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. 5 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 6 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 7 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° 10 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 15C. 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 15C, 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

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