Lesson on using exponents

Lesson on Measurement

MEASUREMENT Convert within measurement systems

M.UN.06.01 Convert between basic units of measurement within a single measurement system, e.g., square inches to square feet.

M.PS.06.02 Draw patterns (of faces) for a cube and rectangular prism that, when cut, will cover the solid exactly (nets).

M.TE.06.03 Compute the volume and surface area of cubes and rectangular prisms given the lengths of their sides, using formulas.

Unwrapping the GLCE’s:

Concepts (what students need to know):

• All basic units of measurement and conversions within the metric and customary systems of measurement.

• Relationship between a two and three dimensional object.

• The concept of surface area and volume and related terminology.

•

Skills (what students need to be able to do):

• To fluidly convert units of measurement within the metric system of measurement.

• To fluidly convert units of measurement within the customary units system of measurement.

• draw geometric objects with specified properties, such as side lengths or angle measures

• use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume

• use geometric models to represent and explain numerical and algebraic relationships.

Prior Knowledge:

• M.UN.02.01 Measure lengths in meters, centimeters, inches, feet, and yards approximating to the nearest whole unit and using abbreviations: cm, m, in, ft, yd.

• M.UN.02.09 Read temperature using the scale on a thermometer in degrees Fahrenheit.

• M.UN.03.01 Know and use common units of measurements in length, weight, and time.

• M.UN.03.02 Measure in mixed units within the same measurement system for length, weight, and time: feet and inches, meters and centimeters, kilograms and grams, pounds and ounces, liters and milliliters, hours and minutes, minutes and seconds, years and months.

• M.UN.03.03 Understand relationships between sizes of standard units, e.g., feet and inches, meters and centimeters.

• M.UN.03.04 Know benchmark temperatures such as freezing (32ºF, 0ºC); boiling (212F, 100¨¬C); and compare temperatures to these, e.g., cooler, warmer.

• M.UN.03.05 Know the definition of area and perimeter and calculate the perimeter of a square and rectangle given whole number side lengths.

• M.UN.03.06 Use square units in calculating area by covering the region and counting the number of square units.

• M.UN.03.07 Distinguish between units of length and area and choose a unit appropriate in the context.

• M.UN.03.08 Visualize and describe the relative sizes of one square inch and one square centimeter.

• M.UN.04.01 Measure using common tools and select appropriate units of measure.

• M.UN.04.03 Measure and compare integer temperatures in degrees.

• M.UN.05.01 Recognize the equivalence of 1 liter, 1.000 ml and 1000 cm3 and include conversions among liters, milliliters, and cubic centimeters.

• M.UN.05.02 Know the units of measure of volume: cubic centimeter, cubic meter, cubic inches, cubic feet, cubic yards, and use their abbreviations (cm3, m3, in3, ft3, yd3).

• M.UN.05.03 Compare the relative sizes of one cubic inch to one cubic foot, and one cubic centimeter to one cubic meter.

• M.UN.05.04 Convert measurements of length, weight, area, volume, and time within a given system using easily manipulated numbers.

Big Ideas:

• To determine appropriate customary and metric units of length, capacity and weight/mass.

• To mentally and accurately convert units of measurement within a metric or customary system of measurement.

• To experiment with the surface area and volume of different prisms.

• To visualize and solve problems involving surface area and volume.

Essential Questions:

1. What are the customary units of measurement?

2. What are the metric units of measurement?

3. Which customary or metric units of measurement are most appropriately used in a specific situation?

4. What strategies can we use to determine the surface area and volume of selected prisms?

Study Guide for Unit:

|Accuracy and precision in measurement can be extremely important. There are two systems of measurement that are commonly used: the |

|metric system and the U.S. customary (or standard) system. |

|The Metric System: |

|The meter is the basis of length measurements in the metric system. Here is a basic breakdown of the metric system of length. |

|          1,000 millimeters (mm) = 1 meter (m) |

|             100centimeters (cm) = 1 meter (m) |

|              10 decimeters (dm) = 1 meter (m) |

|               1 dekameter (dam) = 10 meters (m) |

|               1 hectometer (hm) = 100 meters (m) |

|                1 kilometer (km) = 1,000 meters (m) |

|Example: A fence is 4 meters long. Jim put a gate on the end of the fence that was 20 decimeters long. How long is the fence and the |

