. Q: How do you interpret a histogram?
    • A: Each bar represents a range of data, and the height shows how many observations fall into that range.
15. Q: How can we calculate the range of data?
    • A: Subtract the smallest value from the largest value in the data set.

Presentation:

1. Revision: Recap previous lesson on shapes and counting.
2. Introduction to Data Representation: Explain what statistics and probability mean. Introduce pictograms, histograms, and bar charts as ways to represent data visually.
3. Explanation of Pictograms: Show examples of pictograms and discuss how they represent data using pictures or symbols.
4. Introduction to Histograms: Display sample data and explain how histograms organize data into intervals or ranges.
5. Understanding Bar Charts: Discuss how bar charts use rectangular bars to represent categories of data.
6. Interpreting Data: Practice interpreting information presented in pictograms, histograms, and bar charts.
7. Group Activity: Divide students into groups and provide them with worksheets containing different types of data representations to analyze.
8. Discussion: Allow groups to share their findings and discuss their interpretations.
9. Teacher’s Recap: Summarize key points and clarify any misconceptions.
10. Assessment: Distribute evaluation questions related to the topic for students to complete individually.

Presentation:

• Step 1: Revision of previous lesson on shapes and counting.
• Step 2: Introduction to data representation methods: pictograms, histograms, and bar charts.
• Step 3: Explanation of each method with examples and illustrations.
• Step 4: Group activity and discussion.
• Step 5: Recap of key points and assessment.

Teacher’s Activities:

• Presenting explanations using visual aids and examples.
• Facilitating group activities and discussions.
• Providing guidance and feedback during individual and group work.
• Assessing students’ understanding through observation and evaluation questions.

Learners Activities:

• Participating in class discussions and activities.
• Analyzing and interpreting data representations.
• Collaborating with peers in group work.
• Completing evaluation questions to demonstrate understanding.

Assessment:

• Evaluation questions related to pictograms, histograms, and bar charts.
• Observing students’ participation and contributions during group activities and discussions.
• Reviewing students’ worksheets and responses to gauge understanding.

Evaluation Questions:

1. What is the purpose of using pictograms?
2. How do histograms organize data?
3. Explain how bar charts represent categories of data.
4. What is probability?
5. Describe a situation where you would use a pictogram.
6. What does the height of a bar in a histogram represent?
7. How can you interpret information from a bar chart?
8. Give an example of a probability experiment.
9. How do you calculate the mean of a set of numbers?
10. Can you identify the mode in a data set?

Conclusion:
The teacher will go round to assess students’ understanding and provide necessary assistance. Any misconceptions will be addressed, and students will be encouraged to continue practicing data representation skills.

 Distinguish between 2D shapes and 3D shapes Primary 4 Third Term Lesson Notes Mathematics Week 10

1. A pictogram uses ________ or ________ to represent data.
   a) numbers, lines
   b) pictures, symbols
   c) colors, shapes

2. A histogram is a type of ________ graph that displays data in intervals or ranges.
   a) pie
   b) line
   c) bar

3. In a bar chart, each bar represents a ________ and the height of the bar shows the ________.
   a) number, category
   b) category, value
   c) value, number

4. Pictograms are commonly used to represent data about things we can ________.
   a) measure
   b) count
   c) observe

5. A histogram is useful for understanding patterns and ________ in data.
   a) colors
   b) trends
   c) symbols

6. The x-axis of a graph represents the ________ and the y-axis represents the ________.
   a) frequency, categories
   b) categories, frequency
   c) intervals, values

7. Pictograms help us visualize data in a ________ way.
   a) visual
   b) numerical
   c) logical

8. A bar chart is used to compare different ________ or ________.
   a) symbols, numbers
   b) intervals, ranges
   c) categories, groups

9. The rectangular bars in a histogram represent the ________ of each category.
   a) width
   b) frequency
   c) shape

10. Choosing an appropriate ________ for the axes is important to create a readable graph.
    a) scale
    b) legend
    c) color

Remember to choose the correct option (a, b, or c) that best completes each statement. Good luck!

