Topicm8ed58057f496f41d_1528449000663_0Topic

Number of solutions of the equation

Levelm8ed58057f496f41d_1528449084556_0Level

Second

Core curriculumm8ed58057f496f41d_1528449076687_0Core curriculum

VI. Equations with one unknown. The student:

2) solves first degree equations with one unknown using the method of equivalent equations.

Timingm8ed58057f496f41d_1528449068082_0Timing

45 minutes

General objectivem8ed58057f496f41d_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm8ed58057f496f41d_1528449552113_0Specific objectives

1. Identifying the number of solutions of the equation.

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

Learning outcomesm8ed58057f496f41d_1528450430307_0Learning outcomes

The student:

- identifies the number of solutions of the equation,

- identifies equations: identity, contradiction and conditional.

Methodsm8ed58057f496f41d_1528449534267_0Methods

1. Discussion.

2. Individual task contest.

Forms of workm8ed58057f496f41d_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm8ed58057f496f41d_1528450127855_0Introduction

The student chosen by the teacher does a revision of information about equation that students learn so far.

The teacher introduces the subject of the lesson – identifying the number of solutions of the equation.

Procedurem8ed58057f496f41d_1528446435040_0Procedure

Each student gives an example of an equation and its solution.
Discussion – how many solutions can an equation have? Can we give an example of an equation that is satisfied by 2, 3, 4, ... numbers? Are there equations that have no solutions?

Students answer the questions by giving examples of equations that have no solutions, have one solution or have infinitely many solutions.

Students do the task.

Task
Among the following equations choose those that have:

a) one solution,

b) two solutions,

c) three solutions,

$x(x+2)(x-4)=0$ ; $x^2=9$ ; $x+1=2$.

Are all of these equations first degree equations?

The teacher informs that in the next part of the class we will be considering only equations in which the unknowns are in the first power.

Task
Students work individually, using computers. Their task is to observe what kind of equations are contradictions, conditional equations and identities.

[Interactive illustration]

Conclusions:

- An equation that has one solution is called a conditional equation.m8ed58057f496f41d_1527752263647_0- An equation that has one solution is called a conditional equation.

- An equation that has no solutions is called a contradiction.m8ed58057f496f41d_1527752256679_0- An equation that has no solutions is called a contradiction.

- An equation that has infinitely many solutions is called an identity.m8ed58057f496f41d_1527712094602_0- An equation that has infinitely many solutions is called an identity.

Inidividual task contest.
Students do the contest tasks. They can look for necessary information in available knowledge sources, for example the Internet.

They can go to the next level after verifying results from the previous level.

Three students with the best time score get the highest marks, three following – second highest marks.

Task 
Choose contradictions.

a) $x+3=x$

b) $5x=-5x$

c) $4x-2=4x+2$

Task 
Choose identities.

a) $-(x-3)=3-x$

b) $-7x=-7x$

c) $0x=0$

d) $4(x-2)=4x-2$

Task 
What expression should be inserted in the dotted space so that the obtained equation is an identity?

a) $5x=...+x$

b) $x-3x+1+...=x+1$

c) $5(x-...)=2x$

Task 
What expression should be inserted in the dotted space so that the obtained equation is a contradiction?

a) $2x=...+1$

b) $6x+...=x+3$

c) $3(...-4)=-3x$

An extra task:
What kind of equations are called equivalent equations? Add two equivalent equations do the equation: $2x=8$.

Lesson summarym8ed58057f496f41d_1528450119332_0Lesson summary

Students do the revision exercises.

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

- A number that satisfies the given equation is called the solution of the equation or the root of the equation.

- An equation that has one solution is called a conditional equation.

- An equation that has no solutions is called a contradiction.

- An equation that has infinitely many solutions is called an identity.

Selected words and expressions used in the lesson plan

conditional equationconditional equationconditional equation

contradicitioncontradicitioncontradicition

equivalent equationsequivalent equationsequivalent equations

identityidentityidentity

number that satisfies the equationnumber that satisfies the equationnumber that satisfies the equation

solution of the equationsolution of the equationsolution of the equation