Directions: Fill out the necessary information properly. Read and understand the instructions.<div><span>Answer only </span><span>Activity Nos. 3-5.</span></div>

7
     Mathematics
       Quarter 2 – Module 1:
    Approximating Measurement




CO_Q2_Math 7_ Module 1


 Lesson
                Approximating
    1           Measurement
       Have you ever wondered what the world would be when we use our palm,
handspan, and forearm length instead of rulers, measuring tapes, and meter sticks?
This module connects us to the history where we don’t have to worry about our
physical differences such as sizes of our palm and forearm because the standards
are already set. To appreciate more, let us learn together this module.




                What’s In

   Let us recall first some important terms of measurement. Rearrange the letters
the following highlighted terms and fill in the blanks provided to complete the
sentences.
   1. To EURSEAM _________________ means to give a particular number to a
      particular characteristic of a person, an object, or a concept. When
      measurements are made, they are expressed quantitatively as numbers.
   2. The THLEGN _____________________ is the term used for identifying the size of
      an object by the distance from end to end or commonly referred to as the
      longest dimension of an object.
   3. SAMS ____________________ refers to the amount of matter an object has while
   4. HTIWEG __________________ is the gravitational force acting on an object.
   5. MVOEUL ___________________ is the amount of space an object occupies. In a
      container, it is considered to be the capacity of the container.
   6. ETIM _____________________ is the ongoing and continuous sequence of events
      taking place in succession, from past to the present to the future.
   7. LENAG ____________________ was derived from the Latin word angulus, which
      means corner. It is a figure formed when two rays share a common endpoint
      called the vertex.
   8. ERATEMUPTER ______________________ is the measurement of the degree of
      hotness or coldness of an object or a substance.
   9. ERTA __________________ is the ratio between two related quantities in
      different units.


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                                                                CO_Q2_Math 7_ Module 1


                       What’s New


Activity 1. Let’s do this TOGETHER!
        Determine the dimension of the following objects at home using only the parts
of your arms. Indicate the appropriate part of the arm used for each object. Do this
activity with your parent, guardian or sibling. Record the results in the given table
below. The first two columns were accomplished as your example.



                       envelop         notebook           table            house
                    Length   Width   Length   Width   Length   Width   Length   Width
 What arm part is
 used?
     Palm           palm    palm
     Handspan
     Forearm
       length

 YOU                   6       4

 Parent/
 Guardian/             5       3
 Sibling



Note: Palm – the width of one’s hand excluding the thumb
      Handspan – the distance from the tip of the thumb to the tip of the little finger
      of one’s hand with fingers spread apart
      Forearm length – the length of one’s forearm; the distance from the elbow to
      the tip of the middle finger




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                                                                  CO_Q2_Math 7_ Module 1


                What is It


       How was your experience with the previous activity? Did you find it hard to
do actual measurement? Were there any differences in your data and your other
family member’s data? What do you think is the cause of those differences? These
could explain everything!

                          HISTORY OF MEASUREMENT

       One of the earliest inventions of human beings was the unit of measurement.
In ancient times, people needed measurement to determine how long or wide things
are. They need to measure things to build their houses or make their clothes. Later,
units of measurement were used in trade and commerce. In the 3rd century BC in
Egypt, people used their body parts to determine the measurements of things; the
same body parts that you used to measure the assigned things to you in Activity 1.

      The forearm length was called a cubit. The handspan was considered a half
                                       1
cubit, while the palm was considered       of a cubit. The Egyptians came up with these
                                       6
units to be more accurate in measuring different lengths.

       However, using these units of measurement had a disadvantage. Not everyone
had the same forearm length. Discrepancies arose when the people started
comparing their measurements to one another because measurements of the same
thing differed, depending on who was measuring it. Because of this, these units of
measurement are called non-standard units of measurement which later on evolved
into what is now the inch, foot and yard, the basic units of length in the English
system of measurement.


       The results of measuring are merely approximations since measurements are
not always exact. Oftentimes, there is a relative error involved.

      Accuracy of measurements depends on two factors:

      1. The skill of the person doing the measurement. This can be developed
         through constant practice.
      2. The precision of the instrument used in measuring. This is totally
         dependent to the measuring device.

