MATHEMATICS 7
Quarter 2 Week 1 Module
Republic of the Philippines
Department of Education
National Capital Region
Schools Division Office – Caloocan City
MATH 7 QUARTER 2 WEEK 1 P a g e 1 | 11
NAME: ____________________________________ YR & SEC: _____________________
Competency
The learner approximates the measures of quantities particularly length, weight/mass, volume, time, angle and temperature and rate. (M7ME-IIa-3)
To The Learners
Before starting the module, I suggest that you avoid all distractions that will hinder you from getting quality work done. Read the simple instructions below, focus on the tasks and you’ll be on your way to perform them with exactness!
1. Follow the instructions indicated in every activity.
2. Write on your notebook the concepts about the lessons. Writing preserves ideas and makes learning permanent.
3. Perform all the provided activities in the module.
4. Let your guardian assess your answers using the answer key card.
5. Analyze conceptually the posttest and apply what you have learned.
6. Do your best and have fun studying! Happy learning!
This module was designed to help you master on how to estimate measure of quantities such as length, weight/mass, volume, time, angle, temperature, and rate.
After going through this module, you are expected to:
1. identify different measures of quantities;
2. differentiate one type of measure of quantities from another type;
3. distinguish appropriate measure of quantities to be used; and 4. estimate measures of quantities.
Read and analyse each question carefully. Choose the letter of the correct answer. Write your answer on your answer sheet.
____1. Which of the following is NOT considered as measure of quantities?
A. Hours B. Length C. Mass D. Rate
____2. Which of the following parameters is appropriate in calculating a weight of a man?
A. Hours B. Length C. Mass D. Rate
____3. Which of the following is the most appropriate in determining the capacity of a swimming pool?
A. Angle B. Temperature C. Time D. Volume
____4. What is most likely the height of a flagpole?
A. 1 500 m B. 1 000 m C. 100 m D. 10 m
____5. What is likely to be the temperature on a very hot day in Tuguegarao?
A. 20°C B. 25°C C. 39°C D. 60°C
____6. Which of the following is the best preference for one inch?
A. Diameter of a one-peso coin C. Length of a twenty-peso bill B. Distance of a floor to ceiling D. Thickness of baby’s fingernail
MATH 7
QUARTER 2 Week 1
Pre-Test
Expectations
____7. Rohan wants to know how many inches his basketball is all the way round. Which is the most appropriate tool to use?
A. Measuring tape B. Meter stick C. Ruler D. Yardstick
____8. At 9:45 A.M., Romeo left his house and went to the basketball court. Riding his motorcycle, it took him 10 minutes to get to the court. He promised his wife that they will eat lunch together. What time should he leave the court so that he will be home by 12:00 P.M.?
A. 11:40 A.M. B. 11:45 A.M. C. 11:50 A.M. D. 11:55 A.M.
____9. The distance from Benj’s home to school is 850 meters. He had already walked about 700 meters. Estimate how much of the distance he needs to walk.
A. 50 m B. 100 m C. 150 m D. 200 m
____10. Athena’s bag contains 5 books. Each book weighs 200 grams and the bag weighs 100 grams. How much does the entire bag weigh?
A. 1 000 g B. 1 100 g C. 2 00 g D. 2 100
From your previous lesson, you have learned the real number system, its subsets, operations on real numbers and the real-life situations where you could find solutions to the problems involving real numbers. As you step in another topic, you will still apply what you have learned in real number system especially in simplifying and solving problems.
Since measurement involves quantities, operations on real numbers are still very useful. The looking back lessons below will help you to deal with the latter part of the topics on measurements.
Multiplying and Dividing Numbers by a Power of 10 (10, 100, 1 000, ... )
In multiplying numbers by a power of 10, just move the decimal point to the right depending on the number of zeroes of the given power of 10.
In dividing numbers by a power of 10, just move the decimal point to the left depending on the number of zeroes of the given power of 10.
