Topicmf4d3df849dcb32f0_1528449000663_0Topic

Operations on algebraic expressionsalgebraic expressionsalgebraic expressions

Levelmf4d3df849dcb32f0_1528449084556_0Level

Third

Core curriculummf4d3df849dcb32f0_1528449076687_0Core curriculum

I. Real numbers. The student:

1) performs operations (addition, subtraction, multiplication, division, exponentiation, square roots, logarithms) in a set of real numbers.

Timingmf4d3df849dcb32f0_1528449068082_0Timing

45 minutes

General objectivemf4d3df849dcb32f0_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 objectivesmf4d3df849dcb32f0_1528449552113_0Specific objectives

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

2. Reading and writing algebraic expressionsalgebraic expressionsalgebraic expressions.

3. Transforming algebraic expressions.

Learning outcomesmf4d3df849dcb32f0_1528450430307_0Learning outcomes

The studnet:

- reads and writes algebraic expressions,

- transforms algebraic expressionsalgebraic expressionsalgebraic expressions.

Methodsmf4d3df849dcb32f0_1528449534267_0Methods

1. „Wandering cards”.

2. Competition.

Forms of workmf4d3df849dcb32f0_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmf4d3df849dcb32f0_1528450127855_0Introduction

Students sit in a circle, in the middle of which stands an empty box. With the method of „wandering cards” they review the names of algebraic expressionsalgebraic expressionsalgebraic expressions.

The first student writes an algebraic phrase on the card, e.g. 3x. He or she passes the card to the next student. He or she adds the name of the expression and puts the card back in the box. At that time, the first student speaks aloud what phrase he wrote. The second student takes a blank note, writes an algebraic expression on it (other than the first one) and gives it to the next student. The whole procedure is repeated until students run out of the ideas for new expressions.
Then the volunteer takes out the card from the box and checks if the expressions are correctly signed. If not, he or she shows the card to other students who give the correct name of the expression.

Proceduremf4d3df849dcb32f0_1528446435040_0Procedure

The teacher informs the students that the aim of the lesson will be to review what they know about algebraic expressionsalgebraic expressionsalgebraic expressions.

Task
Students, working in groups, analyze an interactive drawing. They pay attention to the way how the multiplication of the algebraic sumalgebraic sumalgebraic sum by the number and the algebraic sum by the algebraic sum are performed. They formulate the conclusions.

[Interactive illustration]

Conclusion:

- To multiply two algebraic sums, multiply each component of the first sum by each component of the second sum and add the products obtained.
After performing the indicated operations, a reduction of similar expressions should be carried out.mf4d3df849dcb32f0_1527752263647_0- To multiply two algebraic sums, multiply each component of the first sum by each component of the second sum and add the products obtained.
After performing the indicated operations, a reduction of similar expressions should be carried out.

Students, working alone, take part in a task competition.
The competition has three stages. For each correctly performed calculation, the student receives 1 point, for the wrongly done one (-1). Students who have obtained a minimum of 3 points pass to the next stage.

Tasks of the first stage.

Task
Write in the form of an algebraic expression:

a) the sum of the doubled variable x and the tripled variable y,

b) the difference in the number of a and the doubled sum of x and y variables,

c) the product of the square of the number a and the number b,

d) the quotient of the sum of the numbers a and b by their difference.

Task
Bring the expression to the simplest formsimplest formsimplest form:

a) $7m^2-\left(-1\right)·\left[4m^2-3m-\left(m^2-4m\right)\right];$

b) $(2m^2+6nm+5)\cdot 3nm-5nm;$

c) $(-5a^3+15a^2-25a):(-5a)+2;$

d) $(-2b^2+6b^3\cdot c^2-8b^4\cdot c^3):(-2b^2).$

Tasks of the second stage.

Task
Bring the expression to the simplest formsimplest formsimplest form, then calculate its numerical value for the given variable values:

a) $4·\left(\frac{1}{2}x-2\right)+\left(-16x^2+4x\right):(-4x)-(-5x+3)·(-1);$

$x=\frac{2}{3};$

b) $\left(12a^4{b}^4-9a^2{b}^3\right):(-3a^{2}b)-(2+3a^{2}b)·b^2;$

$a=-1$, $b=-2.$

Task
Do the multiplication:

a) $(x+2)(y-5);$

b) $(b+4)(5-3b);$

c) $-2(2x+3)(6-5x).$

Tasks for 3 stage.

Task
Bring the expression to the simplest formsimplest formsimplest form:

a) $(a-b)(2a+3b)+(a+3b)(-a+4b);$

b) $–(n+5m)(3n+m-4)+(6n-3m)(m-n+2)-3\left(n^2+m^2\right).$

The teacher summarizes the results of the competition. The students who scored the most points are rewarded with grades

An extra task:
Simplify fractions. Provide the necessary assumptions:

a) $\frac{x(x+2)}{2x};$

b) $\frac{(3mn-m^2)}{3mn}.$

Lesson summarymf4d3df849dcb32f0_1528450119332_0Lesson summary

Students do the revision exercises.

Together, they formulate conclusions to remember.

-  To multiply two algebraic sums, multiply each component of the first sum by each component of the second sum and add the products obtained.
After performing the indicated operations, similar expression should be reduced.

Selected words and expressions used in the lesson plan

algebraic expressionsalgebraic expressionsalgebraic expressions

algebraic sumalgebraic sumalgebraic sum

multiplication of algebraic sumsmultiplication of algebraic sumsmultiplication of algebraic sums

reduction of similar termsreduction of similar termsreduction of similar terms

similar termssimilar termssimilar terms

simplest formsimplest formsimplest form

value of the algebraic expressionvalue of the algebraic expressionvalue of the algebraic expression