Mathematics pattern questions are common in the PSLE and primary maths curriculum. They test a student's ability to identify, analyse, and predict sequences based on given patterns. Mastering these pattern questions not only boosts confidence but also strengthens a student's overall mathematical problem-solving skills. In this article, we will delve into the four most common types of pattern questions: repeating patterns, square patterns, triangle patterns, and common difference patterns. Each section will provide examples and step-by-step solutions to help you master these concepts.
1. Repeating Patterns
Repeating patterns is a fundamental concept in primary mathematics. These patterns involve a fixed sequence of elements (letters, numbers, or symbols) that repeat continuously. For instance, in the pattern "A B C D E A B C D E A B C D E…", the group "A B C D E" repeats indefinitely. A repeating pattern has a specific group of elements that repeat over and over again.
How to Solve Repeating Pattern Questions
The grouping technique is the most effective method for solving repeating number patterns.
Example: Find the 78th letter in the pattern below.
A B C D E A B C D E A B C D E …
Step 1: Circle the repeating pattern.
1 group = 5 letters (A, B, C, D, E)
Step 2: Find the number of groups and the remainder, if any.
78 ÷ 5
= 15 groups R 3 letters
Tip: The quotient (15) tells us the number of times the pattern is repeated. The remainder (3) tells us the position of the required letter.
Thus, the 78th letter (3rd remainder) is letter C.
2. Square Patterns
Square patterns are formed using square numbers, which are the result of multiplying a number by itself. Square numbers are integers that are the product of a number multiplied by itself. For example, 9 is a square number because it equals 3 × 3. Square patterns utilise these square numbers to create sequences. These patterns are common in PSLE question patterns and require understanding basic multiplication and square numbers.
How to Solve Square Pattern Maths Questions
When solving square pattern questions, it's essential to recognise the pattern of square numbers.
Example: Find the 25th number in the pattern below.
1, 4, 9, 16, 25, 36, 49…
Since the 1st number = 1 × 1
2nd number = 2 × 2
25th number = 25 × 25
= 625
Thus, the 25th number in this pattern is 625.
3. Triangle Patterns
Triangle patterns consist of a sequence where each new figure adds an additional layer of elements, forming a triangular arrangement. These are often visual patterns and require counting the elements in each layer.
How to Solve Triangle Pattern Questions
To solve triangle pattern questions, determine the number of elements (e.g., circles, dots) in each layer and find the total for the desired figure in the sequence.
Example: Fill in the number of circles in each figure below. Then, find the number of circles in the 15th pattern.
4. Common Difference Patterns
A common difference pattern is a sequence in which the difference between consecutive numbers is constant. This difference can be either positive (increasing sequence) or negative (decreasing sequence).
How to Solve Common Difference Pattern Questions
To solve these pattern questions, identify the common difference and use it to find the desired number in the sequence.
Example: Find the 31st number in the pattern below.
7, 10, 13, 16, 19, 22…
Step 1: Find out the common difference.
Common difference = + 3
Step 2: Find the increase in pattern number from the 1st pattern.
31 - 1 = 30
Step 3: Find the total increase.
Total increase = 3 × 30
= 90
Tip: Do not forget to add back the first number!
Step 4: Find the final number.
31st number = 90 + 7
= 97
The 31st number in this pattern is 97.
Mastering the 4 most common PSLE pattern questions and primary maths—repeating patterns, square patterns, triangle patterns, and common difference patterns—is essential for success. By understanding the underlying principles and practising with examples, students can build the confidence and skills needed to excel in these types of questions. Remember to apply the grouping technique for repeating patterns, recognise square numbers, count elements in triangle patterns, and calculate common differences accurately. With these strategies, tackling PSLE maths pattern questions becomes a much more manageable task.
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