Expressions in a table often satisfy some relations. The Math Table interaction allows you to specify such relations and evaluate if these are satisfied.

Relations exist in different types, namely:

- Relation between a cell and its row/column indices
- Relation between a cell and other cells
- Relations for the table as a whole

You can specify all these types of relations with the Math Table interaction type.

## Relation between cell and row/column indices

Every cell, whether it is of type Math, Text, or Input, can use the special variables *row* and *col*. Row 1 is the first non-header row and column 1 is the first non-header column. This implies that the top header in the image above has a row index of 0. If there are multiple headers, the row index will be negative.

## Relation between cell and other cells

You can refer to the content of a Math cell or an Input cell through the *cell* function, which takes the row index and column index as arguments respectively.

The example above shows a table corresponding to the Fibonacci sequence.

**Relations and free input**

A powerful feature of these relations is that the values of the cells do not to be known in advance. You can create a Math Table where a student is free to choose some values. Consider the example below, where the student has to create a table for a given function. The student is free to choose the values for *x*, while the relations enforce that these *x*-values are increasing and that the values for *y* are correct.

## Table conditions

This example illustrates a situation where you want to specify a condition on the table. The student is required to try different divisors of -30, until a pair is found that sums to -13.

The Input cells in columns 2 and 3 are of type Math Entry and allow any integer divisor of -30. The Input cells in the last column are of type Algebra with the task to sum the two divisors.

The student has successfully finished the table when the correct divisors are found, which are -15 and 2. It doesn’t matter in which row these divisors are written or in which order the divisors are given, as long as they exist. This requires a condition like “There exists a cell in the last column with value -13”.

Such a condition can be created under the Table tab:

- Check the ‘Existence’ check box to indicate that the condition is valid if a cell can be found that satisfies it. If this checkbox is not checked, then all cells need to satisfy the condition.
- Click the button ‘change…’ to select the range of cells that apply to this condition. In our case, these are the cells in the last column
- Enter the condition in the formula box. The variables
*r1*and*c1*are the row and column index of the cell that meets the condition (if any). - Specify that the problem is finished if a cell is found that matches this condition. Specify feedback in case it is not found.

Note that the student input is evaluated as correct only if all the conditions in the cells and the table condition are satisfied. So just entering the number -13 in the last column is not a valid answer.

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