|gate combined? |

|          (1) 20 decimeters = 2 meters |

|          (2) 4 meters + 2 meters = ? |

|Step 1: Convert units to like units. |

|Step 2: Add the units. |

|Answer: 6 meters |

| |

|The gram is the basis of weight measurements in the metric system. Here is a basic breakdown of the metric system of weight. |

|          1,000 milligrams (mg) = 1 gram (g) |

|             100centigrams (cg) = 1 gram (g) |

|              10 decigrams (dg) = 1 gram (g) |

|               1 dekagram (dg) = 10 grams (g) |

|               1 hectogram (hg) = 100 grams (g) |

|                1 kilogram (kg) = 1,000 grams (g) |

|Example: |

|          24g = ? mg |

|Since 1 gram equals 1,000 milligrams, 24 grams equal 24,000 milligrams. |

|24 x 1,000 = 24,000 |

|Answer: A |

| |

|The liter is the basis of capacity measurements in the metric system. Here is a basic breakdown of the metric system of capacity. |

|          1,000 milliliters (ml) = 1 liter (l) |

|             100centiliters (cl) = 1 liter (l) |

|              10 deciliters (dl) = 1 liter (l) |

|               1 dekaliter (dal) = 10 liters (l) |

|               1 hectoliter (hl) = 100 liters (l) |

|                1 kiloliter (kl) = 1,000 liters (l) |

| |

|The U.S. Customary System: |

|The foot is the basis of length measurements of the U.S. customary system. Here is a basic breakdown of the U.S. customary system of |

|length. |

|           12 inches = 1 foot |

|              3 feet = 1 yard |

|           12 inches = 1 foot |

|           36 inches = 1 yard |

|           5280 feet = 1 mile |

|          1760 yards = 1 mile |

| Example : A table is 36 inches tall. There are 12 inches in 1 foot. Divide 36 by 12, the result is 3. The table is 3 feet tall. |

|Continue with other objects and also use the metric system.   |

|   |

|The pound is the basis of weight measurements of the U.S. customary system. Here is a basic breakdown of the U.S. customary system of|

|weight. |

|          16 ounces (oz) = 1 pound (lb) |

|             1 ton (ton) = 2,000 pounds (lb) |

| |

|The gallon is the basis of capacity measurements of the U.S. customary system. Here is a basic breakdown of the U.S. customary system|

|of capacity. |

|            16 cups (C) = 1 gallon (gal) |

|           8 pints (pt) = 1 gallon (gal) |

|          4 quarts (qt) = 1 gallon (gal) |

|How to Estimate: Choose the best estimate for the capacity of a cereal bowl. |

|     A. 2 l |

|     B. 2 oz |

|     C. 2 C |

|     D. 2 gal |

| |

|Solution: |

|• 2 liters is 1 large bottle of soda, so it is too large to be the capacity of a cereal bowl. |

|• 2 ounces are less than one cup, so it is much too small to be the capacity of a cereal bowl. |

|• 2 cups is less than two liters, but more than 2 ounces, so it is a possible capacity of a cereal bowl. |

|• 2 gallons is even larger than 2 liters, so it is definitely too large to be the capacity of a cereal bowl. |

|Answer: 2 C |

|Finding the Area of Rectangle: |

|The area of a rectangle is the number of square units needed to cover the surface of the figure.The formula for calculating area of a|

|square or rectangle is: |

|          Area = length x width. |

|Example 1: A figure has a width of 3 inches and a length of 7 inches. What is the area of the figure? |

| |

|          [pic] |

|Step 1: Multiply the width and the length. |

|          Area = 7 x 3 = 21 |

|Answer: 21 square inches |

| |

|It may be useful to use graph paper to develop figures. Help the student determine the area of various figures drawn on the graph |

|paper. |

|Finding the surface area of a solid figure: |

|The surface area of a solid figure is the sum of the areas of all the surfaces.A face is one side of a solid figure. When trying to |

|find the surface area of a figure, first find the area of each face, then add those areas together. |

