Lesson 2: Investigation with Numbers – Patterns, Sequences, and Tricks

📘 Introduction

Welcome! Do you enjoy puzzles, magic number tricks, or figuring out patterns in nature or games?
Then this lesson is for you! In this topic, we’ll explore how numbers can follow rules, repeat in patterns, and surprise us in fun ways.
Number patterns help us understand how math works in our daily lives — from calculating money to solving logic puzzles and predicting what comes next!

🧠 Key Concepts and Explanations

1. What is a Number Pattern?

A number pattern is a sequence of numbers that follow a specific rule.
This rule could involve addition, subtraction, multiplication, division, or even alternating steps.

Example: 2, 4, 6, 8, 10, … → Add 2 each time

2. Types of Sequences

3. Finding the Rule in a Pattern

To find the rule, look at the difference or ratio between each pair of numbers.
Is the pattern adding, subtracting, multiplying, or dividing? Or maybe changing in a special way?

4. Tricks and Hidden Patterns

Some patterns don’t just involve numbers — they involve positions! Look at this:

Example: 1, 4, 9, 16, 25, …

These are square numbers:
= 1, 4, 9, 16, 25

5. General Rule or Formula

For some patterns, you can find a rule to calculate any term in the sequence.

Example: For 2, 4, 6, 8, …, the nth term is:

🧮 Sample Problem Walkthroughs

Example 1: Identify the Pattern

Find the rule in the pattern: 5, 10, 15, 20, …

Solution:
The numbers increase by 5 each time.
So it’s an arithmetic sequence with rule: Add 5

Example 2: Find the Next Two Terms

What are the next two terms in: 1, 3, 6, 10, 15, ?

Solution:
The differences are: +2, +3, +4, +5 → Add 6 next
So next numbers are: 21 and 28

Example 3: General Formula

Find the nth term of the sequence 4, 7, 10, 13, …

Solution:
This is an arithmetic sequence with first term 4 and common difference 3.
Formula:

📝 Practice Exercises

Part A: Number Patterns

1. What comes next in: 2, 5, 8, 11, ___, ___
2. Find the rule in: 81, 27, 9, 3, ___
3. Find the 10th term of the sequence: 6, 9, 12, 15, …
4. Write the nth term of the pattern: 1, 4, 9, 16, 25, …

Part B: Mixed Word Patterns

1. Yaw saves money like this: GHC5 in week 1, GHC10 in week 2, GHC15 in week 3… How much does he save in week 6?
2. Adjoa notices her steps increase by 2 each day: Day 1 = 1 step, Day 2 = 3 steps, Day 3 = 5 steps. How many steps on Day 10?

✔ Answers and Explanations

1. Next: 14, 17 → Rule: Add 3
2. Next: 1 → Rule: Divide by 3
3. Common difference = 3. 10th term =
   
4. These are squares: nth term =
   
5. It’s +5 each week: GHC30 in week 6
6. This is an odd number pattern: 1, 3, 5, 7, 9… Day 10 = 19 steps

📊 Visual Diagram:

🔁 Recap

• Number patterns follow rules — learn to recognize and explain them.
• Arithmetic patterns add or subtract the same number each time.
• Geometric patterns multiply or divide each time.
• Some patterns use positions (like squares or cubes).
• You can write formulas to find any term in a sequence.

🪞 Reflection Prompt

Can you think of a number pattern in your life — maybe in how you walk to school, save money, or play a game?
Try to write it down and explain the rule it follows!