Topicm161621063e6cefc9_1528449000663_0Topic

Calculation of Area or Perimeter of Quadrilaterals.

Levelm161621063e6cefc9_1528449084556_0Level

Second

Core curriculumm161621063e6cefc9_1528449076687_0Core curriculum

XI. Calculations in geometry. Student:

1) calculates the perimeter of a polygon with given side lengths;

2) calculates the areas of: a triangle, a square, a rectangle, a rhombus, a parallelogram, a trapezium, shown in the drawing and in practical situations, including data requiring conversion f units and in non‑standard dimensions, for example a triangle area with 1 km side and 1 mm height.

Timingm161621063e6cefc9_1528449068082_0Timing

45 minutes

General objectivem161621063e6cefc9_1528449523725_0General objective

Using simple, well‑known mathematical objects, interpreting mathematical expressions and manipulating mathematical objects.

Specific objectivesm161621063e6cefc9_1528449552113_0Specific objectives

1. Communicating in English, developing mathematical, scientific, technical and IT competences, developing learning skills.

2. Calculating the perimeter of quadrilaterals.

3. Calculating the area of quadrilaterals.

Learning outcomesm161621063e6cefc9_1528450430307_0Learning outcomes

The student:

1. Student calculates the perimeter of quadrilaterals.

2. Student calculates the area of quadrilaterals.

Methodsm161621063e6cefc9_1528449534267_0Methods

1. „Łańcuszek”

2. Didactic game.

Forms of workm161621063e6cefc9_1528449514617_0Forms of work

1. Group work.

2. Whole class.

3. Pair work.

Lesson stages

Introductionm161621063e6cefc9_1528450127855_0Introduction

Students use the „chain” method to review formulas for the perimeterperimeterperimeter and the areaareaarea of quadrilaterals. The “chain” starts with the random student, and then the students sitting next to him or her, give the appropriate formulas for the areaareaarea and perimeterperimeterperimeter of a given quadrilaterals. The quadrilaterals are indicated by the teacher who presents sample drawings.

[Illustration 1]

Procedurem161621063e6cefc9_1528446435040_0Procedure

The teacher informs students that the aim of the lesson is to calculate quadrilateralquadrilateralquadrilateral areas and perimeters.

Students work in pairs using a computer. The first student changes the position of the vertices of the quadrangle placed in the applet. The other student calculates the areaareaarea of the quadrilateralquadrilateralquadrilateral formed. Students write down their calculations and compare them with the results in the applet. Students take turns and continue with the whole procedure several more times.

[Geogebra applet]

Discussion - How to calculate the areaareaarea of a quadrilateralquadrilateralquadrilateral, which is not a trapezoid (thus neither a rectanglerectanglerectangle nor a parallelogramparallelogramparallelogram).

The students formulate their conclusions on the basis of the task performed.

Conclusions

The areaareaarea of any quadrilateralquadrilateralquadrilateral can be calculated by dividing it into smaller polygons or by supplementing it to larger polygons.

Students are divided into three teams. Each team chooses one player.

The players solve tasks that the teacher reads. If the student is not able to solve the task or solves it incorrectly - he / she drops out of the game. The team can help their player, but to do it they cannot use words. The team, that completes all the tasks first, wins.

Tasks for students

Task 1

The square and the rectangle have equal perimeters. The sides of the rectangle are 2 cm long and 4 cm long. Calculate the side length of the square.m161621063e6cefc9_1527752256679_0The square and the rectangle have equal perimeters. The sides of the rectangle are 2 cm long and 4 cm long. Calculate the side length of the square.

Task 2

If each side of the parallelogramparallelogramparallelogram is increased by 3, how much will its perimeterperimeterperimeter increase?

Task 3

The perimeterperimeterperimeter of a rectanglerectanglerectangle is 20. The length of this rectanglerectanglerectangle is 2 greater than its width. Calculate the areaareaarea of the rectanglerectanglerectangle.

Task 4

Maciej has a meadow in the shape of a parallelogramparallelogramparallelogram. One of the sides of this parallelogramparallelogramparallelogram is 40 m long. The height of this side is 25 m. Is the areaareaarea of this meadow more than 1 ha?

Task 5

Which trapeziumtrapeziumtrapezium has a larger area? How much larger?

[Illustration 2]

Task 6

The areaareaarea of the rectanglerectanglerectangle is equal to the area of the parallelogramparallelogramparallelogram shown in the figure. One of the sides of this rectanglerectanglerectangle is 6 dm long. Calculate the length of the other side.

[Illustration 3]

After the game, participants share their reflections on the tasks.

The teacher assesses the work of the groups, explains all doubts.

Task for volunteers
The square K has a side length of 32. We connect the centres of the sides of this square. A square KIndeks dolny 1₁ is created. We connect the centres of the sides of square KIndeks dolny 1₁ - a square KIndeks dolny 2₂ is created. We proceed in the same way until we get the square KIndeks dolny 6₆. Calculate the area of the square KIndeks dolny 6₆.m161621063e6cefc9_1527752263647_0Task for volunteers
The square K has a side length of 32. We connect the centres of the sides of this square. A square KIndeks dolny 1₁ is created. We connect the centres of the sides of square KIndeks dolny 1₁ - a square KIndeks dolny 2₂ is created. We proceed in the same way until we get the square KIndeks dolny 6₆. Calculate the area of the square KIndeks dolny 6₆.

Lesson summarym161621063e6cefc9_1528450119332_0Lesson summary

Students do the revision exercises.

Then they summarize the lesson together and formulate conclusions to remember.

- The areaareaarea of any quadrilateralquadrilateralquadrilateral can be calculated by dividing it into smaller polygons or by supplementing it to larger polygons.

Selected words and expressions used in the lesson plan

areaareaarea

parallelogramparallelogramparallelogram

perimeterperimeterperimeter

quadrilateralquadrilateralquadrilateral

rectanglerectanglerectangle

squaresquaresquare

trapeziumtrapeziumtrapezium