Constant Sum

### CONSTANT SUM BETWEEN OPPOSITE SIDES: A BOUNDLE OF STRAIGHT LINES

After briefly discussing the concepts of opposite and adjacent sides, ask the students to join together all the pairs of numbers with a certain sum (with the partial tables downloadable at the bottom of the page).

In the example shown in the figure, the sum is 10, but we recommend carrying out the experience twice, starting from a smaller sum.

The configuration obtained is a bundle of lines, a terminology that can be shared with the class.

At the end of the activity, we, therefore, recommend proposing to the class the phrase "if you connect numbers on opposite sides with a constant sum, you get a bundle of straight lines".

### CONSTANT SUM OF ADJACENT SIDES: THE PARABLE

Ask the students to join together all the pairs of numbers with a given sum, but this time by providing the partial tables with the numbers placed on two adjacent sides.

The configuration obtained is a parabola - in the example in the figure, the sum is always 8. We also recommend proposing the phrase "if you connect numbers on adjacent sides with a constant sum, you get a parabola".

While the rule remains unchanged (two figures with one side in common cannot have the same colour), the activity will be more challenging.

### EXPERIENCE OF TESSELLATION WITH THE PARABLE

Quando i bambini hanno finito di colorare le proprie parabole, si può chiedere loro di affiancarle per ottenere varie configurazioni, come quelle mostrata in figura.

### CONSTANT SUM CONFIGURATIONS IN REALITY

After completing each configuration, we recommend that the children find some examples of straight lines or parables, in reality, showing the figures shown here.

A snowflake, the pyramid of Giza.

A satellite dish, a parable shot.

### OBIETTIVI INDICAZIONI NAZIONALI COERENTI CON L'ATTIVITÀ

TERMINE CLASSE TERZA

• Eseguire mentalmente semplici operazioni con i numeri naturali.

TERMINE CLASSE QUINTA

• Eseguire le quattro operazioni con sicurezza;

• riconoscere e descrivere regolarità in una sequenza di numeri o di figure;

• riconoscere figure ruotate, traslate e riflesse;

• riconoscere rappresentazioni piane di oggetti tridimensionali.

Constant Sum

### CONSTANT SUM BETWEEN OPPOSITE SIDES: A BOUNDLE OF STRAIGHT LINES

After briefly discussing the concepts of opposite and adjacent sides, ask the students to join together all the pairs of numbers with a certain sum (with the partial tables downloadable at the bottom of the page).

In the example shown in the figure, the sum is 10, but we recommend carrying out the experience twice, starting from a smaller sum.

The configuration obtained is a bundle of lines, a terminology that can be shared with the class.

At the end of the activity, we, therefore, recommend proposing to the class the phrase "if you connect numbers on opposite sides with a constant sum, you get a bundle of straight lines".

### CONSTANT SUM OF ADJACENT SIDES: THE PARABLE

Ask the students to join together all the pairs of numbers with a given sum, but this time by providing the partial tables with the numbers placed on two adjacent sides.

The configuration obtained is a parabola - in the example in the figure, the sum is always 8. We also recommend proposing the phrase "if you connect numbers on adjacent sides with a constant sum, you get a parabola".

While the rule remains unchanged (two figures with one side in common cannot have the same colour), the activity will be more challenging.

### EXPERIENCE OF TESSELLATION WITH THE PARABLE

Quando i bambini hanno finito di colorare le proprie parabole, si può chiedere loro di affiancarle per ottenere varie configurazioni, come quelle mostrata in figura.

### CONSTANT SUM CONFIGURATIONS IN REALITY

After completing each configuration, we recommend that the children find some examples of straight lines or parables, in reality, showing the figures shown here.

A snowflake, the pyramid of Giza.

A satellite dish, a parable shot.

### OBIETTIVI INDICAZIONI NAZIONALI COERENTI CON L'ATTIVITÀ

TERMINE CLASSE TERZA

• Eseguire mentalmente semplici operazioni con i numeri naturali.

TERMINE CLASSE QUINTA

• Eseguire le quattro operazioni con sicurezza;

• riconoscere e descrivere regolarità in una sequenza di numeri o di figure;

• riconoscere figure ruotate, traslate e riflesse;

• riconoscere rappresentazioni piane di oggetti tridimensionali.