Measures of Central Tendency, Data Collection, Tally Marks and Practice for Primary 6

Class: Primary 6
Term: 3rd Term
Week: 10
Age: 11 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Data Handling and Statistics
Previous Lesson: Capacity, Units, Conversions and Capacity Word Problems.
Topic: MEASURES OF CENTRAL TENDENCY
Subject Matter: Collection of data in groups, organizing data, tally marks and tally tables, constructing tally table from given data, quantitative aptitude involving tally marks.

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain:

• Define data and explain its importance.
• Explain how to collect data in groups.
• Interpret data represented by tally marks.
• Solve quantitative aptitude problems involving tally marks.

Affective Domain:

• Appreciate the importance of accurate data collection.
• Develop a systematic approach to organizing information.

Psychomotor Domain:

• Use tally marks correctly to represent collected data.
• Construct tally tables from given data sets.
• Organize collected data effectively.

Social Domain:

• Work collaboratively when collecting and organizing data in groups.

Reference Materials

The following resources were used in planning this lesson:

• 9 Years Basic Education Curriculum (Primary 4-6)
• State Unified Scheme of Work
• New General Mathematics for Primary Schools 6
• Textbook
• Workbook
• Formula book
• Charts

Instructional Materials

The teacher will teach this lesson with the aid of:

• Charts showing examples of tally marks and tally tables.
• Mathematical set.
• Whiteboard and markers.
• Flashcards with numbers or items for data collection.

Rationale for the Lesson

This lesson helps pupils understand how to gather and arrange information in a simple way. Learning about tally marks and tables is important for organizing daily observations and preparing for more advanced topics in data analysis, making it easier to interpret facts around them.

Prerequisite/Previous Knowledge

Pupils are expected to have basic knowledge of counting, number recognition, and simple categorization of objects.

Lesson Content/Board Summary

Data Collection and Tally Marks

What is Data?

Data refers to facts or information, such as numbers, words, measurements, or observations, collected for analysis.

Why do we collect Data?

We collect data to:

• Understand situations better.
• Make informed decisions.
• Identify patterns and trends.

Collecting Data in Groups

Data can be collected in groups when dealing with many items. This involves categorizing similar items together.

For example, if we count the number of different coloured pens, we group all red pens together, all blue pens together, etc.

What are Tally Marks?

Tally marks are a quick and simple way of recording counts in groups of five. Each vertical line represents one item, and the fifth line crosses the previous four.

Example:

• 1 = |
• 2 = ||
• 3 = |||
• 4 = ||||
• 5 = ||||
• 6 = |||| |

Constructing a Tally Table

A tally table is a table used to organize collected data using tally marks. It usually has three columns: Item, Tally Marks, and Frequency.

Steps to construct a tally table:

1. List the items or categories in the first column.
2. Go through the raw data one by one and make a tally mark for each item in the second column.
3. Count the tally marks for each item and write the total frequency (number) in the third column.

Example 1: Construct a tally table for the following colours of cars seen in a parking lot: Red, Blue, Green, Red, White, Blue, Red, Green, White, Red, Blue, Red.

Solution:

Example 2: A teacher recorded the scores of pupils in a test: 5, 8, 7, 5, 9, 6, 7, 8, 5, 9, 7, 6, 5, 8, 9.

Construct a tally table for these scores.

Solution:

Quantitative Aptitude Involving Tally Marks

Quantitative aptitude problems involving tally marks require pupils to interpret existing tally tables or use tally marks to solve problems.

Example 1: The tally table below shows the number of different fruits eaten by pupils in a week.

Questions:

1. Which fruit was eaten the most?
2. How many pupils ate Mango?
3. What is the total number of fruits eaten?

Solution:

1. Banana (8 times)
2. 6 pupils ate Mango.
3. Total fruits eaten = 7 + 8 + 5 + 6 = 26 fruits.

Example 2: If 15 pupils prefer football, and 10 pupils prefer basketball, represent this information using tally marks.

Solution:

• Football: |||| |||| ||||
• Basketball: |||| ||||

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 3 minutes

Teaching Skill: Set Induction

Teacher’s Activity: The teacher greets the pupils and asks them how they would count and record a large number of items quickly, like the number of pupils present or different coloured books in the class. The teacher introduces the topic of data collection and tally marks as an efficient method.

Pupils’ Activity: Pupils respond to the questions and listen attentively to the introduction of the new topic.

Learning Point: Pupils are introduced to the concept of data collection and the need for efficient recording methods.

