ALGEBRA 1 Version 2009
Revised and highly enlarged.

Algebra 1. April 2010.


Most students entering the 7 th grade have a difficult time understanding the basic notions of algebra. In effect, the main difficulty lies in the introduction of the concept of negative numbers which are written with a “-“ sign, which is also the symbol used in subtraction.

The rules of subtraction and multiplication of negative numbers must be learned by heart, without justification. Without an explaination which is coherent and easily understood, the student will find himself failing before he even gets into the core of the subject and he will have a hard time getting through the 10 th grade.

The Evalutel method aims above all at surmounting these pitfalls. Chapter 1 of this title recalls the properties of the addition of whole numbers, by using graduated axes.The student carries out the addition by drawing segments (vectors) in order to represent the whole numbers and by putting them end to end, which the student is able to do without any difficulty. The chapter ends with the ordering of whole numbers from 1 to 100, chosen and presented in random order.

Having discovered, in chapter 1, the representation of whole numbers using segments, we show the student, in chapter 2, how to carry out the subtraction n 1-n 2 and the impossibility of carrying out this operation on natural numbers for n 2 greater than n 1.

This impossibility is overcome after disarming a fortress (representing the conservatism in our societies), captured in battle with the help of a large piece of timber, and with the introduction of negative numbers by graduating the left part of the axis. The student then draws and carries out additions on the set Z which familiarizes him with addition s including positive and negative whole numbers. The paragraph “What ever happened to subtraction?” prepares the student to understan d that on the set Z, subtraction is no longer a new operation but a form of addition. This chapter ends with the extension of the order relation to positive and negative whole numbers.

Chapter 3 aims to show the link between algebraic addition and subtraction and introduces the first calculations in algebra carried out on additions and subtractions.

The exercises use the drawings of segments corresponding to the proposed numbers and to the traditional calculation. The student also discovers the use of parentheses and the first uses of letters with evaluations.

All the numbers proposed are drawn randomly. By repeating the exercise, the student checks that he has understood the method and not that he has learned the answer by heart.