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Task B: (M B) GEOBOARD PERIMETER AND AREA OF TRIANGLES

Materials

• Geoboards or square dot grids, scissors, and cardstock or other paper to make a unit ruler
• Print the document M_B_Triangles and cut out each numbered triangle

B.1. Visually order the triangles by their geoboard perimeters (by inspection – no measuring)

1. Using visual inspection only, no calculations or measurements, put your triangles in order by perimeter—shortest perimeter to longest perimeter. Take and insert a picture which clearly shows the 7 triangles in your visual inspection ordering (smallest to largest).
2. Give a brief explanation of why you chose this ordering.

B.2. Use a geoboard unit measuring ruler to find triangle perimeters (no calculations – just measuring)

• Don’t forget units with your measurements! – As our units are non-standard geoboard units, just use “u”
1. Construct a new measuring devise: Create and use a “unit” measuring ruler by cutting a straight strip of paper and lining it up horizontally along a row of the Geoboard dot grid in the M_B_Triangles file. Make tick marks on your ruler that correspond to the dots. The “units” of the ruler is one length between neighboring horizontal tick marks. Note: You will use this ruler for Task B.2.b. Insert a picture which clearly shows your ruler lined up with horizontal geoboard dots.
2. Use you unit ruler to measure the perimeter of each triangle using no other measurements or calculations. Put your triangles in order again using these measured perimeters. Do your best to accurately estimate measurements to one decimal place. Take and submit a picture which clearly shows the 7 triangles in order by perimeter and the value your found for each perimeter.

B.3. Use math to calculate the perimeter of each triangle.

• Show you work for all calculations, including sketches on geoboard or dot grid paper of the right triangles you include to calculated diagonal lengths.
• Note – you will need to use the Pythagorean theorem to calculate diagonal lengths.
• Don’t forget units (u) with your measurements!
1. For each triangle, calculate the exact  perimeter in geoboard units, using square root notation when applicable, such as 2 + 2√2 units.
2. i. Convert your exact perimeters (from part a) to their decimal estimates (to the nearest tenth) for any square root expressions (such as 2 + 2√2 u ≈ 4.8 u).

ii. Compare all of your exact perimeter calculations to your visual inspection and unit ruler estimations. If the ordering of the triangles by perimeter has changed, describe these changes.

B.4. Visually order your triangles by their area (by inspection – no measuring)

1. Using visual inspection only, no calculations or measurements, put your triangles in order by area—least area to greatest area. Note that estimations of areas are not asked for, just comparisons of bigger/smaller areas. Take and submit a picture which clearly shows the 7 triangles in your order, by area.
2. Give a brief explanation of why you chose this ordering.

B.5. Use geoboard techniques (no formulas) to measure triangle area and compare to the calculated area using the triangle area formula

• See the “Geoboard Technique Help (Finding area WITHOUT formulas)” help video posted in Canvas. Also, ask for more help/clarification of needed.
• Don’t forget units with your measurements! –  As our units are non-standard just use “u2”
1. Use geoboard techniques such as divide or surround and subtract to determine the area of each triangle (to the nearest tenth of a geoboard square). You can “know” and use the area formula for rectangles, but you are not supposed to use the area formula for triangles.
2. Use math and the area formula for triangles to calculate the area of each triangle precisely (to the nearest tenth of a geoboard square). Show you work for all calculations, including sketches on geoboard or dot grid paper of any needed height computations. Note, you can reference your work and results from B.3. which should help to not redo work.
3. i. Write this ordering down and take a picture which clearly shows the 7 triangles in order by calculated area.

ii. Note any differences between B.4 visual ordering and B.5 computation ordering.

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

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