| |

|Example 1: Find the surface area of the figure. |

| |

|          [pic] |

|          [pic] |

|[pic] |

|Step 1: This three-dimensional figure can be broken down into its six faces (which are rectangles). The front and back are identical,|

|the top and bottom are identical, and the left and right sides are identical. |

|Step 2: Determine the area of each rectangle using the formula Area = length x width. |

|Step 3: Add together the area of each face of the figure. |

| |

|The surface area of the figure is 62 square meters. |

|How to Read Temperature: |

|Celsius is a standard unit in the metric system for measuring temperature. Thermometers are used to measure temperatures. Many times|

|on tests and in textbooks, thermometers are represented by drawings. There are three thermometers below, each with a different scale.|

| |

|          [pic] |

|Example 1: Refer to thermometer A above. If the temperature dropped 2.5°C, what would the temperature read? |

| |

|          (1) 1°C - 2.5°C |

|          (2) -1.5°C |

|Step 1: Thermometer A reads 1°C. Since we want to know what will happen if the temperature drops 2.5°C, we subtract 2.5°C from the |

|current reading (1°C). |

|Step 2: 1°C - 2.5°C = -1.5°C |

|Answer: -1.5°C |

|Finding the Volume of Rectangular Prisms: |

|Volume is the measurement of a three-dimensional figure's interior space. Volume is measured in cubic units. |

|The formula for calculating volume of a rectangular prism is: |

| |

|     Volume = length x width x height |

| |

|Example 1: Find the volume of a rectangular prism with length = 6 inches, width = 4 inches, |

|height = 2 inches. |

|[pic] |

|          (1) Volume = 2 x 4 x 6 |

|          (2) Volume = 48 cubic inches |

| |

|Step 1: Apply the amounts given in the problem to the formula. |

|Step 2: Perform calculations to find the answer. |

|Answer: 48 cubic inches |

Answers for Post Assessment

5 points per question

|1. |Choose the best estimate for the capacity of a soup bowl. |5 |

| | | |Answer: C | |

| | | A. | 1 l | |

| | | B. | 1 oz | |

| | | C. | 1 c | |

| | | D. | 1 gal | |

|2. |[pic] |5 |

| | | |Answer: D | |

| | | A. | 57.6 square meters | |

| | | B. | 102.96 square meters | |

| | | C. | 115.2 square meters | |

| | | D. | 205.92 square meters | |

|3. |1800 in = ? yd |5 |

| | | |Answer: A | |

| | | A. | 50 | |

| | | B. | 1,500 | |

| | | C. | 150 | |

| | | D. | 5 | |

|4. |Which of the following items is most likely measured in pints? |5 |

| | | |Answer: C | |

| | | A. | water in a pool | |

| | | B. | sand on a beach | |

| | | C. | milk in a carton | |

| | | D. | snow on the ground | |

|5. |Solve: |5 |

| |1.5 kL = ? L | |

| | | |Answer: C | |

| | | A. | 15,000 | |

| | | B. | 1.5 | |

| | | C. | 1,500 | |

| | | D. | 0.015 | |

|6. |3 dg = ? g |5 |

| | | |Answer: A | |

| | | A. | 300 | |

| | | B. | 30 | |

| | | C. | 0.003 | |

| | | D. | 0.3 | |

|7. |Which of the following temperatures is the warmest? |5 |

| | | |Answer: D | |

| | | A. | -3.3°C | |

| | | B. | -3°C | |

| | | C. | 0°C | |

| | | D. | 3°C | |

|8. |Patricia bought 47 inches of licorice. |5 |

| |How many feet of licorice did Patricia buy? | |

| | | |Answer: A | |

| | | A. | 3 feet and 11 inches | |

| | | B. | 47 feet | |

| | | C. | 23 feet and 1 inch | |

| | | D. | 1 foot and 11 inches | |

|9. |Solve: |5 |

| |? m = 4 hm | |

| | | |Answer: B | |

| | | A. | 40 | |

| | | B. | 400 | |

| | | C. | 40,000 | |

| | | D. | 400,000 | |

|10. |What is the volume of this figure? |5 |

| | | |

| |Answer: A | |

| | | |[pic][pic] | |

| | | A. | 1,368 cubic inches | |

| | | B. | 144 cubic inches | |

| | | C. | 3,249 cubic inches | |

| | | D. | 684 cubic inches | |

|11. |What is the volume of the block? |5 |

| | | |

| |Answer: C | |

| | | |[pic] | |

| | | A. | 35 cubic centimeters | |

| | | B. | 304 cubic centimeters | |

| | | C. | 520 cubic centimeters | |

| | | D. | 262 cubic centimeters | |

|12. |A bag of potatoes weighs 10 pounds. How many ounces does the bag of potatoes weigh? |5 |

