MATEMATICA SPAZIALE - UDA PROGRAMMAZIONE ANNUALE

START

LA MATEMATICA SPAZIALE - GUIDA PRATICA

PROVE DEI PIANETI

REGOLE MATEMATICHE

GEOMETRIA

PROVE DI CODING

PROBLEMI

INDICE

IN AGGIORNAMENTO

In aggiornamento

In aggiornamento

CLICCA

CLICCA

CLICCA

CLICCA

CLICCA

CLICCA

CLICCA

CLICCA

CLICCA

Our Solar System

Our Solar System

Earth's movement

Day and night

The Moon

Our planet

CLICCA

CLICCA

LA TERRA

Our Solar System

Earth's movement

URANO

SVOLGI LE EQUIVALENZE:1Kg = …………………….g 1 dag = ………………….dg 3 g = ………………………cg 2 g = …………………….. dg 1 mg = …………………..cg 2 cg = …………………… dg 2,2 hg = ……………….. dag 2,2 hg = ……………….. dg 2,3 cg = ……………….. dg 1 Mg = ………………… kg

3,2 l = ……………dl15 dl = …………….l 5,6 cl = …………..dl 5 l =………………dl 2 l = ……………...cl 3,3 dl = …………...l 4 l = ……………...dl 32 ml = …………..cl 5 dl = ……………cl54 dl = …………….l20 cl = …………...dl 5 l = ……………..cl 3,5 l = …………...cl

Le misure di capacità

Guarda lo schema

Guarda il video

LE OPERAZIONI

LE EQUIVALENZE

LE FRAZIONI

I NUMERI DECIMALI

LE POTENZE

INDICE

LE EQUIVALENZE E LE MISURE

Le misure di lunghezza

Le misure di capacità

Le misure di peso

401x24=130x65=330x43=280x37=401x21=66x99=187x39=

PROVA DI NETTUNO

Guarda la regola

Guarda il video

Esegui in colonna

CHE COSA SONO LE EQUIVALENZE?

Fare le equivalenze significa trasformare un'unità di misura in un'altra, in modo tale che si equivalgano. Nella pratica significa trasformare un'unità di misura grande in una più piccola, o viceversa.

Fare le equivalenze significa trasformare un litro in ettolitro, un metro in un centimetro, un grammo in un chilo e così via. Ogni gradino equivale a un valore:

Se immaginiamo queste unità di misura posizionate su una scala, quindi, potremo effettuare equivalenze in salita (dal valore più piccolo al più grande) o in discesa (dal valore più grande a quello più piccolo).

Ricorda che al “centro” c'è sempre il grammo, il litro, il metro: in questo modo, andando verso l’alto ti basterà dividere per 10 a ogni gradino, scendendo invece moltiplicherai per 10 a ogni gradino.

MULTIPLI

SOTTO MULTIPLI

QUIZ

Le misure di capacità

super quiz

Le misure di lunghezza

Le misure di peso

LE OPERAZIONI

ADDIZIONE

SOTTRAZIONE

MOLTIPLICAZIONE

DIVISIONE

Le proprietà della divisione

1) LA PROPRIETÀ INVARIANTIVA Se dividendo e divisore vengono divisi o moltiplicati per uno stesso numero, il risultato della divisione non cambierà. Facciamo un esempio: 150 : 30 = 5 (150 : 10) : (30 : 10) = 15 : 3 = 5 e lo stesso se moltiplichiamo: (150 x 10) : (30 x 10) = 1500 : 300 = 5

Prosegui

2 - LA PROPRIETÀ DISTRIBUTIVA Il primo passaggio è quello di scomporre il dividendo in due numeri la cui somma o la cui differenza dia proprio il numero di partenza, e cioè il dividendo. Una volta fatto questo, se si dividono i numeri ottenuti per il divisore e poi si sommano (o sottraggono) i quozienti ottenuti, si otterrà il risultato della divisione originaria.Guardate: 175 : 25 = 7 (150 + 25) : 25 = (150 : 25) + (25 : 25) = 6 + 1 = 7 Ma anche 175 : 25 = 7 (200 – 25) : 25 = (200 : 25) – (25 : 25) = 8 – 1 = 7