Examples:
A. Find the product of the following:
1. ( 143.98)( 1 000) = 143 980 2. (56)( 100 ) = 5 600 3. ( 0.0078 )( 10 000 ) = 78 Solution: Solution: Solution:
B. Find the quotient of the following:
1. 97 ÷ 100 = 0.97 2. 118.63 ÷ 10 = 11.863 3. 45 900 ÷ 1 000 = 45.9 Solution: Solution: Solution:
Lesson: Measures of Quantities
Measurement is the process of associating numbers with physical quantities and phenomena. We use different measuring tools for a certain quantity to be measured. For example, we use ruler in measuring the length; weighing scale in measuring the mass/weight; and measuring cup in determining the amount of a certain object. There are a lot of tools/devices appropriate in measuring objects. However, these instruments are not yet invented in ancient times. Do you realize how the primitive people measure things around them?
In around 3rd or 4th B.C., all units of measurements were based on something that is familiar to them. Earliest people used body parts and things around them. These are the examples:
Looking Back at your Lesson
Introduction of the Topic
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Figure 4: Measuring the length of a crayon
Table 1: Ancient Measurements
Ancient People Basic Unit Description Image if possible
Egyptians
Cubit Distance from the tip of the middle finger to the elbow
Digit One finger
Span
Distance from the tip of a thumb of a stretched hand to the tip of a pinky finger
The body parts being used during this time can lead to confusion as the measurements varied from one person to another. Due to this situation, many standards of measurement were developed.
English system of measurement is one of the many standards. The basic units of length under this system are:
inch, foot, yard and mile. Pound (lb) and ounce (oz) are the basic measure for weight/mass. Converting from one unit to another requires more time in English system that is why another standard of measurement is being developed; that is the metric system of measurement. Meter (m) is basic unit of length while gram (g) for weight/mass.
Measuring Length
Length is the distance from one point to another. The common units used in measuring length are: inches, feet, yards, and miles in English System; and millimeter (mm), centimeter (cm), meter, and kilometer (km) in Metric System. Inch, foot, millimeter, and centimeter are used for shorter objects. On the other hand, yard, mile, meter and kilometer are units for longer objects. We can also measure length using a variety of measuring tools.
Example 1:
Suppose you were asked to measure the length of a crayon. What do you think is the appropriate measuring device to be used?
Since a crayon is shorter in length, a ruler, which has a unit of both inch and centimeter, can be used in finding the length of a crayon. Using inch as a unit, the crayon is 3 inches (in plural) long.
Observe that the measurement is composed of two parts: a number and a unit of measure. Length should always be accompanied by a unit of measure for us to visualize how long an object is.
Here are some units of length that are commonly used in daily life.
Example1:
The length of the table is 3 span.
Example 2:
The length of the pool is 5 cubit.
Figure 3: Ruler Figure 1: Tape measure Figure 2: Yardstick
Measuring Weight/Mass
Weight and mass are two different quantities. Weight is defined as the measurement of the pull of gravity on an object while mass is a measure of how heavy an object is. The lesson will focus on measuring mass.
In the metric system, gram is the basic unit of mass. It is used for smaller or lighter masses such as ingredients in recipes or nutritional facts at the back of various food labels. Thus, kilogram (kg) is for heavier masses such as rice and meat.
There are different instruments used in measuring mass. Most commonly used and seen are the following:
Example 1:
When selling fruits and vegetables, you need to be precise with the measurement of the product so that you may earn and save more money. Suppose, you are a vendor and a buyer wants 2 kg of pineapple. You have to choose the most appropriate measuring tool. In a weighing scale, make sure that the pointer is at zero mark. As you put the pineapple, the pointer moves and points to its mass.
Example 2:
In the figure below, since the pointer is between 7000g and 8000g, the weight of the fruits is 7500g.
Here are some units of mass that are commonly used in daily life.
Measuring Volume/ Capacity
Volume is the amount of space in any form of solid or liquid matter occupies.
The cubic meter is the standard unit of volume. The related units are:
Capacity is the amount of matter, usually liquid, which a container can hold.