| | | |Answer: D | |

| | | A. | 16 ounces | |

| | | B. | 32 ounces | |

| | | C. | 320 ounces | |

| | | D. | 160 ounces | |

13. Define volume.

Answer: The measure of the number of cubic units contained in a solid figure.

14. Explain in your own words how to find the volume of a rectangular prism using a standard formula.

Answer: Volume(V) = base area(B) x height (h)

15. What is the greatest number of 3 x 4 x 2-inch rectangular boxes of fish food that can fit in a carton with a volume of 3 cubic feet and a width of 1 foot?

Answer: 216 boxes

16. Define surface area.

Answer: The sum of the areas of all of the faces of a solid figure.

17. Explain in your own words how to find the surface area of a rectangular solid.

Answers: Surface Area = 2(lw) + 2(wh) + 2(lw)

18. Find the surface area of a package that is 6 in. tall, 7 in. wide and 4 in. deep.

Answer: 188 inches²

19. Which pattern of squares could be folded to make a cube, so that no square overlaps any

other?

Answer: C

[pic]

|A.   |

|A |

| |

|B.   |

|B |

| |

|C.   |

|C |

| |

|D.   |

|D |

| |

20. You have unfolded a box to fit into the recycling bin. The box is 11 inches long, 6 inches wide and 4 inches tall. How much floor space does the unfolded box cover? Hint: What is the total surface area? Include a diagram with your answer.

Answer: 66+ 66 + 44+ 44+ 24+ 24= 268 in.²

_____________________________________________________________________________________________Student Copy of Post Assessment

