# Math Formula

## Description

The Math Formula question allows students to easily enter complex math as a response, with advanced validation capabilities using math specific scoring methods, in conjunction with our purpose built math engine.

Figure 1 - Math Formula question example.

## Create a Question

Enter the question stem in the Compose Question area. If you want to insert some math in the stimulus, you can use the Math Editor. Note that the student will not be able to interact with math entered this way. To access the Math Editor, click inside the Compose Question text area and select Math Editor from the Rich Text Editor panel (see Figure 2).

Figure 2 - Rich Text Editor panel with Math Editor button.

A new window with a keypad will pop up and you will be able to add a LaTeX or MathML expression. Figure 3 shows an example.

Figure 3 - Question with math expression in the stimulus.

Student response boxes (and math expressions) are added in the Template area. This is a LaTeX only area, and math expressions and response boxes are entered using the LaTeX Keypad - as seen in Figure 4 below.

It is important to remember that everything entered into the Template area must also be entered into the Value field in the validation area, or the question will not validate properly.

Figure 4 - Authoring a Math Question with the LaTeX keypad.

Follow these steps in order to configure validation:

1. Insert a value in the Point(s) box to set the score for the question. The default value is 1.

2. Underneath the Point(s) area, select a suitable math scoring method from the dropdown menu. There are various scoring methods available in math question types. You can learn more about each of them and play with interactive examples on our Formula page. For this example we are going to choose equivSymbolic. This will accept any math that is symbolically equivalent to what the author enters in the Value field, and is the most flexible scoring method.

3. Now insert the correct response into the Value field. In the case below, the correct response must be in the form x+y=z and the sum of two terms must be $$\frac{3}{4}$$. You only need to enter one possible solution in the Value field in order to make it work. Remember that everything that has been entered in the Template area must be copied to the Value field in validation. Figure 5 shows validation settings for this example. EquivSymbolic also validates percentages and decimals as equivalent.

Figure 5 - Setting a value. The entire equation entered into the LaTeX Template area must be entered into the Value area.

4. Each scoring method has additional options that allows authors to set more precise validation conditions. A breakdown of all options associated with certain scoring methods can also be found in our Formula tutorials. When you select a scoring method, all of its extra options will be displayed underneath the Value field.
5. Figure 6 - Additional options.

6. Some more complex math questions will need a second scoring method applied. You can combine several scoring methods to set more strict validation rules. For instance, you may want the system to accept a response that is not only symbolically equivalent but is also presented in a specific syntax. In this case, you would need to add another method called equivSyntax. Below the first scoring method you will see the +Add button. Click on it in order to add a new scoring method. Another module will appear below where you can select equivSyntax as the scoring type. In the Rule dropdown you can choose a specific Syntax, e.g. Fraction or Decimal, among others.
7. Figure 7 - Combining scoring methods.

### More Options

Additional formatting options can be found under More Options:

#### Scoring

Unscored/Practice usage - Removes all scoring from the question.

Penalty point(s) - The value entered here will be deducted from the student for an incorrect answer.

Minimum score if attempted - Set attempt marks for the question.

Check answer button - Show or hide the Check answer button from the student.

Check answer attempts - The value entered here refers to how many times the student can use the Check answer button, before it is disabled.

#### Layout

Transparent background - If this is enabled, the background of the response area will match the colour of the rest of the background area.

Response minimum width (px) - Enter, in pixels, the minimum width of the response area.

Template font scale - Scales the font relative to the question's font size. The default value is 150%.

Response container (global) and Edit invidiual response containers - Configure the Width and the Height, in pixels, for either all response containers, or for specified response containers.

Type - Select from a Floating keypad, a Block keypad, a Block on focus keypad, or no keypad.

Show keypad hints - Enable or disable hints on the keypad, such as keyboard shortcuts and symbol group titles that are shown on the top left corner of the keypad when hovering over a symbol group key.

Number pad - Customise the number pad in this section.

Symbols - Select what symbol groups will be shown to the student, or create custom symbol groups.

#### Text blocks

Use this option when you want to define a list of custom units (such as g, kg, cm, oz, etc.) that will not be rendered as LaTeX.

Example 1 - Math Formula - Default response box.

