GKT101: General Knowledge for Teachers – Math

This lecture series defines the simplest geometric shapes: lines and rays. Watch the videos and complete the interactive exercises.

Watch this lecture series and complete the exercises.

We can also classify angles based on their relationship to another angle. Vertical angles are congruent, supplementary angles add up to 180 degrees, and complementary angles add up to 90 degrees. Watch this lecture series to see the examples of different angle pairs. Complete the interactive exercises.

Complete these exercises and check your answers.

Watch this lecture series, which discusses how to classify triangles by lengths of their sides and measures of their angles.

Right triangles have a unique relationship between the lengths of their sides, known as the Pythagorean theorem. Watch these videos and complete the interactive exercises.

Proving if some shapes, especially triangles, are congruent is an important part of the study of geometry. This lecture series discusses the three theorems that establish the congruence of triangles.

Complete these exercises and check your answers.

Complete these exercises and check your answers.

A quadrilateral is a two-dimensional shape with four sides and four angles. There are a lot of different kinds of quadrilaterals: familiar ones like squares and rectangles and less familiar ones like parallelograms and trapezoids. Quadrilaterals are classified based on the number of parallel lines, equal sides, and angles. Watch this lecture series and complete the interactive exercises.

Read this chapter, which summarizes all properties of various quadrilaterals, including the properties of their diagonals.

Complete these exercises and check your answers.

Watch these videos and complete the interactive exercises to review the basics of solids (three-dimensional shapes).

Symmetry is an intuitive concept, but in geometry, it has a formal definition. Watch this lecture series and complete the interactive exercises.

These resources assume a basic familiarity with the coordinate plane. To review the coordinate plane and related terminology, watch the videos in section 3.4 of Unit 3. Transformation is another term commonly used, but it has a specific meaning in geometry. This lecture series will help you identify different kinds of transformations.

Translation is a type of rigid transformation. Watch this lecture series and complete the interactive exercises.

In this lecture, the transformations you have learned about previously are used to define similar shapes. Watch this video and complete the interactive exercises.

Similar triangles don't only look very much alike, but they also have a unique relationship between the length of their sides. This lecture series describes the properties of similar triangles. Watch the videos and complete the interactive exercises.

Watch the examples in this lecture series to see how to use the similarity to find missing elements of a triangle. Complete the interactive exercises for practice.

Read this section and watch the videos to see the examples of applications of similar triangles in geometric and real-life problems.

Complete these exercises and check your answers.

Watch this lecture series introducing the perimeter, and complete the interactive exercises to practice calculating the perimeter of rectangles.

Area is the measurement indicating how much space on a plane is taken up by a two-dimensional shape. While perimeter is measured in units of length, area is measured in square units. We will discuss units of measurement in more detail in the next section. Watch this lecture series about calculating the area of rectangles, and complete the interactive exercises.

Watch this lecture series that describes how to find the area of a parallelogram given its height and base, and complete the interactive exercises.

You can think of any triangle as half of a parallelogram! This is why its area is half that of the parallelogram: half of height times base. Watch this lecture series and complete the interactive exercises to practice using the triangle area formula.

To calculate the circumference (which is like perimeter) and the area of a circle, you need a special irrational number: pi. Pi is the ratio of the circumference of a circle to its diameter. Watch this lecture series to explore the circumference and area of circles, and complete the interactive exercises.

The boundary of three-dimensional objects consists of several two-dimensional shapes. The total area of these shapes is called the surface area of the object. It gives some idea of how large an object is, but now how much space it takes up. This is measured by volume, which we will discuss next. Watch this lecture series and complete the interactive exercises to practice calculating the surface area of rectangular prisms.

Volume measures how much space is taken up by a three-dimensional object. The volume is measured in cubic units of length, such as cubic feet or cubic centimeters. Watch this lecture series and complete the interactive exercises to practice finding the volume of rectangular prisms and objects composed of several rectangular prisms.

Complete these exercises and check your answers.

Complete these exercises and check your answers.

Complete these exercises and check your answers.

This lecture series introduces the units of length (or distance) in the metric and U.S. customary systems. Watch the videos and complete the interactive exercises.

Watch this lecture series and complete the interactive exercises to get a feel for various units of volume in the metric and U.S. customary systems: liters, pints, gallons, and so on.

This lecture series discusses different units of mass in the metric and U.S. customary systems. Mass and weight are not the same thing, even though they are used interchangeably in everyday language.

Watch this lecture series and complete the interactive exercises to practice converting measurements of length to different units.

Watch this lecture series and complete the interactive exercises to practice converting measurements of time to different units.

Watch this lecture series and complete the interactive exercises to practice converting measurements of volume to different units.

Watch this lecture series and complete the interactive exercises to practice converting measurements of mass to different units.

Complete this section to practice converting units. Then, watch the videos to see the solutions.

Complete these exercises and check your answers.