5 points per question

|1. |Choose the best estimate for the capacity of a soup bowl. |5 |

| | | | | |

| | | A. | 1 l | |

| | | B. | 1 oz | |

| | | C. | 1 c | |

| | | D. | 1 gal | |

|2. |[pic] |5 |

| | | | | |

| | | A. | 57.6 square meters | |

| | | B. | 102.96 square meters | |

| | | C. | 115.2 square meters | |

| | | D. | 205.92 square meters | |

|3. |1800 in = ? yd |5 |

| | | | | |

| | | A. | 50 | |

| | | B. | 1,500 | |

| | | C. | 150 | |

| | | D. | 5 | |

|4. |Which of the following items is most likely measured in pints? |5 |

| | | | | |

| | | A. | water in a pool | |

| | | B. | sand on a beach | |

| | | C. | milk in a carton | |

| | | D. | snow on the ground | |

|5. |Solve: |5 |

| |1.5 kL = ? L | |

| | | | | |

| | | A. | 15,000 | |

| | | B. | 1.5 | |

| | | C. | 1,500 | |

| | | D. | 0.015 | |

|6. |3 dg = ? g |5 |

| | | | | |

| | | A. | 300 | |

| | | B. | 30 | |

| | | C. | 0.003 | |

| | | D. | 0.3 | |

|7. |Which of the following temperatures is the warmest? |5 |

| | | | | |

| | | A. | -3.3°C | |

| | | B. | -3°C | |

| | | C. | 0°C | |

| | | D. | 3°C | |

|8. |Patricia bought 47 inches of licorice. |5 |

| |How many feet of licorice did Patricia buy? | |

| | | | | |

| | | A. | 3 feet and 11 inches | |

| | | B. | 47 feet | |

| | | C. | 23 feet and 1 inch | |

| | | D. | 1 foot and 11 inches | |

|9. |Solve: |5 |

| |? m = 4 hm | |

| | | | | |

| | | A. | 40 | |

| | | B. | 400 | |

| | | C. | 40,000 | |

| | | D. | 400,000 | |

|10. |What is the volume of this figure? |5 |

| | | |[pic][pic] | |

| | | A. | 1,368 cubic inches | |

| | | B. | 144 cubic inches | |

| | | C. | 3,249 cubic inches | |

| | | D. | 684 cubic inches | |

|11. |What is the volume of the block? |5 |

| | | |[pic] | |

| | | A. | 35 cubic centimeters | |

| | | B. | 304 cubic centimeters | |

| | | C. | 520 cubic centimeters | |

| | | D. | 262 cubic centimeters | |

|12. |A bag of potatoes weighs 10 pounds. How many ounces does the bag of potatoes weigh? |5 |

| | | | | |

| | | A. | 16 ounces | |

| | | B. | 32 ounces | |

| | | C. | 320 ounces | |

| | | D. | 160 ounces | |

13. Define volume.

14. Explain in your own words how to find the volume of a rectangular prism using a standard formula.

15. What is the greatest number of 3 x 4 x 2-inch rectangular boxes of fish food that can fit in a carton with a volume of 3 cubic feet and a width of 1 foot?

16. Define surface area.

17. Explain in your own words how to find the surface area of a rectangular solid.

18. Find the surface area of a package that is 6 in. tall, 7 in. wide and 4 in. deep.

19. Which pattern of squares could be folded to make a cube, so that no square will overlap

another?

[pic]

|A.   |

|A |

| |

|B.   |

|B |

| |

|C.   |

|C |

| |

|D.   |

|D |

| |

20. You have unfolded a box to fit into the recycling bin. The box is 11 inches long, 6 inches wide and 4

inches tall. How much floor space does the unfolded box cover? Hint: What is the total surface area?

Include a diagram with your answer.

Pre-Assessment Questions:

Answers for Pre Assessment

5 points per question

|1. |Choose the best choice for measuring the amount of water in a fish tank. |5 |

| | | |Answer: C | |

| | | A. | ounces | |

| | | B. | inches | |

| | | C. | gallons | |

| | | D. | feet | |

|2. |[pic] |5 |

| | | |Answer: D | |

| | | A. |3 ft² | |

| | | B. |3 ft | |

| | | C. | 4 ½ ft² | |

| | | D. | 4 ⅛ ft² | |

|3. |6 lb = ______ oz |5 |

| | | |Answer: A | |

| | | A. | 96 oz | |

| | | B. | 98 oz | |

| | | C. | 48 oz | |

| | | D. | 24 oz | |

|4. |Which of the following items is most likely measured in kilometers? |5 |

| | | |Answer: C | |

| | | A. | Distance between two cities in the United States | |

| | | B. | Walk in a park | |

| | | C. | European cycling race | |

| | | D. | A pencil | |

|5. |Solve: |5 |

| |92 kl = __________L | |

| | | |Answer: C | |

| | | A. | 920 L | |

| | | B. | 920,000 L | |

| | | C. | 92,000 L | |

| | | D. | 0.92 L | |

|6. |425 g =_______ kg |5 |

| | | |Answer: A | |

| | | A. | 0.425 kg | |

| | | B. | 4250 kg | |

| | | C. | 4.25 kg | |

| | | D. | 42.5 kg | |

|7. |Which of the following temperatures is the warmest? |5 |

| | | |Answer: D | |

| | | A. | -1.0°C | |

| | | B. | -10°C | |

| | | C. | 0°C | |

| | | D. | 10°C | |

|8. |You are packing cans into a box that can hold a maximum of 12 lbs. Each can weighs 10 oz. What is the greatest number of |5 |

