Topicm508f820b9cacf18f_1528449000663_0Topic

The area of the deltoid and the regular hexagon

Levelm508f820b9cacf18f_1528449084556_0Level

Second

Core curriculumm508f820b9cacf18f_1528449076687_0Core curriculum

2) uses the formulas to calculate the area of the triangle, the rectangle, the square, the parallelogram, the rhombus and the trapezoid; is able to determine the lengths of line segments in tasks of comparable difficulty:

a) calculate the shortest altitude of the right triangle whose sides are: 5 cm, 12 cm and 13 cm

b) The diagonals of the rhombus ABCD are AC = 8 dm i BD = 10 dm. The diagonal BD is extended to point E in such a way that the line segment BE is twice as long as this diagonal. Calculate the area of the triangle CDE (There are two possible answers.)

Timingm508f820b9cacf18f_1528449068082_0Timing

45 minutes

General objectivem508f820b9cacf18f_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm508f820b9cacf18f_1528449552113_0Specific objectives

1. Calculating the area of the deltoid and the regular hexagon.

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

Learning outcomesm508f820b9cacf18f_1528450430307_0Learning outcomes

The student:

- calculates the area of the deltoid and the regular hexagon.

Methodsm508f820b9cacf18f_1528449534267_0Methods

1. Discussion.

2. Flipped classroom method.

Forms of workm508f820b9cacf18f_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm508f820b9cacf18f_1528450127855_0Introduction

The teacher informs the students that during this class they will learn the formula for the area of the deltoid and the regular hexagon.

Using the internet resources, the students revise the information about the deltoid, especially the way of constructing it.

Procedurem508f820b9cacf18f_1528446435040_0Procedure

Students work individually using computers. Their task is to determine the formula for the area of the deltoid.

[Geogebra applet]

Students write down the following conclusion:

The area of the deltoid is equal to half the product of its diagonals.

Task:

Students calculate the area of the deltoid whose diagonals are 2 dm and 34 cm.

Task:

Students calculate the length of the diagonal of the deltoid whose area is 48 cmIndeks górny 2² and the other diagonal is 8 cm.

Discussion: what type of figures does the regular hexagon consist of?

Task:

Students calculate the area of the regular hexagon whose side is a.

Conclusion:

The area of the regular hexagon whose side is a, is expressed with the following formula:

$P=\frac{3\sqrt{3}}{2}{a}^2$

Task:

Students calculate the area of the regular hexagon whose perimeter is $18\sqrt{3}cm$.

An extra task:

Calculate the length of the shorter diagonal of the regular hexagon whose side is 5 cm.

Lesson summarym508f820b9cacf18f_1528450119332_0Lesson summary

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

The area of the deltoid is equal to half the product of its diagonals.

The area of the regular hexagon whose side is a, is expressed with the following formula:

$P=\frac{3\sqrt{3}}{2}{a}^2$.

Selected words and expressions used in the lesson plan

deltoiddeltoiddeltoid

regular hexagonregular hexagonregular hexagon

regular polygonregular polygonregular polygon

the area of the deltoidthe area of the deltoidthe area of the deltoid

the area of the polygonthe area of the polygonthe area of the polygon

the area of the regular hexagonthe area of the regular hexagonthe area of the regular hexagon