milli centi deci deci hecto kilo. Explain that the same procedure is used for all metric units (meters, grams, and liters).

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1 Week & ay Week 15 ay 1 oncept/skill ompare metric measurements. Standard 7 MG: 1.1ompare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters). Materials HSEE Math Released Item # 93 Overview for Week This week will provide students with a quick review of vocabulary, methods for converting in a measurement system (inches to feet, centimeters to meters) and method for converting from one measurement system to another. Review the units used in the Metric System: o gram weight o meter distance o liter - volume Review the prefixes commonly used in the Metric System: o kilo 1000 (to remember that kilo is large remember that a kilometer is 1000 longer than a meter and a kilogram is 1000 times larger than a gram) o centi 1/100 or.01 (to remember that centi is 1/100 remember that there are 100 cents in a dollar) o milli 1/1000 or.001 (to remember that milli is very small remember that a milligram is a very miniscule amount or that milli sounds like mini and miniskirts are very short) Review how numbers can be arranged by powers of ten. Then draw a line on the board and put the metric names on it. Have students review how units are arranged within the Metric System. Emphasize that they most likely will encounter kilo-, centi-, and milli- on the test milli centi deci deci hecto kilo Explain that the same procedure is used for all metric units (meters, grams, and liters). See example on next page. SUS, Educational Services Week 15 Teacher - Page 1 of 10

2 Steps to change size of the units in the Metric System: 1. raw a number line for the Metric System. 2. Write the number of units you have under the number that corresponds with the unit. 3. ount how many moves it takes to get to the new unit. RULE: To find the conversion factor, use the number 1 and a zero for each move you make to the right or left. 4. Multiply or divide the original number by the conversion factor. RULE: When moving to the right, IVIE by the conversion factor. When moving to the left, MULTIPLY by the conversion factor. Have students do the guided practice on ay 1 of the student HSEE Math Problem of the ay -- Week 15 worksheet. Example: Seven meters is of a kilometer of a kilometer 70 kilometers 7000 kilometers 1. Start by drawing a number line for the Metric System and writing 7 under the meters place. Then count how many moves it takes to get to the meters place milli centi deci deci hecto kilo RULE: To find the conversion factor, use the number 1 and a zero for each move you make to the right or left. 2. In this case, you moved three times, so the conversion factor will be 1 and three zeros, or RULE: When moving to the right, IVIE by the conversion factor. When moving to the left, MULTIPLY by the conversion factor. 3. In the example, since you moved three spaces to the right, you will divide the original 7 m by a conversion factor of Since you had to move to the right you will need to divide by The correct answer is of a kilometer SUS, Educational Services Week 15 Teacher - Page 2 of 10

3 dditional Practice for ay 1: 1. One kilometer is of a centimeter 100 centimeters 1000 centimeters centimeters 2. Three centimeters is of a millimeter 30 millimeters 300 millimeters 3000 millimeters Have students do the HSEE released test item on ay 1 of the student HSEE Math Problem of the ay -- Week 15 worksheet. 93. One millimeter is of a meter of a meter 100 meters 1000 meters Start by drawing the Metric number line milli centi deci deci hecto kilo Since to move from the millimeter to the meter you need to move 3 spaces to the right so you will need to divide 1 by The correct answer is of a meter SUS, Educational Services Week 15 Teacher - Page 3 of 10

4 Week Week 15 ay 2 oncept/skill hange between English and metric measurements. Standard 7 MG: 1.1ompare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters). Materials HSEE Math Released Item # 94, 96 Review the units used for distance in the English system. Remind students that: o 12 inches = 1 foot o 3 feet = 1 yard Tell students that if they are asked to convert from the English system to the Metric system or Metric system to English system they will be given the conversion factor. Example: 1 meter 39 inches means that one meter is approximately 39 inches. 1. To find out how many inches something that is measured in meters is they would multiply the number of meters by If they need to change the answer to feet and inches they would divide by 12 to find the feet and the remainder is the number of inches left over. Note: In questions like these you can often eliminate the wrong answers by estimating the answer. Since a meter is just over 3 feet long you can divide the number of meters by 3 to find the approximate number of feet. ny answer that is less can be eliminated. Have students do the guided practice on ay 2 of the student HSEE Math Problem of the ay -- Week worksheet. Example: wall is 5 meters long. bout how long is the wall in feet (ft) and inches (in)? (1 meter 39 inches) 12 ft 6 in 14 ft 8 in 16 ft 3 in 18 ft 2 in Which two answers can be eliminated because they are less than 5 x 3 (there are about 3 feet in a meter) and How many inches are in 5 meters: 5 x _39 = _195 To find how many feet divide the inches by _12 The number of feet is _16_ so answer is too long. The correct NSWER is. (ay 2 continued on next page) SUS, Educational Services Week 15 Teacher - Page 4 of 10

