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Working alone or in pairs, you will measure the surface area and volume of your donut and donut box. You may use a calculator. Think creatively about the strategies you use, and write down your thoughts using complete sentences and specific math vocabulary. Hand in these worksheets when you are finished. You will be assessed on: 1. Your use of math vocabulary. 2. Your ability to estimate and tell if your estimate is high or low. 3. Your ability to measure the area of circles and rectangles. 4. Your ability to measure the surface area and volume of cylinders and prisms. 5. Your ability to find strategies for measuring the surface area and volume of new shapes.


A. Estimate the surface area and volume of your donut and donut box. donut SA: ___________

donut box SA: ___________

V: ___________

V: ___________

Explain the steps you used to come up with your estimates. Mention any benchmarks you used (use the benchmark worksheet at the end of this packet).

What makes your estimate a good estimate?

B. Consider the size of your donut. What units of measurement would be the most accurate and efficient for measuring its dimensions? _________________ Why?

Consider the shape of your donut. What tools would be the most accurate and efficient for measuring its dimensions? _________________ Why?


C. Measure the following dimensions of your donut and box. Record them in the chart.

D. Are your measurements reasonable? How do you know? (Use your benchmarks.)

Tell what, if anything, you decided to remeasure.


E. Calculate the following areas, showing your work in the workspace that is provided. Note that your calculations will be approximations because of the irregularities of your donut. Record your answer in the answer column. Do not forget to label the units.


F. Eat your donut!

G. What steps will you use to calculate the volume of your donut? Use the information in charts C and E to help you.

Calculate the volume. Label the units. Note that your calculations will be approximations because of the irregularities of your donut. V = ______________ Do you think the volume you calculated for your donut is more or less than its actual volume? ______________ Why?

Compare the volume you calculated with your original estimate in part A. Was your estimate high or low? ______________ Why might this be?

H. What steps will you use to calculate the surface area of your donut?

Using the steps you described, calculate the surface area of your donut. Label the


units. Note that your calculations won’t be exact because of the irregularities of your donut. SA = ______________

Compare the surface area you calculated with your original estimate in part A. Was your estimate high or low? ______________ Why might this be?

Your younger sister asks you, “What do you mean by the surface area of that donut?” What will you tell her?

I. Calculate the volume of air inside the donut box. Show the steps you used. Label your units.

Compare the volume you calculated with your original estimate in part A. What do you notice?

J. If you put a dozen donuts into the box, explain in words how you would determine the volume of air around the donuts in the box.

K. Now use the method you described to find the volume of this air. Label the units.


L. Calculate the surface area of the donut box. Show the steps you used. Label the units.

Compare the surface area you calculated with your original estimate in part A. What do you notice?

M. According to a Dunkin’ Donuts website, “Dunkin’ Donuts sells more than 6 million donuts a day, a whopping 2.3 billion a year.” What is the volume of 2,300,000,000 of your donuts?

The volume of Earth is approximately 1.09×1027 cm3 or 6.7×1025 in3. How many years would it take to fill up Earth with your donuts?


COMMUNICATION Uses specific math vocabulary

A-M

COMPUTATION Makes accurate calculations

E, G-M

ESTIMATION Makes reasonable comparisons with benchmarks Thinks about whether estimates are high or low MEASUREMENT Chooses appropriate units and tools

A, D G B

Measures length and circumference precisely Measures area: circles & rectangles

C

Measures area: complex shapes

E

Measures SA & V: prisms and cylinders

G-L

Measures of SA & V: complex shapes

G, H, J, K

Presentation

E

Challenge section

Spelling

Uses the correct operation

Punctuation

Manipulates numbers in scientific notation

Neatness

Advanced

Proficient

Emergent

Sections

Novice

Critera


middle segment of index 1 in finger outspread hand (from pinky-tip to thumb-tip)

8 in

person’s height (or armspan)

5 ft

floorďƒ ceiling

10 ft

index card

100 cm2 (96.8 cm2)

sheet of paper

8.5*11in (20*30cm) 100 in2 (93.5 in2)

bedroom floor

100 ft2

CD

diameter 12 cm, 450 cm2

pencil

diameter 8mm, 2mm lead


Teacher Scoring Tool – With Standards

Student uses precise vocabulary to communicate mathematical ideas. (area, perimeter, circumference, diameter, face, lateral surface, volume, surface area, efficient, accurate) Student is able to perform math operations with accuracy using a calculator. Student is able to use common benchmarks to select appropriate methods for estimating surface area and volume. Student is able to analyze precision, accuracy, and approximate error in measurement situations Student is able to select appropriate units and tools to measure length and circumference. Student is able to apply techniques and tools to accurately find length and circumference to appropriate levels of precision. Student is able to develop and use formulas to determine the area of circles, rectangles, and morecomplex shapes. Student is able to develop strategies to determine the surface area and volume of selected prisms, cylinders, and more-complex shapes.

Uses specific math vocabulary

A-M

Makes accurate calculations Makes reasonable comparisons with benchmarks Thinks about whether estimates are high or low Chooses appropriate units and tools Measures length and circumference precisely

E, G-M

Measures area: circles & rectangles Measures area: complex shapes Measures SA & V: prisms and cylinders

E

Measures of SA & V: complex shapes

G, H, J, K

A, D G B C

E G-L

Advanced

Sections

Proficient

Critera

Emergent

Standard

Novice

Student Name: _________________________________

Performance Assessment: product  

Notre Dame of Maryland University, 2008 EDU 544