| |cans that can be packed into the box? | |

| | | |Answer: A | |

| | | A. | 19 cans | |

| | | B. | 120 cans | |

| | | C. | 30 cans | |

| | | D. | 10 cans | |

|9. |Solve: |5 |

| |45 m = _______ cm | |

| | | |Answer: B | |

| | | A. | 450 cm | |

| | | B. | 4,500 cm | |

| | | C. | 45.00 cm | |

| | | D. | 0.45 cm | |

|10. |What is the volume of this figure? |5 |

| | | |

| |Answer: A | |

| | | |[pic][pic] | |

| | | A. | 60 m³ | |

| | | B. | 12 m³ | |

| | | C. | 15 m³ | |

| | | D. | 30 m³ | |

|11. |What is the volume of the block? |5 |

| | | |

| |Answer: C | |

| | | |[pic] | |

| | | A. | 256 cubic centimeters | |

| | | B. | 768 cubic centimeters | |

| | | C. | 7,680 cubic centimeters | |

| | | D. | 512 cubic centimeters | |

|12. |How many gallons are 6 quarts of strawberries? |5 |

| | | |Answer: D | |

| | | A. | 12 gallons | |

| | | B. | 2 gallons | |

| | | C. | 1 gallon | |

| | | D. | 1½ gallons | |

13. Define volume.

Answer: The measure of the number of cubic units contained in a solid figure.

14. Explain in your own words how to find the volume of a rectangular prism using a standard formula.

Answer: Volume(V) = base area(B) x height (h)

15. What is the storage capacity of an area that is 8 feet long, 6 feet wide, and 10 ft high in cubic feet?

Answer: 480 ft³

16. Define surface area.

Answer: The sum of the areas of all of the faces of a solid figure.

17. Explain in your own words how to find the surface area of a rectangular solid.

Answers: Surface Area = 2(lw) + 2(wh) + 2(lw)

18. Find the surface area of a package that is 10 inches high, 7 inches long, and 2 inches wide?.

Answer: 208 inches²

19. Which pattern of squares could be folded to make a cube, so that no square overlaps any

other?

Answer: C

[pic]

|A.   |

|A |

| |

|B.   |

|B |

| |

|C.   |

|C |

| |

|D.   |

|D |

| |

20. A box is 12 inches wide, 6 inches long. Its volume is 1296 cubic inches. Can it fit in a 12 -inch-wide space on a shelving unit that has 17 inches of space between its shelves? Explain.

Answer: No because the box is 18 inches high.

Pre Test Student Copy

5 points per question

|1. |Choose the best choice for measuring the amount of water in a fish tank. |5 |

| | | | | |

| | | A. | ounces | |

| | | B. | inches | |

| | | C. | gallons | |

| | | D. | feet | |

|2. |[pic] |5 |

| | | | | |

| | | A. |3 ft² | |

| | | B. |3 ft | |

| | | C. | 4 ½ ft² | |

| | | D. | 4 ⅛ ft² | |

|3. |6 lb = ______ oz |5 |

| | | | | |

| | | A. | 96 oz | |

| | | B. | 98 oz | |

| | | C. | 48 oz | |

| | | D. | 24 oz | |

|4. |Which of the following items is most likely measured in kilometers? |5 |

| | | | | |

| | | A. | Distance between two cities in the United States | |

| | | B. | Walk in a park | |

| | | C. | European cycling race | |

| | | D. | A pencil | |

|5. |Solve: |5 |

| |92 kl = __________L | |

| | | | | |

| | | A. | 920 L | |

| | | B. | 920,000 L | |

| | | C. | 92,000 L | |

| | | D. | 0.92 L | |

|6. |425 g =_______ kg |5 |

| | | | | |

| | | A. | 0.425 kg | |

| | | B. | 4250 kg | |

| | | C. | 4.25 kg | |

| | | D. | 42.5 kg | |

|7. |Which of the following temperatures is the warmest? |5 |

| | | | | |

| | | A. | -1.0°C | |

| | | B. | -10°C | |

| | | C. | 0°C | |

| | | D. | 10°C | |

|8. |You are packing cans into a box that can hold a maximum of 12 lbs. Each can weighs 10 oz. What is the greatest number of |5 |

