Topicm659af3b4dc1b9d48_1528449000663_0Topic

Operations on algebraic expressions

Levelm659af3b4dc1b9d48_1528449084556_0Level

Second

Core curriculumm659af3b4dc1b9d48_1528449076687_0Core curriculum

III. Creating algebraic expressions with one and more variables.

The student:

2) calculates numerical values of algebraic expressions;

3) writes the relations presented in exercises in the form of algebraic expressions with one or more variables.

IV. Transformation of algebraic expressions. Algebraic sums and operations performed on them.

Timingm659af3b4dc1b9d48_1528449068082_0Timing

45 minutes

General objectivem659af3b4dc1b9d48_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm659af3b4dc1b9d48_1528449552113_0Specific objectives

1. Creating and transforming algebraic expressionstransforming algebraic expressionstransforming algebraic expressions.

2. Calculating numerical values of algebraic expressions

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

Learning outcomesm659af3b4dc1b9d48_1528450430307_0Learning outcomes

The Student:

- creates and transforms algebraic expressions,

- calculates numerical values of algebraic expressions.

Methodsm659af3b4dc1b9d48_1528449534267_0Methods

1. Discussion.

2. Thematical contest.

Forms of workm659af3b4dc1b9d48_1528449514617_0Forms of work

1. Work in pairs.

2. Group work.

Lesson stages

Introductionm659af3b4dc1b9d48_1528450127855_0Introduction

The teacher introduces the subject of the class: transforming algebraic expressionstransforming algebraic expressionstransforming algebraic expressions and calculating numerical values of algebraic expressions.

Task:

The teacher asks students to recall how we perform operations on algebraic sumalgebraic sumalgebraic sum and how we calculate the numerical value of an algebraic expression.

Procedurem659af3b4dc1b9d48_1528446435040_0Procedure

Students sort out the information about operations on algebraic expressions.

Note

In order to calculate the numerical value of the algebraic expressions, we insert numbers in the place of variables and perform operations.m659af3b4dc1b9d48_1527752263647_0In order to calculate the numerical value of the algebraic expressions, we insert numbers in the place of variables and perform operations.

[Geogebra applet]

Students work individually, using computers. Their task is to create algebraic expressions that illustrate the content of given exercises and calculate the numerical values for these expressions.

The teacher announces a thematical contest. Students work in pairs. The pair who first solves the obligatory and extra tasks get the highest mark.

Task

Perform the following operations:

a) $(2x^{2}y-3x)(-6y+2xy)-(xy+4y)(-3x+1)$

b) $-7a(ab+2a^2{b}^3)+(3a-5b)(4b-8a)$

c) $5x^{2}y(-2x+4y)-(2x^{3}y-7x^2{y}^2)+4x^2{y}^2-xy$

d) $(4\sqrt{3}x-\sqrt{3}y)(3\sqrt{2}x-\sqrt{3}y)-(3\sqrt{2}x-\sqrt{3}y)(4\sqrt{2}x+\sqrt{3}y)$

Task

Calculate the numerical value of the following expressions:

a) $(\frac{1}{a}+6a)·\frac{2}{3}$ for $a=-3$

b) $(-2x^{2}y{z}^4{)}^2$ for $x=\frac{1}{2},y=-2,z=2$

c) $2b^2-2d+3e^3$ for $b=-3,d=\frac{-1}{5},e=\frac{1}{2}$

Task

Write the expression describing the area of the ADCFE pentagon in the simplest form.

[Illustration1]

Task

Number M is a three‑digit number, whose hundreds digit is x, the tens digit is y and the units digit is z. Number K was obtained by exchanging the tens digit with the units digit in number M.

Write the expression $M·K$ in the simplest form.

An extra task:

Prove that the equation below is true for any x.

$x(x-4)+4x-4=(x-2)(x+2)$

Lesson summarym659af3b4dc1b9d48_1528450119332_0Lesson summary

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

In order to calculate the numerical value of algebraic expressions, we insert numbers in the place of variables and perform operations.

Selected words and expressions used in the lesson plan

algebraic sumalgebraic sumalgebraic sum

multiplication of an algebraic sum by a monomialmultiplication of an algebraic sum by a monomialmultiplication of an algebraic sum by a monomial

reduction of similar expressionsreduction of similar expressionsreduction of similar expressions

similar monomialssimilar monomialssimilar monomials

terms of a sumterms of a sumterms of a sum

multiplication of algebraic sumsmultiplication of algebraic sumsmultiplication of algebraic sums

transforming algebraic expressionstransforming algebraic expressionstransforming algebraic expressions