5 dditional Practice for ay 2: (HSEE Math Released Item # 96) 96. If Jill is driving at 65 miles per hour, what is her approximate speed in kilometers per hour? ( 1 mile 1.6 kilometers) To change the miles per hour to km per hour you need to multiply the 65 miles/hour by 1.6 km/mile. The units of the new answer will be km/hour. The correct answer is 104 Note: If students divide instead of multiply they will get the incorrect answer of. Have students do the HSEE released test item on ay 2 of the student HSEE Math Problem of the ay -- Week15 worksheet. ay 2 PO (HSEE Math Released Item # 94) 94. boy is two meters tall. bout how tall is the boy in feet (ft) and inches (in.)? (1 meter 39 inches) 5 ft 0 in. 5 ft 6 in. 6 ft 0 in. 6 ft 6 in. First calculate the number of inches: 2 x 39 = 78 Then divide 78 by 12 to find the number of feet. You will get 6 feet with a remainder of 6 inches left over. SUS, Educational Services Week 15 Teacher - Page 5 of 10

6 Week Week 15 ay 3 oncept/skill onvert hours to minutes to seconds. Standard 7 MG: 1.1ompare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters). Materials HSEE Math Released Item # 95 Review the units used for time: o 60 seconds = 1 minute o 60 minutes = 1 hour o 24 hours = 1 day Review the steps to change time from one unit to another: 1. ircle the unit you are starting with and ending with. 2. Multiply if you are going from larger units to smaller units. ivide if you are going from smaller units to larger units. Have students do the guided practice on ay 3 of the student HSEE Math Problem of the ay -- Week 15 worksheet. (Remind the students that they should circle the units they are starting and ending with and that it is ok to write in the HSEE test booklets) Julia did homework for 240 minutes. How many hours did Julia do homework? The unit of time you are starting with is _minutes_. The unit you are changing to is hours. To do this you will need to divide 240 by _60_ The correct NSWER is _4 hours. ay 3 continued on next page. SUS, Educational Services Week 15 Teacher - Page 6 of 10

7 dditional Practice for ay 3 television show covers a time period of seconds. How many hours does the show cover? 1 hour 24 hours 48 hours 60 hours Since you are starting with seconds and converting to hours, a larger unit, you will need to divide. First divide seconds by 60 to change it to 1440 minutes. Then, divide 1440 minutes by 60 to change it to 24 hours. Have students do the HSEE released test item on ay 3 of the student HSEE Math Problem of the ay -- Week15 worksheet. ay 3 PO (HSEE Math Released Item #95 ) 95. Juanita exercised for one hour. How many seconds did Juanita exercise? ,600 Since you are starting with an hour and converting to seconds, a smaller unit, you will need to multiply. First multiply one hour by 60 to change it to 60 minutes. Then, multiply 60 minutes by 60 to change it to 3600 seconds. SUS, Educational Services Week 15 Teacher - Page 7 of 10

