Geostrips – Quadrilaterals

  1. One of the constructions in front of you is a quadrilateral with only two equal sides. You can move its sides to add or take other characteristics. Using its shadow, can you draw a square?
  2. Use now the rigid rhombus. Can you use its shadow to draw a square?
  3. Use the rigid rhombus again. Can you use its shadow to draw an equilateral triangle?
  4. Use the flexible rhombus. Can you use its shadow to cast only one square from one of the internal holes?
  5. If you do that what is the shape shown by the other holes?
  6. Can you make four squares using the holes?

Geostrips – Lines

  1. Use the flexible construction.

a)Make the two big strips parallel and their shadows parallel

b)Make the two big strips parallel and their shadows not parallel

c)Make the two big strips non parallel and their shadows parallel

  1. Use the two yellow strips construction.

a)Make their shadows perpendicular

b)See if you can make the light passing through the hole make an equilateral triangle

  1. Use the two blue strips construction. Make the light passing through the hole turn into:

a)An equilateral triangle

b)A rectangular triangle

c)A rectangular and isosceles triangle

Foam Solids

  1. Sphere – what is the geometric shape of its shadow? Can you make a different shape?
  2. Cylinder – What shapes can its shadow form? Can one of them be a kite (two pairs of consecutive sides equal)?
  3. Chose one solid (neither the sphere or the cylinder) whose shadow can make a kite. Indicate the conditions related to its position to the light so we can have a kite.
  4. Which of the solids make a shadow square and on what conditions?
  5. Which of the solids make a circle-shadow and on what condition?

Frameworks – platonic solids

  1. Connect two of the triangles.
  2. Verify that you cannot close anything with only two triangles. They just turn around one the other.
  3. Join a third triangle so that it closes around a vertex.
  4. Join another triangle and close totally.
  5. Construct a 3D-figure by joining (and closing) 4 triangles around vertices.
  6. Construct a 3D-figure by joining (and closing) 5 triangles around vertices.
  7. What do you think each of the three 3D figures shadows will be when placed directly below the light?
  8. Check it out!

Frameworks – platonic solids

  1. Connect two of the triangles.
  2. Verify that you cannot close anything with only two triangles. They just turn around one the other.
  3. Join a third triangle so that it closes around a vertex.
  4. Join another triangle and close totally.
  5. Construct a 3D-figure by joining (and closing) 4 triangles around vertices.
  6. Construct a 3D-figure by joining (and closing) 5 triangles around vertices.
  7. What do you think each of the three 3D figures shadows will be when placed directly below the light?
  8. Check it out!

Geoboards

  1. In one of the geoboards, you have two long parallel lines. How can you make the parallel lines produce non-parallel shadows? And what are the conditions for that happening?
  2. In another geoboard, you have two long non-parallel lines. How can you make them produce two parallel shadows and on what conditions?
  3. In another geoboard, you have two perpendicular lines. How can you make non-perpendicular shadows (conditions?)?
  4. In yet another geoboard, you can find two non-perpendicular lines. How can you make the shadows perpendicular?

Frameworks – big pyramid

  1. Place the construction on the table.
  2. See all the different shapes that are formed by light and shadow.
  3. What is the most symmetric shape you can get?

Solids to construct

  1. Choose one of the nets to construct a solid.
  2. Imagine that light is being projected on the solid.
  3. Conjecture what shapes can the shadows have and write them down.
  4. Construct the solid.
  5. Verify your conjecture.
  6. Write down every shape that you have not anticipated.

Escher’s nets

  1. Choose one of the nets to construct a solid.
  2. Imagine that light is being projected on the solid.
  3. Conjecture what shapes can the shadows have and write them down.
  4. Construct the solid.
  5. Verify your conjecture.
  6. Write down every shape that you have not anticipated.

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