GimmeFive is constituted by 8 environments. A single interface gives access to these environments.

The first 5 environments support students in developing basic skills and mental calculation for performing addition and subtraction. The last 3 environments give students opportunities to develop strategies in mental calculations for addition and subtraction of two-, three- and four-digits numbers.

**Environment 1**

This environment is addressed to develop skills concerning known number pairs with a total of 10. In this activity numbers are represented through hand fingers. This representation allows students to visualize the process leading to the addition result.

In this activity numbers are expressed in analogical format. The number in Arabic format can be seen tapping up over each corresponding analogical representation. The activity leads student to perform additions observing relationships among the two represented numerical quantities and the corresponding result. It is not possible for student to insert an incorrect result. This feature was designed to prevent them from incorrect experiences.

**Environment 2 **

** **This environment is addressed to automatize the ability to add number pairs with a total of 10. In this environment the activity requires to perform additions with numbers pairs with a total of 10 where the two numbers are expressed as symbols.

Skills involved in this activity are similar to those required in the previous environment; the only difference is the change in number representation. As before, it is not possible for student to insert an incorrect result. This feature was designed to prevent them from incorrect experiences.

**Environment 3 **

** **This environment is addressed to automate the ability to add number pairs with a total of 10, 100 and 1000. There are three different kinds of activity that can be performed from student. The first activity present one addend of an operation and requires student to select a second addend to have 10 as result (complement to 10). The second and third activities are very similar to the first one. They requires students to select the second addend of an operation having respectively 100 (complement to 100) and 1000 (complement to 1000) as result.

Automating skills and mastering relationship about pairs of numbers which total 10, 100 and 1000 is very important for mental calculation. The activity supports students in visualising numbers of complement 10, 100 and 1000 through a symmetrical relationship between the two number sequences represented on the screen. As in the previous environments, it is not possible for student to insert an incorrect result. This feature was designed to prevent them from incorrect experiences.

**Environment 4 **

** **This environment is addressed to automate the ability to add number pairs with a total under 10, 100 and 1000. The activity is similar to the previous one; the difference is that the result in this environment is not 10, 100 or 1000 but it is a number smaller than 10, 100 or 1000. There are three different kinds of activity that can be performed from student. The first activity presents the result of an operation, a number smaller than 10, and one addend of this operation and requires student to select the second addend of this operation. The second and third activities are similar to the first one. They require students to select the second addend of an operation having respectively a number smaller then 100 and smaller than 1000 as result.

Automating skills and mastering relationship about pairs of numbers which total under 10, 100 and 1000 is very important for mental calculation. The activity supports students in visualising relationships between pairs of numbers of required complement through a symmetrical relationship between the two number sequences represented on the screen. As in the previous environments, it is not possible for student to insert an incorrect result. This feature was designed to prevent them from incorrect experiences.

**Environment 5**

** **This environment is addressed to automate the ability to decompose numbers to simplify addition between them. Their total is a number between 11 and 18. The activity requires student to decompose the two addends through analogical representation. There is a best decomposition among the possible ones: it is that using 5

**Environment 6 **

** **This environment is addressed to develop strategies of mental calculation to solve additions decomposing the two addends of the operation. There are three different kinds of activity student can chooses. In the first kind of activity addition has result under 20, in the second and third activity the result of the operation is respectively under 99 and 999.

For each task the system provides a grade. The max value of this grade corresponds to a correct answer given in only one step. The grade decreases if mistakes are made. The grade also depends on the number of steps used to solve the operation and the time taken to provide the answer. This app monitors the student activity and records in a pdf document the performed tasks, the eventual mistakes, the number of steps taken to solve the task, the acquired grade. An option in the app allows the user to send the pdf document. In this environment the user can learn to decompose each addend of the operation through an additive relationship among hundreds, tenth and ones. The user can tap the number to obtain this decomposition. Numbers can be dragged to make closer hundreds, tenth and ones to add respectively among them hundreds, tenth and ones. This spatial proximity can facilitate mental calculation. Finally the number can be recomposed. In this environment it is possible to directly experience strategies involved in mental calculations. Through this experience, student can succeed to interiorize these strategies to eventually perform them mentally.

**Environment 7 **

This environment is addressed to develop strategies of mental calculation to solve subtractions decomposing the minuend and/or the subtrahend in the operation. There are three different kinds of activity student can chooses. In the first kind of activity subtraction has result between 10 and 19, in the second and third activity the result of the operation is respectively between 20 and 99, and between 100 and 999.

For each task the system provides a grade. The max value of this grade corresponds to a correct answer given in only one step. The grade decreases if mistakes are made. The grade also depends on the number of steps used to solve the operation and the time taken to provide the answer. This app monitors the student activity and records in a pdf document the performed tasks, the eventual mistakes, the number of steps taken to solve the task, the acquired grade. An option in the app allows the user to send the pdf document. In this environment the user can learn to decompose the minuend and the subtrahend of the operation through an additive relationship among hundreds, tenth and ones. The user can tap the number to obtain this decomposition. Numbers can be dragged to make closer hundreds, tenth and ones to subtract respectively among them hundreds, tenth and ones. This spatial proximity can facilitate mental calculation. Finally the number can be recomposed. In this environment it is possible to directly experience strategies involved in mental calculations. Through this experience, student can succeed to interiorize these strategies to eventually perform them mentally.

**Environment 8 **

This environment is addressed to develop strategies of mental calculation to solve additions and subtractions decomposing the operands of the operation. In this environment the user is completely free to choose the appropriate strategy to decompose the operands to solve the task. The app supports the development of all strategies for mental calculation that can be involved in additions and subtractions.

For each task the system provides a grade. The max value of this grade corresponds to a correct answer given in only one step. The grade decreases if mistakes are made. The grade also depends on the number of steps used to solve the operation and the time taken to provide the answer. This app monitors the student activity and records in a pdf document the performed tasks, the eventual mistakes, the number of steps taken to solve the task, the acquired grade. An option in the app allows the user to send the pdf document.