1. A pictogram is a graph that uses ________ or ________ to represent data. a) numbers, lines b) pictures, symbols c) colors, shapes
2. In a pictogram, each ________ represents a certain number of data. a) picture b) symbol c) color
3. A histogram is useful for displaying data in ________ or ________. a) ranges, intervals b) colors, shapes c) lines, patterns
4. The height of the bars in a histogram represents the ________ or ________ of the data. a) width, length b) frequency, value c) shape, size
5. Bar charts are commonly used to compare different ________ or ________. a) colors, shapes b) categories, groups c) patterns, trends
6. The x-axis of a graph represents the ________ and the y-axis represents the ________. a) intervals, values b) categories, frequency c) frequency, categories
7. Pictograms are a visual way to represent ________. a) numbers b) data c) trends
8. Histograms are useful for understanding the ________ and ________ of data. a) patterns, trends b) colors, shapes c) symbols, numbers
9. Bar charts use rectangular bars to represent data, where the height of each bar represents the ________. a) width b) frequency c) color
10. To create a readable graph, it is important to choose an appropriate ________ for the axes. a) scale b) legend c) title

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1. The mean is also known as the ________ of a set of numbers.
   a) average
   b) middle value
   c) most common value

2. The median is the ________ value in a data set.
   a) highest
   b) lowest
   c) middle

3. The mode represents the value that occurs ________ frequently in a data set.
   a) least
   b) most
   c) randomly

4. The range is calculated by subtracting the ________ value from the ________ value.
   a) highest, lowest
   b) lowest, highest
   c) middle, average

5. The mean is calculated by ________ all the values and then dividing by the ________.
   a) adding, total number of values
   b) multiplying, range
   c) subtracting, median

6. The median is useful for finding the ________ value in a data set.
   a) smallest
   b) largest
   c) middle

7. The mode helps us identify the ________ value in a data set.
   a) average
   b) most common
   c) range

8. The range gives us an idea of how ________ or ________ the data is.
   a) spread out, varied
   b) average, normal
   c) small, large

9. If a data set has two middle values, the median is the ________ of the two values.
   a) sum
   b) product
   c) average

10. The mode represents the value with the ________ frequency in a data set.
    a) highest
    b) lowest
    c) equal

1. The mean is also known as the ________ of a set of numbers.
   a) average
   b) middle
   c) largest

2. The median is the ________ value in a data set.
   a) highest
   b) middle
   c) smallest

3. The mode represents the value that occurs ________ frequently in a data set.
   a) least
   b) most
   c) randomly

4. The range is calculated by subtracting the ________ value from the ________ value.
   a) largest, smallest
   b) smallest, largest
   c) middle, average

5. The mean is calculated by ________ all the values and then dividing by the ________.
   a) adding, total number of values
   b) multiplying, range
   c) subtracting, median

6. The median is useful for finding the ________ value in a data set.
   a) smallest
   b) largest
   c) middle

7. The mode helps us identify the ________ value in a data set.
   a) average
   b) most common
   c) range

8. The range gives us an idea of how ________ or ________ the data is.
   a) spread out, varied
   b) average, normal
   c) small, large

9. If a data set has two middle values, the median is the ________ of the two values.
   a) sum
   b) product
   c) average

10. The mode represents the value with the ________ frequency in a data set.
    a) highest
    b) lowest
    c) equal

Reference For Further Reading

1. Math is Fun (https://www.mathsisfun.com/): This website provides explanations, examples, and interactive activities for various mathematical topics, including statistics and probability.
2. National Council of Teachers of Mathematics (NCTM) Illuminations (https://illuminations.nctm.org/): NCTM Illuminations offers a wide range of lesson plans, activities, and games for teaching mathematics, including statistics and probability.
3. Khan Academy (https://www.khanacademy.org/): Khan Academy provides video lessons, practice exercises, and quizzes on various math topics, including statistics and probability.
4. BBC Bitesize – Maths (https://www.bbc.co.uk/bitesize/subjects/z826n39): BBC Bitesize offers interactive lessons, quizzes, and activities to help students understand and practice different mathematical concepts, including statistics and probability.
5. Math Playground (https://www.mathplayground.com/): Math Playground features math games, activities, and interactive tools that cover various mathematical topics, including statistics and probability
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