8 Week Week 15 ay 4 oncept/skill hange of scale of measurement. Standard 7 MR: 2.4 Relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1square foot = 144 square inches or [1 ft 2 ] = [144 in 2 ], 1 cubic inch is approximately cubic centimeters or [1 in 3 ] = [16.38 cm 3 ]). Materials HSEE Math Released Item # 119 Orally quiz the students to see if they know the following: o 1 foot = 12 inches o 1 square foot = 12 in. x 12 in. = 144 in 2 Review the Steps to find the area when given measurements in different units: 1. ircle the unit the answers are in. 2. hange all the units given in the problem to the unit that the answer is given in. 3. Multiply to find the area. Have students do the guided practice on ay 4 of the student HSEE Math Problem of the ay -- Week 15 worksheet. Remind students to circle the all of the units. EXMPLE: The width of the rectangle shown below is 4 feet (ft). The length is 24 inches (in). 4 ft. 24 in. Inches which need to be changed to feet What is the area of the rectangle in square feet? The units for the answer are feet. To change 24 in. to feet you will _divide_ 24 by _ in = _2 ft To find the area of the rectangle in ft: _2_ ft x _4_ ft = 8 square feet The correct NSWER is 8. ay 4 continued on next page. SUS, Educational Services Week 15 Teacher - Page 8 of 10

9 dditional Practice for ay 4: The width of the rectangle shown below is 1 yard. The length is 2 feet (ft). What is the area of the rectangle in square inches? feet 1 yard Since you are starting with a yard and feet and converting to inches, a smaller unit, you will need to multiply. First multiply 1 yard by 36 to change it to 36 inches. Then, multiply 2 feet by 12 to change it to 24 inches. To find the area multiply 36 in. x 24 in. = 864 in. Remind students that many of the multiplication problems are not easily computed in their heads. Students should write computations in the HSEE test booklet. Have students do the HSEE released test item on ay 4 of the student HSEE Math Problem of the ay -- Week15 worksheet. ay 4 PO (HSEE Math Released Item #119 ) 119. The width of the rectangle shown below is 6 inches (in.). The length is 2 feet (ft). What is the area of the rectangle in square inches? ft 6 in. needs to be changed to inches Since you are starting with inches and feet and the answer is in inches, you will need to change feet to inches. Multiply 2 feet by 12 to change it to 24 inches. Then, find the area by multiply 24 inches by 6 inches. 24 in. x 6 in. = 144 sq in. This problem is an example where students can estimate and eliminate all the incorrect answers. Since 2 feet is just over 20 inches and 6 x 20 is 120, answers,, and can not be correct. The key is to look at the units and to make sure they have changed all the units to the same kind as the answer SUS, Educational Services Week 15 Teacher - Page 9 of 10

10 Week Week 15 ay 5 oncept/skill onversion between units. Standard 7 MR: 2.1 Relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic feet) and to conversions between units (1square foot = 144 square inches or [1 ft2] = [144 in2], 1 cubic inch is approximately cubic centimeters or [1 in3] = [16.38 cm3]). Materials HSEE Math Released Item # 121, # 120 ay 5 Students will have an opportunity to practice the strategies they used during Week 15 to find the answers to two released items for the HSEE. Have students do the HSEE released test item on ay 5 of the student HSEE Math Problem of the ay -- Weekvv15 worksheet. ay 5 PO (HSEE Math Released Item # 121 ) 121. rectangular field is 363 feet long and 240 feet wide. How many acres is the field? (1 acre = 43,560 square feet) First find the area of the field in square feet: 363 ft x 240 ft = sq ft Then divide by to find the number of acres which is 2. Here is another problem where estimation will enable students to easily eliminate the wrong answers. Since x 2 is 88000, the answer has to be 2. Try multiplying by 3 and you get over so any answer 3 and above would not be correct. dditional Practice for ay 5 (HSEE Math Released Item # 120 ) 120. One cubic inch is approximately equal to cubic centimeters. pproximately how many cubic centimeters are there in 3 cubic inches? This is another example where students can easily eliminate the wrong answers without having to do a large multiplication problem. To find the exact answer you would need to multiply 3 x and can be eliminated since they are less than can be eliminated since it is only slightly larger than must be the correct answer. You can check by doing an estimate of 15 x 3 = 45 which is very close to t the end of the week remind students to keep the student HSEE Math Problem of the ay -- Week 15 worksheet to use as a study guide as they continue to prepare for the HSEE. SUS, Educational Services Week 15 Teacher - Page 10 of 10

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