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Patterns and Relationships in Numbers (Algebraic Thinking)


For many parents, seeing the word “algebra” in your child’s math curriculum often brings about a sense of uncertainty and fear. Algebra is an area of mathematics more commonly associated with high school classes and problems involving the letters “x” and “y”. While middle school and high school was the normal time for the introduction of algebra, most math classrooms incorporate the early stages of algebraic thinking and problem-solving to young learners.

Math is an area of learning that involves relationships between numbers and patterns. Early in your child’s math instruction, algebraic thinking begins with recognizing and making generalizations about patterns. These patterns might be numeric in nature (5, 10, 15, 20…counting by fives), positional (up, down, up, down) or geometric (shapes). 

Recognizing repeated patterns (red, blue, red, blue) are introduced first and then children experience growing patterns (1, 2, 4, 7…in which children will conclude that you increase what you add by each time starting with 1, then 1 + 1= 2, then 2 + 2 =4, then  4 + 3= 7, and so on).

Children will also begin to see relationships in number sentences that will be further explored later in their education experience. For example, we know that 2 + 3 = 5 and therefore 3 + 2 = 5. The equal sign “=” is also taught as more than the symbol used to show the answer to a number sentence. For later success in algebra, children must understand the equal sign as meaning “the same as”. In many classrooms, this concept is taught using the playground equipment – seesaw. Children understand relatively early that a seesaw needs to be balanced and that if one side is heavier or lighter than the other side, it isn’t nearly as fun. So it is with early algebraic thinking.
This early introduction to balance in a number sentence begins with finding the missing part of a problem (2 + ___ = 5) and then progresses to finding the missing number that makes both sides equal (2 + 3 = ____ + 4  explanation: since 2 + 3 = 5, the numbers on the other side of the equal sign must also equal 5, so the missing number is 1 since 1 + 4 = 5 as well). This early exploration prepares children for more complex thinking and problem-solving later on in their schooling.