| |cans that can be packed into the box? | |

| | | | | |

| | | A. | 19 cans | |

| | | B. | 120 cans | |

| | | C. | 30 cans | |

| | | D. | 10 cans | |

|9. |Solve: |5 |

| |45 m = _______ cm | |

| | | | | |

| | | A. | 450 cm | |

| | | B. | 4,500 cm | |

| | | C. | 45.00 cm | |

| | | D. | 0.45 cm | |

|10. |What is the volume of this figure? |5 |

| | | |

| | | |[pic][pic] | |

| | | A. | 60 m³ | |

| | | B. | 12 m³ | |

| | | C. | 15 m³ | |

| | | D. | 30 m³ | |

|11. |What is the volume of the block? |5 |

| | | |[pic] | |

| | | A. | 256 cubic centimeters | |

| | | B. | 768 cubic centimeters | |

| | | C. | 7,680 cubic centimeters | |

| | | D. | 512 cubic centimeters | |

|12. |How many gallons are 6 quarts of strawberries? |5 |

| | | | | |

| | | A. | 12 gallons | |

| | | B. | 2 gallons | |

| | | C. | 1 gallon | |

| | | D. | 1½ gallons | |

13. Define volume.

.

14. Explain in your own words how to find the volume of a rectangular prism using a standard formula.

15. What is the storage capacity of an area that is 8 feet long, 6 feet wide, and 10 ft high in cubic feet?

16. Define surface area.

17. Explain in your own words how to find the surface area of a rectangular solid.

18. Find the surface area of a package that is 10 inches high, 7 inches long, and 2 inches wide?.

19. Which pattern of squares could be folded to make a cube, so that no square overlaps any

other?

[pic]

|A.   |

|A |

| |

|B.   |

|B |

| |

|C.   |

|C |

| |

|D.   |

|D |

| |

20. A box is 12 inches wide, 6 inches long. Its volume is 1296 cubic inches. Can it fit in a 12 -inch-wide space on a shelving unit that has 17 inches of space between its shelves? Explain.

INSTRUCTIONAL LESSON AND ACTIVITIES:

Resource: gibbarh@cape.k12.mo.us

Mrs. Gibbar

Central Junior High School * 205 Caruthers Street

Cape Girardeau, MO * 573-334-2923

Adapted from site by Rob Frescoln

rfrescoln@chccs.k12.nc.us

The Process:

-Part 1, Individual work

1. Divide into groups of 5 students. Print out a copy of the Research Sheet (below) for each student.

2. Have each student choose a topic to research: length, mass, temperature, surface area and volume. Individuals within the group will go to the recommended sites and gather/record the following information:

• What are the units, smallest to largest, in metric and US/English standard?

• What does each type of measurement truly measure (examples)?

• How do you convert from one unit to another in both metric and US/English Standard (Ex. centimeters to meters, inches to feet)?

• On what is each measurement based (Where did it come from? WHY is a foot called a foot)?

• In your opinion, which system, metric or US/English, is easier to use and WHY?

-Part 2: Group Work

1. The group will come together and share information summarizing each section of the

Research Sheet and recording on the Group Decision Sheet, answering the question:

• What system, metric or US/English, will you recommend for all of the measurements?

2. The group will also peer teach standard conversions using recommended web sites or

practice sheets for practice purposes.

Evaluation:

Students will be graded on the quality of the two worksheets. Emphasis is placed on the depth to which the topics are covered. See the Rubric (below) for more details.

Resources:

Factual information on units

A Dictionary of Units of Measurement -Russ Rowlett and UNC at Chapel Hill

The International System of unit (SI) -Bureau International des Poids et Mesures

More “opinionated” information, pros and cons.

US Metrication Association -pro metric. Click through the links in the "Metric system information" section

English Weights & Measures -has Pro English arguments, with good info. on units.

STUDENT PACKET

Introduction:

Your school has decided to secede from the United States and become its own nation, “The United People of Knowledge.” There are many tasks ahead of your new country: electing a leader, writing a new set of laws, choosing a currency, creating a new flag, etc. One very important task to be preformed is to establish a standard set of Weights and Measures.

Part One: Your Group Task

The provisional government has assigned a group of their top scientists, including you, the task of choosing the official units of measurement for your country. You will compare the metric system (Also called SI) and the US/English systems for length, mass, and volume, and answer the following question:

• Overall, which system is better and why?

Your Individual Task:

• Go to each one of the sites below and gather the following information for your measurement:

What are the units, smallest to largest, in metric and US/English standard?

• What does each type of measurement truly measure (examples)?

• How do you convert from one unit to another in both metric and US/English Standard (Ex. centimeters to meters, inches to feet)?

