April 12: Today’s activities:
1. Fold a circle to a ….
2. Movie (& cutting)
3. Four triangle problem (three parts)
a. Making polygons
b. Same and different
c. Polygon designs
Time? Repeat four triangle with tangrams
April 12: Today’s posters
1. While you are working, ADD new terms
with simple sketch to the “Geometry
Words” poster.
2. While you are working, if you use a
CCSS practice, ADD a brief description
of how you used the practice to the
appropriate practice poster.
Folding Circles to a ….
• Cut out your circle
• Guess where the center of the circle is. Mark it.
• See if you can figure out a way to find the exact
center of the circle.
• Share / how close was your guess?
Folding Circles to a ….
• What do you call the crease you get when you
fold a circle in half?
• (diameter) Add to Geometry Words poster
• Mark a point on the circumference of the circle
and fold that point to the center point. What is
the new crease called?
• (chord)
Folding Circles to a ….
• Fold again to the center, using one endpoint of
the first chord as an endpoint of your new
chord.
• Fold the remaining arc to the center.
• What shape did you make?
• (equilateral triangle)
Folding Circles to a ….
• Can you figure out how to find the midpoint of
one of the sides of your equilateral triangle?
Mark it.
• Fold the opposite vertex to the midpoint. What
shape have you made?
• (isosceles trapezoid)
Folding Circles to a ….
• If the area of the original triangle is “1 triangular
unit”, what is the area of the isosceles
trapezoid?
Folding Circles to a ….
• Fold one of the three congruent triangles of the
trapezoid over the middle triangle. What shape
did you make?
• (rhombus)
• What is the area of the rhombus?
Folding Circles to a ….
• Fold the remaining triangle over the middle
triangle. What shape did you make?
• (equilateral triangle)
• What is the area of the triangle?
Folding Circles to a ….
• The small triangle is similar to the large (unit)
triangle we started with.
• How do the lengths of the sides of the two
triangles compare?
• (small is 1/2 the length of the unit edge)
• How do the areas of the triangles compare?
• (small is 1/4 the area of the unit area)
Folding Circles to a ….
• When the tips of the three folded over triangles
are brought together, a three dimensional
shapes is formed. What shape is it?
• (Tetrahedron / triangular pyramid)
Folding Circles to a ….
• What is the surface area of the tetrahedron?
Folding Circles to a ….
• Open back up to the unit triangle.
• Fold each vertex to center of the circle. What
shape have you made?
• (regular hexagon)
• What is the area of the regular hexagon?
Folding Circles to a ….
• Turn the hexagon over and shade it.
• Turn the figure back over, push gently towards
the center so the hexagon forms a truncated
tetrahedron. What is the surface area of the
truncated tetrahedron?
Another fun fold
Stepping through a piece of paper
CUT on alternating dashed lines
The more cuts, the bigger the hole
For kids, start with 3 cuts, then repeat with more
MOVIE: FLATLAND
Please cut out triangles
during the movie.
The Four Triangle problem
• Geometry words & practices posters (keep filling
in as we go)
Materials
• 20 of each color “1/2 square” triangles
• Kid Idea: Pass out only squares, have them cut
• Paper
• Glue and / or tape
The Four Triangle problem
Question 1: How many ways can you put two
triangles together following the rule that the sides
that touch must be the same length and match
exactly?
OK
NOT OK
NOT OK
• What shapes did you make? Tape & name.
• Share!
The Four Triangle problem
Question 2: How many ways can you put four
triangles together following the rule that the sides
that touch must be the same length and match
exactly? Use two of each color triangles.
• What different shapes did you make?
• Tape to your paper & name the shapes
• Add shapes/names to chart
• Share!
The Four Triangle problem
Question 3: Same and different
• Each team pick two different four-triangle
polygons (three different pairs)
Use your Same/Different table
• Describe how the polygons are the same and
how they are different in as many ways as you
can
• Share!
The Four Triangle problem
Question 4: Designs
• Each person pick one four-triangle polygon
• Trace the whole polygon on cardstock and cut it
out, mark one vertex
• Draw a dot in the middle of your paper
• Place the vertex on the dot and trace the
polygon
• Rotate, trace again until you have a fun picture
The Four Triangle problem
Question 4: Design Example
The Tangram problem (if time)
• Repeat the four triangle problem with tangrams
• What shape is each tangram piece?
• What shapes can you make with two pieces?
With three? With four? With five? With six?
With seven? (Use the rule: The sides that touch
must be the same length and match exactly)
• Pick several shapes, what is the same, what is
different?