Topicm53bbfc7c2a14a0c7_1528449000663_0Topic

Monomials

Levelm53bbfc7c2a14a0c7_1528449084556_0Level

Second

Core curriculumm53bbfc7c2a14a0c7_1528449076687_0Core curriculum

III. Creating algebraic expressionsalgebraic expressionsalgebraic expressions with one or more variables.

The student:

1) writes down the results of a given operation in the form of algebraic expressions with one or more variables.

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

3) writes down the solutions to the exercises in the form of algebraic expressions, like in the example below:

Bartek and Grześ were picking up chestnuts. Bartek collected n chestnuts and Grześ collected 7 times more. Then, on the way home, Grześ lost 10 chestnuts and gave half of the rest to Bartek. How many chestnuts do Bartek and Grześ have now?

Timingm53bbfc7c2a14a0c7_1528449068082_0Timing

45 minutes

General objectivem53bbfc7c2a14a0c7_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm53bbfc7c2a14a0c7_1528449552113_0Specific objectives

1) Arranging monomials.

2) Writing down the content of exercises in the form algebraic expressionsalgebraic expressionsalgebraic expressions.

3) Communicating in English, developing basic mathematical, computerand scientific competences, developing learning skills.

Learning outcomesm53bbfc7c2a14a0c7_1528450430307_0Learning outcomes

The student:

- arranges monomials,

- writes down the content of exercises in the form algebraic expressionsalgebraic expressionsalgebraic expressions.

Methodsm53bbfc7c2a14a0c7_1528449534267_0Methods

1) Discussion.

2) Brainstorming.

Forms of workm53bbfc7c2a14a0c7_1528449514617_0Forms of work

1) Individual work.

2) Group work.

Lesson stages

Introductionm53bbfc7c2a14a0c7_1528450127855_0Introduction

The teacher informs students that during this class they will extend their knowledge about algebraic expressionsalgebraic expressionsalgebraic expressions.

Students revise the definitions of algebraic expression and the monomialmonomialmonomial.

An algebraic expression consists of numbers and letters, which are connected with each other by the signs of arithmetic operations and/or parentheses. A single letter or number is also an algebraic expression. The letters occurring in algebraic expressions are variables.
A monomial is an expression that is a single number, a letter or a product of numbers and letters.m53bbfc7c2a14a0c7_1527752263647_0An algebraic expression consists of numbers and letters, which are connected with each other by the signs of arithmetic operations and/or parentheses. A single letter or number is also an algebraic expression. The letters occurring in algebraic expressions are variables.
A monomial is an expression that is a single number, a letter or a product of numbers and letters.

Procedurem53bbfc7c2a14a0c7_1528446435040_0Procedure

Task
Student work individually, using computers. The aim of the exercise is to revise the ways of creating the names of algebraic expressionsalgebraic expressionsalgebraic expressions.

[Geogebra applet]

Note
The name of an algebraic expression is determined by the operation which, according to the order of operations, would be done as the last one.

Students use the revised knowledge in exercises.

Task
Write in the form of an algebraic expression:

a) the sum of the square of 5 and cube of the number x,

b) the quotient of the sum of x and y and their difference,

c) the square of the sum of the numbers -2 and y.

The teacher gives examples of monomials and the students’ task is to write them down in the ordered form. In this way, they revise the principles of creating and arranging monomials.

Note
A monomial is arranged if its first part is a number and then it includes letters in alphabetical order.
The letter which occurs at the beginning of an arranged monomial is called the numerical coefficient of the monomial.m53bbfc7c2a14a0c7_1527752256679_0A monomial is arranged if its first part is a number and then it includes letters in alphabetical order.
The letter which occurs at the beginning of an arranged monomial is called the numerical coefficient of the monomial.

Students arrange the monomials and identify their numerical coefficients.

Task
Arrange the monomials and identify their numerical coefficients.

a) $-4\cdot \sqrt[3]{9}{a}^2{b}^2·\sqrt[3]{3}{a}^{3}b$

b) $4^2\cdot x{y}^4{z}^3·(-2\sqrt{5})x^{2}y$

c) $–z^2·(-x{)}^2·(-\mathrm{1,5}z)·\mathrm{0,4}x$

d) $\frac{(0,2x{y}^2)}{4}·(-0,8)x$

Task
Fill the blanks with the monomials which make the equations true:

a) $1,5a^4{b}^3=0,5a{b}^2·\dots$

b) $4x{y}^2=\sqrt{2}y·\dots$

c) $-5k{l}^2=-0,5l·\dots$

d) $5a^2{k}^{3}l=\frac{1}{5}akl·\dots$

Task
Students write down arranged monomials which describe the perimeter and the area of the rectangle in which:

a) one of the sides has the length z and the other is 30% shorter,

b) the width w is equal to 0,2 of the length,

c) the length x is $\frac{11}{3}$ of its width.

An extra task
In the ABC triangle, the AB base is equal to $\frac{1}{2}x$. The altitude between the vertex C and the base AB is twice longer than the AB side. Write down the expression describing the area of this triangle in the form of an arranged monomialmonomialmonomial.

Lesson summarym53bbfc7c2a14a0c7_1528450119332_0Lesson summary

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

An algebraic expression consists of numbers and letters, which are connected with each other by the signs of arithmetic operations and/or parentheses. A single letter or number is also an algebraic expression. The letters occurring in algebraic expressionsalgebraic expressionsalgebraic expressions are variables.

A monomialmonomialmonomial is an expression that is a single number, a letter or a product of numbers and letters.

A monomial is arranged if its first part is a number and then it includes letters in alphabetical order.

The letter which occurs at the beginning of an arranged monomialmonomialmonomial is called the numerical coefficient of the monomial.

Selected words and expressions used in the lesson plan

algebraic expressionsalgebraic expressionsalgebraic expressions

algebraic productalgebraic productalgebraic product

algebraic quotientalgebraic quotientalgebraic quotient

monomialmonomialmonomial

variablevariablevariable