{
"instant_feedback": true,
"is_math": true,
"stimulus": "Enter the equation \$$x + 1\$$",
"type": "formulaV2",
"ui_style": {
"type": "block-keyboard"
},
"validation": {
"scoring_type": "exactMatch",
"valid_response": {
"score": 1,
"value": [
{
"method": "equivLiteral",
"value": "x+1",
"options": {
"ignoreOrder": false,
"inverseResult": false
}
}
]
}
}
}

Example 2 - Math Formula question with 1 response box.

{
"instant_feedback": true,
"is_math": true,
"stimulus": "Enter any value that is equal to \$$5m\$$. You may use \$$km\$$, \$$cm\$$, \$$ft\$$, \$$in\$$ or other units (rounded to two decimal places).",
"symbols": [
"units_us",
"units_si"
],
"template": "{{response}}",
"text_blocks": [],
"type": "formulaV2",
"ui_style": {
"type": "block-keyboard"
},
"validation": {
"scoring_type": "exactMatch",
"valid_response": {
"score": 1,
"value": [
{
"method": "equivValue",
"value": "5m",
"options": {
"decimalPlaces": 2,
"inverseResult": false
}
}
]
}
}
}

Example 3 - Math Formula - Default response box with Matrices keyboard.

{
"instant_feedback": true,
"is_math": true,
"stimulus": "<p>Complete the matrix addition:<\/p>\n\n<p>\$$\\begin{bmatrix}3&amp;1\\\\-2&amp;4\\end{bmatrix}+\\begin{bmatrix}-1&amp;5\\\\-3&amp;1\\end{bmatrix}=\$$<\/p>\n",
"symbols": [
"matrices"
],
"text_blocks": [],
"type": "formulaV2",
"ui_style": {
"response_font_scale": "normal",
"type": "block-keyboard"
},
"validation": {
"scoring_type": "exactMatch",
"valid_response": {
"score": 1,
"value": [
{
"method": "equivSymbolic",
"value": "\\begin{bmatrix}2&6\\\\-5&5\\end{bmatrix}",
"options": {
"allowDecimal": false,
"inverseResult": false
}
}
]
}
}
}

Example 4 - Math Formula - with customised response container size.

Hint Insert 10-31.

{
"instant_feedback": true,
"is_math": true,
"response_containers": [
{
"width": "60px",
"height": "40px"
}
],
"stimulus": "<p>\n<p>Complete the&nbsp;formula to calculate mass of an electron.<\/p>\n",
"symbols": [
"basic",
"qwerty",
"units_si"
],
"template": "m_e=9.109\\times{{response}}{ }kg",
"text_blocks": [],
"type": "formulaV2",
"ui_style": {
"type": "block-keyboard"
},
"validation": {
"scoring_type": "exactMatch",
"valid_response": {
"score": 1,
"value": [
{
"method": "equivLiteral",
"options": {
"allowDecimal": false,
"inverseResult": false,
"ignoreOrder": false
},
"value": "m_e=9.109\\times10^{-31}kg"
}
]
}
}
}

Example 5 - Math Formula with 2 response boxes.

{
"instant_feedback": true,
"is_math": true,
"stimulus": "Complete the equation so that the two sides are equal.",
"symbols": [],
"template": "{{response}} + {{response}} = 10",
"text_blocks": [],
"type": "formulaV2",
"ui_style": {
"type": "block-keyboard"
},
"validation": {
"scoring_type": "exactMatch",
"valid_response": {
"score": 1,
"value": [
{
"method": "equivValue",
"options": {
"decimalPlaces": 10,
"inverseResult": false,
"ignoreOrder": false
},
"value": "1+9=10"
}
]
}
}
}

Example 6 - Math Formula - With Fraction and exponent responses.

Hint Correct answer is V=43π r3

{
"instant_feedback": true,
"is_math": true,
"stimulus": "\n<p>Complete a formula to find volume of a sphere.<\/p>\n\n<p><img alt=\"\" height=\"200\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/a\/a3\/Linalg_great_circle.png\" width=\"200\" \/><\/p>\n\n<p>&nbsp;<\/p>\n",
"template": "V=\\frac{ }{ }\\pi r^{ }",
"text_blocks": [],
"type": "formulaV2",
"ui_style": {
"type": "block-keyboard"
},
"validation": {
"scoring_type": "exactMatch",
"valid_response": {
"score": 1,
"value": [
{
"method": "equivLiteral",
"options": {
"allowDecimal": false,
"inverseResult": false,
"ignoreOrder": false
},
"value": "V=\\frac{4}{3}\\pi r^3"
}
]
}
}
}