Topicme5360c42b7db2475_1528449000663_0Topic

Adding and subtracting rational numberssubtracting rational numberssubtracting rational numbers

Levelme5360c42b7db2475_1528449084556_0Level

Second

Core curriculumme5360c42b7db2475_1528449076687_0Core curriculum

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

9) calculates values of arithmetic expression that require arithmetic calculations on integers or numbers written as common fractionsfractionsfractions, mixed numbers and decimal fractionsfractionsfractions, also rational negative, not more difficult than: $-\frac{1}{2}:025+5,25:0,05-7\frac{1}{2}\cdot (2,5-3\frac{2}{3})+1,25$.

Timingme5360c42b7db2475_1528449068082_0Timing

45 minutes

General objectiveme5360c42b7db2475_1528449523725_0General objective

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

Specific objectivesme5360c42b7db2475_1528449552113_0Specific objectives

1. Adding and subtracting rational numberssubtracting rational numberssubtracting rational numbers.

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

Learning outcomesme5360c42b7db2475_1528450430307_0Learning outcomes

The studnet:

- adds and subtracts rational numbersrational numbersrational numbers.

Methodsme5360c42b7db2475_1528449534267_0Methods

1. Discussion.

2. Mental map.

Forms of workme5360c42b7db2475_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionme5360c42b7db2475_1528450127855_0Introduction

Students revise their knowledge about rational numbersrational numbersrational numbers. They give examples of such numbers.

The teacher introduces the subject of the lesson – adding and subtracting rational numberssubtracting rational numberssubtracting rational numbers.

Procedureme5360c42b7db2475_1528446435040_0Procedure

Students work individually, using computers. Their task is to observe the way of adding rational numbersadding rational numbersadding rational numbers, depending on their sign.

[Geogebra applet]

In groups, students discuss presented examples, make theories and verify them on specific examples, possibly by using calculators. Then they make a note in the form of a mental map, including various cases of adding rational numbersadding rational numbersadding rational numbers.

Conclusions:
- If we add two numbers of the same sign, then the sign of the sum is the same as the sign of both terms.
- If we add two rational numbers of different signs, then the sign of the sum is the same as the sign of the number located further from 0 on the number line.
- Subtraction of a number can be replaced with addition of the additive inverse of this number. Students use obtained information to do exercises.me5360c42b7db2475_1527752263647_0- If we add two numbers of the same sign, then the sign of the sum is the same as the sign of both terms.
- If we add two rational numbers of different signs, then the sign of the sum is the same as the sign of the number located further from 0 on the number line.
- Subtraction of a number can be replaced with addition of the additive inverse of this number. Students use obtained information to do exercises.

Task
Without doing the calculation, decide if the result is a positive or negative number.

a) $2\frac{3}{8}-2\frac{1}{2}$

b) $-3,21+3\frac{1}{5}$

c) $-5\frac{2}{3}-(-5,6)$

d) $-1,7+1\frac{3}{4}$

Task
Calculate.

a)  $(-36)-(-16)+(-21)-5$

b) $1243+(-1250)-(-237)+534$

c) $-1\frac{2}{5}+(-2,6)-(3,75)+(-4\frac{1}{4})$

d) $0,55+(2,36)-(-3,4)-1,345$

Task
Do the difference of numbers 45 and -15 add the sum of numbers 17 and -24.

Task
Lena put 26 candies in a box. The next day, she took out 5 candies and put in 13 different candies. The third day, she ate 7 candies from the box and added 4 other candies. How many candies are in the box?

Task
Miss Jola bought a fridge and it turned out that she had a debit on her account of 2300 zł. Next day she got transferred 3500 zł on her account. Miss Kinga had 4350 zł on her account and she bought a washing machine for 1640 zł. Which one of them has more money on the account and how much more?

An extra task:
Give two rational numbersrational numbersrational numbers such that their sum is smaller from each one of these numbers.

Lesson summaryme5360c42b7db2475_1528450119332_0Lesson summary

Students do the revision exercises.

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

- If we add two numbers of the same sign, then the sign of the sum is the same as the sign of both terms.

- If we add two rational numbersrational numbersrational numbers of different signs, then the sign of the sum is the same as the sign of the number located further from 0 on the number linenumber linenumber line.

- Subtraction of a number can be replaced with addition of the additive inverse of this number.

Selected words and expressions used in the lesson plan

adding rational numbersadding rational numbersadding rational numbers

fractionsfractionsfractions

number linenumber linenumber line

rational numbersrational numbersrational numbers

sign of the sum of numberssign of the sum of numberssign of the sum of numbers

subtracting rational numberssubtracting rational numberssubtracting rational numbers