Step 2: Explanation of Data and its Collection

Time: 7 minutes

Teaching Skill: Explanation/Discussion

Teacher’s Activity: The teacher explains what data is (facts or information) and why it is collected (e.g., to understand things, make decisions). The teacher also explains the idea of collecting data in groups, giving examples like counting different types of animals or vehicles.

Pupils’ Activity: Pupils listen, ask questions for clarification, and provide examples of data they have encountered.

Learning Point: Pupils understand the definition of data and the purpose of collecting it, especially in groups.

Step 3: Introduction to Tally Marks

Time: 7 minutes

Teaching Skill: Demonstration/Explanation

Teacher’s Activity: The teacher introduces tally marks as a way to quickly record counts. The teacher demonstrates how to make tally marks, especially the group of five (||||), using examples on the board (e.g., counting pupils wearing blue shirts).

Pupils’ Activity: Pupils observe the demonstration and practice making tally marks in their notebooks as guided by the teacher.

Learning Point: Pupils learn to use tally marks correctly to represent counts.

Step 4: Constructing Tally Tables

Time: 8 minutes

Teaching Skill: Demonstration/Guided Practice

Teacher’s Activity: The teacher explains what a tally table is and its components (Item, Tally Marks, Frequency). The teacher then demonstrates constructing a tally table using a simple data set (e.g., favourite fruits of 15 pupils), guiding pupils through each step on the board.

Pupils’ Activity: Pupils follow along, copy the example into their notebooks, and participate in counting the tally marks to determine the frequency.

Learning Point: Pupils understand how to construct a tally table from given data.

Step 5: Quantitative Aptitude with Tally Marks

Time: 7 minutes

Teaching Skill: Problem Solving/Application

Teacher’s Activity: The teacher presents examples of quantitative aptitude problems involving tally marks and tally tables. These problems will require pupils to interpret data from a given tally table or use tally marks to represent given numerical data. The teacher guides pupils through solving these problems.

Pupils’ Activity: Pupils attempt to solve the problems presented by the teacher and ask questions if they face difficulties.

Learning Point: Pupils develop skills in interpreting and solving problems using tally marks and tables.

Step 6: Class Activity/Practice

Time: 4 minutes

Teaching Skill: Group Work/Monitoring

Teacher’s Activity: The teacher divides pupils into small groups and provides each group with a small data set (e.g., colours of shoes in the class, types of pencils) to collect and organize using tally marks and a tally table. The teacher moves around to monitor and provide assistance.

Pupils’ Activity: Pupils work in their groups to collect data and construct a tally table based on the given instructions.

Learning Point: Pupils apply their knowledge of tally marks and tables in a practical, collaborative setting.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. What is data?
2. Explain how to make a tally mark for the number 7.
3. List the three main columns of a tally table.
4. If a tally table shows |||| || for ‘Red’ cars, how many ‘Red’ cars are there?

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 4 minutes

Teaching Skill: Summarization/Reinforcement

Teacher’s Activity: The teacher reviews the key points of the lesson, emphasizing the importance of collecting and organizing data using tally marks and tables. The teacher assigns homework, which includes constructing a tally table for a given set of data or interpreting an existing one.

Pupils’ Activity: Pupils listen to the summary, ask any final questions, and copy down the homework assignment.

Learning Point: Pupils reinforce their understanding and are prepared for further practice.

Home Task: Solve three new exercises on MEASURES OF CENTRAL TENDENCY. Show each step and check each answer.

Lesson Keywords

• Data – Facts or information collected for analysis.
• Tally Marks – A simple way of recording counts in groups of five.
• Tally Table – A table used to organize collected data using tally marks and frequencies.
• Frequency – The number of times an item or value appears in a data set.
• Collection – The act of gathering information.
• Organization – The act of arranging information in a systematic way.

Differentiation

For pupils who grasp concepts quickly, the teacher will provide more complex data sets for tally table construction and quantitative aptitude problems. For pupils needing additional support, the teacher will provide simpler data sets, offer one-on-one guidance, and use visual aids more extensively to reinforce understanding of tally mark formation and table construction.

Note for teachers using this lesson plan

Teachers should ensure to use real-life examples relevant to the pupils’ environment to make the concept of data collection and tally marks relatable. Encourage active participation and hands-on activities to reinforce learning. Visual aids like charts showing various tally mark representations and completed tally tables are highly recommended. Emphasize the systematic approach to making tally marks and constructing tables.