Perpendicular Lines

Perpendicular lines are two lines that intersect at a 90-degree angle. This means that if you were to place a protractor at the point where the two lines meet, the angle formed would measure exactly 90 degrees.

Visually, perpendicular lines look like the letter "T" when they intersect. One line goes horizontally, and the other goes vertically, creating a right angle where they meet.

It's important to note that the slopes of perpendicular lines are negative reciprocals of each other. For example, if the slope of one line is 2, the slope of the line perpendicular to it would be -1/2.

Perpendicular lines are commonly encountered in geometry and can be found in various shapes and structures, such as the corners of rectangles, the sides of a square, or the edges of a cube.

Understanding perpendicular lines is essential in geometry, architecture, engineering, and many other fields where precise angles and intersections are important.

Remember, when two lines are perpendicular, they form right angles, and their slopes are negative reciprocals of each other.

◂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.