The liter is the basic unit of capacity and is equivalent to a cubic decimeter. The other units of capacity are:
Like the first two measurements discussed, measuring volume has also different devices to be used. A medicine dropper, spoon, teaspoon, measuring cup can be used in finding the volume of smaller objects.
Figure 6: Weighing
scale Figure 7: Electronic digital weighing scale
Figure 8: Beam balance
Figure 9: Medicine dropper
Figure 10:
Standardized tablespoon
Figure 11: Measuring cup
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Figure 12: Junah's typing rate
Example 1:
In the figure below, since the water level is between40 and 60, then the capacity is 50 units.
Example 2:
While it is complicated to measure larger objects, you can do some indirect measurements. For example, you are about to measure the volume of a huge pail. You can use a 2-liter drinking bottle to fill in a huge pail. This is done until the pail is in full
capacity. Count how many times you fill in the pail. In this manner, you can estimate its volume.
Measuring Time and Angle
Time describes how long it takes to do something. Both English and metric system uses the same units of measurement for time. The table below represents the units of time and their equivalence:
Table 2: Basic Units of Time and Their Equivalence 60 seconds (s) = 1 minute (min)
60 minutes = 1 hour (hr)
24 hours = 1 day
7 days = 1 week (wk)
52 weeks = 1 year (yr)
12 months (mo) = 1 year
365 days = 1 year
366 days = 1 leap year
Clocks and watches are the devices used to show the passage of time. A.M. means ante meridiem which denotes before midday while P.M. means post meridiem which denotes after midday. Elapsed time is the amount of time that has passed from a given time to another given time.
Example 1:
Suppose, your mother went to the market by 9:00 A.M. and went back home by 11:30 A.M. How much time does she spend outside the house?
Using a clock, the starting time will be at 9:00 A.M. From 10:00 A.M., that is 1 hour.
From 10:00 A.M. to 11:00 A.M., another 1 hour, accumulated of 2 hours. All we have to do is to add 2 hours and the remaining 30 minutes. Therefore, mother is outside the house for about 2 hours and 30 minutes.
Example 2:
Another example is when Aunt Guia is cooking your favorite adobo. She started cooking around 8:05 A.M. She prepared the ingredients for 25 minutes and cooked for about 35 minutes. At what time will adobo be served?
Adding all of them, that will be:
Preparing ingredients - 25 minutes Cooking - 35 minutes
Total time consumed 60 minutes or 1 hour
Since the total time consumed is 60 minutes or 1 hour, the adobo of Aunt Guia will be served at 9: 05 A.M.
Angle is the union of the endpoints of a ray. The space between the two rays is the angle. In the figure below, angle (symbol for angle: ∠) ABC is formed when ray 𝐵𝐴⃗⃗⃗⃗⃗ and ray 𝐵𝐶⃗⃗⃗⃗⃗ intersect at common endpoint which is B. The common endpoint is called the vertex while rays 𝐵𝐴⃗⃗⃗⃗⃗ and 𝐵𝐶⃗⃗⃗⃗⃗ are the sides. Angle ABC, in symbols is: ∠𝐴𝐵𝐶.
Protractor is the instrument used in measuring angles. Angles are measured in degrees (°). A complete rotation of a ray is 360°. Therefore, one degree is 1
360 of its complete rotation.
The picture illustrates the proper way of measuring angles using a protractor. The vertex of the angle should coincide with the midpoint of the base of the protractor. One side of the angle should be aligned with the zero marking of the protractor. In reading the measure of an angle; start from zero up to the point where the other side of the angle coincides. Hence, the measurement of ∠𝐴𝐵𝐶 is 130°.
Measuring Rate
Rate is a quantity, amount, or degree of something measured per unit of something else. It is a comparison of two different quantities. There is no specific unit for rate. It depends on the two quantities that we are relating to each other . Typically, rate refers a specific quantity over time.
