Topicm15720c13a4eab9d8_1528449000663_0Topic

The volumevolumevolume of the cuboidcuboidcuboid

Levelm15720c13a4eab9d8_1528449084556_0Level

Second

Core curriculumm15720c13a4eab9d8_1528449076687_0Core curriculum

XI. Calculations in geometry. The student:

5) calculates the volumevolumevolume and the area of the cuboidcuboidcuboid knowing the lengthlengthlength of the edges;

6) uses the units of volume and capacity: millilitre, litre, cmIndeks górny 3³, dmIndeks górny 3³, mIndeks górny 3³.

Timingm15720c13a4eab9d8_1528449068082_0Timing

45 minutes

General objectivem15720c13a4eab9d8_1528449523725_0General objective

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

Specific objectivesm15720c13a4eab9d8_1528449552113_0Specific objectives

1. Calculating the volume of the cuboidvolume of the cuboidvolume of the cuboid and the cubecubecube.

2. Solving the tasks in practical contexts which require calculating the volume of the cuboid and converting the units.

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

Learning outcomesm15720c13a4eab9d8_1528450430307_0Learning outcomes

The student:

- calculates the volume of the cuboid and the cube knowing the length of its edges,

- describes in English the tasks which are required to calculate the volume of the cuboid.

Methodsm15720c13a4eab9d8_1528449534267_0Methods

1. Mind map.

2. Situational analysis.

Forms of workm15720c13a4eab9d8_1528449514617_0Forms of work

1. Individual work.

2. Class work.

Lesson stages

Introductionm15720c13a4eab9d8_1528450127855_0Introduction

The students use the brainstorming method to revise the basic properties of the cuboidcuboidcuboid and the cubecubecube and the most popular units of volumevolumevolume. They also point out the objects in the shape of cuboidcuboidcuboid which exist around them.

The cuboidcuboidcuboid is a spatial figure whose all faces are rectangles.

The cubecubecube is a cuboidcuboidcuboid with all equal edges.

The main units of volumevolumevolume are presented below:

- 1 cubic millimetre (1 mmIndeks górny 3³),

- 1 cubic centimetre (1 cmIndeks górny 3³),

- 1 cubic decimetre (1 dmIndeks górny 3³),

- 1 cubic metre (1 mIndeks górny 3³),

- 1 millilitre,

- 1 litre.

The teacher introduces the topic of the lesson: calculating the volume of the cuboidvolume of the cuboidvolume of the cuboid and the cubecubecube and solving tasks using this skill.

Procedurem15720c13a4eab9d8_1528446435040_0Procedure

The students look at the interactive illustration to revise the method for calculating the volume of the cuboidvolume of the cuboidvolume of the cuboid.

[Interactive illustration]

Task

Put on 3 D glasses and watch the animation. After watching it answer the following question: How many blocks is the cuboidcuboidcuboid made of ?

On the basis of their observations the students draw the following conclusion:

To calculate the volume cuboid of the we multiply its dimensions: the length, the width and the height.m15720c13a4eab9d8_1527752256679_0To calculate the volume cuboid of the we multiply its dimensions: the length, the width and the height.

[Illustration 1]

The volume of the figure is represented with the letter V.
The cube is a cuboid so we calculate its volume in the same way as we calculate the volume of the cuboid. The edges coming out of one vertex of the cube are equal.
The volume of the cube equals the cube of the length of its edges.m15720c13a4eab9d8_1527752263647_0The volume of the figure is represented with the letter V.
The cube is a cuboid so we calculate its volume in the same way as we calculate the volume of the cuboid. The edges coming out of one vertex of the cube are equal.
The volume of the cube equals the cube of the length of its edges.

[Illustration 2]

The students calculate and compare the volumevolumevolume of the cuboids.

Task
Calculate the volume the cuboids below and answer the following questions.m15720c13a4eab9d8_1527712094602_0Calculate the volume the cuboids below and answer the following questions.

[Illustration 3]

Which of the cuboids has a smaller volumevolumevolume? What is the difference in their volumes?

What is the difference between the cuboids?

What is the sum of the volumes both cuboids?

Students calculate the volume of the cubevolume of the cubevolume of the cube knowing the sum of the lengthlengthlength of all its sides.

Task
Calculate the volume of the cube, if the sum of the length of all its edges is 72 cm.

The students calculate the volume of the cuboidvolume of the cuboidvolume of the cuboid and convert the units.

Task
A container with dimensions of: 60 cm, 80 cm, 50 cm was filled with water. How many liters of water were used?

Students calculate the volume of the cubevolume of the cubevolume of the cube knowing the lengthlengthlength of its edges and calculate the lengthlengthlength of the edges of the cube knowing its volumevolumevolume.

Task
Complete the following sentences:

a) The volume of the cubevolume of the cubevolume of the cube with the edge of 5 m is … mIndeks górny 3³.

b)The edge of the cubecubecube with volumevolumevolume of 8 dmIndeks górny 3³ is … dm long.

c) The volume of the cubevolume of the cubevolume of the cube with the edge of 40 cm is … dmIndeks górny 3³.

d) The edge of the cubecubecube with volumevolumevolume of $\frac{27}{64}$ litre is … dm long.

Self‑study work:
Heavy rain flooded the basement. The room was 4 m long and 3 m wide. The level of water reached 25 cm.

a) How many litres was poured into the basement?

b) How many buckets with the capacitycapacitycapacity of 12 litres can be filled with water?

Lesson summarym15720c13a4eab9d8_1528450119332_0Lesson summary

Students do the exercises summarizing the class.

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

- To calculate the volume the cuboid you should multiply its dimensions: the length, the width, the height.
- The volume of the figure is represented with the letter V.
- The cube is a cuboid so we calculate its volume in the same way as we calculate the volume of the cuboid. The edges coming out of the vertex of the cube are equal.
- The volume of the cube equals the cube of the length of its edges.m15720c13a4eab9d8_1527712094602_0- To calculate the volume the cuboid you should multiply its dimensions: the length, the width, the height.
- The volume of the figure is represented with the letter V.
- The cube is a cuboid so we calculate its volume in the same way as we calculate the volume of the cuboid. The edges coming out of the vertex of the cube are equal.
- The volume of the cube equals the cube of the length of its edges.

Selected words and expressions used in the lesson plan

capacitycapacitycapacity

cubecubecube

cuboidcuboidcuboid

heightheightheight

lengthlengthlength

volumevolumevolume

volume of the cubevolume of the cubevolume of the cube

volume of the cuboidvolume of the cuboidvolume of the cuboid

widthwidthwidth