Topicmca3890eea6d3f17a_1528449000663_0Topic

Solving word problems – a cuboid

Levelmca3890eea6d3f17a_1528449084556_0Level

Second

Core curriculummca3890eea6d3f17a_1528449076687_0Core curriculum

XI. Calculations in geometry. Student:

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

Timingmca3890eea6d3f17a_1528449068082_0Timing

45 minutes

General objectivemca3890eea6d3f17a_1528449523725_0General objective

Drawing a mathematical model for a simple situation and building it in various contexts, also in a practical context.

Specific objectivesmca3890eea6d3f17a_1528449552113_0Specific objectives

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

2. The use of cuboid properties in geometric and practical problems.

3. Developing the skills of calculating the surface areasurface areasurface area and volume of a cuboid.

Learning outcomesmca3890eea6d3f17a_1528450430307_0Learning outcomes

The student:

- the student uses the properties of a cuboidcuboidcuboid in geometrical and practical tasks,

- the student solves word problems in which he/she calculates the total surface area and volume of a cuboid.

Methodsmca3890eea6d3f17a_1528449534267_0Methods

1. Conceptual hooks.

2. Controlled discussion.

Forms of workmca3890eea6d3f17a_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmca3890eea6d3f17a_1528450127855_0Introduction

The students review the most important terminology related to the rectangular prism with the „conceptual hooks” method.

The teacher point to a volunteer student. This student chooses from his „list of hooks” words that other students should associate with the relevant concepts of a rectangular prism. For example, the student says - cherry, the students answer - the apex. The student says - bridge, students answer - diagonaldiagonaldiagonal, etc.

The teacher informs that the aim of the lesson will be to develop and systematize knowledge and skills related to the cuboidcuboidcuboid.

Proceduremca3890eea6d3f17a_1528446435040_0Procedure

Students work in groups using their group instructions.

They solve tasks by checking the correctness of results on sheets attached to the board. If they correctly solved the task - they set 1 point. If they made a mistake they score (-1) point.

Instructions for group work:

High in the mountains Geometric Dragon lives alone. The dragon promised the prize to anyone who visited it. The uphill road is not easy. Different obstacles are awaiting the visitors. Try to overcome these obstacles and win the prize.

Obstacle 1

What is it?

- It is similar to a shoe box,
- it is similar to a book,
- it is an interesting object,
- it has four faces and two bases.

Obstacle 2

Draw any cuboidcuboidcuboid. Use the computer and applet now.

[Geogebra applet]

Mark on your drawing all the cuboid parts, mentioned in the applet. Give properties to these elements. Check the correctness of the solution every time.

Obstacle 3

Geometric Dragon always eats a rectangular cubecubecube of butter with dimensions of 2 dm·3 dm·4 dm for breakfast. Calculate the volumevolumevolume of this cube.

Obstacle 4

Geometric Dragon lives in the summer in Palace A, while in winter - in Palace B. Both palaces are built of identical cubic elements.

The dragon wants to cover the palace roofs with a gold sheet and the walls – with the silver one.
Which roof needs more metal?
Which palace needs less metal to cover its walls?

[Illustration]

Obstacle 5

In front of you there is a ditch, which contains 120 l of water. The ditch has a rectangular shape with a length of 0.5 m and a width of 0.4 m. Calculate the depth of this ditch.mca3890eea6d3f17a_1527752263647_0In front of you there is a ditch, which contains 120 l of water. The ditch has a rectangular shape with a length of 0.5 m and a width of 0.4 m. Calculate the depth of this ditch.

Obstacle 6

There is an aquarium on the side of the road. Goldfish swim in it. The aquarium has the shape of a cubecubecube with an edgeedgeedge length of 2 m. 
The dragon claims that the diagonaldiagonaldiagonal of the face of this cube is shorter than 400 cm. Justify that he is right.

Obstacle 7 - the last and the most difficult one

The dragon stores his hats in a box of 80 000 cmIndeks górny 3³. The base of this box is a square with a surface area of 16 dmIndeks górny 2². How much carton was used to make this box?mca3890eea6d3f17a_1527752256679_0The dragon stores his hats in a box of 80 000 cmIndeks górny 3³. The base of this box is a square with a surface area of 16 dmIndeks górny 2². How much carton was used to make this box?

If you received more than 4 points for solving the tasks, you have overcome all obstacles. You can visit the Geometric Dragon and win the prize.

The groups discuss the results of their work. The teacher explains the doubts.
Discussion - which tasks were the most difficult to solve and why.

Conclusion from the discussion:
In geometrical tasks, careful attention should be paid to the fact that all quantities used in a given calculation are presented in the same units.

The group who first solved all the tasks correctly receive a prize from the Geometric Dragon - for example, it can be very good grade.

An extra task:

EdgeedgeEdge lengths coming out of one vertex of a cuboidcuboidcuboid are expressed by consecutive integers. The volumevolumevolume of this cuboid is equal to 60. Calculate thesurface areasurface areasurface area of this cuboid.

Lesson summarymca3890eea6d3f17a_1528450119332_0Lesson summary

Students do the revision exercises.

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

- In geometrical tasks, pay careful attention to the fact that all the quantities used in a given calculation are presented in the same units.

Selected words and expressions used in the lesson plan

basebasebase

cubecubecube

cuboidcuboidcuboid

diagonaldiagonaldiagonal

edgeedgeedge

heightheightheight

lateral facelateral facelateral face

surface areasurface areasurface area

volumevolumevolume