Topicmdc20ea4c01735001_1528449000663_0Topic

The area of the cuboidcuboidcuboid

Levelmdc20ea4c01735001_1528449084556_0Level

Second

Core curriculummdc20ea4c01735001_1528449076687_0Core curriculum

XI. Calculations in geometry. The student:

3) uses the units of the area: mmIndeks górny 2², cmIndeks górny 2², dmIndeks górny 2², mIndeks górny 2², kmIndeks górny 2², are, hectare;

5) calculates the volume and the area of the cuboidcuboidcuboid knowing the length of its edges.

Timingmdc20ea4c01735001_1528449068082_0Timing

45 minutes

General objectivemdc20ea4c01735001_1528449523725_0General objective

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

Specific objectivesmdc20ea4c01735001_1528449552113_0Specific objectives

1. Calculating the area of the cuboidcuboidcuboid and the cubecubecube.

2. Solving tasks in practical contexts which require calculating the area of the cuboid.

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

Learning outcomesmdc20ea4c01735001_1528450430307_0Learning outcomes

The student:

- calculates the area of the cuboidcuboidcuboid and the cubecubecube,

- calculates the edge length knowing the total surface areasurface areasurface area of the cube.

Methodsmdc20ea4c01735001_1528449534267_0Methods

1. Situational analysis.

2. Brainstorming.

Forms of workmdc20ea4c01735001_1528449514617_0Forms of work

1. Individual work.

2. Class work.

Lesson stages

Introductionmdc20ea4c01735001_1528450127855_0Introduction

The students identify elements of the cuboidcuboidcuboid and the cubecubecube using the models below.

[Illustration 1]

Look at the models and match the following properties with the appropriate solid:

All edges are of the same length.

All faces are rectangles.

It has got six faces.

It has got twelve edges.

It has got eight vertices.

Three edges come out from each vertex.

The lateral faces are rectangles, but they are not the squares.

All faces are squares.

The teacher introduces the topic of the lesson: revising how to calculate the area of the cuboidcuboidcuboid and the cubecubecube.

Proceduremdc20ea4c01735001_1528446435040_0Procedure

Students watch the slideshow to revise how to calculate the area of the cuboidcuboidcuboid.

Task
Watch how to calculate the area of the faces of the cuboid and the area of the cuboidcuboidcuboid.

[slideshow 1]

The students answer the following questions:

- How many faces does the cuboid have?

- What rectangles does the net of the cuboidcuboidcuboid consist of?

- How do we calculate the area of the rectanglerectanglerectangle and the squaresquaresquare?

- How can we calculate the area of the total surface of the cuboid?

The students and the teacher draw the following conclusion:

We can calculate the area of the cuboidcuboidcuboid using the following formulas:

P = 2 ∙ (a ∙ b + a ∙ c + b ∙ c)

or

P = 2 ∙ a ∙ b + 2 ∙ a ∙ c + 2 ∙ b ∙ c

The area of the cuboid is the sum of the areas of all its faces.
P = P1 + P2 + P3 + P4 + P5 + P6mdc20ea4c01735001_1527752256679_0The area of the cuboid is the sum of the areas of all its faces.
P = P1 + P2 + P3 + P4 + P5 + P6

Task
The figure below consists of seven identical cuboids with the dimensions of 1 dm x 1 dm x 2 dm. Calculate how many dm2 of paint will be used to paint the figure once.

[Illustration 2]

Students watch the slideshow to revise the method for calculating the area of the cubecubecube.

Task

Revise the method for calculating the area of the cubecubecube.

[slideshow 2]

We calculate the area of the cube using the following formula:
P = 6 ∙ aIndeks górny 2²mdc20ea4c01735001_1527752263647_0We calculate the area of the cube using the following formula:
P = 6 ∙ aIndeks górny 2²

Task
Calculate the area of the cubecubecube, if the sum of lengths of all its edges is 120 cm.

A self‑study task
A rectangular‑shaped classroom has the following dimensions: the length of 10 m, the width of 6 m and the height of 3,2 m. There are the doors with the dimensions of 1,2 m x 2 m and three windows with the dimensions of 2 m x 1,8 m. The walls of the classroom (without the ceiling) will be painted twice. We use 1 liter of paint to cover 12mIndeks górny 2² of the surface. How many tins of paint should we buy if one tin contains 5 liters of liquid?

Lesson summarymdc20ea4c01735001_1528450119332_0Lesson summary

Students do the exercises summarizing the class.

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

1. To calculate the area of the cuboidcuboidcuboid you should add the areas of all its faces.

2. We can calculate the area of the cuboid using the following formulas:
P = 2 ∙ (a ∙ b + a ∙ c + b ∙ c) or P = 2 ∙ a ∙ b + 2 ∙ a ∙ c + 2 ∙ b ∙ c, where a, b and c are the dimensions of the cuboidcuboidcuboid.

3. We calculate the area of the cubecubecube using the formula: P = 6 ∙ aIndeks górny 2², where a is the length of the edge of the cube.

Selected words and expressions used in the lesson plan

area of rectanglearea of rectanglearea of rectangle

area of squarearea of squarearea of square

base areabase areabase area

cubecubecube

cuboidcuboidcuboid

face areaface areaface area

lateral arealateral arealateral area

rectanglerectanglerectangle

squaresquaresquare

surface areasurface areasurface area