Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus! ... https://www.youtube.com/watch?v=AUqeb9Z3y3k
Separation of Powers and Checks and Balances and Federalist 51
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https://www.youtube.com/watch?v=APcKEHAPYEg
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Watch the next lesson: https://www.khanacademy.org/science/biology/macromolecules/nucleic-acids/v/molecular-structure-of-dna?utm_source=YT&utm_medium=Desc&utm_campaign=biology
Missed the previous lesson? https://www.khanacademy.org/science/biology/macromolecules/nucleic-acids/v/dna-deoxyribonucleic-acid?utm_source=YT&utm_medium=Desc&utm_campaign=biology
Biology on Khan Academy: Life is beautiful! From atoms to cells, from genes to proteins, from populations to ecosystems, biology is the study of the fascinating and intricate systems that make life possible. Dive in to learn more about the many branches of biology and why they are exciting and important. Covers topics seen in a high school or first-year college biology course.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
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https://www.youtube.com/watch?v=6gUY5NoX1Lk
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Proving the triangle inequality for vectors in Rn
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/dot_cross_products/v/defining-the-angle-between-vectors?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/dot_cross_products/v/proof-of-the-cauchy-schwarz-inequality?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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https://www.youtube.com/watch?v=PsNidCBr5II
Note: All Khan Academy content is available for free at (www.khanacademy.org)
An overview of the Khan Academy today and what I see as its potential social impact
More free lessons at: http://www.khanacademy.org/video?v=wRf6XiEZ_Y8
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https://www.youtube.com/watch?v=wRf6XiEZ_Y8
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Given a dot plot with different measurements of trail mix in bags, find the amount of trail mix each bag would contain if the total amount in all the bags were redistributed equally.
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-measurement-topic/cc-5th-data/e/interpreting-line-plots-with-fraction-multiplication-and-division?utm_source=YT&utm_medium=Desc&utm_campaign=5thgrade
Watch the next lesson: https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-geometry-topic/cc-5th-coordinate-plane/v/graphing-points-exercise?utm_source=YT&utm_medium=Desc&utm_campaign=5thgrade
Missed the previous lesson? https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-measurement-topic/cc-5th-data/v/redistributing-trail-mix?utm_source=YT&utm_medium=Desc&utm_campaign=5thgrade
Grade 5th on Khan Academy: Whether you are a robot, possum, magic unicorn, or just a normal human being, 5th grade is incredible! You will deepen your knowledge of the decimals that you were first exposed to in 4th grade. In particular, you'll learn to do all the arithmetic operations--addition, subtraction, multiplication, division--with them and really understand what a decimal represents. This will be complemented by building your fraction muscles where you'll learn to add, subtract, and multiply any fractions (and begin to divide them). On the measurement front, you'll explore volume (or how much "space" something takes up) and continue the unit conversion journey begun in 4th grade. 5th grade is also the first time that you get exposed to the fundamental concept of graphing points on a coordinate plane, and you'll get a very brief exposure to the concept of exponents (when exploring "powers" of 10)! (Content was selected for this grade level based on a typical curriculum in the United States.)
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https://www.youtube.com/watch?v=4vNloi-zNjU
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Use number lines to find missing numbers in subtraction equations with integers. Arrows to the left equivalently mean adding a negative number and subtracting a positive number of the same magnitude. Arrows to the right equivalently mean adding a positive number and subtracting a negative number of the same magnitude.
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https://www.youtube.com/watch?v=HsPEStiHQS0
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Kim discusses how modern American political culture began to emerge in the early nineteenth century as the right to vote was extended to a broader segment of American citizens.
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https://www.youtube.com/watch?v=o0K8bb9uJQ4
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Showing that a projection onto a subspace is a linear transformation
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthogonal_projections/v/linear-algebra-subspace-projection-matrix-example?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/orthogonal_projections/v/linear-alg-visualizing-a-projection-onto-a-plane?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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https://www.youtube.com/watch?v=cTyNpXB92bQ
Note: All Khan Academy content is available for free at (www.khanacademy.org)
Find the volume of an irregular 3D figure by dividing the figure into two rectangular prisms and finding the volume of each part.
Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-measurement-topic/cc-5th-volume/e/decompose-figures-to-find-volume?utm_source=YT&utm_medium=Desc&utm_campaign=5thgrade
Watch the next lesson: https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-measurement-topic/cc-5th-volume/v/volume-word-problem-example?utm_source=YT&utm_medium=Desc&utm_campaign=5thgrade
Missed the previous lesson? https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-measurement-topic/cc-5th-volume/v/volume-in-unit-cubes-by-decomposing-shape?utm_source=YT&utm_medium=Desc&utm_campaign=5thgrade
Grade 5th on Khan Academy: Whether you are a robot, possum, magic unicorn, or just a normal human being, 5th grade is incredible! You will deepen your knowledge of the decimals that you were first exposed to in 4th grade. In particular, you'll learn to do all the arithmetic operations--addition, subtraction, multiplication, division--with them and really understand what a decimal represents. This will be complemented by building your fraction muscles where you'll learn to add, subtract, and multiply any fractions (and begin to divide them). On the measurement front, you'll explore volume (or how much "space" something takes up) and continue the unit conversion journey begun in 4th grade. 5th grade is also the first time that you get exposed to the fundamental concept of graphing points on a coordinate plane, and you'll get a very brief exposure to the concept of exponents (when exploring "powers" of 10)! (Content was selected for this grade level based on a typical curriculum in the United States.)
...
https://www.youtube.com/watch?v=feNWZEln6Nc
Note: All Khan Academy content is available for free at (www.khanacademy.org)