Patterns are an essential part of mathematics, helping students develop critical thinking and problem-solving skills. In Grade 7, students learn about numeric and geometric patterns, which form the foundation for algebra and geometry. Understanding these patterns allows students to recognize sequences, predict future terms, and analyze mathematical relationships.
This guide will cover everything you need to know about numeric and geometric patterns, including definitions, types, rules, and examples.
1. What Are Patterns in Mathematics?
A pattern is a set of numbers, shapes, or objects arranged in a specific order according to a rule. Patterns can be numeric (related to numbers) or geometric (related to shapes).
Patterns help in:
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Identifying relationships between numbers.
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Predicting future terms in a sequence.
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Understanding algebraic concepts.
2. Numeric Patterns
Definition of Numeric Patterns
A numeric pattern is a sequence of numbers that follows a specific rule. Each number in the pattern is called a term, and the rule determines how to get from one term to the next.
Types of Numeric Patterns
A. Arithmetic Sequences
An arithmetic sequence is a pattern where the difference between consecutive terms is constant. This difference is called the common difference.
Formula for an arithmetic sequence:
Where:
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a_n = nth term
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a_1 = first term
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d = common difference
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n = position of the term
Example:
2, 5, 8, 11, 14, …
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The common difference is +3.
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The next term is 14 + 3 = 17.
B. Geometric Sequences
A geometric sequence is a pattern where each term is found by multiplying the previous term by a constant value called the common ratio.
Formula for a geometric sequence:
Where:
- r = common ratio
Example:
3, 6, 12, 24, 48, …
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The common ratio is à2.
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The next term is 48 à 2 = 96.
C. Square and Cube Number Patterns
Some numeric patterns are based on square or cube numbers.
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Square number pattern: 1, 4, 9, 16, 25, … (Each term is n^2 ).
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Cube number pattern: 1, 8, 27, 64, 125, … (Each term is n^3 ).
D. Fibonacci Sequence
A special numeric pattern is the Fibonacci sequence, where each term is the sum of the two previous terms.
Example:
0, 1, 1, 2, 3, 5, 8, 13, …
The next term is 8 + 13 = 21.
3. Geometric Patterns
Definition of Geometric Patterns
A geometric pattern is a sequence of shapes or objects that follows a specific rule. These patterns involve transformations, symmetry, and repetition.
Types of Geometric Patterns
A. Repeating Patterns
A repeating pattern consists of shapes arranged in a repeating sequence.
Example:
ðº ðµ ðº ðµ ðº ðµ (Triangle, Circle, Triangle, Circle, …)
B. Growing Patterns
A growing pattern increases in size or number according to a rule.
Example:
ð¦
ð¦ð¦
ð¦ð¦ð¦
ð¦ð¦ð¦ð¦
Here, each row adds one more square.
C. Symmetry and Reflection
A symmetrical pattern looks the same when divided along a line of symmetry.
Example: A butterfly has reflectional symmetry because both sides are identical.
D. Tessellations
A tessellation is a pattern of shapes that fit together without gaps.
Example: A honeycomb pattern of hexagons.
4. Identifying and Extending Patterns
Steps to Identify Patterns
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Look for a rule – Find the difference (addition, multiplication, etc.).
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Check for repetition – See if shapes or numbers repeat.
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Find missing terms – Use the rule to complete the sequence.
Example – Finding the Next Number
5, 10, 15, 20, __ , __ , __
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The rule is +5.
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The missing terms are 25, 30, 35.
5. Real-Life Applications of Patterns
Patterns are not just in textbooks! They appear in nature, art, music, and science.
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Nature: Sunflowers, seashells, and pinecones follow Fibonacci sequences.
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Architecture: Buildings use symmetrical and tessellation patterns.
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Music: Notes and beats follow rhythmic patterns.
6. Practice Questions
A. Numeric Patterns
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Identify the pattern: 3, 6, 9, 12, __ , __
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What is the next term in 2, 4, 8, 16, __ , __?
B. Geometric Patterns
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Draw the next shape in a repeating pattern: ð ð¢ ðº ð ð¢ __
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Identify the type of symmetry in a snowflake.
7. Tips for Mastering Patterns
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Practice daily – Solve different types of patterns.
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Use visuals – Draw shapes and sequences.
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Look for clues – Find common differences or ratios.
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Apply in real life – Observe patterns in nature and surroundings.
Understanding numeric and geometric patterns in Grade 7 helps students build strong math skills. Whether working with number sequences or shape transformations, recognizing patterns improves problem-solving and logical thinking.
Keep practicing, and soon, patterns will become easy to identify and extend! ð