Tasks

Define the problem, not the answer

A core feature of Multistep is its ability to evaluate substeps and give automated support. This is possible only if Multistep knows what problem students must solve. Therefore, you don't prescribe answers; you prescribe the tasks students should perform.

Example

a task could be to simplify $\frac{2y^2\sqrt{5}}{xy}$ . An answer is $2\sqrt{5}\frac{y}{x}$ .
a task could be to solve $3(x-1)=2x+4$ . The answer is $x=7$ .

Algebrakit derives hints, error feedback, worked solutions, and answers from the task, so you don't need to enter them. You can add custom hints or error feedback, as we will see later.

Multistep supports several tasks organised into the following categories:

Simplifying expressions
Rewriting expressions, such as expanding, factoring, or rewriting expressions into different forms.
Solving equations or inequalities

You can build more complex tasks from these. For example:

Finding the equation of a line through two points, which requires:

Calculating the slope (Simplify).
Substitute coordinates to get the $y$ -intercept (Solve).
Writing the equation (Simplify).

Finding the coordinates of the maximum of a function, which requires:

Finding the derivative of the function (Simplify)
Setting the derivative to zero and solving the equation (Solve)
Writing the coordinates of the maximum (Simplify)

How to create such composed tasks will be discussed in chapter Multistep (advanced)

Defining a task

Now let's create a new Multistep question. You can use the Testbench if you have no access to an Algebrakit-enabled content management system.

There are two available Multistep editors. Select the simple editor. Selecting the Multistep question type Left: Selecting the Multistep question type. Right: Setting task "Simplify $x(x-1)+x$ "

The default Task is to simplify an expression. In the input field, type $x(x-1)+x$ . Now press the Test button at the bottom of the page to see a preview of our question.

Previewing an exercise Figure: Previewing our exercise.

The preview shows an interactive question on the left. You can answer the question step by step, and request hints as a student would. The worked solution on the right shows how Algebrakit solves the problem. Click to expand the steps.

Note

The Accuracy, Units and Form settings are not covered here, but have their own dedicated section.

The Simplify task

Simplifying is required for all tasks. Students must evaluate calculations and simplify expressions as much as possible.

$1+1$ must be evaluated to $2$
$x+y+x$ must be simplified to $2x+y$
$x(x+1)-x$ must be simplified to $x^2$
$\frac{d}{dx}\sin\left(x^2+1\right)$ must be simplified to $2x \sin\left(x^2+1\right)$
$\int_0^T \left(at+b\right) dt$ must be simplified to $\frac12aT^2+bT$

Multistep will only rewrite an expression if that simplifies the result. For example, Multistep will not rewrite the following expressions:

$x(x+1)$ . An equivalent form is $x^2+x$ .
Use the task Rewriting expressions - Expand brackets if you want students to expand the expression.
$\frac{1}{x}+\frac{2}{3}$ . An equivalent form is $\frac{3+2x}{3x}$ .
Use the task Rewriting expressions - Combine fractions if you want students to combine the fractions.

Multistep will accept as a final answer any equivalent form that cannot be simplified further.

Simplifying does not include solving equations, so Multistep will not require students to rewrite $2x=4$ into $x=2$ . Use the Solve task if students are supposed to solve for $x$ .

Solving equations

In the category Solving Equations, you can find tasks for finding solutions to equations, inequalities, or systems of equations.

Task: Solving Equations Figure: Task: Solving Equations

You can use the "Solving Equations: Single Variable" task to solve a wide variety of relations. The table shows some examples:

Relation	Result	Explanation
$6(p-1)=4p+10$	$p=8$	A linear equation
$a\cdot x=b$	$x=\frac{b}{a}$	Algebraic solutions are allowed
$2(1-x)\leq4$	$x\geq -1$	Inequalities are supported
$\frac{1}{\sqrt{1-x}}>1$	$0<x<1$	Algebrakit keeps track of the domain
$2\sin \left(2x-\frac{1}{4}\pi \right)=\sqrt{2}$ , $0<x<\pi$	$x=\frac{\pi}{4}, x=\frac{\pi}{2}$	Trigonometry
$\begin{cases}2x-1=y\\x+y=1\end{cases}$	$\begin{cases}x=\frac{2}{3}\\y=\frac{1}{3}\end{cases}$	System of equations

As always, Multistep offers support through hints and substep evaluations. You can try them here:

Note

The following types of equations are not yet supported:

Systems of inequalities
Equations with solutions in the complex plane

The Rewrite Task

Multistep provides several tasks that require students to rewrite an expression. Most of them will be self-explanatory.

The table below shows some examples.

Task	Example	Result
Expand	$x(x-1)$	$x^2-x$
Factor	$x^2-x$	$x(x-1)$
Combine Fractions	$\frac{1}{x}+\frac{2}{3}$	$\frac{3+2x}{3x}$
Complete the Square	$x^2+6x+7$	$\left(x+3\right)^2-2$

Custom Initial hints

You can define hints that Algebrakit must show before the automatic hints. For example, you can add custom hints to help students get started by rephrasing the question.

Click the Multistep dropdown and choose Hints
Adding a custom initial hint Figure: Navigating to the Hints settings

You can add multiple hints using the plus icon on the right. Adding multiple custom hints Figure: Adding multiple custom hints

Multistep settings

Click the Multistep dropdown and choose Settings
Navigating to the Settings panel Figure: Navigating to the Settings panel

Setting: Disabling automated hints

Students can request multiple hints by repeatedly clicking the Hint button. If you defined custom hints (see below), these will appear first. The automated hints follow next.

Configuring hints in the settings panel Figure: Configuring hints in the settings panel

Set Hints to Disable automated hints to disable the automated hints for this question. Any custom initial hints will still appear.

Setting: Initial expression

By default, Multistep shows the first expression of the derivation. If you don't want to give this expression away, you can configure this Initial Expression to be "Not visible". You can also define a custom expression.

A Multistep with and without an initial expression Figure: A Multistep with and without an initial expression.