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Operations andAlgebraic Thinking

In mathematics, an operation is an action or procedure that produces a new value from one or more input values. In fourth grade, students build on their understanding of the properties of addition, subtraction, multiplication, and division for whole numbers.

Students know the concrete and symbolic representations pertaining to equations and solve multi-step word problems using the four operations. Students work to ensure that answers make sense and are reasonable. For example, they interpret what remainders mean within the real-world context of division problems. They use mental computation and estimation strategies.

In fourth grade, students also learn about factors and multiples of whole numbers. They come to know the terms prime and composite. A prime number has exactly two factors (1 and itself). A composite number has more than two factors.

Additionally, students learn and apply concepts that will help build a foundation necessary for later work in algebra. In particular, they generate outputs based on a given rule, such as “add 5.” They identify patterns in generating outputs with rules. Such understanding will help them be successful with later algebraic functions and equations.

The following hands-on activities will enable students to learn the concepts of operations and algebraic thinking in a meaningful way. Mathematically proficient students in fourth grade look closely to discover patterns in numbers while using different operations. They also notice repetitive actions in computations to make generalizations.

Using the activities, teachers can provide students with opportunities to use models to explain computations and why algorithms work. Concrete experiences help students construct their own understanding.

The Grade 4 Common Core State Standards for Operations and Algebraic Thinking specify that students should—