Pyramid

Maria Hochpöchler, Math Teachers' Adventure of ICT Integration, Oct 2, 2017

In this book you learn about the pyramid, it's net and the calculation of it's surface.

Table of Contents

  1. Lesson Plan
    1. Lesson Plan PYRAMID
  2. Geometric solids
    1. Can you sort these geometric solids?
    2. Do you recognize the shape of these objects?
    3. Do you know the name of these solids?
    4. Do you know the name of the objects' shape?
    5. Find the solid matching the name
    6. Find the matching object
    7. Recognising solids
  3. Nets of geometric solids
    1. Which solid can be built from this net?
    2. Which net matches the displayed solid?
    3. Build the net of a prism
    4. Build net of a cube
    5. Build the net of a pyramid
  4. Basic terms: squared pyramid
    1. Basic terms for a pyramid
    2. Net of a pyramid
  5. Surface ares of a squared pyramid
    1. Lateral surface and surface of a squared pyramid

1.

Lesson Plan

  • 1. Lesson Plan PYRAMID

1.1.

Lesson Plan PYRAMID

Lesson Information
[table][tr][td]Subject: [/td][td]Mathematics[/td][/tr][tr][td]Grade Level:[/td][td]7[/td][/tr][tr][td]Duration:[/td][td]1 to 2 lessons[/td][/tr][tr][td]Technology setting:[/td][td][i]computer/ tablets for students, computer and projector for teacher[/i][/td][/tr][/table]
Topic
Pyramid - Recognising a pyramid and its net and calculate its surface area.
Learning Outcomes
Students know the characteristics of pyramids and are aware of the differences between a pyramid, a cube and a cuboid.[br]Students know how the nets of squared pyramids look like.[br]Students can calculate the surface area of a squared pyramid.
Lesson Objectives and Assessment
[u]Lesson Objectives[/u][br]Studens elaborate a mathematical problem on their own.[br][br][u]Assessment[br][/u]Review of the task "model of a pyramid" by the teacher.
Teaching Strategies
Sequence:[br][list][*]Introduction into GeoGebra (10 min)[br][br][/*][*]Students edit the worksheets in this book. ( 30 -50 min)[br](Starting with simple materials, since the students are not familiar with GeoGebra jet.)[br][br][/*][*]Next the students have to complete the task "model of a pyramid" (10 - 30 min)[br]Therefor they get one pyramid out of different models. [br]They have to measure it, make a graphic presentation, insert a suitable dimensioning, describe the pyramid and calculate its surface area. This task will be done during the lesson and will be evaluated by the teacher. [br]Practical relevance and the use of suitable measuring instruments are importent in this task.[br]Questions can be answered individually.[br][br][/*][*]Opportunity for differentiation: [br]additional models (f.i. pyramids with different bases)[/*][/list]
Technology Integration
This lesson plan can be used for students with no or little experience with GeoGebra,[br]since there is hardly any prior knowledge needed.[br]The worksheets are simple and self-explanatory in usage.[br]Students who have already had computer lessons, should not have problems with this technology setting.[br][br]If there are problems with this technology setting anyway, you have alternative options:[br][list=1][*]Team teaching: A second teacher can help to support students individually.[/*][*]Plenum: Worksheets that are to hard can be discussed with the whole class. Therefor the projector should be used.[br][/*][/list]
– Math Teachers' Adventure of ICT Integration, Maria Hochpöchler, Judith Hohenwarter

2.

Geometric solids

  • 1. Can you sort these geometric solids?
  • 2. Do you recognize the shape of these objects?
  • 3. Do you know the name of these solids?
  • 4. Do you know the name of the objects' shape?
  • 5. Find the solid matching the name
  • 6. Find the matching object
  • 7. Recognising solids

2.1.

Can you sort these geometric solids?

– GeoGebra Team German, GeoGebra Translation Team German

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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3.

Nets of geometric solids

  • 1. Which solid can be built from this net?
  • 2. Which net matches the displayed solid?
  • 3. Build the net of a prism
  • 4. Build net of a cube
  • 5. Build the net of a pyramid

3.1.

Which solid can be built from this net?

– GeoGebra Team, GeoGebra Team German, GeoGebra Translation Team German

3.2.

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3.3.

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3.4.

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3.5.

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4.

Basic terms: squared pyramid

  • 1. Basic terms for a pyramid
  • 2. Net of a pyramid

4.1.

Basic terms for a pyramid

Fulfill this tasks to get an overview of the basic terms used for a pyramid.[br][list][*][b][size=150]Write the following heading into your book "Squared pyramids"![/size][/b][/*][/list][list][*][b][size=150]Draw a sketch of a net of a squared pyramid![/size][/b][/*][/list][list][*][b][size=150]Label all impotant things as shown in the applet below![/size][/b][/*][/list]
– Sabrina Azesberger, Carolin Kern, Math Teachers' Adventure of ICT Integration, Maria Hochpöchler, lisa.fink

4.2.

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5.

Surface ares of a squared pyramid

Three tasks on the topic solids for secondary school.

  • 1. Lateral surface and surface of a squared pyramid

5.1.

Lateral surface and surface of a squared pyramid

Surface area of a squared pyramid
1. A squared pyramid with base line [i]a = 4cm[/i] and height [i]h = 5cm[/i] is given. [br]Calculate the lateral surface and the surface of the pyramid.[br][br]An arbitrary squared pyramid with base line [i]a[/i] and height [i]h[/i] is given.[br]1. Find a formula to calculate the area of [i]polygon 1[/i] and [i]2![/i][br]2. How do you get the lateral surface and the surface of the pyramid using [i]polygon 2[/i]?[br][br]
– Sabrina Azesberger, Carolin Kern, Math Teachers' Adventure of ICT Integration, Szyska

Information