       The English System of Measurement was widely used until the 1800s and
the 1900s when the Metric System of Measurement started to gain ground and
became the most used system of measurement worldwide. First described by Belgian
Mathematician Simon Stevin in his booklet, De Thiende (The Art of Tenths) and
proposed by English philosopher, John Wilkins, the Metric System of Measurement
was first adopted by France in 1799. In 1875, the General Conference on Weights
and Measures (Conférence générale des poids et mesures or CGPM) was tasked to


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                                                                  CO_Q2_Math 7_ Module 1


define the different measurements. By 1960, CGPM released the International
System of Units (SI) which is now being used by majority of the countries with the
biggest exception being the United States of America. Since Philippines used to be a
colony of the United States, earlier Filipinos were taught in the use of the English
instead of the Metric System of Measurement. Thus, they preferred English System
rather than the Metric System although the Philippines have already adopted the
Metric System as its official system of measurement.

       The Metric System of Measurement is easier to use than the English System
of Measurement since its conversion factors would consistently be in the decimal
system, unlike the English System of Measurement where units of lengths have
different conversion factors. The base unit for length is the meter and units longer
or shorter than the meter would be achieved by adding prefixes to the base unit.
These prefixes may also be used for the base units for mass, volume, time and other
measurements.

       Here are the common prefixes used in the Metric System:
 PREFIX         SYMBOL                           FACTOR
 yyota-             Y     x 1 000 000 000 000 000 000 000 000 or 1024
 zeta-              Z     x 1 000 000 000 000 000 000 000 or 1021
 exa-               E     x 1 000 000 000 000 000 000 or 1018
 peta-              P     x 1 000 000 000 000 000 or 1015
 tera-              T     x 1 000 000 000 000 or 1012
 giga-              G     x 1 000 000 000 or 109
 mega-              M     x 1 000 000 or 106
 kilo-              k     x 1 000 or 103
 hecto-             h     x 100 or 102
 deka-              da    x 10 or 101
 deci-              d     x 1/10 or 10-1
 centi-              c    x 1/100 or 10-2
 milli-             m     x 1/1 000 or 10-3
 micro-              µ    x 1/1 000 000 or 10-6
 nano-              n     x 1/1 000 000 000 or 10-9
 pico-              p     x 1/1 000 000 000 000 or 10-12
 femto-              f    x 1/1 000 000 000 000 000 or 10-15
 atto-               a    x 1/1 000 000 000 000 000 000 or 10-18
 zepto-              z    x 1/1 000 000 000 000 000 000 000 or 10-21
 yocto-              y    x 1/1 000 000 000 000 000 000 000 000 or 10-24

      The seven SI base units are comprised of:
               QUANTITY                                  BASE UNIT
                 Length                                   meter (m)
                  Time                                    second (s)
          Amount of Substance                            mole (mol)
             Electric current                            ampere (A)
              Temperature                                 kelvin (K)
           Luminous Intensity                           candela (cd)
                  Mass                                  kilogram (kg)




                                         8
                                                               CO_Q2_Math 7_ Module 1


      In both English and Metric system, there is a basic unit for length, mass,
volume, time, temperature and angle. Though these basic units are still widely used,
the adoption of the International System of Units will serve its purpose which is to
provide the same values of measurements wherever it is performed.

Questions to ponder:
   1. When a Filipina is described as 1.7 meters tall, would she be considered tall
      or short? How about if she is described as 5 ft and 7 in tall, would she be
      considered tall or short?
          Chances are, you will find it difficult to answer the first question. For the
            second question, a Filipina with a height 5 ft and 7 in would be
            considered tall by Filipino standards.

   2. Which particular unit of height were you more familiar with? Why?
         Possibly, in measuring height, the use of feet and inches is more familiar
            to you than that of meters because the English system is still being
            widely used in the Philippines for this quantity.

Example 1. Estimate your Non-Standard Units.

       Use a measuring tool (tape measure or ruler) to measure your Non-Standard
Units to Metric Units. Note your answer for the next activity.
                                         Table 1

                                palm               handspan            forearm length


    centimeters


       meters


       Using the data in Table 1, estimate the lengths of the following objects in
Table 2 without using any measuring tool.

