Topicme2dd7aacd2043c1c_1528449000663_0Topic

Equations and inequalities

Levelme2dd7aacd2043c1c_1528449084556_0Level

Third

Core curriculumme2dd7aacd2043c1c_1528449076687_0Core curriculum

III. Equations and inequalities. The student:

1) transforms equations and inequalities with the equivalent method;

2) interprets contradiction and identity equations and inequalities;

3) solves linear inequalities with one unknown.

Timingme2dd7aacd2043c1c_1528449068082_0Timing

45 minutes

General objectiveme2dd7aacd2043c1c_1528449523725_0General objective

Interpreting and manipulating information presented in both mathematical and popular science texts, as well as in the form of graphs, diagrams, tables.

Specific objectivesme2dd7aacd2043c1c_1528449552113_0Specific objectives

1. Communicating in English, developing mathematical and basic scientific and technical and IT competences, developing learning skills.

2. Solving equations with the equivalent equationequationequation method.

3. Solving inequalities using the equivalent inequalityinequalityinequality method.

Learning outcomesme2dd7aacd2043c1c_1528450430307_0Learning outcomes

The student:

- solves equations with the equivalent equationequationequation method,

- solves inequalities using the equivalent inequalityinequalityinequality method.

Methodsme2dd7aacd2043c1c_1528449534267_0Methods

1. Throw the Ball.

2. Case study.

Forms of workme2dd7aacd2043c1c_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionme2dd7aacd2043c1c_1528450127855_0Introduction

Students, using the „ball” method, review their knowledge of equations and inequalities and methods of solving them. They all stand in a circle and throw a ball at one another.

The student who gets the ball has to answer the question posed by the teacher. If he does not know the answer to the question, he or she falls leaves the circle.

Examples of questions that the teacher may ask:

- What do we call an equationequationequation?

- What does it mean to solve the equationequationequation?

- What equations are called equivalent equations?

- Does each equationequationequation have a solution?

- What is inequalityinequalityinequality?

- What inequalities are called equivalent inequalities?

The game ends when the teacher gets all the answers. After completing the game, the teacher verifies students' answers and explains all doubts.

Procedureme2dd7aacd2043c1c_1528446435040_0Procedure

The teacher informs students that the aim of the lesson is to review and consolidate knowledge of equations and inequalities and methods of solving them.

Task
Students, working in groups, analyze the Interactive illustration which illustrates the method of solving the equationequationequation. Students’ task is to provide the stages of solving the equationequationequation. They formulate the conclusions.

[Interactive illustration 1]

Conclusion:

- Stages of solving the equationequationequation.

1. The unknown are transferred to the left side of the equation and the numbers to the right.me2dd7aacd2043c1c_1527752263647_0The unknown are transferred to the left side of the equation and the numbers to the right.

2. By moving the expression to the other side of the equation, we change its sign to the opposite one.me2dd7aacd2043c1c_1527752256679_0By moving the expression to the other side of the equation, we change its sign to the opposite one.

3. We carry out the reduction of similar terms.

4. If there is a number with the unknown, we divide both sides of the equationequationequation by this number.

Discussion - What additional steps should be performed if the numeric coefficients are written in the form of fractions or the expression contains brackets?

Students formulate the conclusions together.

Conclusion:

- If in the equationequationequation appear numerical coefficients in the form of fractions, then we can multiply both sides of the equation by the common denominator of these fractions.

- We get rid of the brackets by performing the indicated operations.

Students work independently and check their skills by solving problems.

Task
Calculate the equations.

a) $\frac{x+3}{2}-\frac{x-4}{3}=0$

b) $\frac{2+x}{3}+\frac{3-x}{6}=1$

c) $\frac{x-4}{3}-\frac{2x-1}{5}=x+\frac{11-2x}{15}$

d) $\frac{3(x-11)}{4}=\frac{3(x+1)}{5}-\frac{2(2x-5)}{11}$

Task
For which value of the number a, the solution of the given equationequationequation is the number 0,5?

$(3x+1)\left(x+a\right)-3\left(x-1\right)(x-a)=4$

Task
Students, working in groups, analyze the Interactive illustration that illustrates how to solve inequalities. Their task is to provide stages of the solution of inequalityinequalityinequality. They formulate the conclusions.

[Interactive illustration 2]

Conclusion:

- Stages of solving inequalityinequalityinequality.

1. We transfer the unknowns to the left of the inequalityinequalityinequality and the numbers to the right.

2. By moving the expression to the other side of the inequalityinequalityinequality, we reverse its symbol to the opposite one.

3. We carry out the reduction of similar terms.

4. If there is a number with the unknown, we divide both sides of the inequalityinequalityinequality by that number.

5. Dividing the sides of inequalityinequalityinequality by a negative number requires changing the direction of the inequalityinequalityinequality to the opposite one.

Students, working independently, check their skills by solving problems.

Task
Solve the inequalityinequalityinequality and mark the set of the solutions on the numerical axis.

a) $2\left(x-1\right)-3\left(x-2\right)<6$

b) $x-\frac{3(x+2)}{4}>1+x$

c) $\frac{x-5}{2}-\frac{3-x}{6}\le \frac{x+4}{3}$

d) $\frac{4-x}{5}-\frac{x+2}{3}\ge \frac{2-8x}{15}$

Task
For what value of the number a, a set of solutions of inequalityinequalityinequality $2\left(x-5\right)<ax-16$ is the set $(1,\infty )$.

After solving all the tasks, students present their results. The teacher evaluates their work, explains all doubts.

An extra task:
Solve the inequalityinequalityinequality $1-\frac{x-3}{3}\le {(x-1)}^2-x^2$.

a) Indicate integers greater than -3 belonging to the set of inequalityinequalityinequality solutions.

b) Write three numbers that are not rational that belong to the set of inequalityinequalityinequality solutions.

c) Is the number $\frac{1}{7}$ a part of the set of inequalityinequalityinequality solutions?

Lesson summaryme2dd7aacd2043c1c_1528450119332_0Lesson summary

Students do the revision tasks.

Then they summarize the lesson together and formulate conclusions to remember.

- Stages of solving the equation (inequalityinequalityinequality).

1. The unknowns are transferred to the left side of the equationequationequation (inequalityinequalityinequality), and the numbers to the right.

2. By moving the expression to the other side of the equationequationequation (inequalityinequalityinequality), we reverse its symbol to the opposite one.

3. We carry out the reduction of similar terms.

4. If there is a number with the unknown, we divide both sides of the equationequationequation (inequality) by that number.

5. Dividing the sides of inequalityinequalityinequality by a negative number requires changing the direction of this inequalityinequalityinequality to the opposite one.

Selected words and expressions used in the lesson plan

equationequationequation

inequalityinequalityinequality

left side of the equationleft side of the equationleft side of the equation

right side of the equationright side of the equationright side of the equation

set of inequality solutionsset of inequality solutionsset of inequality solutions

solution of the equationsolution of the equationsolution of the equation