Topicm507f0a023e9e179e_1528449000663_0Topic

Monomials and algebraic sums

Levelm507f0a023e9e179e_1528449084556_0Level

Second

Core curriculumm507f0a023e9e179e_1528449076687_0Core curriculum

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

1) arranges monomials and adds similar monomialssimilar monomialssimilar monomials (that differ only by the coefficient);

2) adds and subtracts algebraic sums, while doing the reduction of similar expressions.

Timingm507f0a023e9e179e_1528449068082_0Timing

45 minutes

General objectivem507f0a023e9e179e_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm507f0a023e9e179e_1528449552113_0Specific objectives

1. Identifying and arranging monomials.

2. Adding similar monomialssimilar monomialssimilar monomials.

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

Learning outcomesm507f0a023e9e179e_1528450430307_0Learning outcomes

The student:

- identifies and arranges monomials,

- adds similar monomialssimilar monomialssimilar monomials.

Methodsm507f0a023e9e179e_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workm507f0a023e9e179e_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm507f0a023e9e179e_1528450127855_0Introduction

The teacher introduces the subject of the class: expanding knowledge concerning algebraic expressions. Students will learn two kinds of expressions and the ways in which they can be transformed.

Task
Using the internet resources, students look for the information about the simplest algebraic expressions, i.e. monomials. They analyse their examples, their construction and ways of writing them down.

Procedurem507f0a023e9e179e_1528446435040_0Procedure

Together students create the definition of a monomialmonomialmonomial.

- A monomial is an expression which is a number, a letter or a product of numbers and letters.m507f0a023e9e179e_1527752263647_0- A monomial is an expression which is a number, a letter or a product of numbers and letters.

Students identify monomials among other algebraic expressions.

Task
Choose monomials from the algebraic expressions below.

$\frac{2a+b}{ab}$

$\frac{x^{2}y}{x+3y}$

$-4$

$-2ab\cdot 2c$

$x$

$(7-n)h^2$

$2y^4$

The teacher gives examples of ordered and unordered monomials. The student’s task is to notice the regularities in the construction of ordered monomials and to identify the difference between an ordered and an unordered monomial. The result of the discussion should be writing down the definition of an ordered monomialmonomialmonomial.

Note:

- A monomial is ordered when its first coefficient is a number and followed by letters in the alphabetical order. The number than occurs at the beginning of an ordered monomial is the numerical coefficient of this monomial.m507f0a023e9e179e_1527752256679_0- A monomial is ordered when its first coefficient is a number and followed by letters in the alphabetical order. The number than occurs at the beginning of an ordered monomial is the numerical coefficient of this monomial.

Students arrange the monomials and identify their numerical coefficients.

Task
Arrange the monomialmonomialmonomial.

a) $-5ad·2c$

b) $\frac{3}{5}x·(-4y)·(-2xy)·0,2x$

c) mathematics

Task
Arrange the monomialmonomialmonomial and give its numerical coefficient.

a) $3a·(-4c)$

b) $4\frac{1}{4}·(-7)·xx·yyy$

c) $-0,6a^{2}b·10a{b}^2$

d) $\frac{2}{3}{x}^4{y}^{2}z·(-8xy{z}^3)$

Task
Students work individually, using computers. Their task is to notice what kind of monomials can be considered similar.

[Geogebra applet]

Students discover that similar monomialssimilar monomialssimilar monomials are monomials in which the letter coefficients have the same powers. They can differ only by the numerical coefficient.

Students together find the way to add similar monomialssimilar monomialssimilar monomials. First, they show the operation graphically and then they write down the algebraic result.

Task
Show graphically the addition and write the result in the form of a monomialmonomialmonomial.

a) $2x+3x$

b) $x+4x$

c) $6x+(-3x)$

The teacher defines the algebraic sum as an algebraic expression in which we add monomials. The parts of the sum are terms.m507f0a023e9e179e_1527712094602_0the algebraic sum as an algebraic expression in which we add monomials. The parts of the sum are terms.

An extra task:
Students give examples of monomials which are similar to the monomialmonomialmonomial below.

a) $6\frac{2}{7}{x}^2·(-11x)·0,4x{y}^2$

b) $-4baba·caaac$

c) $\frac{5}{11}k{t}^4·4k^4·ht·\frac{2}{15}{h}^{3}t$

Lesson summarym507f0a023e9e179e_1528450119332_0Lesson summary

Students do the revision exercises.

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

Definition of the monomialmonomialmonomial:
- A monomial is an expression which is a number, a letter or a product of numbers and letters.

- A monomialmonomialmonomial is ordered when its first coefficient is a number and followed by letters in the alphabetical order. The number than occurs at the beginning of an ordered monomial is the numerical coefficient of this monomialmonomialmonomial.

- Similar monomialssimilar monomialsSimilar monomials are monomials in which the letter coefficients have the same powers. They can differ only by the numerical coefficient.

- An algebraic sumalgebraic sumalgebraic sum is an expression which is a sum of monomials.

Selected words and expressions used in the lesson plan

algebraic expressionalgebraic expressionalgebraic expression

algebraic sumalgebraic sumalgebraic sum

monomialmonomialmonomial

similar monomialssimilar monomialssimilar monomials

terms of a sumterms of a sumterms of a sum