Task Settings

What are task settings?

We have seen how tasks define what problems students have to solve. However, students often have to do extra work after solving the task. Examples are:

• Numerically evaluating and possibly rounding the result
• Writing the result with the proper unit.
• Writing the result in scientific notation.

You can configure such post-processing through the Task Settings.

Figure: Rounding and adding a unit after solving an equation. Left: an interactive session. Right: a worked solution.

Accuracy settings

Click on the accuracy option to reveal its settings.

Figure: Accuracy settings

The default setting is 'exact', meaning students should not approximate their answers. So students should keep roots and fractions if these cannot be written in an exact decimal form.

• The exact solution of $3x=10$ is $x=\frac{10}{3}$ or $x=3\frac{1}{3}$, but not $3.333333$.
• The exact solution of $2x=3$ is $x=\frac{3}{2}$, $x=1\frac{1}{2}$, or $x=1.5$.

Any other option than 'exact' implies that students must numerically approximate the result. We will discuss the various types of approximations below.

Rounded to .. decimals

Students must round the answer to the prescribed number of decimal places.

Example: Round $\pi$ to two decimals

• $3.142\rightarrow$ intermediate step. Too many decimal places.
• $3.1\rightarrow$ incorrect. Not enough decimal places.
• $3.15\rightarrow$ incorrectly rounded.
• $3.14\rightarrow$ final answer

Accurate to ... decimals

The answer must be accurate to at least the prescribed number of decimals.

Example: Write $\pi$ accurate to two decimals

• $3.142\rightarrow$ final answer
• $3.14\rightarrow$ final answer
• $3.1\rightarrow$ incorrect, not accurate enough.

Significant figures

Significant figures are the number of digits in a value. For example, 3.1415 has five signification figures. This type of accuracy is expected in STEM problems where calculations usually depend on measured values.

Example: Approximate $\frac{5}{2}$ to three significant figures

• $2.5\rightarrow$ intermediate step. Not enough significant figures.
• $2.500\rightarrow$ intermediate step. Too many significant figures.
• $2.50\rightarrow$ final answer.

Range

Sometimes you want to set the upper and lower bounds explicitly. An example is a length which students must measure with their ruler. Note that the range always includes the lower bound but excludes the upper bound.

Units

You can use Multistep for calculations that involve quantities and units. Algebrakit recognizes the notations of many standard units and can convert one unit into another.

Just like rounding, adding the unit is something you usually do at the end of a derivation. This way of working, and some other settings, can be configured in the Unit Settings.

Figure: Unit settings

The elements in the Unit Settings are divided into three categories, as indicated by the yellow labels in the image.

• (A) The unit of the result. If also the task has a unit, then it will be converted. Otherwise, it will be added. See the figure below.
• (B) Whether equivalent units are allowed as a final answer or if students need to convert these to the desired unit.
• (C) Is the unit optional or required? Is it allowed to postpone adding the unit toward the end of the derivation (which is the default behavior), or must it be written with every intermediate step?

Figure: Left: Adding units at the end of a calculation. Right: converting units

Didactical configurations

Didactical configurations configure properties of the final answer. For example, the worked solution to a STEM question should be in scientific notation. Or, you may require students to give their final answer as a mixed fraction rather than an improper fraction. You can find didactical configurations under the Form menu toggle when editing a multistep exercise.

Figure: The didactical configurations menu

You can define three types of didactical configurations.

• The Numbers section defines number notation, such as decimal, fraction, or scientific notation.
• The Radicals setting defines notation requirements for roots.
• The Fractions setting defines what fraction types are allowed, such as improper or mixed fractions

If you don't choose an option, Algebrakit will use the default settings from the student profile.

Numbers

The Numbers setting determines accepted notations for student answers. You can enforce decimal, fractional, and scientific notation. You can also choose the preferred notation in worked solutions.

The default setting allows both fractions and decimal notation. For example, a student can answer $1.25$ if the expected answer is $\frac{5}{4}$.

Radicals

The Radicals setting has only two options. The default option follows the student profile. The option "Students must extract perfect squares and rationalize denominators" requires students to normalise radicals. For example, students must rewrite $\sqrt{8}$ into $2\sqrt{2}$ and $\frac{1}{1-\sqrt{5}}$ into $\frac{-1-\sqrt{5}}{4}$.

Figure: An example of a worked solution where students must simplify radicals

Fractions

You can require students to write fractions as improper fractions or as mixed fractions.