Topicm75b132a3cf64677a_1528449000663_0Topic

Multiplying algebraic sums

Levelm75b132a3cf64677a_1528449084556_0Level

Second

Core curriculumm75b132a3cf64677a_1528449076687_0Core curriculum

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

4) multiplies binomials by binomials, while doing the reduction of similar expressionsreduction of similar expressionsreduction of similar expressions.

Timingm75b132a3cf64677a_1528449068082_0Timing

45 minutes

General objectivem75b132a3cf64677a_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm75b132a3cf64677a_1528449552113_0Specific objectives

1. Multiplying algebraic sums by algebraic sums.

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

Learning outcomesm75b132a3cf64677a_1528450430307_0Learning outcomes

The student:

- multiplies algebraic sums by algebraic sums.

Methodsm75b132a3cf64677a_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workm75b132a3cf64677a_1528449514617_0Forms of work

1. Work in pairs.

2. Group work.

Lesson stages

Introductionm75b132a3cf64677a_1528450127855_0Introduction

The teacher introduces the subject of the lesson: multiplying algebraic sums by algebraic sums.

Task
The teacher asks the students to recall how to multiply algebraic sumalgebraic sumalgebraic sum by the monomial. They illustrate their answers with examples.

Procedurem75b132a3cf64677a_1528446435040_0Procedure

Students work individually, using computers. Their task is to observe how to multiply an algebraic sumalgebraic sumalgebraic sum by an algebraic sumalgebraic sumalgebraic sum.

[Geogebra applet]

Using the information they obtained, the students draw conclusions and do the exercises.

Note:

- In order to multiply two algebraic sums, we multiply each term of the first sum by each term of the second sum and add the resulting products.m75b132a3cf64677a_1527752263647_0- In order to multiply two algebraic sums, we multiply each term of the first sum by each term of the second sum and add the resulting products.

Task
Do the multiplication of the algebraic sums below.

a) $(-5a+3b)(7a-3b)$

b) $(3x^2 – 3y)(-2x + 6y^2)$

c) $(5\mathrm{xy} – 3x)(-3x + 7\mathrm{xy})$

d) $(-2a^3 + 4b – 3)(2b^2 – 5a + 1)$

Task
Calculate the values of the following expressions, using the multiplication of algebraic sums.

a) $(\sqrt{3}-\sqrt{2})(-2\sqrt{3}+3\sqrt{2})$

b) $(\sqrt{3}+2\sqrt{6})(-\sqrt{3}+\sqrt{2})$

c) $(\sqrt{5}+1)(3\sqrt{5}-6)$

d) $(\sqrt{6}-2\sqrt{2})(\sqrt{3}-3\sqrt{6})$

Task
Write the expression in the form of an algebraic sumalgebraic sumalgebraic sum ${(x+2)}^2$. On the basis of this example, write the expression $x^2 + 6x + 9$ as the square of the sum of two expressions.

Task
Write the area of the trapezium below in the form of an algebraic expression.

[Illustration 1]

An extra task:
Calculate the area of the rhombus whose longer diagonal of the length 2x is extended by y, and the shorter diagonal of the length y was reduced by x.

Lesson summarym75b132a3cf64677a_1528450119332_0Lesson summary

Students do the revision exercises.

Then together they sum‑up the classes, by formulating the conclusions to memorise.

- In order to multiply two algebraic sums, we multiply each term of the first sum by each term of the second sum and add the resulting products.

Selected words and expressions used in the lesson plan

algebraic sumalgebraic sumalgebraic sum

multiplication of algebraic sumsmultiplication of algebraic sumsmultiplication of algebraic sums

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