Topicmc7bf72abb77bb3eb_1528449000663_0Topic

Arithmetic problems

Levelmc7bf72abb77bb3eb_1528449084556_0Level

Second

Core curriculummc7bf72abb77bb3eb_1528449076687_0Core curriculum

V. Operations on ordinary and decimal fractions. The Student:

7) calculates the value of simple arithmetic expressions, applying the rules of order of operations.

Timingmc7bf72abb77bb3eb_1528449068082_0Timing

45 minutes

General objectivemc7bf72abb77bb3eb_1528449523725_0General objective

Performing uncomplicated calculations using mental maths skills or in more difficult cases in a written form and the use of these skills in practical situations.

Specific objectivesmc7bf72abb77bb3eb_1528449552113_0Specific objectives

1. Communicating in English, developing mathematical, scientific, technical and IT competences, developing learning skills.

2. Calculation of the values of arithmetic expressions.

3. The use of rules for the order of operations.

Learning outcomesmc7bf72abb77bb3eb_1528450430307_0Learning outcomes

The Student:

- calculates the values of arithmetic expressions,

- uses the rules for the order of operationsthe order of operationsthe order of operations.

Methodsmc7bf72abb77bb3eb_1528449534267_0Methods

1. Miming method.

2. Didactic game – ‘Our home’.

Forms of workmc7bf72abb77bb3eb_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmc7bf72abb77bb3eb_1528450127855_0Introduction

Students use the miming method and review the information regarding the order of performing operations on rational numbers.

The teacher writes on the board a simple arithmetic expressionarithmetic expressionarithmetic expression. A student who wants to do the calculations, approaches the board and solves the task. At the same time, without using words, he or she explains in which order he or she performed all the operations. At the end of the task volunteers complete the rule of the order of operationsthe order of operationsthe order of operations initiated by the teacher.

To sum up this part of the lesson, the teacher does not use words, but uses gestures, symbols, etc.

Proceduremc7bf72abb77bb3eb_1528446435040_0Procedure

The teacher informs students that the aim of the lesson will be to develop the ability to calculate the value of arithmetic expressions, taking into account the rules for order of operations.

Work in small groups - Didactic game „Our home”. Each group has to solve a set of tasks. They have calculators at their disposal to check the correctness of their calculations. Each calculation done correctly is rewarded with new elements to build a house, which are collected from the warehouse. The group that will „build” a house with a smoking chimney is rewarded with an excellent grade.

[Table 1]

[Illustration 1]

Tasks for groups.

Task 1

Calculate quickly:

$\frac{1+2+3+4+\dots \dots +98+99+100}{100}$

Task 2

The number 144 is 12 times greater than the number 12. The number 12 is 6 times greater than the number 2. How many times is the number 2 less than the number 144?mc7bf72abb77bb3eb_1527752256679_0The number 144 is 12 times greater than the number 12. The number 12 is 6 times greater than the number 2. How many times is the number 2 less than the number 144?

Task 3

Use the computer. Do 3 turns of calculations included in the applet. To download the next element of the „house”, you can only make a mistake once.mc7bf72abb77bb3eb_1527752263647_0Use the computer. Do 3 turns of calculations included in the applet. To download the next element of the „house”, you can only make a mistake once.

[Geogebra applet]

Task 4

Decide if the number M is even or odd:

$M=\left[\left(-\frac{1}{2}+\frac{3}{4}\right)·2\right]:0,5$

Task 5

Indicate the largest number:

$A=0,8:0,08$, $B=2^3:8$, $C=8·\frac{1}{8}:\frac{2}{8}$.

Task 6

Jola had PLN 300. First, she bought 5 kilograms of apples for the price of 6,50 zloty per kilogram and 2 packs of butter at a price of 6,20 zloty per piece. Then she bought a table for PLN 128 and a chair for PLN 150. Did she have enough money to buy all the items? If yes, how much money has she still got? Or maybe she had to borrow money from a friend? If so, how much did she borrow?mc7bf72abb77bb3eb_1527712094602_0Jola had PLN 300. First, she bought 5 kilograms of apples for the price of 6,50 zloty per kilogram and 2 packs of butter at a price of 6,20 zloty per piece. Then she bought a table for PLN 128 and a chair for PLN 150. Did she have enough money to buy all the items? If yes, how much money has she still got? Or maybe she had to borrow money from a friend? If so, how much did she borrow?

An extra task

Ada is 26 years old. Bogdan is twice younger than her. Czesia is six years older than Bogdan. Daniel is as old as Bogdan and Czesia together. How many years ago was Daniel the same age as Bogdan is now?

Groups present their houses. The teacher evaluates their work and explains any doubts.

Lesson summarymc7bf72abb77bb3eb_1528450119332_0Lesson summary

Students do revision exercises.

Then they summarize the lesson together and formulate conclusions to remember.

The rule for the order of operationsthe order of operationsthe order of operations:

- operations in brackets,

- exponentiationexponentiationexponentiation,

- multiplicationmultiplicationmultiplication and divisiondivisiondivision (in order of occurrence),

- additionadditionaddition and subtractionsubtractionsubtraction (in order of occurrence).

Selected words and expressions used in the lesson plan

additionAdditionaddition

arithmetic expressionArithmetic expressionarithmetic expression

divisionDivisiondivision

exponentiationexponentiationexponentiation

expression in bracketsExpression in bracketsexpression in brackets

multiplicationMultiplicationmultiplication

subtractionSubtractionsubtraction

the order of operationsThe order of operationsthe order of operations

value of expressionValue of expressionvalue of expression

word problemWord problemword problem