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Glacius

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Foundations

Get comfortable with the language of mathematics: numbers, algebra, functions, and graphs.

Start with signed numbers 41 lessons · 5 units
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01Signed Numbers and Arithmetic6 lessons
  1. 01
    Signed numbers

    Interpret a signed integer as a position relative to zero.

  2. 02
    Adding signed numbers

    Add two signed integers.

  3. 03
    Subtracting signed numbers

    Subtract one signed integer from another.

  4. 04
    Multiplying signed numbers

    Multiply two signed integers.

  5. 05
    Dividing signed numbers

    Divide signed integers when the quotient is an integer and the divisor is nonzero.

  6. 06
    Absolute values

    Compute a real number’s distance from zero.

02Algebra essentials17 lessons
  1. 01
    Fractions

    Interpret a fraction as a quotient with a nonzero denominator.

  2. 02
    Equivalent fractions

    Generate an equivalent fraction by scaling its numerator and denominator by the same nonzero integer.

  3. 03
    Adding fractions

    Add two fractions using a common denominator.

  4. 04
    Subtracting fractions

    Subtract two fractions using a common denominator.

  5. 05
    Multiplying fractions

    Multiply two fractions.

  6. 06
    Dividing fractions

    Divide a fraction by a nonzero fraction.

  7. 07
    Powers

    Evaluate a positive whole-number power.

  8. 08
    The zero exponent

    Evaluate a nonzero base raised to the zero power.

  9. 09
    Negative exponents

    Evaluate a nonzero base raised to a negative integer power.

  10. 10
    Multiplying powers

    Rewrite a product of powers with the same nonzero base as one power.

  11. 11
    Dividing powers

    Rewrite a quotient of powers with the same nonzero base as one power.

  12. 12
    A power raised to a power

    Rewrite a power raised to an integer power as one power for a nonzero base.

  13. 13
    Square roots

    Evaluate a real square root with its domain restriction.

  14. 14
    Rearranging equations

    Isolate one scalar variable in a linear equation.

  15. 15
    Distributing products

    Expand a scalar product over a sum.

  16. 16
    Factoring

    Factor a common scalar factor from a sum.

  17. 17
    Inequalities

    Solve a one-step scalar inequality.

03Functions and graphs6 lessons
  1. 01
    Coordinates

    Locate a point from an ordered coordinate pair.

  2. 02
    Function notation

    Evaluate a scalar function at a supplied input.

  3. 03
    Function domains

    Determine which real inputs a scalar expression allows.

  4. 04
    Reading graphs

    Read the output of a scalar function from its graph.

  5. 05
    Straight-line slope

    Compute the slope between two distinct points.

  6. 06
    Affine functions

    Evaluate a scalar affine rule from its slope and intercept.

04Composition and growth5 lessons
  1. 01
    Function composition

    Evaluate a composition in the correct order.

  2. 02
    Inverse functions

    Recover an input using an invertible scalar function.

  3. 03
    Exponential functions

    Predict multiplicative change from an exponential rule.

  4. 04
    Logarithms

    Evaluate a logarithm as an inverse exponent.

  5. 05
    Logarithms of products

    Rewrite a positive product using logarithms.

05Mathematical language7 lessons
  1. 01
    Set membership

    Decide whether an object belongs to a specified finite set.

  2. 02
    Set union

    Form the union of two finite sets.

  3. 03
    Set intersection

    Form the intersection of two finite sets.

  4. 04
    Summation notation

    Expand and evaluate a finite indexed sum.

  5. 05
    Product notation

    Expand and evaluate a finite indexed product.

  6. 06
    Quantifiers

    Distinguish a universal claim from an existence claim.

  7. 07
    Counterexamples

    Refute a universal claim with a valid counterexample.