                                         Table 2
                                                         length of
                                                        your foot
                                                                          length of
                                         length of    (from the tip
                      ballpen                                            your dining
                                       window pane     of your heel
                                                                            table
                                                       to the tip of
                                                        your toes)

 Non-Standard
     Unit


  Metric Unit




                                            9
                                                                 CO_Q2_Math 7_ Module 1


Example 2. Mass/ Weight

       Anna plans to buy plants and vermi cast at nearby garden shop but has a
vehicle with limited weight capacity of 800 kilograms for the items to be bought. If
the sacks of vermi cast weigh 250 kilograms and each plant weighs approximately
4.5 kilograms, what is the maximum number of plants that Anna can buy and
transport regardless of the size?


Solution.     Step 1:      Find the available capacity the vehicle can hold.

                           capacity – weight of vermi cast
                           800 kg – 250 kg = 550 kg
                                      550 ????????
              Step 2:                           = 122.22 ≈ 122
                                      4.5 ????????

      Therefore, 122 is the maximum number of plants that Anna can buy and
transport.

Example 3. Volume

        A rectangular container van needs to be filled with identical cubical
balikbayan boxes. If the container van’s length, width and height are 16 ft, 4 ft and
6ft, respectively, while each balikbayan box has an edge of 2 ft, what is the maximum
number of balikbayan boxes that can be placed inside the van?

Solution.     Step 1:      Vvan   =
                                  lwh
                                  =
                                  (16 ft)(4 ft)(6 ft)
                                  =
                                  384 ft3
              Step 2:      Vbox   =
                                  e3
                                  =
                                  (2 ft)3
                                  =
                                  8 ft3
                                                   V????????????
              Step 3:      Number of boxes      =
                                                    V????????????
                                                        384 ???????? 3
                                                    =
                                                         8 ???????? 3
                                                    = 48 boxes

Example 4. Angle
      In estimating measurement of angle, we need to recall the different kinds of
angles such as:
              1. Acute angle – angle whose measure is less than 90°
              2. Right angle – angle whose measure is exactly 90°
              3. Obtuse angle - angle whose measure is more than 90°

1. Estimate the measurement of the angle below. Use your protractor to check your
estimate.

                                  Estimate _______________
                                  Measurement using the protractor _______________
             Measurement = 50°


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                                                                   CO_Q2_Math 7_ Module 1


2. What difficulties did you meet in using your protractor to measure the angles?
          One of the difficulties you may encounter would be on the use of the
             protractor and the angle orientation. Aligning the cross bar and base line
             of the protractor with the vertex and an angle leg, respectively, might
             prove to be confusing at first, especially if the angle opens in the
             clockwise orientation. Another difficulty arises if the length of the leg is
             too short such that it won’t reach the tick marks on the protractor. This
             can be remedied by extending the leg.

3. What can be done to improve your skill in estimating angle measurements?
          You may familiarize yourself with the measurements of the common
            angles like the angles in the first activity, and use these angles in
            estimating the measurement of other angles.

Example 5. Temperature

       Zale, a Cebu resident, was packing his suitcase for his trip to New York City
the next day for a 2-week vacation. He googled New York weather and found out the
average temperature there is 15C. Should he bring a sweater? What data should
Zale consider before making a decision?

       Solution.
       1. What data should Zale consider before making a decision?
           In order to determine whether he should bring a sweater or not, Zale
             needs to compare the average temperature in New York City to the
             temperature he is used to which is the average temperature in Cebu.
             Compared average temperatures should always be expressed in same
             units and be converted if it differs.

       2. Should Zale bring a sweater?
            The average temperature in Cebu is between 24 – 32 C. Since the
             average temperature in New York City is 15C, Zale should probably
             bring a sweater since the latter’s temperature is way below the
             temperature he is used to. Better yet, he should bring a jacket just to be
             safe.

Example 6. Time/ Rate

   The concept of time is very basic and is integral in the discussion of other
concepts such as speed. Currently, there are two types of notation in stating time,
the 12-hr notation (standard time) or the 24-hr notation (military or astronomical
time). Standard time makes use of a.m. and p.m. to distinguish between the time
from 12midnight to 12 noon (a.m. or ante meridiem) and from 12 noon to 12 midnight
(p.m. or post meridiem). This sometimes leads to ambiguity when the suffix of a.m.
and p.m. are left out. Military time prevents this ambiguity by using the 24-hour
notation where the counting of the time continues all the way to 24. In this notation,
1:00 p.m. is expressed as 1300 hours and 5:30 p.m. is expressed as 1730 hours.



