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Long addition of natural numbers

Source: licencja: CC 0.

Dodawanie liczb naturalnych sposobem pisemnym

Learning objectives

  • You will learn to add natural numbers using the long method.

Learning effect

  • You apply long addition of natural numbers to do text exercises.

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nagranie abstraktu

Revise various methods of mental additionadditionaddition of natural numbers.

Do additionadditionaddition using the calculator:

  1. 155 + 234

  2. 135 + 288

Think:

  • Do we always carry calculator with ourselves?

  • Is it easy to make such calculations mentally?

Task 1
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nagranie abstraktu

Open the slideshow and observe how we perform long addition of natural numberslong addition of natural numberslong addition of natural numbers. After having completed the exercise, present results of your observations.

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Pokaz multimedialny - pisemne dodawanie liczb naturalnych. Instrukcja obsługi z poziomu klawiatury: 1. Uruchomienie aplikacji - ENTER, 2. Na każdym ze slajdów czytany jest automatycznie tekst alternatywny po polsku, 3. Przy pierwszym uruchomieniu na pierwszym slajdzie, czytanie tekstu po angielsku - TAB, 4. Przejście między slajdami: do następnego slajdu - TAB, do poprzedniego slajdu - TAB + SHIFT, 5. Przejście do czytania napisu po angielsku - strzałka w górę + strzałka w dół (czyta tekst po angielsku widoczny na slajdzie).
Long addition of natural numbers
Source: GroMar, licencja: CC BY 3.0.

Conclusions:

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nagranie abstraktu
  • Long addition of natural numberslong addition of natural numbersLong addition of natural numbers starts with writing numbers under one another, in such a way that ones are under ones, tens under tens, etc. We put a linelineline under the numbers.

  • Then we add ones and write the result under the linelineline, in the place of ones. Then we add tens and write the result under the linelineline, in the place of tens, etc.

  • If during additionadditionaddition in one of the places we exceed the ten threshold, then we add the first digit to the higher place.

Task 2
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nagranie abstraktu

Do the long addition:

  1. 254 + 645

  2. 6325 + 1564

  3. 2645 + 9654

  4. 3698 + 4587

Task 3
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nagranie abstraktu

Do the exercises by performing long additionadditionaddition. Give the answers:

  1. 36 students from IV class, 47 from V class and 46 from VII class took part in the mathematical contest. How many students from this school were taking part in this contest?

  2. Tomek has 125 stickers and Marcel has 30 stickers more. How many stickers do they have together?

  3. Magda had 365 zł. Her granddad gave her 350 zł and her aunt 300 zł. Does she have enough savings to buy a bike that costs 1000 zł?

Task 4
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nagranie abstraktu

Using the ‘Price cards’ do the ‘shopping’ in such a way that the amount you spend is as high as possible but does not exceed 1000 zł.

Price cards

Ham
package 1 kg
22 zł

Ice cream
package 1 l
12 zł

Bread crumbs
package 500 g
3 zł

Baguette
item
1 zł

Bread
item
3 zł

Juice
1 l 
4 zł

Sparking water
1 l 
2 zł

Sausages
package 250 g 
4 zł

Yellow cheese
package 250 g 
7 zł

Milk
carton 1 l 
3 zł

Notebook A4
item
8 zł

Margarine
package 500 g 
4 zł

Set of 3 pens
package
15 zł

Set of 12 markers
package
16 zł

Milk chocolate
item 100 g 
3 zł

Paper towels
package 4 items
9 zł

Dish soap
1 l 
6 zł

Fabric softener
1 l 
15 zł

Washing capsules
package 32 items
28 zł

Tissues
10 packages
5 zł

A1 batteries
package 4 items
7 zł

Toothpaste
item
9 zł

Toothbrush
item
8 zł

Dishwasher tablets
package 80 items
49 zł

Shaving cream
item
11 zł

Female perfume
item
55 zł

Hair shampoo
250 ml
11 zł

Liquid handsoap
250 ml
5 zł

Cookbook
item
34 zł

Backpack
item
53 zł

Task 5

An extra task:

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nagranie abstraktu

In the magical squaremagical squaremagical square the sum of numberssum of numberssum of numbers written along each diagonal, each column and each row is the same. The numbers cannot be repeated. Fill in the picture so that is shows a magical squaremagical squaremagical square.