Example 1:
Junah can type 1 200 words in 30 minutes. Her typing rate is 400 words per minute. Rate can be associated to an average speed.
Junah’s typing rate = 1 200 𝑤𝑜𝑟𝑑𝑠
30 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 =400 𝑤𝑜𝑟𝑑𝑠
𝑚𝑖𝑛
Example 2:
Romeo drives at the rate of 60 𝑘𝑚
ℎ𝑟 . He reached his office after 4 hours of driving. How far is his office from home?
There are different ways in finding the answer. Still, we will arrive at the same answer. One way of solving the problem is by drawing a diagram. Based on the illustration, we can say that the distance between Romeo’s home and office is 240 km.
Measuring Temperature
Temperature is the measure of hotness or coldness of an object. Temperature of an object does not depend on its size. That is, the temperature of boiling water in a cup is similar to the temperature of boiling water in a large bowl.
The basic units used in temperature are degree Fahrenheit (°F) and degree Celsius (°C). Celsius scale is easier to remember as 0°C is the freezing point and 100°C is the boiling point. Thermometer is the device used to measure temperature.
Example 1:
In the figure on the right, the temperature is 41°C since the mercury level is on that level.
Example 2:
It is easier to read temperature using a digital thermometer since the digit is already seen in its monitor. The temperature is 36.8°C.
Activity 1: Ancient Crossword Puzzle
Direction: Read the clues and fill in the correct answer.
Activity 2: Guess the Word
Activity 2: What is the longest word without vowel?
Activities
Figure 13: Romeo's driving rate
Across:
3 One of the many standards develop but converting from one unit to another takes more time
5 One of the basic units of mass in English system
6 One of the basic units of mass in metric system
7 Width of one finger
8 One of the basic units of length in English system
9 Distance from the tip of a thumb of a stretched hand to the tip of a pinky finger 10 One of the many standards develop and
converting from one unit to another makes it easier
Down:
1 One of the ancient people who used their body parts in measuring objects
2 One of the familiar things around primitive people that is used in measuring
4 It is a process of measuring or quantifying
MATH 7 QUARTER 2 WEEK 1 P a g e 7 | 11
Answer each item by finding its length. Notice that below the given are letters with corresponding values. Write this letter in each box at the bottom that contains the number of the exercise. Keep on working until you discover the answer to the question.
1. 4.
2. 5.
3.
6.
T - 4 inches H - 1.5 inches
Y - 7.5 inches R - 5 inches S - 5 inches M - 2.25 inches
Activity 3: Let’s be Healthy
Below are the nutrition facts of two different brands of sardines.
Miss Sardines Serving Size ……… 2 oz Serving Per Container ………. 3 Calories …….……..………… 50 Total Fat ………..… 2.5 g Cholesterol ……….……...…..15 mg Sodium ………..……610 mg Protein ………...……..….6 g
Lucky 9 Sardines Serving Size ……… 4 oz Serving Per Container ………. 3 Calories …….……..………… 80 Total Fat ………..… 3.5 g Cholesterol ……….……...….. 10 mg Sodium ………..….. 710 mg Protein ………...………. 5 g _____________ 1. What is the serving size of Miss Sardines based on the label?
_____________ 2. How many calories would be there in one ounce of Miss Sardines?
_____________ 3. What is the serving size of Lucky 9 Sardines based on the label?
_____________ 4. How many calories would be there in one ounce of Lucky 9 Sardines?
_____________ 5. Comparing the calorie content per ounce of the two brands, which of them has lower calorie content?
Activity 4: Tricky Liters
Direction: Find the solution to the given situation.
1. A box of juice containing 10 pieces of tetra pack costs P95.00. Each pack is 250 mL. Another is a 1 000 mL bottle of juice costs P65.00. Which of the two is more economically cost effective?
2. Millie’s Milktea grand opening offers two special deals. Here are the special deals: 1) if you buy 1L milktea for Php 90, you will get another 1L for free; 2) if you buy two 500ml milktea for Php 80, you will get one 500 ml for free. Which of the two is the best deal?
