Math Summative criterion B

Pattern Finding

Identifying relationships between numbers, shapes, or mathematical structures.

Definition of a Pattern

A sequence or series of numbers, shapes, or objects that follow a defined rule.

Arithmetic Patterns

Patterns involving a constant difference between consecutive terms.

Geometric Patterns

Patterns involving a constant ratio between consecutive terms.

Quadratic Patterns

Patterns defined by a quadratic function, with a constant second difference.

Numeric Patterns

Sequences based on numerical relationships, such as arithmetic or geometric sequences.

Geometric Patterns (Shapes)

Figures that repeat or follow a certain arrangement.

Algebraic Patterns

Patterns represented using algebraic expressions or equations.

Common Differences

The difference between consecutive terms in numeric patterns.

Analyze Ratios

Examine how each term relates to the next through multiplication or division in geometric patterns.

visual representations

Using charts, graphs, or diagrams to visualize patterns.

Test the Rule

Formulating a general rule based on identified patterns and validating it with new data.

Example of Numeric Pattern

Sequence like 2, 4, 6, 8, where the pattern is adding 2 to the previous term.

Example of Geometric Pattern

Alternating shapes like Triangle, Square, Triangle, Square.

Application of Pattern Finding

Using patterns to solve problems in algebra, statistics, and geometry.

Tips for Success in Pattern Finding

Practice with various patterns and discuss reasoning in groups.

Notation $U_n$

Denotes the nth term of a sequence or pattern.

Understanding $U_n$

Represents the nth term value in a sequence, based on specific rules.

Deriving the Rule for $U_n$

A rule can be derived by observing initial terms of the sequence.

Arithmetic Sequence Example

For the sequence 4, 7, 10, 13, the rule is $U_n = 4 + 3(n-1)$.

Geometric Sequence Example

For the sequence 2, 6, 18, 54, the rule is $U_n = 2 \times 3^{(n-1)}$.

Calculate Terms using $U_n$

Use $U_n$ to find any term in the sequence based on its position.

First Few Terms in Patterns

Determine them to identify a potential pattern.

Development of General Formula

Derive it based on observed patterns in sequences.

Testing the Formula

Ensure it generates correct terms for the sequence.

Identify Next Terms

Example problem: Identify the next three terms in 5, 10, 15, , , __.

Shape Series Pattern

Identify the pattern in the shapes: Circle, Circle, Square, __.

Understanding Pattern Applications

Recognizing patterns aids in making predictions and understanding complex concepts.