16

2

13

10

8

9

7

14

1

Do the revision exercises.

Remember:

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nagranie abstraktu
  • Long addition of natural numberslong addition of natural numbersLong addition of natural numbers starts with writing numbers under one another, in such a way that ones are under ones, tens under tens, etc. We put a linelineline under the numbers.

  • Then we add ones and write the result under the linelineline, in the row of ones. Then we add tens and write the result under the linelineline, in the row of tens, etc.

  • If during additionadditionaddition in one of the rows we exceed the ten threshold, then we add the first digit to the higher row.

Exercises

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Exercise 1
Adam and his parents made a road trip. From Warsaw they went to Berlin and then from Berlin to Paris. How many kilometres did they make, if from Warsaw to Berlin there is 575 km and from Berlin do Paris 1065 km? Możliwe odpowiedzi: Pierwszy wariant: 1645 km, Drugi wariant: 1630 km, Trzeci wariant: 1640 km, Czwarty wariant: 1635 km
Exercise 2

Calculate using the long method:

  1. 452 + 365

  2. 258 + 3695

  3. 2542 + 1237 + 548

Exercise 3

Find information about the number of inhabitants of each voivodeship in 2017. How many people together inhabited the three most populated voivodeships?

Write the appropriate calculation. Give the answer in English.

Exercise 4
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Wersja alternatywna ćwiczenia: Indicate which pairs of expressions or words are translated correctly. Możliwe odpowiedzi: 1. dodawanie liczb naturalnych sposobem pisemnym - long addition of natural numbers, 2. przekroczenie progu dziesiątkowego - exceeding the ten threshold, 3. rząd jedności - the ones row, 4. rząd dziesiątek - the tens row, 5. rząd tysięcy - the hundreds row, 6. rząd setek - the thousands row
zadanie
Source: GroMar, licencja: CC BY 3.0.
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Interaktywna gra, polegająca na łączeniu wyrazów w pary w ciągu jednej minuty. Czas zaczyna upływać wraz z rozpoczęciem gry. Jeden ruch to odkrywanie najpierw jednej potem drugiej karty z wyrazem. Każdy wyraz jest odczytywany. Kolejny ruch to odkrywanie trzeciej i czwartej karty. W ten sposób odsłuchasz wszystkie wyrazy. Nawigacja z poziomu klawiatury za pomocą strzałek, odsłuchiwanie wyrazów enterem lub spacją. Znajdź wszystkie pary wyrazów.
Source: Zespół autorski Politechniki Łódzkiej, licencja: CC BY 3.0.

Glossary

addition
addition

dodawanie

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wymowa w języku angielskim: addition
exceeding the ten treshold
exceeding the ten treshold

przekroczenie progu dziesiątkowego

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wymowa w języku angielskim: exceeding the ten treshold
hundreds row
hundreds row

rząd setek

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wymowa w języku angielskim: hundreds row
line
line

prosta

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wymowa w języku angielskim: line
long addition of natural numbers
long addition of natural numbers

dodawanie liczb naturalnych sposobem pisemnym

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wymowa w języku angielskim: long addition of natural numbers
magical square
magical square

kwadrat magiczny

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wymowa w języku angielskim: magical square
ones row
ones row

rząd jedności

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wymowa w języku angielskim: ones row
sum of numbers
sum of numbers

suma liczb

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wymowa w języku angielskim: sum of numbers
tens row
tens row

rząd dziesiątek

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wymowa w języku angielskim: tens row
thousands row
thousands row

rząd tysięcy

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wymowa w języku angielskim: thousands row

Keywords

hundreds rowhundreds rowhundreds row

long addition of natural numberslong addition of natural numberslong addition of natural numbers - starts with writing numbers under one another, in such a way that ones are under ones, tens under tens, etc.

magical squaremagical squaremagical square - the sum of numbers written along each diagonal, each column and each row is the same

ones rowones rowones row

tens rowtens rowtens row