Folding Geometric Shapes

Nets  A net is a two-dimensional figure that, when folded, forms a three-dimensional figure.

Identical Nets  Two nets are identical if they are congruent; that is, they are the same if you can rotate or flip one of them and it looks just like the other.

Nets for a Cube  A net for a cube can be drawn by tracing faces of a cube as it is rolled forward, backward, and sideways.  Using centimeter grid paper (downloadable), draw all possible nets for a cube.

Nets for a Cube  There are a total of 11 distinct (different) nets for a cube.

Nets for a Cube  Cut out a copy of the net below from centimeter grid paper (  Write the letters M,A,T,H,I, and E on the net so that when you fold it, you can read the words MATH around its side in one direction and TIME around its side in the other direction.  You will be able to orient all of the letters except one to be right-side up.

Nets for a Rectangular Prism  One net for the yellow rectangular prism is illustrated below. Roll a rectangular prism on a piece of paper or on centimeter grid paper and trace to create another net.

Another Possible Solution  Are there others?

Nets for a Regular Pyramid  Regular pyramid Tetrahedron - All faces are triangles Find the third net for a regular pyramid (tetrahedron)  Hint – Pattern block trapezoid and triangle

Nets for a Square Pyramid  Square pyramid Pentahedron - Base is a square and faces are triangles

Nets for a Square Pyramid  Which of the following are nets of a square pyramid?  Are these nets distinct?  Are there other distinct nets? (No)

Great Pyramid at Giza  Construct a scale model from net to geometric solid (downloadable*) Materials per student:  8.5” by 11” sheet of paper  Scissors  Ruler (inches)  Black, red, and blue markers  Tape * id2.html

Great Pyramid at Giza Directions  Fold one corner of the paper to the opposite side. Cut off the extra rectangle. The result is an 8½" square sheet of paper.  Fold the paper in half and in half again. Open the paper and mark the midpoint of each side. Draw a line connecting opposite midpoints. 4 ¼” 8 ½”

More Great Pyramid Directions  Measure 3¼ inches out from the center on each of the four lines. Draw a red line from each corner of the paper to each point you just marked. Cut along these red lines to see what to throw away.  Draw the blue lines as shown

Great Pyramid at Giza Scale Model  Print your name along the based of one of the sides of the pyramid.  Fold along the lines and tape edges together.

Creating Nets from Shapes  In small groups students create nets for triangular (regular) pyramids ( es/ _M1MUTM18.pdf), square pyramids, rectangular prisms, cylinders, cones, and triangular prisms. Materials needed – Geometric solids, paper (plain or centimeter grid), tape or glue Questions for students: How many vertices does your net need? How many edges does your net need? How many faces does your net need? Is more than one net possible?

GPS Addressed  M6M4 Find the surface area of cylinders using manipulatives and constructing nets Compute the surface area of cylinders using formulae Solve application problems involving surface area of cylinders  M6A2 Use manipulatives or draw pictures to solve problems involving proportional relationships  M6G2 Compare and contrast right prisms and pyramids Compare and contrast cylinders and cones Construct nets for prisms, cylinders, pyramids, and cones  M6P3  Organize and consolidate their mathematical thinking through communication  Use the language of mathematics to express mathematical ideas precisely

Websites for Additional Exploration  Equivalent Nets for Rectangular Prisms 7_geometry.pdf 7_geometry.pdf  Nets ls/6.html ls/6.html  ESOL On-Line Foil Fun nstream/classroom/units/foil_fun/home_e.php