# Properties of Operations in Algebraic Thinking

This unit examines the properties of addition and subtraction within 20. It introduces students to the concepts of differentiation and accommodations for assessment. In addition, the unit focuses on the representation of problems involving three or more whole numbers. A student is able to recognize these patterns using the properties of operations. The unit includes 15 mathematical performance tasks that require the use of mental models. The content is relevant and engaging for all grades.

Students learn about algebra by manipulating symbols and rules to represent patterns. They learn to use symbols to express mathematical ideas and relationships. The symbol “x” indicates the same as another number, such as “five times three.” But the “x” in a question is not an operation. It’s a relational symbol that means the same as “X,” not necessarily “y.” This means that the answer to a problem is the same for each group of five.

The first grade standard involves identifying and describing number patterns. They apply basic facts and develop strategies for solving word problems. They also practice addition and subtraction by modeling with objects such as their fingers. In addition to the above-mentioned concepts, they develop their problem-solving skills. They apply algebraic thinking, logical reasoning, and mathematical models to solve problems. In the process, they develop a strong understanding of how the system works and how to solve problems.

The fourth grade standard teaches students to use the equal sign. It is not an operations symbol. It means the same as. For example, three x five = nine. The third grade standard is “five x five=25.” This can be written as five x five + five=25. The last two standards build on each other, so that a student learns to generalize arithmetic and make patterns.

The first grade standards emphasize the use of symbols to model and solve problems. For instance, in a five-by-five-by-five-foot array, the student can find the total number of objects in the array. Then, the student writes the equation to represent the sum: the answer to this problem is five plus five. A similar question in the second grade can be expressed as two-by-two.

In the second grade standards, students are introduced to the use of symbols. In addition to using symbols to represent operations, students also apply the properties of addition and multiplication. For instance, four times a number will always be even. A five-by-five array will be written as five + five. By defining the properties of multiplication and division, the third grade is well on its way to becoming an algebraic thinker.

The fourth grade standards involve multiplication and division. Despite the name, these two concepts can be interpreted as comparisons. For example, 35 x seven is seven, while a 7×7 is seven, and a ten is five. Both are additive. Arithmetic and adding are inexact, but they can be used as a tool to help students solve multiplication problems. This is a very powerful strategy for extending and applying the learning of mathematics.