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Mental and written calculations on natural numbers

Source: licencja: CC 0.

Działania pamięciowe i pisemne na liczbach naturalnych

Learning objectives

  • You will discover the method of doing the complex operations on natural numbers.

Learning effect

  • You add, subtract, multiply and divide the natural numbers.

  • You use the correct order of operations.

  • You use English to describe the correct order of operations on natural numbers.

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nagranie abstraktu

Prepare for the lesson:

  • The cubic dice. There are following writings on the faces of the dice concerning multiplication, division, addition or subtraction by given number: 8, 57, : 3, + 2918,- 92, - 201.

  • A set of 11 cards. There is one of the following numbers on each card: 4167, 9021, 2001, 708, 324, 6012, 8001, 402, 315, 2700, 4050.

  • Calculator.

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nagranie abstraktu

Revise the written method of addition, subtraction, multiplication and division of the natural numbersnatural numbersnatural numbers.

Task 1
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nagranie abstraktu

Use the set the set you have prepared earlier: the cards and the dice. Throw the dice and choose the operation you are going to do. Next, draw one of the cards and do the proper calculations. Check if the result is correct by using the calculator.

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nagranie abstraktu

Today you are going to do the operations on the natural numbersnatural numbersnatural numbers by using the proper order of operationsorder of operationsorder of operations.

Task 2
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nagranie abstraktu

Analyse the slideshow concerning the order of operationsorder of operationsorder of operations on the natural numbersnatural numbersnatural numbers.

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Ilustracja interaktywna przedstawia sześć aut na torze wyścigowym. Auta ponumerowane w kolejności od 1 do 5 od pierwszego od góry: auto na torze trzecim od lewej, auto na torze szóstym od lewej, auto na torze pierwszym od lewej, auto na torze czwartym od lewej (na tej samej wysokości co poprzednie auto), auto na torze drugim od lewej, auto na torze piątym od lewej (na tej samej wysokości co poprzednie auto). Na ilustracji widoczne są numery, a na nich podpisy. 1. brackets {audio}, 2. exponentiation {audio}, 3. multiplication {audio}, 4. division {audio}, 5. addition {audio}, 6. subtraction {audio}.
Order of operations on the natural numbers
Source: GroMar, licencja: CC BY 3.0.
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nagranie abstraktu

Consider:

  • Which operation should be done at the same time?

  • Which operation should be done at the same time?

  • What order should be used to do the operations in brackets?

Note, that:

  • We do the multiplication and the division, the addition and the subtraction at the same time.

  • We do the operation in brackets first. If there are some operations in the bracket we use the order of operation.

Use gained information to do the operations on the natural numbersnatural numbersnatural numbers.

Task 3
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nagranie abstraktu

Calculate:

a) 848 : 4 ∙ 3

b) (560+ 304) ∙ 11

c) 3200 : 16 + 25 ∙ 100

d) 14 ∙ (51 - 45)3

Task 4
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nagranie abstraktu

Write the task in the form of the arithmetic expression and calculate its value:

a) Reduce the number of 5821 by the productproductproduct of the numbers 35 and 103.

b) Increase by 9 times the differencedifferencedifference of the numbers 1942 and 197.

c) Reduce the quotationquotationquotation of the number 5664 by 12 by the squaresquaresquare of the number 8.

d) Calculate the cubecubecube of the differencedifferencedifference of the numbers 1505 and 1494.

Task 5
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nagranie abstraktu

An extra task:

Using exactly four numbers of four and writing the mathematical symbols such as addition, subtraction, multiplication, division and brackets among them write down the following numbers: 0, 1, 2, 6, 7 and 9.

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nagranie abstraktu

Remember:

When you do the operations on the natural numbersnatural numbersnatural numbers:

  • you do the operations in bracketsoperations in bracketsoperations in brackets first,

  • next you do the exponentiationexponentiationexponentiation,

  • then you do multiplication or division (in order they appear),

  • finally you do the addition or subtraction (in order they appear).

If there are some operations in the bracket you use the  described above.

Do the summarizing tasks.

Exercises

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Exercise 1
Determine which sentences are true. Możliwe odpowiedzi: 1. The difference between the numbers 17000 and 6543 is less than 10000., 2. Doing the operation 8 + 24 : (23  22) one should do the exponentiation first., 3. The result of the operation of 3600 : 100 + 25·4 equals the result of the operation 25·4 + 3600 : 100., 4. The result of the operation of 540·23000 has got four zeros at the end., 5. There is an equality of 145  35  · 0 + 5 = 145.
zadanie
Source: PŁ, licencja: CC BY 3.0.
Exercise 2

Increase the quotation of number 30485 by 13 by the square of the number 307.

Exercise 3

Calculate:
90201 – (16375 + 4444 : 101)
Describe in English step by step the operations you have done.

Exercise 4
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Wersja alternatywna ćwiczenia: Indicate which pairs of expressions or words are translated correctly. Możliwe odpowiedzi: 1. liczby naturalne - natural numbers, 2. kolejność wykonywania działań - order of operations, 3. działania w nawiasach - operations in brackets, 4. kwadrat - square, 5. różnica - product, 6. suma - difference
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

natural numbers
natural numbers

liczby naturalne – 0, 1, 2, 3, 4, …

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wymowa w języku angielskim: natural numbers
order of operations
order of operations

kolejność wykonywania działań

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wymowa w języku angielskim: the order of operations
operations in brackets
operations in brackets

działania w nawiasach

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wymowa w języku angielskim: operations in brackets
square
square

kwadrat – druga potęga

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wymowa w języku angielskim: square
cube
cube

sześcian – trzecia potęga

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wymowa w języku angielskim: cube
sum
sum

suma

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wymowa w języku angielskim: sum
difference
difference

różnica

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wymowa w języku angielskim: difference
product
product

iloczyn

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wymowa w języku angielskim: product
quotation
quotation

iloraz

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wymowa w języku angielskim: quotation
exponentiation
exponentiation

potęgowanie

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wymowa w języku angielskim: exponentiation

Keywords

cubecubecube

natural numbersnatural numbersnatural numbers

operations in bracketsoperations in bracketsoperations in brackets

order of operationsorder of operationsorder of operations

squaresquaresquare