Objective: Illustrate an arithmetic sequence.
Subject: Mathematics
Grade Level: Grade 10
Learning across curriculum:
- Science: Analyzing patterns in scientific data
- Social Studies: Studying historical population growth rates
- English: Analyzing the structure of literary texts
Review Motivation:
1. Show a video clip of a fast-paced race, and ask students to identify any patterns
they notice in the order in which the runners cross the finish line.
2. Display a series of numbers on the board and ask students to identify the pattern
or rule behind the sequence.
3. Distribute a set of number cards to each student and ask them to arrange the
cards to create a sequence that follows a specific pattern.
Activity 1: Identifying Arithmetic Sequences
Materials:
- Whiteboard or blackboard
- Markers or chalk
- Number cards
Instructions:
1. Begin by reviewing the definition of an arithmetic sequence with the students.
2. Write a sequence of numbers on the board and ask students to identify whether it
is an arithmetic sequence or not.
3. Divide the class into small groups and distribute number cards to each group.
4. In their groups, students will create their own arithmetic sequences using the
number cards.
5. Each group will present their sequence to the class, explaining the pattern or rule
they used.
Rubrics:
Criteria:
- Correct identification of arithmetic sequences
- Clear explanation of the pattern or rule
Points:
- Correct identification: 10 points
- Clear explanation: 10 points
Assessment questions:
1. Identify whether the following sequence is arithmetic or not: 2, 5, 8, 11, 14.
2. Explain the pattern or rule behind the arithmetic sequence: 3, 7, 11, 15, 19.
Activity 2: Finding the Common Difference
Materials:
- Whiteboard or blackboard
- Markers or chalk
- Worksheets
Instructions:
1. Review the concept of the common difference in an arithmetic sequence.
2. Provide each student with a worksheet containing incomplete arithmetic
sequences.
3. In pairs, students will complete the missing terms in the sequences and find the
common difference.
4. Students will exchange worksheets with another pair to check their answers.
5. Discuss the correct answers as a class, emphasizing the importance of the
common difference in an arithmetic sequence.
Rubrics:
Criteria:
- Correct completion of missing terms
- Accurate determination of the common difference
Points:
- Correct completion: 15 points
- Accurate determination: 10 points
Assessment questions:
1. Complete the missing terms in the arithmetic sequence: 2, __, __, 8, 10. What is
the common difference?
2. Determine the common difference in the arithmetic sequence: 12, 9, 6, 3, 0.
Activity 3: Applying Arithmetic Sequences
Materials:
- Whiteboard or blackboard
- Markers or chalk
- Real-life problem scenarios
Instructions:
1. Present real-life problem scenarios that involve arithmetic sequences, such as
calculating the monthly salary increase of an employee.
2. In groups, students will analyze and solve the given scenarios, using the concept
of arithmetic sequences.
3. Each group will present their solution to the class, explaining their thought process
and the steps they took to solve the problem.
Rubrics:
Criteria:
- Correct application of arithmetic sequences
- Clear explanation of the solution process
Points:
- Correct application: 15 points
- Clear explanation: 10 points
Assessment questions:
1. A student saves Php 500 every month. If the initial amount is Php 1,000, how
much will the student have saved after 10 months?
2. The temperature in a city increases by 2 degrees Celsius every day. If the initial
temperature is 20 degrees Celsius, what will be the temperature after 5 days?
Analysis:
- Discuss with the students the patterns and trends they observed in the arithmetic
sequences during the activities.
- Emphasize the importance of the common difference in determining the next term
in the sequence.
Abstraction:
- Summarize the key concepts learned about arithmetic sequences, including the
definition, common difference, and application in real-life scenarios.
Application:
- Provide the students with a real-life problem related to arithmetic sequences, such
as calculating the growth rate of a population over a certain period.
- Ask the students to solve the problem individually and present their solutions to the
class.
Assessment:
- Teachers can assess students' learning by evaluating their performance in the
activities, including their ability to identify arithmetic sequences, find the common
difference, and apply the concept to real-life problems.
- Teachers can also conduct quizzes or tests to assess students' understanding of
arithmetic sequences.
Assignment:
- Assign the students to create their own arithmetic sequence and write a short
explanation of the pattern or rule behind it.
- Students should also provide a real-life scenario where their arithmetic sequence
can be applied.