                                           11
                                                                  CO_Q2_Math 7_ Module 1


   Consider the given situation:

   An airplane bound for Beijing took off from the Ninoy Aquino International Airport
at 11:15 a.m. Its estimated time of arrival in Beijing is at 1555 hrs. The distance
from Manila to Beijing is 2839 km.

   Questions:
      1. What time (in standard time) is the plane supposed to arrive in Beijing?
      2. How long is the flight?
      3. What is the plane’s average speed?

   Solution.
      1. What time (in standard time) is the plane supposed to arrive in Beijing?
          3:55 P.M.
      2. How long is the flight?
          1555 hrs – 1115 hrs = 4 hrs, 40 minutes or 4.67 hours
      3. What is the plane’s average speed?
                    ????
           S=
                    ????
                    2839 ????????
                =
                    4.67 ℎ????????
                = 607.92 kph

Example 7. Determine a practical SI unit for each of the following:


   1. Length of the provincial road                   Answer: kilometer
   2. Total area of a farm                            Answer: square meter
   3. The mass of a baby                              Answer: kilogram
   4. The volume of a small pail of water             Answer: liter
   5. The mass of a 24k gold bracelet                 Answer: gram
   6. A bottle of juice drink                         Answer: milliliter
   7. The length of wire of a phone charger           Answer: meter
   8. A squash bought at the market                   Answer: kilogram
   9. An extension wire                               Answer: meter
   10. A small bottle of alcohol                      Answer: milliliter




                                         12
                                                               CO_Q2_Math 7_ Module 1


Directions: ANSWER ME! Type the word " degrees" after the number. Ex: 15 degrees

                    What’s More


 Activity 2.
        Using the data from Example 1, Table 1, convert the dimensions of the sheet
 of paper, teacher’s table, and the classroom into Metric units. Recall past lessons
 on perimeter and area and fill in the appropriate columns:


               sheet of intermediate
                                              dining table               house
                       paper

                              Peri-                   Peri-                   Peri-
               Length Width         Area Length Width       Area Length Width       Area
                              meter                   meter                   meter
Non-
Standard
Unit
Metric
Unit


 Activity 3.
       Estimate the measurement of the given angles, then check your estimates by
 measuring the same angles using your protractor.




  angle



                                 A                    B                     C


  estimate




  measurement




                                             13
                                                                  CO_Q2_Math 7_ Module 1


Directions: ANSWER ME! Fill out the box using the appropriate SI unit of measure for the given objects. Do not put a dot to your answer. If the answer is in square unit, type ^2 after the unit.

Type your answer on the box. Write the word "degrees" before the temperature.<div>Ex. 22 degrees Celsius. Capitalize the first letter of the temperature. </div>

Activity 4.
        Choose an appropriate SI unit of measure for each of the following:
Length:

   1. A pencil
   2. A flagpole
   3. A highway


Mass:
   4. A sack of rice
   5. A 10-year old boy


Liquid measure:

   6. A jug of water
   7. A tank of gasoline
   8. A dose of medicine


Area:
   9.  The area of the front cover of a book
   10. The surface area of a microchip

Activity 5.
Choose the best approximation of temperature for the following:
   1.   A   good day to go swimming:             15°C, 32°C, 55°C
   2.   A   feverish condition:                  29°C, 33°C, 38°C
   3.   A   moderate oven temperature:           300°F, 400°F, 450°F
   4.   A   good night to sleep:                 15°C, 34°C, 58°C
   5.   A   glass of hot milk:                   10°C, 15°C, 40°C




                   What I Have Learned



        Let’s recap! Fill in the blanks to complete the following sentences.

        1. At around 3rd century BC in _______________, people use their body parts
           to determine the measurement of things.
        2. In 1800s, the _______________ is widely used and later in 1900s,
           _______________ started to gain ground.



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                                                                  CO_Q2_Math 7_ Module 1


7
     Mathematics
       Quarter 2 – Module 1:
    Approximating Measurement




CO_Q2_Math 7_ Module 1