Topicm3eb836e07817d8e4_1528449000663_0Topic

The area of the cuboidcuboidcuboid and the cube

Levelm3eb836e07817d8e4_1528449084556_0Level

Second

Core curriculumm3eb836e07817d8e4_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 cuboid knowing the length of the edges.

Timingm3eb836e07817d8e4_1528449068082_0Timing

45 minutes

General objectivem3eb836e07817d8e4_1528449523725_0General objective

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

Specific objectivesm3eb836e07817d8e4_1528449552113_0Specific objectives

1. Calculating the area of the cuboid and the cube.

2. Solving the 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 outcomesm3eb836e07817d8e4_1528450430307_0Learning outcomes

The student:

- calculates the area of the cuboid and the cube,

- solves practical tasks connected with calculating the area of the cuboid and the cube.

Methodsm3eb836e07817d8e4_1528449534267_0Methods

1. Situational analysis.

2. Brainstorming.

Forms of workm3eb836e07817d8e4_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm3eb836e07817d8e4_1528450127855_0Introduction

The student brings a prism‑shaped, cardboard box to class and cuts it out along some of its edges to get the net of the prism.

The teacher introduces the topic of the lesson: learning about the area of the solid and finding out how to calculate the area of the cuboid and the cube.

Students point out the cuboids and the cubes among other models of the solids. They describe their construction and revise the calculation of the area of the rectanglerectanglerectangle and the squaresquaresquare.

The cuboid is a spatial figure whose all faces are rectangles.
The cubecubecube is a cuboid with all equal edges.
The area of the rectangle equals the product of its two adjacent sides.
The area of the square equals the product of its two adjacent sides.

Procedurem3eb836e07817d8e4_1528446435040_0Procedure

Students watch the slideshow to find out how to calculate the area of the specified faces of the cuboidcuboidcuboid and the total surface areasurface areasurface area of the cuboid.

[slideshow]

Task 1

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

The students and the teacher draw the following conclusion:

The area of the total surface areasurface areasurface area of the cuboid equals the sum of the areas of all its faces.

Each student sticks the net of the cuboid he has brought into his notebook. He measures the length of appriopriate segments and calculates the area of the cuboid.

Task 2

Stick the net of the cuboidcuboidcuboid into your notebook. Measure the length of the edges. Calculate the area of each face. Then, calculate the area of the cuboid.

The area of the cuboid is the sum of the areas of all its faces.m3eb836e07817d8e4_1527752256679_0The area of the cuboid is the sum of the areas of all its faces.

[Illustration1]

Students calculate the area of the cuboidcuboidcuboid knowing the areas of three different faces.

Task 3

The drawing below shows the areas of some faces of the cuboid. Calculate the area of the cuboid.

[Illustration2]

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

or

[Illustration3]

Students watch different nets of the cubecubecube and answer the following questions.

Task 4

Here is the net of a cube below. Look at it carefully and answer the following questions.

[Illustration4]

What figures are the faces of the cube?

How many faces are there in the cube?

What is the area of one face of the cube?

How large is the area of the cube?

The students and the teacher draw the following conclusion:

We can calculate the area of the cube with the edge length a by using the formula:m3eb836e07817d8e4_1527752263647_0We can calculate the area of the cube with the edge length a by using the formula:

[Illustration5]

An extra task:

Parents want to paint the walls and the ceiling in the cuboid‑shaped room with the length of 4m, the width of 3,5m and the height of 2,5m. How many square meters will be painted, if the area of the door and the window equals  3,8 mIndeks górny 2²?

Lesson summarym3eb836e07817d8e4_1528450119332_0Lesson summary

Students do the exercises summarizing the class.

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

- The area of the cuboid is the sum of the areas of all its faces. $P=P_1+P_2+P_3+P_4+P_5+P_6$.

- We can also calculate the area of the cuboid using the following formulas: $P=2·(a·b+a·c+b·c)$
or $P=2·a·b+2·a·c+2·b·c$ a, b and c are the dimensions of the cuboid.

- We can calculate the area of the cubecubecube by using the formula: $P=6·a^2$, where a is the length of the cube edge.

Selected words and expressions used in the lesson plan

cuboidcuboidcuboid

cubecubecube

surface areasurface areasurface area

base areabase areabase area

face areaface areaface area

lateral arealateral arealateral area

rectanglerectanglerectangle

squaresquaresquare

rectangle arearectangle arearectangle area

square areasquare areasquare area