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Task C: (M C) GEOBOARD PERIMETER AND AREA OF QUADRILATERALS (see course page for .docx & PDF typing & writing outlines)

Materials

• Geoboards or square dot grids
• Scissors, and cardstock or other paper to make a unit ruler
• Print the document M_C_Quadrilaterals and cut out each numbered quadrilateral

C.1. Visually order your quadrilaterals by their perimeter (by inspection – no measuring)

1. Using visual inspection only, no calculations or measurements, put your quadrilaterals in order by perimeter—shortest perimeter to longest perimeter. Note that estimations of perimeters are not asked for, just comparisons of longer/shorter perimeters. Take and insert a picture which clearly shows the 14 quadrilaterals in your visual inspection ordering (smallest to largest).
2. Give a brief explanation of why you chose this ordering.

C.2. Use a unit measuring ruler to estimate quadrilateral perimeters (estimation, no calculations)

• Don’t forget units with your measurements! (u)
1. Create a new Unit Measuring Ruler that is aligned with the geoboard dot grid in the M_C_Quadrilaterals file. Note: You will use this ruler for Task C.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 quadrilateral using no other measurements or calculations. Put your quadrilaterals in order again using these measured perimeters. Do your best to accurately estimate measurements to one decimal place.Take and insert a picture which clearly shows the quadrilaterals in order by perimeter and the value your found for each perimeter

C.3. Use math to calculate the perimeter of each quadrilateral.

• Show you work for all calculations, including sketches on geoboard or dot grid paper of the right quadrilaterals you include to calculated diagonal lengths in geoboard units.
• Note – you will need to use the Pythagorean theorem to calculate diagonal lengths.
• Don’t forget units with your measurements! (u)
1. For each quadrilateral, calculate the exact perimeter, using square root notation when applicable, such as 2 + 2√2 units.
2. Calculate the decimal estimates (to the nearest tenth) of any square root expressions (such as 2 + 2√2 ≈ 4.8 u) and compare all of your exact perimeter calculations to your visual inspection and unit ruler estimations. If the ordering of the quadrilaterals by perimeter has changed, describe these changes.

C.4. Visually order your quadrilaterals by their area (by inspection – no measuring)

1. Using visual inspection only, no calculations or measurements, put your quadrilaterals in order by area—least area to most area. Take and insert a picture which clearly shows the 14 quadrilaterals in your visual inspection ordering (smallest to largest).
2. Give a brief explanation of why you chose this ordering.

C.5. Use geoboard techniques (not formulas) to determine quadrilateral area and compare to the calculated area using the quadrilateral area formula

• Don’t forget units with your measurements! (u2)
1. Use geoboard techniques such as divide or surround to determine the area of each quadrilateral (to the nearest tenth of a geoboard square). You can “know” the area of rectangles; however, you are not supposed to use the area formulas for rhombi, parallelograms or trapezoids. See the “Geoboard Technique Help (Finding area WITHOUT formulas)” help video posted in Canvas. Insert picture(s) that show how you determined each geoboard area.
2. Use math and the area formulas for quadrilaterals to calculate the area of each quadrilateral 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 marks you include. Note, you can reference your work and results from C.3. which should help to not redo work.
3. i. Write this ordering down and take a picture which clearly shows the 14 quadrilaterals in order by calculated area.

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

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

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