Topicm9f0337bccdd65f2d_1528449000663_0Topic

Solving first degree equation with one unknown

Levelm9f0337bccdd65f2d_1528449084556_0Level

Second

Core curriculumm9f0337bccdd65f2d_1528449076687_0Core curriculum

VI. Equations with one unknown. The student:

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

Timingm9f0337bccdd65f2d_1528449068082_0Timing

45 minutes

General objectivem9f0337bccdd65f2d_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm9f0337bccdd65f2d_1528449552113_0Specific objectives

1. Solving equations using the equivalent equationsequivalent equationsequivalent equations method.

2. Identifying equivalent equationsequivalent equationsequivalent equations.

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

Learning outcomesm9f0337bccdd65f2d_1528450430307_0Learning outcomes

The student:

- solves equations using the equivalent equationsequivalent equationsequivalent equations method,

- identifies equivalent equationsequivalent equationsequivalent equations.

Methodsm9f0337bccdd65f2d_1528449534267_0Methods

1. Discussion.

2. Task tables.

Forms of workm9f0337bccdd65f2d_1528449514617_0Forms of work

1. Work in a small group.

2. Group work.

Lesson stages

Introductionm9f0337bccdd65f2d_1528450127855_0Introduction

At home, students search available knowledge sources (films, animations, educational materials) for information about types of systems of equations and methods of solving them. Then, they make notes to systemize obtained knowledge.

Procedurem9f0337bccdd65f2d_1528446435040_0Procedure

Class representatives chosen by the teacher shortly discuss results of their research and answer teachers’ questions.

To solve an equation – means to find all numbers that satisfy this equation or prove that the equation has no solution.m9f0337bccdd65f2d_1527752263647_0To solve an equation – means to find all numbers that satisfy this equation or prove that the equation has no solution.

Solving equations using the equivalent equationsequivalent equationsequivalent equations method mean that we can:

- add to both sides of the equation or subtract from the same equation the same number or expression,

- multiply both sides of the equation or divide both sides of the equation by the same number different than zero.

[Geogebra applet]

Students work individually, using computers. Their task is to observe the way of solving equations using the equivalent equationsequivalent equationsequivalent equations method.

Work in pairs
Students do exercises using the method of task tables is pairs. The fastest pair that solves also the extra task gets the highest mark. Next three pairs – the second best.

Table 1 – a task to do
In an equilateral trapezium, the angle at the longer base is 36 ˚ smaller than the angle at the shorter base. Calculate angles of this trapezium.

Table 2 – a task to do
Add a second side of the equation so that any real number satisfies it.

a. $5x-4=1+...$

b. $\sqrt{3}-2x=x+...$

c. $7+\sqrt{3}=-2+...$

Table 3 – a task to do
Knowing solution of the equationsolution of the equationsolution of the equation, identify number a.

a. $3x-5(a-1)=4(x-2),x=-1$

b. $4z-2a+3=a-a(z-5),z=2$

c. $2a-3(v+a)=4(a-1),v=-\frac{1}{4}$

Table 4 – a task to do
Add two equivalent equationsequivalent equationsequivalent equations to each equation.

a. $2x+3(1-x)=5$

b. $x-\frac{1}{2}+4(x-1)=-x+2$

c. $\frac{1}{4}x=1$

Table 5 – a task to do
Solve equations.

a. $x-\frac{3}{4}=\frac{2x-2}{\sqrt{2^4}}-5(x-1^0)$

b. $-2^{2}x-2\frac{1}{5}(x+3)=-\sqrt[3]{-8}-\frac{1}{3}(\sqrt[3]{\frac{1}{27}}-x)$

An extra task:
Give two numbers whose sum is twice greater than their difference.

Students discuss solutions and the teacher evaluates their work and clarifies doubts.

Lesson summarym9f0337bccdd65f2d_1528450119332_0Lesson summary

Students do the revision exercises. Then together they sum‑up the classes, by formulating the conclusions to memorise.

To solve an equationto solve an equationTo solve an equation – means to find all numbers that satisfy this equation or prove that the equation has no solution. Equivalent, first degree equations with one unknown are such equations that have the same set of solutionsset of solutionsset of solutions. Solving equations using the equivalent equationsequivalent equationsequivalent equations method mean that we can:

- add to both sides of the equation or subtract from the same equation the same number or expression,

- multiply both sides of the equation or divide both sides of the equation by the same number different than zero.

Selected words and expressions used in the lesson plan

contradictioncontradictioncontradiction

equivalent equationsequivalent equationsequivalent equations

identityidentityidentity

set of solutionsset of solutionsset of solutions

solution of the equationsolution of the equationsolution of the equation

to solve an equationto solve an equationto solve an equation