• On what is each measurement based (Where did it come from? WHY is a foot called a foot)? IMPORTANT: You are looking for reasons not just conversions!

• Record the information you gather in the appropriate columns on your Research Sheet.

• In your opinion, which system, metric or US/English, is easier to use and WHY?

Part 2: More Group Work

1. Come together and present to the group what each member found out, summarizing each section of the Research Sheet.

2. Print out a copy of the Group Decision Sheet. (in your packet)

3. Make sure you have gone to all of the sites below. If it will help with your discussion, return to any of the sites as a group.

4. As a group fill out your Group Decision Sheet, answering the question:

o What system, metric or US/English, will you recommend for all of the measurements?

Conclusion:

In the United States, the Metric System will some day be the rule of the land. Congress passed legislation back in 1975 to move the United States towards metrication. Since that time, many initiatives have come and gone, many without any success. After this activity, you should be able to decide for yourself if you think the metric system is the way to go!

Factual information on units

A Dictionary of Units of Measurement -Russ Rowlett and UNC at Chapel Hill

The International System of unit (SI) -Bureau International des Poids et Mesures

More “opinionated” information, pros and cons.

US Metrication Association -pro metric. Click through the links in the "Metric system information" section

English Weights & Measures -has Pro English arguments, with good info. on units.

Research Sheet

Research Topic (circle): Length, Mass, Volume, Surface Area

[pic]

|Group Decision Sheet |

| |

| |

|As a group, we decided: |

| |

|Metric |

|US/English Standard |

| |

|Advantages |

| |

| |

| |

| |

| |

| |

| |

| |

|Disadvantages |

| |

| |

| |

| |

| |

| |

| |

|As a group, we recommend the __________________________________ system for Length, Mass, Volume, Surface Area and Temperature because: |

| |

| |

| |

| |

| |

|(What process did you use? Did you vote? Did one person make the decision? Describe the process.) |

|To come to a group decision, we did the following: |

| |

| |

| |

| |

| |

| |

Rubric:

|Individual Grade (from Research Sheet) |

|Points |25 |20 |10 |5 |

|Units |6+ units found for |4-5 units found for each |3-4 units found for each system|3 or fewer units found for each |

| |each system, in order |system, in order |in order |system, or more, if ut of order |

|Conversions |Conversions found for |Conversions found for 4-5 |Conversions found for 3-4 |Conversions found for 3 or fewer |

| |6 unique units for |unique units |unique units |unique units, or more if incorrect|

| |each system | | | |

|Advantages and |4+ unique & factual |2-3 unique & factual |1 unique & factual argument |1 or more non-factual argument(s) |

|Disadvantages |arguments given for |arguments given for each |given for each system |or repetition of single argument |

| |each system |system | |given |

|Decision |Well reasoned, based |Well reasoned, based on pros |Poorly reasoned, based on pros |Poorly reasoned, not based on pros|

| |on pros and cons, |and cons, two or fewer |and cons, one reason given |and cons, and one or no reason |

| |multiple reasons given|reasons given | |given |

| |

|Group Grade (from Group Decision Sheet) |

|Points |50 |44 |39 |34 |

|Advantages and |4+ unique & factual |2-3 unique & factual |1 unique & factual argument |1 or more non-factual argument(s) |

|Disadvantages |arguments given for |arguments given for each |given for each system |or repetition of single argument |

| |each system |system | |given |

|Decision |Well reasoned, based |Well reasoned, based on pros |Poorly reasoned, based on pros |Poorly reasoned, not based on pros|

| |on pros and cons, |and cons, two or fewer |and cons, one reason given |and cons, and one or no reason |

| |multiple reasons given|reasons given | |given |

-----------------------

19 In.

15.6 m

Find the area.

13.2 m

8 in.

9 in.

20 cm

13 cm

2 cm

19 In.

13.2 m

15.6 m

Find the area.

8 in.

9 in.

20 cm

13 cm

2 cm

2 [pic]ft

Find the area.

1 ½ ft

5 m

4 m

3 m

30 cm

16 cm

16 cm

2 [pic]ft

Find the area.

1 ½ ft

5 m

4 m

3 m

30 cm

16 cm

16 cm

................
................

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