Topicmdf9221188d847c33_1528449000663_0Topic

Operations in the set of rational numbers

Levelmdf9221188d847c33_1528449084556_0Level

Second

Core curriculummdf9221188d847c33_1528449076687_0Core curriculum

V. Calculations on common and decimal fractions. The student:

9) calculates values of arithmetic expression that require arithmetic calculations on integers or numbers written as common fractions, mixed numbers and decimal fractions, also rational negative, not more difficult than:

$-\frac{1}{2}÷0,25+5,25÷0,05-7\frac{1}{2}\cdot (2,5-3\frac{2}{3})+1,25$.

Timingmdf9221188d847c33_1528449068082_0Timing

45 minutes

General objectivemdf9221188d847c33_1528449523725_0General objective

Doing simple calculations mentally or using the long method in more difficult examples, using these abilities in practical situations.

Specific objectivesmdf9221188d847c33_1528449552113_0Specific objectives

1. Doing operations in the set of rational numbers.

2. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesmdf9221188d847c33_1528450430307_0Learning outcomes

The student:

- does operations in the set of rational numbers.

Methodsmdf9221188d847c33_1528449534267_0Methods

1. Discussion.

2. Thematical contest.

Forms of workmdf9221188d847c33_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmdf9221188d847c33_1528450127855_0Introduction

Students revise the order of operations in the set of natural numbers.

The teacher introduces the subject of the class – doing operations in the set of rational numbersrational numbersrational numbers, while remembering about the order of operations.

Proceduremdf9221188d847c33_1528446435040_0Procedure

Task

Students work individually, using computers. Their task is to determine the order of operations in the given example.

[Slideshow]

Conclusions:

Operations on rational numbersrational numbersrational numbers are done similarly to operations on natural numbers, according to a defined order:

- operations in parenthesesparenthesesparentheses,
- exponentiationexponentiationexponentiation,
- multiplicationmultiplicationmultiplication or divisiondivisiondivision – in the order it is written,
- additionadditionaddition or subtractionsubtractionsubtraction – in the order it is written.

Thematical contest.

Students do contest tasks in groups, using properties of operations in the set of rational numbersrational numbersrational numbers. Each group does the same set of exercises prepared by the teacher. The prize in the contest is getting a mark for correct solutions.

Task contest

Calculate the number that is the multiplicative inverse of the expression.

$2\frac{3}{5}÷(1\frac{3}{5}-3\frac{1}{4})+(-5)$

Task contest

Multiply the sum of numbers -3,14 and $-2\frac{1}{2}$ by the square of the difference of numbers -4,5 and -2.

Task contest

Zosia bought 0,4 kg of candies in the price of 24 zł for a kilogram and 0,6 kg of cookies in the price of 18,5 zł for a kilogram. How much change will she obtain if she paid with a 50 zł banknote?mdf9221188d847c33_1527752256679_0Zosia bought 0,4 kg of candies in the price of 24 zł for a kilogram and 0,6 kg of cookies in the price of 18,5 zł for a kilogram. How much change will she obtain if she paid with a 50 zł banknote?

Task contest

A cake that mum made was 1,2 kg. Kids ate $\frac{1}{3}$ of the whole cake, and dade ate half of what was left after he came back from work. How much did the part that dad ate weigh?

An extra task:

Search the Internet for the highest and the lowest temperature noted in Poland last year. Calculate the amplitude of these temperatures.

After having completed the exercises, the fastest group presents their solutions. If the obligatory tasks and the extra task are done correctly, they get the highest mark.

The teacher clarifies the doubts and rewards groups that did the exercises using the most effective or the most original ways.

Lesson summarymdf9221188d847c33_1528450119332_0Lesson summary

Students do the revision exercises.

Then together they sum‑up the classes, by formulating the conclusions to memorise.

Operations on rational numbersrational numbersrational numbers are done according to a defined order:

- operations in parenthesesparenthesesparentheses,
- exponentiationexponentiationexponentiation,
- multiplicationmultiplicationmultiplication or divisiondivisiondivision – in the order it is written,
- additionadditionaddition or subtractionsubtractionsubtraction – in the order it is written.

Selected words and expressions used in the lesson plan

additionadditionaddition

divisiondivisiondivision

exponentiationexponentiationexponentiation

multiplicationmultiplicationmultiplication

parenthesesparenthesesparentheses

rational numbersrational numbersrational numbers

subtractionsubtractionsubtraction