Introduction
Hello! Welcome to Grade 10!
Did you ever notice that there are patterns all around you? They occur in the tiles of the floor, the stripes on your clothes, the patterns on your bags, how the chairs are arranged, and even in buildings and their windows. You will also find patterns in nature, for instance, how the branches of the tree branch out, how the seashells are formed, and how the wings of butterflies are arranged. There are repetitive movements and patterns even in sports. These are all examples of patterns in our everyday life.
Patterns can be found not only in the things around us but also in mathematics. We might be able to guess what will happen next by recognizing the patterns and the rules that govern them.
You will be a Pattern Detective in this WebQuest! You will notice a variety of patterns, determine their guidelines, and understand why numbers are arranged in particular ways. Additionally, you will learn how to solve for the next terms in arithmetic sequences.
Task
Your task is to become a Pattern Detective. You will explore patterns in everyday objects and numbers using the Internet as your learning resource.
At the end of this activity, you are expected to:
1. Identify patterns in your environment.
2. Describe a sequence.
3. Learn to classify arithmetic sequences.
4. Determine the sequence's common difference.
5. Determine the arithmetic sequence's next and missing terms.
Your Final Activity:
Let's assume you are a math investigator. Your objective is to identify three real-world examples of patterns or sequences.
You'll need the following for your activity:
Three examples of sequences or patterns in your everyday life. Explain how each of these patterns functions.Make sure to include at least two sequences of arithmetic. Show the common differences of the given arithmetic sequences and determine the next three terms for each of them.
Process
Follow these steps to complete the WebQuest.
Step 1: Examine Your Environment for Patterns
Look around you for patterns in clothing, tiles, plants, flowers, and other household objects.
Name three items that show a pattern, then give a brief explanation of it.
Step 2: Recognize Number Sequences
Learn about number sequences and that numbers appear in a specific order by visiting the resources provided on educational websites.
This is an illustration of a numerical sequence.
5, 10, 15, 20, 25, ____
What is going on with the numbers, you ask?
To get the next number, we add five.
Consequently, thirty will be the following number.
Step 3: Learn about Arithmetic Sequences
Understand how an arithmetic sequence looks like. An arithmetic sequence is a series of numbers which can be obtained by adding or subtracting the same number repeatedly.
Example:
2, 4, 6, 8, 10
The common difference is 2 as we keep adding 2 to obtain the next number.
Step 4: Test Your Understanding
Complete the following activities:
1. Find the next two terms: 4, 8, 12, 16, ___, ___.
2. Find the next two terms: 9, 18, 27, 36, ___, ___.
3. What is the common difference of 6, 12, 18, 24, 30?
4. Find the missing term: 7, 14, ___, 28, 35.
5. Is 2, 5, 8, 11, 14 an arithmetic sequence? Why?
Step 5: Create Your Own Number Patterns
Create three different arithmetic sequences. Discuss the similarities among the sequences and give an explanation of how you generated the terms.
Step 6: Complete Your Final Task
Identify three examples of sequences or patterns in your day-to-day life. Provide a short description of each. Two of the sequences must be arithmetic. Give the next three terms as well as the common difference.Illustrate your ideas using pictures/drawings if you like. Use your imagination!
Evaluation
The following criteria will be used to evaluate your work:
Points of Criteria
| Three instances of real life patterns | 20 |
| Arithmetic sequences correctly solved | 30 |
| Common difference and next term | 20 |
| Explanation of answers | 20 |
| Neatness and completion | 10 |
| Total | 100 |
Grade:
- 90-100 = Excellent
- 80-89 = Very Good
- 75-79 = Good
- Below 75 = Needs Improvement
Conclusion
Excellent work! You completed the WebQuest on patterns and arithmetic sequences with success.
This exercise has taught you how to recognize patterns, recognize arithmetic sequences, determine the common difference, and forecast the sequence's next term. Always remember that learning Mathematics becomes easier when mathematics is connected to real-world situations, it becomes
I hope that this exercise has improved your understanding of mathematics. Never forget that when you observe, experiment, practice, and learn from your surroundings, mathematics gets simple.
Keep looking for patterns because sometimes observation is the first step toward learning!
Credits
1. Private Education Assistance Committee. (2017). Sequences and series: Mathematics 10, Quarter 1.1 learning module. https://peac.org.ph/wp-content/uploads/2020/05/2017_MATHG10Q1.1.pdf
2. Siyavula. 3.2 Describing sequences. https://www.siyavula.com/read/za/mathematics/grade-10/number-patterns/03-number-patterns-01
3. Tipay, E. L. Grade 10 math: Sequences Module 1. Scribd. https://www.scribd.com/document/534990831/MATH10-QUARTER1-MODULE-1-MELC-123
4. Introduction to sequences . YouTube. https://www.youtube.com/watch?v=p-rc5mTDt9E