Khan Academy has free math courses for kindergarten through high school (and beyond). In this review, I focus on courses for students up through eighth grade. You can access courses without signing in, but creating an account allows the system to track progress.
These math courses use voice-over video instruction, practice problems, a limited amount of written instruction that includes one or more practice problems, online quizzes, and a final exam. All problems are scored by the computer. Both the amount of lesson material and the number of practice problems increase with each grade level.
Each course has several units, with each unit divided into several lessons. Khan Academy math courses teach one topic at a time in brief videos (usually just a few minutes long) and do not include cumulative review of material taught in previous units until the final exam. I will describe the content of the fifth-grade unit titled “Multiply Fractions” to give you a better idea of the lesson components.
The goal of this unit is to teach four different methods for multiplying fractions. This unit is split into three parts, with a quiz at the end of each part. In the first part, lessons are grouped under two headings: Multiplication as scaling and Multiplying fractions and whole numbers. Under the first heading are two videos and a set of seven practice problems. Under the second are four videos and two sets of practice problems, with seven problems each. Students need to get at least five correct in each set to “level up.” A five-question quiz concludes this first part. The second part of the unit also has two headings: Multiplying fractions and Multiplying mixed numbers. The first heading has three videos and three sets of practice questions. Two of the sets of questions have only four questions each while the third has seven. Under the second heading are one video and one set of four questions. Again, a five-question quiz concludes this part. The third part of the unit has two headings: Area of rectangles with fraction side lengths and Multiplying fractions word problems. There are two videos under the first heading and three under the second. Each heading has only one set of four practice problems. The second heading adds another component that appears more frequently as the math becomes more complex—material for students to read with example problems. In this case, the material to read is titled “Multiply fractions: FAQ,” and it reviews concepts and links back to practice problems in earlier lessons. (These sections usually include one or more practice problems rather than links to problems in previous lessons.) The unit concludes with a ten-question quiz.
The lack of cumulative review allows most students to move through the lessons more quickly than in other courses. Still, some students might have trouble retaining the knowledge without recurring practice. On the other hand, a dedicated student who wants to advance quickly is more likely to appreciate this aspect of the courses. Also, if students think they already know a topic, they can take the quiz and advance if they pass.
The courses are generally plain in their design. The course presenters use a computerized whiteboard or blackboard to illustrate their voice-over presentations. As in the example unit, there are frequent sets of practice problems but not for every video. Questions are most often presented in multiple-choice format, but some questions use other types of responses such as typing in a number or manipulating a dot on a number line.
Students are not given instructions on how much lesson material to complete in one sitting. The videos are so brief that students might watch two or three (or even more) in a session if they can complete the practice problems quickly. If you want help with scheduling, you might check out Homeschool Planet’s lesson plans for these courses.
In addition to the grade-level courses, Khan Academy offers "Get Ready" courses that can be used before math courses, beginning with third-grade math. These are brief, review courses that utilize content from the complete courses.
Course Content
The math courses begin with “Early Math Review” which teaches counting, addition (up to 1,000), subtraction, and place value, along with work in measurement, data, and geometry—most of which is covered in kindergarten and first grade in other math programs. This is a review course since it moves too quickly to offer sufficient practice with each new concept for kindergarten or first grade.
Next in line, the second-grade course covers similar content, although it begins with addition and subtraction within 20. It also teaches place value and advanced addition and subtraction up to 1,000 (with regrouping), with briefer units on money and time, measurement (both standard and metric), graphs, and introductory geometry. I expect that many second graders will need more practice than is provided in this course.
The course covers addition, subtraction, estimation, multiplication, division, introductory fractions, arithmetic patterns and problem-solving, quadrilaterals, area, perimeter, time, measurement (metric), and data (creating and interpreting bar graphs and line plots).
Fourth graders do more advanced work with addition, subtraction, multiplication, and division. They have several units on fractions, a unit on decimals, and an introduction to factors and multiples. Three units teach plane geometry, including topics such as types of angles, measuring angles with a protractor, and determining area and perimeter. The final unit teaches about time (e.g., travel word problems) and both standard and metric systems of measurement with a focus on mass, volume, and distance.
The fifth-grade course covers decimal place value, all four functions with both fractions and decimals, powers of ten, volume, the coordinate plane, algebraic thinking, converting units of measure, line plots, and geometry (triangles, quadrilaterals, and polygons).
In sixth grade, students learn about ratios, rational numbers, rates, percentages, exponents, the order of operations, negative numbers, variables and expressions, equations, inequalities, geometry (area of parallelograms, triangles, and composite shapes), the coordinate plane, 3D figures (volume, nets, and surface area), and introductory data and statistics (e.g., mean, median, and mode).
The seventh-grade course is essentially a pre-algebra course with an extensive unit on expressions, equations, and inequalities. It also covers proportions, rates, percentages, integers, rational numbers, negative numbers, statistics, probability, scaled images, and geometry (e.g., radius, diameter, and circumference of circles; complementary and supplementary angles; and vertical angles as proof of congruence).
The eighth-grade course has students review numbers and operations in the first unit and solve equations with one unknown in the second. The third unit covers linear equations and functions, with several lessons on slope-intercept, simple functions, and linear-equation word problems. The fourth unit addresses systems of equations where students solve problems with two variables. Geometry in the fifth unit includes work with triangles, the Pythagorean theorem, cylinders, and cones. Units six and seven cover geometric transformations, data, and modeling. This course is quite advanced, covering some of what is typically addressed in Algebra 1 and high-school geometry.
Summary
The Khan Academy math courses for kindergarten through eighth grade are very easy to navigate, the videos are brief and concise, and students can advance as quickly as they want. This makes the Khan math courses a great choice for students with gaps in their math knowledge who want to catch up quickly, as well as for bright students who grasp concepts without a lot of explanation and practice.
