Chapter 1
Numbers and Operations
Course: Elementary Education Multiple Subjects 5001
Subject: Elementary Education Mathematics Subtest 5003
Chapter: Algebraic Thinking
Understanding patterns is essential in developing mathematical reasoning. Patterns appear across all areas of math, including algebra, geometry, and number sense. Recognizing and describing them prepares students for analyzing functions, writing expressions, and solving problems logically.
1. Identifies, extends, describes, or generates number and shape patterns
Explanation:
Students should be able to observe a sequence of numbers or shapes, identify how the pattern progresses, and apply that rule to extend the pattern or describe it. They should also be able to create new patterns following a rule.
Types of patterns:
a) Number patterns
- Arithmetic pattern: Each term is created by adding or subtracting a fixed number. Example: 2, 5, 8, 11, 14... (Add 3 repeatedly)
- Geometric pattern: Each term is created by multiplying or dividing by a fixed number. Example: 1, 3, 9, 27... (Multiply by 3)
- Nonlinear growing patterns: Numbers increase by a changing difference or involve powers. Example: 1, 4, 9, 16... (These are square numbers)
- Alternating pattern: Terms switch between operations or categories. Example: A, B, A, B, A...