Modulus

The modulus, denoted by the symbol "%", is a mathematical operation that returns the remainder of a division between two numbers. In other words, it gives us the amount left over after dividing one number by another.

For example, if we have the expression 10 % 3, the modulus operation would return the value 1, because 10 divided by 3 is 3 with a remainder of 1.

Here's the general formula for the modulus operation:

a % b = r

Where a is the dividend, b is the divisor, and r is the remainder.

The modulus operation is commonly used in programming to check for divisibility, determine even or odd numbers, and cycle through a range of values.

It's important to note that the modulus operation only makes sense for integers, as it calculates the remainder of a division. When working with non-integer numbers, the concept of modulus can be extended using the modulo function.

Overall, the modulus operation is a useful and versatile tool in mathematics and computer programming, allowing us to efficiently work with remainders and solve a wide range of problems.

◂Math Worksheets and Study Guides Third Grade. Commutative Property

The resources above cover the following skills:

Number and Operations (NCTM)

Understand meanings of operations and how they relate to one another.

Understand and use properties of operations, such as the distributivity of multiplication over addition.

Compute fluently and make reasonable estimates.

Develop fluency in adding, subtracting, multiplying, and dividing whole numbers.

Select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools.

Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Identify such properties as commutativity, associativity, and distributivity and use them to compute with whole numbers.

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

Grade 3 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing understandings of multiplication and division and strategies for basic multiplication facts and related division facts

Students understand the meanings of multiplication and division of whole numbers through the use of representations (e.g., equal-sized groups, arrays, area models, and equal 'jumps' on number lines for multiplication, and successive subtraction, partitioning, and sharing for division). They use properties of addition and multiplication (e.g., commutativity, associativity, and the distributive property) to multiply whole numbers and apply increasingly sophisticated strategies based on these properties to solve multiplication and division problems involving basic facts. By comparing a variety of solution strategies, students relate multiplication and division as inverse operations.