Topicm9d979affbc4b79c4_1528449000663_0Topic

Solving equations and inequalities with the use of short multiplicationmultiplicationmultiplication formulas

Levelm9d979affbc4b79c4_1528449084556_0Level

Third

Core curriculumm9d979affbc4b79c4_1528449076687_0Core curriculum

II. Algebraic expressions. The student:

1) applies short multiplicationmultiplicationmultiplication formulas for:
 $(a+b{)}^2$ , $(a-b{)}^2$ , $a^2-b^2$ , $(a+b{)}^3$ , $(a-b{)}^3$ , $a^3-b^3$ , $a^{\mathrm{n}}-b^{\mathrm{n}}$.

Timingm9d979affbc4b79c4_1528449068082_0Timing

45 minutes

General objectivem9d979affbc4b79c4_1528449523725_0General objective

Interpretation and the use of information presented both in a mathematical and popular science texts also using graphs, diagrams and tables.

Specific objectivesm9d979affbc4b79c4_1528449552113_0Specific objectives

1. Communication in English, developing mathematical, IT and basic scientific and technical competence, developing learning skills.

2. Applying short multiplicationmultiplicationmultiplication formulas for converting algebraic expressions.

3. Solving equations and inequalities with the use of short multiplication formulas.

Learning outcomesm9d979affbc4b79c4_1528450430307_0Learning outcomes

The student:

- applies short multiplication formulas for converting algebraic expressions,

- solves equations and inequalities with the use of short multiplicationmultiplicationmultiplication formulas.

Methodsm9d979affbc4b79c4_1528449534267_0Methods

1. Speaking cards.

2. Situational analysis.

Forms of workm9d979affbc4b79c4_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm9d979affbc4b79c4_1528450127855_0Introduction

The students revise their information about short multiplicationmultiplicationmultiplication formulas using the „speaking cards” technique. Every student gets a card, where he/she writes one formula. Next, one of the students collects the cards and reads the formulas. The teacher develops or completes the information if needed.

Procedurem9d979affbc4b79c4_1528446435040_0Procedure

The teacher informs the students that the aim of the class is consolidation of the short multiplicationmultiplicationmultiplication formulas and solving equations and inequalities with the use of the formulas.

Task
Working in groups the students analyse the material shown in the Slideshow 1. They formulate hypotheses, check them and write down all the stages of solving the equationequationequation.

[Slideshow 1]

The stages of solving the equation:
1. First, we perform the operations in the parentheses. We use the short multiplication formulas.
2. We move the unknown to the left side of the equation and the expressions without unknowns to the right side of the equation, remembering about changing the symbols to the opposite.
3. We simplify the like terms.
4. We divide both sides of the equation by the number next to the unknown.
5. We calculate the root of the equation.m9d979affbc4b79c4_1527752263647_0The stages of solving the equation:
1. First, we perform the operations in the parentheses. We use the short multiplication formulas.
2. We move the unknown to the left side of the equation and the expressions without unknowns to the right side of the equation, remembering about changing the symbols to the opposite.
3. We simplify the like terms.
4. We divide both sides of the equation by the number next to the unknown.
5. We calculate the root of the equation.

Using the information, the students solve the tasks individually.

Task
Solve the equations.

a) $(x+5{)}^2-(x-3{)}^2=x+1$

b) $(x+3{)}^2-(4-x\left)\right(4+x)=2(x-1{)}^2+1$

c) $(x-\sqrt{3})(x-\sqrt{3})-(x+\sqrt{3})(x+\sqrt{3})-\sqrt{12}=0$

d) $(x+2\sqrt{5}{)}^2+(x-2\sqrt{5}{)}^2=46$

Task
Working in groups the students analyse the material shown in the Slideshow 2. They formulate hypotheses, check them and write down all the stages of solving the inequalityinequalityinequality.

[Slideshow 2]

The stages of solving the inequalityinequalityinequality:
1. First, we perform the operations in the parentheses. We use the short multiplicationmultiplicationmultiplication formulas.
2. We move the unknown to the left side of the inequality and the expressions without unknowns to the right side of the inequality, remembering about changing the symbols to the opposite.
3. We simplify the like terms.
4. We divide both sides of the inequalityinequalityinequality by the number next to the unknown. If the number next to the unknown is a negative number, we switch the direction of inequality.
5. We find the solutionsolutionsolution of the inequality.
6. We present the set of solution on the number line.

Using the information, the students solve the tasks individually.

Task
Solve the inequalityinequalityinequality and present the set of solutionsolutionsolution on the number line.

a) $(2x+3)(2x-3)-8x>(2x-3{)}^2-18$

b) $x^2-\frac{{(x-1)}^2}{2}<\frac{(x-2)(x+2)}{2}+2x-1$

c) $(x+\sqrt{2})(x-\sqrt{2})-(x+\sqrt{2}{)}^2<0$

d) $(2-x{)}^2-5\ge (x-\sqrt{3}{)}^2$

Task
For what value of number a the solutionsolutionsolution of equationequationequation

$(x-a{)}^2=(x+2\left)\right(x-2)-(1,5·x-4)$ is number 2?

Having solved all the tasks, the students present their results. They assess their work. The teacher verifies the students’ answers and explains the doubts.

An extra task:
Solve equations.

a) $x^2·(x^2-4)-3·(x^2-4)=0$

b) $-4·(x^2-12)=x^2·(12-x^2)$

Lesson summarym9d979affbc4b79c4_1528450119332_0Lesson summary

The students do the consolidation tasks.

They formulate the conclusions to memorize.

The stages of solving the equationequationequation:
1. First, we perform the operations in the parentheses. We use the short multiplicationmultiplicationmultiplication formulas.
2. We move the unknown to the left side of the equation and the expressions without unknowns to the right side of the equation, remembering about changing the symbols to the opposite.
3. We simplify the like terms.
4. We divide both sides of the equationequationequation by the number next to the unknown.
5. We calculate the root of the equation.

The stages of solving the inequality:
1. First, we perform the operations in the parentheses. We use the short multiplication formulas.
2. We move the unknown to the left side of the inequality and the expressions without unknowns to the right side of the inequality, remembering about changing the symbols to the opposite.
3. We simplify the like terms.
4. We divide both sides of the inequality by the number next to the unknown. If the number next to the unknown is a negative number, we switch the direction of inequality.
5. We find the solution of the inequality.
6. We present the set of solution on the number line.m9d979affbc4b79c4_1527752256679_0The stages of solving the inequality:
1. First, we perform the operations in the parentheses. We use the short multiplication formulas.
2. We move the unknown to the left side of the inequality and the expressions without unknowns to the right side of the inequality, remembering about changing the symbols to the opposite.
3. We simplify the like terms.
4. We divide both sides of the inequality by the number next to the unknown. If the number next to the unknown is a negative number, we switch the direction of inequality.
5. We find the solution of the inequality.
6. We present the set of solution on the number line.

Selected words and expressions used in the lesson plan

difference of the squaresdifference of the squaresdifference of the squares

equationequationequation

inequalityinequalityinequality

multiplicationmultiplicationmultiplication

set of solutions of an inequalityset of solutions of an inequalityset of solutions of an inequality

short multiplication formulashort multiplication formulashort multiplication formula

solutionsolutionsolution

solution of an equationsolution of an equationsolution of an equation

square of the differencesquare of the differencesquare of the difference

square of the sumsquare of the sumsquare of the sum