Topicm823e2bc9f1429f67_1528449000663_0Topic

Linear equation

Levelm823e2bc9f1429f67_1528449084556_0Level

Third

Core curriculumm823e2bc9f1429f67_1528449076687_0Core curriculum

III. Equations and inequalities. The student:

1) transforms equations and inequalities in the equivalent way;

2) interprets contradictions and identities.

Timingm823e2bc9f1429f67_1528449068082_0Timing

45 minutes

General objectivem823e2bc9f1429f67_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm823e2bc9f1429f67_1528449552113_0Specific objectives

1. Identifying the type of the equation.

2. Solving equations using the method of equivalent equationsmethod of equivalent equationsmethod of equivalent equations.

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

Learning outcomesm823e2bc9f1429f67_1528450430307_0Learning outcomes

The student:

- identifies the type of the equation,

- solves equations using the method of equivalent equations.

Methodsm823e2bc9f1429f67_1528449534267_0Methods

1. Discussion.

2. Chain of associations.

Forms of workm823e2bc9f1429f67_1528449514617_0Forms of work

1. Work in pairs.

2. Group work.

Lesson stages

Introductionm823e2bc9f1429f67_1528450127855_0Introduction

The teacher introduces the subject of the lesson – methods of solving equations and types of linear equations.

Procedurem823e2bc9f1429f67_1528446435040_0Procedure

A few days earlier, the teacher asks one of the students to prepare information about equation students learnt earlier. This student present gathered information at the beginning of the class. Student gives examples of first and higher degree equations, with one or more unknowns. Student discusses types of first degree equations with regard to the number of solutions.

Students work with the method of the chain of associations. They obtain a chain drawn on a big cardboard, that consists of empty links. They fill the links with terms, formulas and associations connected with ways of solving equations.

Students present their chains and discuss most important links.

Task
Solve equations using the equivalent equations method and determine its type based on the number of solutions.

a) $\frac{x+\sqrt[3]{-8}}{2}=\frac{x}{6}-\frac{-2x^2+2}{3}$

b) $2x+\sqrt{3}=x+x+\sqrt{3}$

c) $1+\sqrt{2}x=-4+3+\sqrt{2}x$

Task
Students work individually, using computers. Their task is to observe the way of calculating the root of the functionroot of the functionroot of the function.

[Geogebra applet]

Discussion – what is the relations between the root of the function and solving equations?

Conclusion:

- Calculating the root of the functionroot of the functionroot of the function is solving an equation in the form ax + b = 0, for set a and b coefficients.

Students use obtained information in the exercises.

Task
Calculate the root of the function defined by the formula.

a) f(x) = -2x

b) f(x) = 3x + 1

c) f(x) = $\frac{1}{4}$x + 5

Task  
Calculate the root of the function defined by the formula.

a) $f\left(x\right)=3\sqrt{3}x+3$

b) $f\left(x\right)=-\frac{\sqrt{5}}{2}x-1$

c) $f\left(x\right)=-\frac{2}{5}x+3\sqrt{5}$

Task
Give formula for the linear function whose plot is presented in the picture and then calculate its root.

[Illustration 1] 

Task
For what value of z does the point A (1, -2) belong to the plot of the function
f(x) = (z - 4)·x + 2?m823e2bc9f1429f67_1527752256679_0For what value of z does the point A (1, -2) belong to the plot of the function
f(x) = (z - 4)·x + 2?

The teacher evaluates students’ work and clarifies doubts.

An extra task:
Is there such number m for which the function defined by the formula 
f(x) = (-m + 2)x - 5 has no roots?

Lesson summarym823e2bc9f1429f67_1528450119332_0Lesson summary

Students do the revision exercises.

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

- 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.m823e2bc9f1429f67_1527752263647_0- 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.

- Calculating the root of the functionroot of the functionroot of the function is solving an equation in the form ax + b = 0, for set a and b coefficients.

Selected words and expressions used in the lesson plan

contradictioncontradictioncontradiction

identityidentityidentity

linear equationlinear equationlinear equation

method of equivalent equationsmethod of equivalent equationsmethod of equivalent equations

root of the functionroot of the functionroot of the function