**Mod 2 M EXPLORE**

**Task A: (M A) SURFACE AREA & VOLUME **(see course page for .docx & PDF typing & writing outlines)

**Materials**

- 8.5” × 11” scratch paper, scissors, tape and a ruler and a compass (if you are fancy)
- Volume estimation fill such as rice, beans, popcorn, packing peanuts, pom-pom cotton balls or?

**Construction **

- Use 8.5” × 11” scratch paper, scissors and tape to make cylinder and prisms I, II, III and IV (below)
- The 8.5” × 11” paper is the faces of the prism; fold, align and tape without overlapping edges
- For each prism, make a base to hold the fill for #3. You can use a wrapping method (like plastic wrap on a bowl), or precisely measure and cut your base; your choice.

**A.1. Construction:** Construct figures I – IV as described.

**Figure I: Cylinder**

- Curl the 11” edge of the sheet into the circumference of the base of the cylinder.
- Label the paper with a large “
**I**”.

**Figure II: Square Prism **

- Crease a sheet of 8.5” × 11” paper, perpendicular to the 11” side, into four identical rectangles.
- Fold and tape the paper into the shape of a square prism.
- Label the paper with a large “
**II**”.

**Figure III: Equilateral Triangular Prism**

- Crease a sheet of 8.5” × 11” paper, perpendicular to the 11” side, into three identical rectangles.
- Fold and tape the paper into the shape of a triangular prism.
- No need to cut extra paper for the bases – just pretend they are there.
- Label the paper with a large “
**III**”.

**Figure IV: Regular Hexagonal Prism**

- Crease a sheet of 8.5” × 11” paper, perpendicular to the 11” side, into six identical rectangles.
- Fold and tape the paper into the shape of a hexagonal prism.
- Label the paper with a large “
**IV**”.

**A.2. Visually order your cylinder & prisms by volume (by inspection – no measuring)**

- Using visual inspection only, no calculations or measurements, put your figures in order by volume—least volume to greatest volume. Note that estimations of volumes are not asked for, just comparisons of bigger/smaller volumes. Take and insert a picture which clearly shows the visual inspection order (least to greatest) and the I, II, III and IV labels on the figures.
- Give an explanation of why you chose this ordering.

**A.3. Use fill to compare cylinder & prism volume (estimation, no calculations)**

This task is not meant to be complicated, keep it simple and fun.

- Use a uniform volume fill material of your choice to fill each figure. The smaller grained the fill material, the more accurate. Put your figures in order again (small to large) by comparing the amount of fill used but using no other measurements or calculations. Take and insert a picture which clearly shows the figure order and the I, II, III and IV labels.
- Give a brief description of your fill and compare procedure.

**A.4. Use math to calculate the volumes and surface areas of each cylinder & prism**

- For each figure, calculate the area of one base, in inches squared, accurate to
**2 decimal places**. [Do this completely in inches – do not compute in cm and then convert to inches] - For each figure, calculate the volume, in inches cubed, accurate to
**2 decimal places**. Note, you can reference your work and results from A.4.a. which should help to not redo work. [Do this completely in inches – do not compute in cm and then convert to inches] **i.**Order the figures by the volumes you computed and give that order (no need to take another picture).

**ii. **Comment on computed volume ordering compared to visual inspection ordering and fill estimation ordering.

**HINTS & Requirements:**

- Show your work for all calculations, including sketches of the polygonal bases with measurements labeled on the sketch. Use a protractor, a template or a drawing tool. Your physical constructions should be to scale, but your sketches of the nets (sides and bases) don’t need to be to scale, but they do need to be clearly labeled and precisely regular polygons. Sketching nets will help with surface area calculations.
- For the base of the cylinder: You know the circumference, so use the circumference formula to find the radius and then use the area formula.
- For the bases of the triangular prism: “Cut” in ½ from one vertex to the midpoint of the opposite side to make 2 right triangles. Use the Pythagorean Theorem to find the height. Then use the area formula.
- For the bases of the hexagonal prism: Make 3 “cuts” between opposite vertices to make 6 congruent (and equilateral) triangles.

- Surface Area review at mathisfun.com à plane geometry à area of plane shapes
- Volume review at mathisfun.com à solid geometry à click on the desired shape in the “Polyhedra and Non-Polyhedra” section

**A.E Enhancement:** Enhanced with relevant connections, references or resources beyond the given materials.

*Possible examples *

- Connections to other mathematical ideas or contexts from other mathematical domains
- Educationally relevant web resource (examples described and referenced (and not part of assignment))
- Solving the problem in more than one way
- Extending the solution beyond the question asked
- Connecting the problem-solving
*strategy*to a related math idea or question

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