# 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.

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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?

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)

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? Folding Circles to a ….

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.

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 Four Triangle problem

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? The Tangram problem (if time)

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