Activity 5: Let’s be Covid Free
What is the safest way to keep Covid-19 away?
Answer each item. Notice that below the given are letters with corresponding values. Write this letter in each box at the bottom that contains the number of the exercise. Keep on working until you discover the answer to the question.
1. What tool is used to measure angle?
2. Mace studied for about 2 hours and 10 minutes. If she started at 4:50 P.M., at what time will she be finished studying?
5 2 1 6 2 4 3
3. Chardie went to the market at 6:45 A.M. He bought necessary supplies for 2-day concern lockdown at their place.
He went back home around 8:35 A.M. How long did he spend outside the house?
4. What do you call the intersection of the endpoints of two rays?
5. It takes 2 hours and 10 minutes to travel from Manila to Palawan by plane. Alecsa needs to be in Palawan by 10:30 A.M. At what time does she need to travel?
6. How many minutes had elapse between 6:35 A.M. to 8:55 A.M.?
7. What device is used to indicate passage of time?
8. What is formed when the endpoint of two rays unite?
A - Clock T - Vertex
E - 8:20 A.M. O - Protractor
H - 140 minutes S - 7:00 P.M.
M - Angle Y - 1 hour and 50 minutes
2 4 7 3 7 4 6 1 8 5
Activity 6: Inverted Word
What is a five-letter word that reads the same upside down and right side up?
Answer each item. Notice that below the given are letters with corresponding values. Write this letter in each box at the bottom that contains the number of the exercise. Keep on working until you discover the answer to the question.
1. The technician received P900 for repairing three appliances. How much does he received for repairing one appliance?
2. A school bus traveled 2 hours at a constant rate. The bus traveled 80 km. What is its rate in kilometers per hour?
3. If the speed of a car is 55 km/hr, how long does the car travel for 2 hours?
4. A factory worker received a payment of P 450 for 2 working days. How much will he receive after working for 10 days?
I - 110 km W - P2 250
S - 40 km per hour M - P300
2 4 3 1 2
Activity 7: Match Making
Direction: Match the items in Column A with the appropriate temperature readings in Column B.
Column A 1. Normal body temperature 2. Boiling water in a kettle 3. Normal room temperature 4. Ice freezer
5. Freezing point
Column B A. -20°C B. 0°C C. 30°C D. 37°C E. 100°C
There are different quantities to be measured such as length, mass, volume, time and angle, rate and temperature.
Each quantity had certain unit and measuring tools to be used. The table below shows the summary for each quantity.
Quantity Common Units Common Measuring Tools
Length Inch, feet, yard, mile, meter,
kilometer Tape measure, ruler, yardstick
Mass Pound, ounce, gram, kilogram
Weighing scale, Electronic digital weighing scale, beam balance
Remember
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Volume Liter (liquid volume); cubic
decimeter (solid volume)
Medicine dropper, standardized tablespoon, measuring cup
Time Second, minute, hour Clock, watch
Angle Degree Protractor
Rate Depends on the quantities being
compared
Depends on the quantities being measured
Temperature Degree Fahrenheit, degree
Celsius Thermometer
Direction: Choose the best estimate for each measure of quantity.
1. Medicine dropper 1 mL l0 mL 100 mL
2. Medium-sized apple 200 kg 200 g 200 mg
3. Length of a car 4 cm 4 m 4 km
4. Loaf of bread 500 g 5000 g 50 000 g
5. Bottle of soda 3.5 mL 35 mL 350 mL
6. Width of a window 4 inches 4 feet 4 yards
7. Medium-sized fish 250 mg 250 g 250 kg
8. Diameter of a clock 1 inch 1 foot 1 mile
9. Tank of car gasoline 3 L 30 L 300 L
10. Boiling chocolate drink 1°C 10°C 100°C
Read and analyze each questions carefully. Choose the letter of the correct answer.