LA DIVISIONE A DUE CIFRE IN COLONNA

320

12

2

4

2

320

12

2

8

0

0

6

2

1) Osserva le prime due cifre del dividendo: (in questo caso h e da) se sono più piccole o più grandi del divisore. In questo caso, il 32 è maggiore del 12 (dividendo). 2) Adesso calcola quante volte il 12 è contenuto (sta) nel 32. In questo caso ci sta 2 volte. (12x2=24). 3)Dal 32 si toglie 24. Il resto è 8. 4)A questo punto si tira giù lo 0. Quante volte il 12 sta nell'80? 6 volte! (12x6= 72). Si sottrae dall'80 il 72 ed il resto è 8!

7

8

8

Osserva bene:

320:12=

LA MOLTIPLICAZIONE

MOLTIPLICANDO XMOLTIPLICATORE=--------------------PRODOTTO

Le moltiplicazioni possono presentarsi con una o più cifre al moltiplicatore. Lo svolgimento diventa più complesso, man mano che aumentano le cifre al moltiplicatore.Nella prossima pagina vedremo alcuni esempi.

Segue

Segue

MOLTIPLICAZIONE CON UNA CIFRA AL MOLTIPLICATORE

312 x 6=1872

312 x 6 =-----

1) si moltiplica ogni cifra del moltiplicando per l'unità del moltiplicatore .

312 x 6= ------- 2

SVOLGI L'ESERCIZIO

312 x 6=------- 72+

2) Si parte dall'unità.

+1 (RIPORTO)

(6x2)=12

3) Si parte dall'unità e poi si prosegue con la decina

312 x 6=------- 1872

(1x6)=6 (6+1) = il riporto

ESERCITAZIONE

SEGUE

MOLTIPLICAZIONE CON 2 CIFRE AL MOLTIPLICATORE

312 x 41=

312 x 41=----- 312

1) si moltiplica il moltiplicando per l'unità .

2) si moltiplica il moltiplicando per la decina.

312 x 41=------- 312 1248/

312 x 41=------- 312+ 1248/=-------- 12792

3) si sommano i due risultati.

2) Lascia uno spazio sotto l'unità (vale 0)

401+24=2340+165=439+765=263+378=401+274=1250+3766 =

ADDIZIONI CON LA PROVA

Guarda la regola

Guarda il video

Esegui in colonna con i 2 metodi di prova

Guarda il video

Scrivi sul quaderno, con parole tue, la proprietà commutativa ed i 2 metodi per fare la prova dell'addizione.BUON LAVORO!!

RISOLVI LE OPERAZIONI:

IL SOLE

5.400 – 2324 = 3672 – 1835 = 6320 – 2500,33 =

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LA PROVA

IL RESTO è quel numero che, addizionato al SOTTRAENDO dà come somma il MINUENDO

500 -100 =------400

400 + 100 =------ 500

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E ORA QUALCHE CALCOLO MENTALE:

VENERE

8 + 50 + 4 + 30 + 2 + 9 + 100 + 6 + 15 =2500 + 700 + 60 + 11 + 9 + 40 = 2,5 + 1,5 + 6 + 3,3 =

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LE SOTTRAZIONI IN COLONNA

Le sottrazioni in colonna si impostano come le addizioni, ma invece di aggiungere si toglie. Non esiste il riporto, ma c'è il prestito tra decine, centinaia e migliaia.

3108-1877 =

3 1 0 8 -1 8 7 7 =-------1 2 3 1

1

0

1

2

E ORA QUALCHE CALCOLO MENTALE:

VENERE

8 + 50 + 4 + 30 + 2 + 9 + 100 + 6 + 15 =2500 + 700 + 60 + 11 + 9 + 40 = 2,5 + 1,5 + 6 + 3,3 =

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La scala delle misure di capacità

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PARLIAMO DI TEMPO (Ricorda che 1 ora è formata da 60 minuti)

MERCURIO

12.45: quanto manca alle 13.30?8.30: quanto manca alle 15.00? 23.12: quanto manca alle 1.30?

