Topicma17809ce6a64ccf9_1528449000663_0Topic

Multiplying an algebraic sum by a monomialmultiplying an algebraic sum by a monomialMultiplying an algebraic sum by a monomial

Levelma17809ce6a64ccf9_1528449084556_0Level

Second

Core curriculumma17809ce6a64ccf9_1528449076687_0Core curriculum

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

3) multiplies algebraic sums by the monomial and adds expressions obtained by multiplying algebraic sums by monomials.

Timingma17809ce6a64ccf9_1528449068082_0Timing

45 minutes

General objectivema17809ce6a64ccf9_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesma17809ce6a64ccf9_1528449552113_0Specific objectives

1. Multiplying an algebraic sum by a monomialmultiplying an algebraic sum by a monomialMultiplying an algebraic sum by a monomial.

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

Learning outcomesma17809ce6a64ccf9_1528450430307_0Learning outcomes

The student:

- multiplies an algebraic sumalgebraic sumalgebraic sum by a monomial.

Methodsma17809ce6a64ccf9_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workma17809ce6a64ccf9_1528449514617_0Forms of work

1. Work in pairs.

2. Group work.

Lesson stages

Introductionma17809ce6a64ccf9_1528450127855_0Introduction

Students revise the distributive property of multiplication over additiondistributive property of multiplication over additiondistributive property of multiplication over addition. They give examples.

Procedurema17809ce6a64ccf9_1528446435040_0Procedure

The teacher introduces the topic of the class: learning to multiply an algebraic sumalgebraic sumalgebraic sum by a monomial.

Task
Students work individually, using computers. Their task is to notice how to multiply an algebraic sumalgebraic sumalgebraic sum by a monomial using the distributive property of multiplication over additiondistributive property of multiplication over additiondistributive property of multiplication over addition.

[Geogebra applet]

Using the obtained information, students do the exercises and formulate conclusions.

Task
Change the following products $-3x^2(3+7x),8ab(3a^2-2b^3)$ into sums. Use the formulaformulaformula.

The conclusion students should draw:

- To multiply an algebraic sum by a monomial we need to multiply the monomial by every term of the sum and add the obtained products.ma17809ce6a64ccf9_1527752263647_0- To multiply an algebraic sum by a monomial we need to multiply the monomial by every term of the sum and add the obtained products.

Students do the multiplication using the same method.

Task
Multiply the monomial by the following algebraic sums.

a) $2x^{2}y(-4,5x^3{y}^2 + 2{\mathrm{xy}}^2 + y)$

b) $-\frac{1}{4}ab(\frac{1}{2}a{b}^3-\frac{4}{17}a+3a^4{b}^2)$

c) $-\mathrm{2,5}{k}^2{l}^3(\mathrm{1,2}{\mathrm{kl}}^2 + 2l^3 – 3,5k^4 - \mathrm{kl})$

Task
Fill in the blanks in such a way that the following equations are correct.

a) $3a{b}^2(-2a+3b-\dots )=-6a^2{b}^2+9a{b}^3-18a^2{b}^3$

b) $-0,5ab(-4a^2+12a{b}^3-\dots )=...-6a^2{b}^4+8ab$

c) $-\frac{1}{3}a(\dots +9a^{2}b+12a{b}^2)=2a^{2}b-3a^{3}b-4a^2{b}^2$

The teacher announces the task contest. The group which does correctly all the exercises as first gets the highest mark.

Task
Match the following operations and the corresponding results.

a) $2ab(-3a{b}^2+a^{2}b)$

b) $-a^2(6ab-\sqrt{9}a{b}^2)$

c) $0,5b(\sqrt{36}a{b}^3+4ab)$

d) $-\sqrt{\frac{1}{9}}a\left(6a^2 + 9b^2\right)$

1. $-6a^{3}b+2a^3{b}^2$

2. $3a{b}^4+2a{b}^2$

3. $-6a^2{b}^3+2a^3{b}^2$

4. $-2a^3-3a{b}^2$

Task
There are 18 animals in the backyard: x are hens and the other are dogs. How many legs do all the animals have?

An extra task:
The shorter base of the trapezoid has the length x + 3. The longer one is longer by 5y. The altitude equals 3xy. Calculate the area of the trapezoid.

Lesson summaryma17809ce6a64ccf9_1528450119332_0Lesson summary

Students do the revision exercises.

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

- To multiply an algebraic sum by a monomial we need to multiply the monomial by every term of the sum and add the obtained products.ma17809ce6a64ccf9_1527752263647_0- To multiply an algebraic sum by a monomial we need to multiply the monomial by every term of the sum and add the obtained products.

Selected words and expressions used in the lesson plan

algebraic productalgebraic productalgebraic product

algebraic sumalgebraic sumalgebraic sum

distributive property of multiplication over additiondistributive property of multiplication over additiondistributive property of multiplication over addition

formulaformulaformula

measuremeasuremeasure

multiplying an algebraic sum by a monomialmultiplying an algebraic sum by a monomialmultiplying an algebraic sum by a monomial

reduction of similar termsreduction of similar termsreduction of similar terms

similar monomialssimilar monomialssimilar monomials

sumsumsum

terms of the sumterms of the sumterms of the sum