Topicm41605bb25811d3f0_1528449000663_0Topic

Geometric problems

Levelm41605bb25811d3f0_1528449084556_0Level

Second

Core curriculumm41605bb25811d3f0_1528449076687_0Core curriculum

XI. Calculations in geometry. Student:

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

5) calculates the volume and area of the cuboid with given edge lengths.

Timingm41605bb25811d3f0_1528449068082_0Timing

45 minutes

General objectivem41605bb25811d3f0_1528449523725_0General objective

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

Specific objectivesm41605bb25811d3f0_1528449552113_0Specific objectives

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

2. Consolidation and expanding knowledge of flat (2D) and spatial figures (3D).

3. Performing simple geometric calculations.

Learning outcomesm41605bb25811d3f0_1528450430307_0Learning outcomes

The student:

- consolidates and expands his/ her knowledge of flat (2D) and spatial figures (3D),

- performs simple geometric calculations.

Methodsm41605bb25811d3f0_1528449534267_0Methods

1. Discussion.

2. Puzzle Circle.

Forms of workm41605bb25811d3f0_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm41605bb25811d3f0_1528450127855_0Introduction

Prior to the lesson, at home, the students were supposed to review their knowledge of the flat and spatial figures.

The lesson starts with a mini‑test. Students work individually. Their task is to complete the classification of quadrangles with examples of appropriate figures.

[Geogebra applet]

The test ends with peer assessment, discussion of results and clarification of doubts.

Procedurem41605bb25811d3f0_1528446435040_0Procedure

The teacher informs students about the aim of the lesson – consolidation and expanding knowledge flat and spatial figures.

Discussion - How to review information in geometry in the most effective way?

Conclusions students can draw:

- the most important geometric formulas have to be memorizedm41605bb25811d3f0_1527752256679_0the most important geometric formulas have to be memorized,
- it is good to learn in a group,
- it is good to use computer self‑checking tests,
- all the necessary information can be found in the textbooks available online.m41605bb25811d3f0_1527712094602_0all the necessary information can be found in the textbooks available online.

Students are divided into four groups. They will take part in the „mysterious password” game.

Each group receives a set of tasks to solve. Tasks should be solved in writing. Each correct answer is assigned a letter or a group of letters. The letters received should be entered in the indicated blank spaces, prepared by the teacher. Letters form a common „mysterious password”.

A table for entering letters.

[Table]

Task fo group 1

Task 1
The sum of angles  $\alpha$ and $\beta$ is equal

1. 105 - TY
2. 110 - AT

Task 2
The wall has the shape of a rectangular trapezoid with a base length of 4 m and 6 m. To paint this wall, 3 paint cans were used. The paint can is enough to paint 5mIndeks górny 2² of surface. Calculate the height of the wall.

1. 3 m - E
2. 4 m - P

Tasks for group 2

Task 3
How many triangles are there in the drawing?

1. 2 - TY
2. 3 - A

[Illustration 1]

Task 4
On the plan drawn on a scale of 1: 2,500, the distance from Anka's house to Danka's house is 5 cm. How many metres divides Anka's house from Danka's house?

1. 125 m - M
2. 1250 m - EK

Task for group 3

Task 5
The CE section has a length of 16. The CD and AB sections are equal. The length of the CD section is therefore equal

1. 8 - A
2. 4 - WI

[Illustration 3]

Task 6
The surface area of the cube is equal to 96 cmIndeks górny 2². Calculate the volume of this cube.

1. 16 cmIndeks górny 3³ - A
2. 64 cmIndeks górny 3³ - K

Tasks for group 4

Task 7
An empty vessel in the shape of a rectangular prism, similar to the one in the drawing, was filled with water to the half of the height. Calculate how many litres of water were poured into the vessel.

1. 18 l - A
2. 36 l - E

[Illustration 4]

Task 8
The diamond area is 24. One of the diagonals is 8. The length of the second diagonal is

1. greater than 5 - M
2. less than 5 - PR

Students read the received password - MATHEMATICS. The teacher evaluates their work, explains the doubts.

An extra task:
In a given polygon, each angle has a measure of 1440°, and each side has a length of 10. Calculate the perimeter of this polygon.

Lesson summarym41605bb25811d3f0_1528450119332_0Lesson summary

Students do the revision exercises.

Together, they summarize the lesson and formulate the conclusions to remember:

- the most important geometric formulas have to be memorized,
- it is good to learn in a group,
- it is worth using computer self‑checking tests,
- all the necessary information can be found in e‑textbooks.

Selected words and expressions used in the lesson plan

angleangleangle

cubecubecube

geometrygeometrygeometry

parallelogramparallelogramparallelogram

perimeterperimeterperimeter

revisionrevisionrevision

rhombusrhombusrhombus

scalescalescale

surface areasurface areasurface area

volumevolumevolume