Topicm9ff3c3299921b70d_1528449000663_0Topic

The properties and the types of triangles

Levelm9ff3c3299921b70d_1528449084556_0Level

Second

Core curriculumm9ff3c3299921b70d_1528449076687_0Core curriculum

IX. Polygons and circles. The student:

1) recognises and identifies the acute, the right, the obtuse, the isosceles, the equilateral triangles.

Timingm9ff3c3299921b70d_1528449068082_0Timing

45 minutes

General objectivem9ff3c3299921b70d_1528449523725_0General objective

Matching a mathematical model to a simple situation and using it in various contexts, including practical ones.

Specific objectivesm9ff3c3299921b70d_1528449552113_0Specific objectives

1. Recognising and identifying the acute, right obtuse, isosceles, equilateral triangles.

2. Describing the properties of triangles.

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

Learning outcomesm9ff3c3299921b70d_1528450430307_0Learning outcomes

The student:

- recognises and identifies the acute, right, obtuse, isosceles, equilateral triangles,

- knows and uses the properties of the acute, right, obtuse, isosceles, equilateral triangles.

Methodsm9ff3c3299921b70d_1528449534267_0Methods

1. Flipped classroom.

2. Mind map.

Forms of workm9ff3c3299921b70d_1528449514617_0Forms of work

1. Individual work.

2. Whole‑class work.

Lesson stages

Introductionm9ff3c3299921b70d_1528450127855_0Introduction

Students prepare colourful markers, crayons and the following cardboard triangles:

- two with all acute angles,

- two with one right angle,

- two with obtuse angles.

All the things will be used while completing the summarising tasks.

Students are going to work using the flipped classroom method.

At home they become familiar with the material included in the e‑book:

https://www.epodreczniki.pl/reader/c/119603/v/latest/t/student‑canon/m/i5vfddYyU2 The types of triangles

Procedurem9ff3c3299921b70d_1528446435040_0Procedure

The teacher introduces the topic of the lesson: recognising and identifying various types of triangles.

Part 1

The students revise the basic properties of triangles: the triangle is a polygon with three sides and three angles. Triangles have different shape but they can be divided into three groups with similar features.m9ff3c3299921b70d_1527752263647_0the triangle is a polygon with three sides and three angles. Triangles have different shape but they can be divided into three groups with similar features.

On the basis of the material the students have studied they answer the following question:

What properties can we consider to classify triangles?

Task
Students work individually using their computers. They are going to watch different properties of triangles.

[Geogebra applet]

Task
The teacher divides the class into groups of 3 or 4 and gives each group large cardboard sheets. On the basis of the material they have studied at home students make a mind map illustrating the types of triangles.

Task
On the basis of the mind maps and the material they have studied so far students answer the following questions:

Is it possible for a triangle to have two right angles at the same time?

Is it possible for a triangletriangletriangle to have two obtuse angles at the same time?

Is it possible for a triangle to have the right and the obtuse angle at the same time?

Can the equilateral triangleequilateral triangleequilateral triangle have the right or the obtuse angle?

Is every equilateral triangletriangletriangle an isosceles one?

Is the triangle with the sides of: 3 cm, 4 cm, 3 cm an isosceles triangleisosceles triangleisosceles triangle?

Is the triangle with the angles of 50°, 50°, 50° an equilateral triangleequilateral triangleequilateral triangle?

Is the triangletriangletriangle with the angles of 45°, 45°, 90° an isosceles triangleisosceles triangleisosceles triangle?

Part 2

Selected students summarise the material they have learned by answering the following questions:

1) What are the types of triangles depending on the values of the angles?

2) What are the types of triangles depending on the length of the sides?

An extra task
Make a construction of the equilateral triangleequilateral triangleequilateral triangle using the compass. Use the Internet and the mathematical literature to find out how to construct it.

Lesson summarym9ff3c3299921b70d_1528450119332_0Lesson summary

Students do the exercises summarizing the class.

Then, together they sum up the classes, drawing conclusions to memorize:

Depending on the values of the angles we classify the triangles as:
- acute‑angled triangles with three acute angles,
- right‑angled triangles with one right and two acute angles,
- obtuse‑angled triangles with one obtuse and two acute angles.m9ff3c3299921b70d_1527752256679_0Depending on the values of the angles we classify the triangles as:
- acute‑angled triangles with three acute angles,
- right‑angled triangles with one right and two acute angles,
- obtuse‑angled triangles with one obtuse and two acute angles.

Depending on the lengths of the sides we classify the triangles as:
- equilateral triangles having three equal sides,
- isosceles triangles having two equal sides,
- scalene triangle having the sides of different length.m9ff3c3299921b70d_1527712094602_0Depending on the lengths of the sides we classify the triangles as:
- equilateral triangles having three equal sides,
- isosceles triangles having two equal sides,
- scalene triangle having the sides of different length.

Selected words and expressions used in the lesson plan

acute‑angled triangleacute‑angled triangleacute‑angled triangle

arm of trianglearm of trianglearm of triangle

base of trianglebase of trianglebase of triangle

equalityequalityequality

equilateral triangleequilateral triangleequilateral triangle

interior angleinterior angleinterior angle

isosceles triangleisosceles triangleisosceles triangle

obtuse‑angled triangleobtuse‑angled triangleobtuse‑angled triangle

right‑angled triangleright‑angled triangleright‑angled triangle

triangletriangletriangle