Topicmc71aafdfaf187ad6_1528449000663_0Topic

Using simple formulas

Levelmc71aafdfaf187ad6_1528449084556_0Level

Second

Core curriculummc71aafdfaf187ad6_1528449076687_0Core curriculum

VI. The elements of algebra. The student:

1) uses simple formulas with the letter marking, describes the formulas verbally;

2) uses the letter marking of unknown figures and writes down simple algebraic expressions on the basis of the information filled in with a practical contents, e.g. writes the perimeter of the triangle with the sides: a, a+2, b; solves linear equation in one unknown occurring in one side of the equation ( by guessing completing, or doing the opposite) e.g. $\frac{x-2}{3}=4$

Timingmc71aafdfaf187ad6_1528449068082_0Timing

45 minutes

General objectivemc71aafdfaf187ad6_1528449523725_0General objective

Matching the mathematical model to a simple situation and using it in various contexts.

Specific objectivesmc71aafdfaf187ad6_1528449552113_0Specific objectives

1. Writing the information and data of the content of the task in a form of the algebraic expression or the equation.

2. Solving the equations with one unknown.

3. Communicating in English; developing mathematical and basic scientific, technical and digital competences; developing learning skills.

Learning outcomesmc71aafdfaf187ad6_1528450430307_0Learning outcomes

The student:

- writes the information and data of the content of the task in a form of the algebraic expression or the equation,

- solves the equations with one unknown.

Methodsmc71aafdfaf187ad6_1528449534267_0Methods

1. Situational analysis.

Forms of workmc71aafdfaf187ad6_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmc71aafdfaf187ad6_1528450127855_0Introduction

Every student brings the box of matches for the lesson.

The students revise the material about the algebraic expressions and the equations.

Proceduremc71aafdfaf187ad6_1528446435040_0Procedure

The teacher introduces the topic of the lesson: writing the algebraic expressions and equations concerning the natural numbers and the figures drawn or made of the matches.

The students work individually using their computers. They are going to analyse the slideshow concerning the natural, even and triangular numbers.

Title: Even and triangular numbers

[SLIDESHOW]

The students work in groups of three or four. Using the gained information they write the algebraic expressions and the equations. Finally the leaders of the groups present the solutions of the tasks 1to 3 in the class.

Task 1
Write the algebraic expression describing the following:

a) the natural number divided by 3,

b)the sum of two subsequent natural numbers divided by 3,

c) the odd number,

d) the sum of four subsequent odd natural numbers.

Task 2
a) The sum of three subsequent even natural numbers equals 228. What are the numbers? Rearrange the appropriate equation and solve it.

b) The sum of four subsequent natural odd numbers equals 376. What are these numbers? Rearrange the appropriate equation and solve it.

Task 3
a) How much is the tenth triangular number? And the fourteenth one?

b) Calculate the sum of seventh, tenth, and the fourteenth triangular number.

The students work in pairs. They use the matches they have brought for the lesson. They are going to make the figures according to the rules and describe them by using the formulas.

Task 4
Look at the drawings.

Title: The squares of the matches

[illustration 1]

a)Make four squares in the presented way. How many matches will you need?

b) Make five squares in the presented way. How many matches will you need?

c) Write the algebraic expression describing the number of matches you need to construct n number of the squares.

Hint: Note, that to make any new square you need three matches (the fourth side belongs to the next square). We have to add another match when we want to finish our puzzle.

d)How many matches should be used to construct a hundred of squares in such a way?

Task 5
a) Make a polygon using five matches.

b) Add the matches in such a way the polygons you have made have the common side. Make the second and the third figure using that method. How many matches do the figures consist of?

c) Write down the algebraic expression describing the number of matches used to construct the n number of polygons.

d) Which figure will be made of 45 matches?

An extra task:
Find out on the Internet the information about the square numbers and their geometric interpretation.

a) Calculate the sum of the fifth, the seventh and the ninth square number.

b) Write down the algebraic expression describing  the sum of two subsequent square numbers.

Lesson summarymc71aafdfaf187ad6_1528450119332_0Lesson summary

The students do the summarising tasks.
Then they sum up the class drawing the conclusions to memorise:

- The even natural number can be described by using the algebraic expression 2n, where n means any natural number.mc71aafdfaf187ad6_1527752263647_0The even natural number can be described by using the algebraic expression 2n, where n means any natural number.

- The odd natural number can be described by using the algebraic expression 2n + 1,where n means any natural number.mc71aafdfaf187ad6_1527752256679_0The odd natural number can be described by using the algebraic expression 2n + 1,where n means any natural number.

Selected words and expressions used in the lesson plan

algebraic expressionalgebraic expressionalgebraic expression,

equationequationequation,

even numbereven numbereven number,

figurefigurefigure,

natural numbernatural numbernatural number,

odd numberodd numberodd number,

squaresquaresquare,

square numbersquare numbersquare number,

sumsumsum,

triangular numbertriangular numbertriangular number