Welcoming negative numbers in 1st of ESO!

Welcoming negative numbers in 1^st of ESO!

The previously published unit “Integer numbers”, pretends students of 1^st of ESO Bilingual Mathematics to realize both the importance and the necessity of negative numbers in common day, as well as in other subjects that they are studying like natural and social sciences. This is why we start with an introductory class, in which we can force our students to think about, while we practice English (listening and speaking). We can try the following questions with the whole group: “Why negative numbers are necessary, give examples in common life, how are these situation correctly expressed in English: Underline the correspondent study guide in English and write down the examples collected on the board.” Doing the last proposition, they are practicing also reading and writing.

Some nice expressions and vocabulary should have been aroused here: 

·          Three degrees below zero ·         Four metres below sea level or ground level. ·         Year 450 after or before Christ. ·         ……….

 

Our next objective is the students to collocate both positive and negative numbers on the number line, understanding the concept of opposite numbers and absolute value. 

This activity is also very helpful for them to understand how to order positive and negative numbers, as well as to get a better learning of the next goals: To know and to apply the different properties of the operations involving integer numbers, to solve combined operations involving integer numbers and finally to solve arithmetic problems involving integer numbers.

In order to use the English language while we are achieving our mathematical goals too, the students have a short study guide in English; an two extra worksheet in English, including the different activities we desire they to do, including word problems and a criss-cross with the most important vocabulary; a worksheet to practice mental calculationinvolving integers (an oral correction will help us again to practice speaking and listening); and another “AICLE style” worksheet to especially reinforce the four language skills (listening, speaking, reading and writing)  by using the expressions and the vocabulary related to our unit. This “AICLE style” is ideal to be practiced with our language assistant.

Some nice expressions, grammar and vocabulary should have been appeared:

 Nouns: numbers in English, negative, integer, below, above, subtraction, addition, sum, difference, subtrahend, minuend, multiplication, product, factor, division, remainder, dividend, divisor, bracket, solution, result…

Verbs: to equal, to solve, to apply, to add, to subtract, to divide, to multiply, to practice, to understand,….

Adjectives: Below, above, after, before, greater, less…

Expressions: : If …..then……,  plus negative #, minus negative #,  greater than, less than, …plus…equals, …minus….is, …times…, …divided by,…., to solve, better than, worse than, better than, worse than..

Grammar: Conditionals ( type 0 and type 1), imperatives, interrogatives sentences.

 Different methods and organizations should be used for each activity. Then, in the introductory class, will be the whole group giving ideas; the mental calculation will be an individual work of 15-20 minutes, and then the whole class correcting; they will do exercises in class comparing solutions, helping and being helped by their partner/s and finally, they will be in small groups with the language assistant.

For the two first objectives, will need two sessions respectively, in which we will read in loud voice and will underline de part of the study guide in which this contents appear and we will work out the exercises from both the study guide (from 1 to 4) and the worksheet in English (ex 1).

The third session will be dedicated to explain by using examples the addition and the subtraction of integer numbers. We will practice them doing the correspondent exercises of this worksheet about Operation involving integer numbers.

The four session will be dedicated to correct some of the previous exercises (the ones that could not be done in the previous session) and then we will work both the multiplication and the division of integer numbers. We will do the correspondent exercises in Operation involving integer numbers.

During the fifth session we will correct some of the previous exercises and will learn about the distributive property and te extraction of the common factor.  We will do the correspondent exercises in Operation involving integer numbers.

The sixth session is a nice moment to practice the  “AICLE style” worksheet with our language assistand, half of the time with half of the class and then changing.

In the seventh session wi will start practising a quarter of hour solving the two first column of worksheet to practice mental calculationinvolving integers. Then ten minutes for an oral correction.In the second part of the class we will practise some combined operations. We will work out some of them from the worksheet Operation involving integer numbers.

The eighth class will be dedicated again to practise and correct exercises about combined operations and to solve some easy word problems from the book.

The ninth class will be a class to review before the exam. We will practice different exercises from our worksheet in English and to solve questions. We will also work out the two las column from
worksheet to practice mental calculationinvolving integers.

The tenth class is for the TEST.

 

Having learned Maths as well as English language, we have developed cognitive process like analysis, relationship ability, operational skills and self evaluation. We will have worked key competences like mathematical thinking applied to real situations and real problems.

Finally, we will have collected different notes to correctly evaluate the language skills according to our general assessment criteria: oral corrections, work done on the board, daily work and attitude, written test.