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LA SOTTRAZIONE

Si tratta della differenza di due numeri di cui il primo è più grande o uguale al secondo.

MINUENDO

SOTTRAENDO

RESTO

500 -100 =-----400

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PARLIAMO DI TEMPO (Ricorda che 1 ora è formata da 60 minuti)

MERCURIO

12.45: quanto manca alle 13.30?8.30: quanto manca alle 15.00? 23.12: quanto manca alle 1.30?

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La differenza di due numeri non cambia se a entrambi si aggiunge o si sottrae lo stesso numero. Pensate di avere dei numeri molto grandi, con questo piccolo trucchetto potrete calcolare la sottrazione più facilmente.

La proprietà invariantiva

ESEMPIO:132 – 122 = 10Ora proviamo ad aggiungere uno stesso numero sia al minuendo, che al sottraendo. (132 + 3) – (122 + 3) = 135 - 125 = 10

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L'addizione è quell'operazione che consente di sommare i numeri fra di loro.Ad esempio se ho un numero (10) e aggiungo un altro numero (25), ottengo un numero più grande, cioè il totale (35).I numeri che compongono la somma sono gli addendi, mentre il risultato si chiama somma.

LA PROPRIETÀ COMMUTATIVA cambiando l'ordine degli addendi il risultato non cambia. Questo vuol dire che: 18 + 2 = 20 così come 2 + 18 = 20

LA PROPRIETÀ ASSOCIATIVA In un'addizione composta da tre o più addendi, possiamo sostituire due qualsiasi addendi consecutivi con la loro somma.18 + 2 + 5 = 25Ma possiamo farlo anche diversamente: 18 + (2 + 5) = 18 + 7 = 25

LA PROPRIETÀ DISSOCIATIVA La proprietà dissociativa stabilisce che in un'addizione si può sostituire un addendo con due numeri la cui somma restituisca proprio quel numero, senza che il risultato cambi.(10 + 8) + 2 = 20

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LE PROVE DELL'ADDIZIONE

1° METODO:Usa la proprietà commutativa.

35+36= 7136+35 = 71

Dopo aver eseguito la prima addizione, basterà invertire gli addendi e calcolare di nuovo. Se il risultato è lo stesso, vuol dire che è giusto!

2° METODO:Usa la sottrazione.

35+36= 7171-36 = 35

Dopo aver eseguito la prima addizione, basterà sottrarre dal totale il secondo addendo. Se il risultato è uguale al primo addendo è giusto!

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PROVA DEL PIANETA MARTE

• 1° giorno = 18,5 °C
• 2° giorno = 20,3 °C
• 3° giorno = 24 °C
• 4° giorno = 17,2 °C
• 5° giorno = 23 °C
• 6° giorni = 25,8 °C

Marte è l’unico pianeta sul quale si potrebbe ipotizzare l’esistenza di una qualsiasi forma di vita; infatti sono stati ritrovati numerosi fossili di fiumi che assicurano l’esistenza di acqua nel passato. Inoltre questo pianeta ha delle temperature estive di 25 °C. Ecco i dati che sono stati raccolti negli ultimi sei giorni in merito alla temperatura su Marte:

Costruisci un grafico con questi dati, sul quaderno.

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• Generate experiences with your content.
• It’s got the Wow effect. Very Wow.
• Make sure your audience remembers the message.

With Genially templates, you can include visual resources to wow your audience. You can also highlight a particular sentence or piece of information so that it sticks in your audience’s minds, or even embed external content to surprise them: Whatever you like!Do you need more reasons to create dynamic content? No problem! 90% of the information we assimilate is received through sight and, what’s more, we retain 42% more information when the content moves.

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La divisione ha un elemento neutro, che è il numero 1. Questo perché se si divide un qualsiasi numero per uno, il quoto sarà sempre uguale al dividendo. 1.543 : 1 = 1.543 Un'altra caratteristica della divisione riguarda lo zero: in matematica non esiste il risultato di una divisione per zero. Se, invece, provo a dividere lo zero per un qualsiasi numero, il risultato sarà sempre zero. 0 : 85 = 0

ATTENZIONE!