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Building Solids using Unit Cubes
  Learning Outcomes:
  In this lesson, you will learn to
  • build solids with unit cubes
  • count the number of unit cubes in a solid
  • create a 3-D structure using cubes




Integrating Mathematics with Art
Mrs Cynthia Seto / Master Teacher
Academy of Singapore Teachers
Main Menu
1    Introduction: A cube
2    Same number of cubes with different arrangements
3    Count the number of unit cubes
4    Build your own solids
5    Hidden Unit Cube
6    Practice 1
7    Practice 2
8    Practice 3
9    How many more unit cubes are needed?
10   Real-life designs based on cubes
11   Create your own 3-D design based on cubes
Introduction: A cube
This is a cube.
A single cube is called a unit cube.



                                  face




                             edge
Same number of units cubes
     with different arrangements




Did you notice that all these solids are made of
3 unit cubes but they are arranged differently?
Count the number of unit cubes
How many unit cubes are used to build this solid?




                 7 unit cubes
Build Your Own Solids
Use 4 unit cubes to build as many different solids as
you can. You may use Lego bricks (if you have them at
home) or click on the url below to build your solids.
    http://illuminations.nctm.org/ActivityDetail.aspx?ID=125




  Once you are
  at this website,
  click on this to
  learn how to use
  the tools to
  build your solid.

Source:
NCTM Illuminations
How well have I done?
Click on the screen capture or the yellow box below to do a self-assessment
of how well you have done in building different solids with 4 cubes.

             Self Assessment on “Build Your Own Solids”
Hidden unit cube




Did you notice that 1 unit cube is hidden?
How many unit cubes are used to build this solid?

             4 unit cubes
Practice 1




How many unit cubes are used to build this solid?

   8 unit cubes    11 unit cubes   19 unit cubes
Practice 2




How many unit cubes are used to build this solid?

 9 unit cubes    10 unit cubes   12 unit cubes
Practice 3




How many unit cubes are used to build this solid?

  37        39        40        41
How many more unit cubes are needed?




                              ? cubes




 Post your answer and explain your strategy to
 your class online forum or blog. After that,
 review your partner’s strategy in working out
 his/her answer.
A gentle reminder to return to this online lesson to watch a video
on how cubes are used in real-life designs.
Real-life Designs based on Cubes
Click on this picture below to
watch a video on cube tower
Create your 3-D Design based on Cubes
In your group, form your own cubes or collect
boxes that are in the shape of a cube to build
a 3-D design during your Art lesson.

Take a digital photo and then upload it for
art appreciation of each group’s design.
Congratulations!
   By completing this online lesson,
you have demonstrated self-leadership.

 Do the online quiz (only 6 questions)
 and then you will be awarded with a
  Certificate of Achievement.
Great! You have
considered the 3 hidden cubes.
Please Count Again!
You have left out the
  3 hidden cubes.
Please Count Again!
  You have counted the
number of faces instead of
  the number of cubes.
Great Job!




 12 unit cubes are used to build this solid.
Did you count them one by one or did you count
in this way: There are 6 rows. There are 2 cubes
in each row. So, 6 x 2 = 12.
Consider these in your counting ?
 How many cubes are there in one row?
 How many rows are there in this solid?
Try Again!




Study the arrangement of this solid, eg look at
the number of unit cubes in a row and the
number of rows etc
Bravo!




I have counted them in this way:
There are 7 rows of 4 cubes, 3 rows of 3 cubes and
a group of 4 cubes.
So, (7 x 4) + (3 x 3 ) + 4 = 41

Did you do it in this way?

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Building solids using unit cubes

  • 1. Building Solids using Unit Cubes Learning Outcomes: In this lesson, you will learn to • build solids with unit cubes • count the number of unit cubes in a solid • create a 3-D structure using cubes Integrating Mathematics with Art Mrs Cynthia Seto / Master Teacher Academy of Singapore Teachers
  • 2. Main Menu 1 Introduction: A cube 2 Same number of cubes with different arrangements 3 Count the number of unit cubes 4 Build your own solids 5 Hidden Unit Cube 6 Practice 1 7 Practice 2 8 Practice 3 9 How many more unit cubes are needed? 10 Real-life designs based on cubes 11 Create your own 3-D design based on cubes
  • 3. Introduction: A cube This is a cube. A single cube is called a unit cube. face edge
  • 4. Same number of units cubes with different arrangements Did you notice that all these solids are made of 3 unit cubes but they are arranged differently?
  • 5. Count the number of unit cubes How many unit cubes are used to build this solid? 7 unit cubes
  • 6. Build Your Own Solids Use 4 unit cubes to build as many different solids as you can. You may use Lego bricks (if you have them at home) or click on the url below to build your solids. http://illuminations.nctm.org/ActivityDetail.aspx?ID=125 Once you are at this website, click on this to learn how to use the tools to build your solid. Source: NCTM Illuminations
  • 7. How well have I done? Click on the screen capture or the yellow box below to do a self-assessment of how well you have done in building different solids with 4 cubes. Self Assessment on “Build Your Own Solids”
  • 8. Hidden unit cube Did you notice that 1 unit cube is hidden? How many unit cubes are used to build this solid? 4 unit cubes
  • 9. Practice 1 How many unit cubes are used to build this solid? 8 unit cubes 11 unit cubes 19 unit cubes
  • 10. Practice 2 How many unit cubes are used to build this solid? 9 unit cubes 10 unit cubes 12 unit cubes
  • 11. Practice 3 How many unit cubes are used to build this solid? 37 39 40 41
  • 12. How many more unit cubes are needed? ? cubes Post your answer and explain your strategy to your class online forum or blog. After that, review your partner’s strategy in working out his/her answer. A gentle reminder to return to this online lesson to watch a video on how cubes are used in real-life designs.
  • 13. Real-life Designs based on Cubes Click on this picture below to watch a video on cube tower
  • 14. Create your 3-D Design based on Cubes In your group, form your own cubes or collect boxes that are in the shape of a cube to build a 3-D design during your Art lesson. Take a digital photo and then upload it for art appreciation of each group’s design.
  • 15. Congratulations! By completing this online lesson, you have demonstrated self-leadership. Do the online quiz (only 6 questions) and then you will be awarded with a Certificate of Achievement.
  • 16. Great! You have considered the 3 hidden cubes.
  • 17. Please Count Again! You have left out the 3 hidden cubes.
  • 18. Please Count Again! You have counted the number of faces instead of the number of cubes.
  • 19. Great Job! 12 unit cubes are used to build this solid. Did you count them one by one or did you count in this way: There are 6 rows. There are 2 cubes in each row. So, 6 x 2 = 12.
  • 20. Consider these in your counting ? How many cubes are there in one row? How many rows are there in this solid?
  • 21. Try Again! Study the arrangement of this solid, eg look at the number of unit cubes in a row and the number of rows etc
  • 22. Bravo! I have counted them in this way: There are 7 rows of 4 cubes, 3 rows of 3 cubes and a group of 4 cubes. So, (7 x 4) + (3 x 3 ) + 4 = 41 Did you do it in this way?