Intro: Algebra Interaction

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The three core principles of the algebra interaction are:

AlgebraKiT automatically simplifies an expression.

The default task when creating an algebra interaction is set to Simplify. With this task selected, AlgebraKiT automatically simplifies the given expressen.

Example

With a task katex is not defined, AlgebraKiT will evaluate the sum, because katex is not defined is a simpler expression than katex is not defined.

Try it yourself:

  • katex is not defined
    AlgebraKiT will combine the like terms.
  • katex is not defined
    AlgebraKiT will do nothing. Expanding the brackets is not necessarily ‘simpler’.
  • katex is not defined
    Now AlgebraKiT will expand the brackets, because it can then cancel terms and reach a simple result.
  • katex is not defined
    Using the mathematical knowledge that AlgebraKiT has, it decides to factor both numerator and denominator and cancel factors to reach a simpler result.

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The interaction tasks indicate what the student should do.

An important principle in AlgebraKiT is that an author does not specify the answer, but the problem. This allows AlgebraKiT to evaluate intermediate steps and support the student with the derivation.

You can use the dropdown elements to choose from the available tasks.

Try it yourself:

  • Solve katex is not defined
  • Expand katex is not defined
  • Factor katex is not defined
  • Write katex is not defined into scientific notation.
You can use audience and modes to influence how AlgebraKiT solves the problem.

Audience

The audience defines the type of student for which the exercise was meant. It influences what mathematical steps are available and how expressions are written.

Note

In a low-level audience such as Arithmetic, AlgebraKiT will not be able to solve more advanced problems, like equations.

Modes

With modes you can give AlgebraKiT more information about the problem.

Examples


AlgebraKiT will interpret katex is not defined by default as the sine of 30 radians. To use degrees, you can set mode gonio_degrees.

To force AlgebraKiT (and the student) to write the fraction katex is not defined into the mixed fraction 1¼,  set mode nf_rational.  

AlgebraKiT will solve the equation katex is not defined by default by factoring. To force use of the Quadratic Formula (‘abc-formula’), set mode solve_quadratic_abc.

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