You will learn to formulate rules about the order of operations.
Learning effect
You apply rules about the order of operations.
Give examples of addition, subtraction, multiplication and division of natural numbers:
Write down the operations according to the description:
add the result of the multiplication of the number 3 by number 4 to the number 2,
add the number 2 to number 3 and multiply by 4.
Think whether you obtain the same result in both cases. Propose different ways of calculations, for example ‘step by step’ or by using graphs.
After obtaining different results, look for the causes.
Think how to write the operation using one expression.
Conclusion
Different results are caused by the different order of operations.
Expressions made of numbers, signs of operations and, possibly, parentheses are called arithmetic expressions. Arithmetic is a science about numbers and operations on them.
Task 1
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Open the slideshow and observe the ‘Operations car race’.
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After having finished the exercise, present the results of your observations and write down the order in which we should do the operations.
Conclusion
Operations should be done in the following order:
operations in parentheses,
multiplication or division – in the order it is written,
addition or subtraction – in the order it is written.
Task 2
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Play the board game according to the following rules:
Rules of the game:
Place your pawn on the START field.
Throw the dice and move as many fields as the dice showed.
Calculate the value of the expression on the card placed on the field you are at.
Check your results on the calculator, consult the doubts with the teacher.
If the result is correct, you stay at the field and wait for your next turn.
If the result is wrong, you go back to the field you were at before.
The person that gets first to the final field, gets the highest mark.
GOOD LUCK!
The board for the game:
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Use obtained information in the exercises.
Task 3
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Write down the solution of the task using one arithmetic expression. Calculate the value of this expression.
In a school there are two fourth grades in which there are 25 students are three fourth class in which there are 20 students. How many fourth‑graders there are in the school?
Tomek had 35 zł, he bought 4 bars 3 zł each and a chocolate that cost 5 zł. How many złoty did he have left after the shopping?
Task 4
An extra task:
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Write the number 100 as the arithmetic expressionthe arithmetic expressionthe arithmetic expression, using signs of operations and parentheses and each one of the nine digits, only once.
Do the revision exercises.
Remember:
Operations should be done in the following order:
operations in parentheses,
multiplication or division – in the order it is written,
addition or subtraction – in the order it is written.
Exercises
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Exercise 1
Exercise 2
Calculate while paying attention to the order of operations.
a) b) c)
a) b) c)
Exercise 3
Write the operations that solves the text exercise in the form of one arithmetic expression. Calculate its value and give the answer in English.
Ania has 4 banknotes 20 zł each, 5 coins 5 zł each, 6 coins 2 zł each and 4 coins 1 zł each. How much money will she have left after she buys a jacket for 85 zł and a t‑shirt for 25 zł?
11 zł
Exercise 4
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Glossary
graph
graph
graf
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a paranthesis
a paranthesis
nawias zwykły
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arithmetics
arithmetics
arytmetyka
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the arithmetic expression
the arithmetic expression
wyrażenia arytmetyczne
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the operation in parentheses
the operation in parentheses
wyrażenie w nawiasie
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the order of operations
the order of operations
kolejność wykonywania działań
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Keywords
arithmeticsarithmeticsarithmetics – a science about numbers and operations on them
the arithmetic expressionthe arithmetic expressionthe arithmetic expression – expressions made of numbers, signs of operations and parentheses