____1. Which of the following is NOT considered as measure of quantities?
A. Hours B. Length C. Mass D. Rate
____2. Which of the following parameters is appropriate in calculating a weight of a man?
A. Hours B. Length C. Mass D. Rate
____3. Which of the following is the most appropriate in determining the capacity of a swimming pool?
A. Angle B. Temperature C. Time D. Volume
____4. What is most likely the height of a flagpole?
A. 1 500 m B. 1 000 m C. 100 m D. 10 m
____5. What is likely to be the temperature on a very hot day in Tuguegarao?
A. 20°C B. 25°C C. 39°C D. 60°C
____6. Which of the following is the best preference for one inch?
A. Diameter of a one-peso coin C. Length of a twenty-peso bill B. Distance of a floor to ceiling D. Thickness of baby’s fingernail
____7. Rohan wants to know how many inches his basketball is all the way round. Which is the most appropriate tool to use?
A. Measuring tape B. Meter stick C. Ruler D. Yardstick
____8. At 9:45 A.M., Romeo left his house and went to the basketball court. Riding his motorcycle, it took him 10 minutes to get to the court. He promised his wife that they will eat lunch together. What time should he leave the court so that he will be home by 12:00 P.M.?
A. 11:40 A.M. B. 11:45 A.M. C. 11:50 A.M. D. 11:55 A.M.
____9. The distance from Benj’s home to school is 850 meters. He had already walked about 700 meters. Estimate how much of the distance he needs to walk.
A. 50 m B. 100 m C. 150 m D. 200 m
____10. Athena’s bag contains 5 books. Each book weighs 200 grams and the bag weighs 100 grams. How much does the entire bag weigh?
A. 1 000 g B. 1 100 g C. 2 00 g D. 2 100 g
Check Your Understanding
Post-Test
After learning history of measurements and the different measure of quantities, it is now time for you to create a graphic organizer which will help you remember words associated to the topic such as definition, basic units and measuring tools. Supply and complete the diagram below. As much as possible, try not to look back on the previous pages. Good luck!
To better understand the lesson, watch the following:
History of Measurement
- https://www.slideshare.net/MirasolRalo/history-of-measurements
Measuring Length - https://www.youtube.com/watch?v=ftB5VU64yGA&t=68s - https://www.youtube.com/watch?v=fcAl2g92NyY
Measuring Mass - https://www.youtube.com/watch?v=ybEU-6U7s8k - https://www.youtube.com/watch?v=a3uy4H9kjB0
Measuring Volume - https://www.youtube.com/watch?v=HuwKlGpzqB8 - https://www.youtube.com/watch?v=--tKaWlHz3E
Measuring Time and Angle - https://www.youtube.com/watch?v=yWENh35QT1k - https://www.youtube.com/watch?v=Gzd_lsNwTOI
Measuring Temperature - https://www.youtube.com/watch?v=K2CH1cUkMgs
Reflection
Additional Activities
Measurement
Length Mass Volume
Time Rate Temperature
Measurement
MATH 7 QUARTER 2 WEEK 1 P a g e 11 | 11
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Content from:
Crisostomo, R.M., et,al. (2013). “Our World of Math 7”. Page 84-131
Oronce, O.A., et.al. (2003). “Exploring Mathematics: Elementary Algebra I”. Pages 1-74
Mallari, M.T.G, et.al. (2019). “MathTIME Vol XXIII No. 2 Grade 7”. Pages 1-16
https://www.dattapolytechnic.com/physics/UNITS.pdf
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https://www.bced.gov.bc.ca/exams/search/grade10/english/sample/exam/1112fmp_p_m.pdf
https://www.seaford.k12.ny.us/cms/lib/NY01000674/Centricity/Domain/807/Mathematics%20grade%207%20practice%20final%20exam.pdf
https://www.britannica.com/technology/measurement
https://www.nyu.edu/pages/mathmol/textbook/weightvmass.html#:~:text=1)%20Mass%20is%20a%20measurement,an%20unknown%20amount%
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https://www.ipracticemath.com/learn/measurement/measurement-units
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References