# Tutorial

## Actions

The following actions can be applied to an algebra step:

Add a description for this step

The description of a step defines ‘what’ this step means and is used by AlgebraKiT to generate the step hint.

Note: In case you have multiple steps defined in your interaction, make sure to give each step a description, also the solution step. Otherwise, step hints won’t work as expected.

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To define the solution model of your algebra interaction, you define for each step the possible tasks to find the final result of that step. The definition of these tasks should all have the same result.

In case the student is allowed to submit a different answer as final result of that step, you can use the alternative answer option. When the student submits this alternative answer, his input will be considered correct as well.

Clicking on the Action button on the left bottom of the interaction field and select Add alternative answer. An alternative answer field appears below the step task(s).

Click on the new field. A new definition field opens.

Select the task and the expression for the alternative answer that should also be considered correct.

##### Example

Let’s look at the question where the student needs to find a certain probability. A probability can be written either as a fraction or as a percentage. As an author, one of the two forms can be authored as a task, but the other form needs to be added as an alternative answer.

Consider the question where the student needs to find the chance for an even number when throwing with a die.

For this question, we have created an algebra interaction with $\frac{3}{6}$ as task, together with an alternative answer $50\%$:

Now try it yourself by entering either $\frac{3}{6}$ or $50\%$ in the interactive exercise below.

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A students might make a (common) mistake in finding the answer to the task. AlgebraKiT has a number of common mathematical mistakes included in the knowledge set of the student, in which automated feedback is given on the possible mistake the student made. However, AlgebraKiT might not recognise all mathematical errors. Furthermore, there are also exist context-specific mistakes where a student makes mistakes in selecting the wrong context value for the task calculation.

Click on the Action button on the bottom left of the interaction field and select the Add incorrect answer option. An incorrect answer field appears below the step task(s).

Click on the new field. A new definition field opens.

Select the task of the incorrect answer and enter the expression. The specific feedback should be entered in the text-editor on the right of the field.

Removing an incorrect answer can be done by clicking on the bin on the top right side of the field. Adding another incorrect answer is done by clicking on the + icon on the top right side or by selecting the Add incorrect answer option in the actions menu once more.

Note: this field is intended to define incorrect answers for the step you are adding the incorrect answer to. You also have the concept of defining an incorrect step on step level, which is intended for strategic errors, rather than task errors.

##### Example

Let’s look at the question where the student needs to find the square root of $-4$. This is a trick question, as they have not learned complex numbers yet, so the answer is $no solution$. However, some students consider $\sqrt{-2}$ as a valid answer. In this case, we want to give feedback that they can verify their answer.

We have created an algebra interaction with $\sqrt{-4}$ as task, together with an incorrect answer $-2$:

Now try it yourself by entering $-2$ in the interactive exercise below.

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Set accuracy

On top of the selected algebra task, you can set the accuracy. The student must write their final answer according to this accuracy for the step to be final.

When you click on the “Actions” button on the left bottom and select the “Set Accuracy” option, an Accuracy field appears. Select one of the available options and fill in their corresponding fields.

For the algebra interaction, AlgebraKiT currently supports four different accuracy settings. To add this setting, click Actions > Accuracy.

You will then be able to select one of the following settings.

Exact

The default behaviour of AlgebraKiT is the exact accuracy setting. That means that no answer other than the mathematically exact answer to the question is accepted. The knowledge set of the selected audience defines what is mathematically exact for the student.

Rounded to

With the rounded to setting, the student has to write the answer rounded to exactly the selected number of decimals.

In the worked solution, AlgebraKiT will show the answer rounded to the selected number of decimals.

Accurate to

With the accurate to setting selected, the student has to write the answer rounded to at least the selected number of decimals correctly.

In the worked solution, AlgebraKiT will show the answer rounded to the least number of decimals.

Range

With the range setting selected, the answer of the student should lie between the boundaries entered ($minimum \le student input \le maximum$).

In the worked solution, AlgebraKiT will show the $maximum$ boundary value as solution.

Note that there is also some change in behavior related to the accuracy setting. This is explained below.

Accuracy settings – accepted input behavior

Answer rounded to 1 d.p. means that any input of the student is correct (not finished) if that input rounded to 1 d.p. will result in the original required value rounded to 1 d.p.

Why? A student might need to do more advanced calculations to calculate the final value. If a student chooses to round the intermediate steps to a different amount of decimals than you authored (but still enough to get to the correct final answer), it might be that the intermediate calculations differ from the exact value of the original result before rounding.

##### Example

$x=\frac{1}{7}$
$x^3=0.00291545189$ rounded to 11 d.p.
$x^3=0.003$ rounded to 3 d.p.

When calculating $x^3$ using $x$ rounded to $6$ decimals gives $(0.142857)^3=0.00291544314$. The margin of error seems quite small, but it is still there. However, rounded to 3 d.p. it yields the same result as using the exact value of $x$ for the calculation.

When calculating $x^3$ using $x$ rounded to $3$ decimals gives $(0.143)^3=0.002924207$. The margin of error gets bigger, but still, rounded to 3 d.p. it yields the same result as using the exact value of $x$ for the calculation.

As we can’t limit the student by always using exact values in their calculation, the above behavior applies to questions with accuracy settings applied.

In the below interactive exercise you can try all of the above (the exercise definition can be found here in the AlgebraKiT library):

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Set units

In AlgebraKiT, a unit is referring to a unit of measurement, which is a definite magnitude of a quantity.

As an author, you do not have to worry about the different forms of notation of common (SI) units, this is automatically recognised by AlgebraKiT.

For the algebra interaction, more advanced unit settings are available.

##### Example

$€10$ is interpreted by AlgebraKiT as a quantity for currency, with € the accounting unit. The quantity is representing ten euros. Whether the student writes $€10$, $10 \ euro$ or $10\ Euro$, does not matter.

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In an algebra or math entry task, you can write units in the task which AlgebraKiT is able to interpret as the actual unit, allowing enhanced student interactions. In case AlgebraKiT is not sure whether you referred to a unit, AlgebraKiT will give a popup to confirm. Refer to the item on symbols for more information.

There are several settings you can adapt as an author regarding the behavior of units. By clicking on the Actions button at the left bottom of the step field and selecting the Set Units option, a Units field appears beneath the task input. The following options are available.

By default, AlgebraKiT has the setting Allow other units enabled. This means that the student can choose in which unit the final answer is given.

##### Example

For an algebra interaction with a simplify task of $2.5km$, all of the following student inputs are accepted as a correct and final answer:
$2.5\ \text{kilometer}$, $2.5\ \text{kilometers}$, $25\ \text{m}$, $25\ \text{meters}$, etc.

If the answer is required in a specific unit, you can use the setting Convert to this unit. This setting is the oppposite of the Allow other units setting.

In case the Discard unit in task checkbox is not selected, AlgebraKiT will try to convert the task unit (if present) to the given unit in the unit field. In case this is not possible (AlgebraKiT cannot convert e.g. meters to seconds), the task unit will remain.

Consider the following example:

In this example, the student will need to convert the area of $300 \times 700 \text{meters}$ to the simplified answer in $\text{kilometers}$.

Unit not required in final answer

If a step is defined with a unit, (either in the task or the unit field), then the question is not finished until the student has written the final answer with a correct unit. If you want to accept a final answer without the unit, you can use the setting Unit not required to allow a final answer without the given unit.

For example:

In this case, the final answers $50$ and $50\ m$ are both correct and final answers.

Unit required at every input

By default, AlgebraKiT allows a student to write intermediate steps of a calculation without a unit, as is common in mathematical and physical calculations regarding units. In case you want the unit to be written at every input, you can use the setting Unit required at every step.

For example:

Intermediate steps now require units to be written explicitly.

Ignore the unit in the task

In some cases, the task is defined by using step references, where these steps might use units in their definition/answer. These units might not be useful in the calculation at this task. Therefore, you have the option to Discard unit from task.

##### Worked solution:

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Set modes

Refer to the section on modes for more information. Modes can be set on multiple levels (exercise-, interaction- and step level). This action sets the selected mode(s) on step level.

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Most of the above actions were already used in the section Creating a solution model. Refer to this section for the examples.

You now have seen all basic settings for the algebra interaction type. Let’s continue to the math entry interaction type, which is also useful when authoring algebra questions.