PASIG CATHOLIC COLLEGE Grade School Department School Year MATHEMATICS 5 THIRD QUARTER Activity Sheet No. 1

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1 Activity Sheet No. 1 TYPE OF ACTIVITY: Concept Development LEARNING OBJECTIVES : Place Value and Value of Decimals : Identify the place value and value of each decimal digit. Read and write decimals. REFERENCE : Soaring 21 st Century Mathematics 2 nd Edition, pp Manuel T. Kotah, et al. Math for Life 5 Revised Edition, p Adelaida Celeridad-Wright & Adela C. Villamayor A decimal is a number less than one that represents units divided equally into powers of ten of which is separated by a decimal point from the whole number. Whole Numbers Ones Example: 1.) Decimal Point Recall: Place Value System Decimals Tenths Hundredths Thousandths Ten Hundred thousandths thousandths 1 1/10 1/100 1/1000 1/ / In reading decimals the standard way, follow these steps: 1.) Read the whole numbers as it is, 2.) Read the decimal point as and, 3.) Read the decimal digits like that of a whole number, 4.) State the place value of the last decimal digit. Therefore, is read as four and sixty-seven thousand two hundred fifty-three hundred thousandths. In cases where the whole number is zero (0), steps 1 and 2 should be omitted. 2.) is read as five thousand nine hundred thirteen ten thousandths. Note: To emphasize the decimal point in numbers less than one, a zero should be written as the digit in the ones place.

2 , PASIG CATHOLIC COLLEGE Activity Sheet No. 2 : Fractions to Decimals LEARNING OBJECTIVES : Rename fractions as decimals. REFERENCE : Math for Life 5 Revised Edition, p. 172 AUTHOR/S : Adelaida Celeridad-Wright & Adela C. Villamayor A fraction can be changed to decimal easily if the denominator is a power of ten. However, not all fractions has a denominator which is a power of ten. Case 1: If the denominator of the simplest form is a factor of any power of ten, change the fraction to an equivalent fraction with a denominator of a power of ten of which it is a factor. Simplifying the given fraction first may also help. 1.) 2.)!! à!!" =!"!!" 100 (seventy-five hundredths). Therefore,!! = 0.75!! à!! =!" = 2!!! 10!" (two and five tenths). Therefore,!! = 2.5 [Hint: A fraction can be changed to an equivalent fraction if the denominator of its simplest form is a power of 2 or a power of 5.] Case 2: If the fraction cannot be changed to an equivalent fraction that has a denominator of any power of ten, divide the numerator by the denominator. 3.)!! Note: If the divisor is larger than the dividend, affix a decimal to the dividend without changing its value. Thus, affix zero (0) every time a number can t be divided. Then, divide the dividend like whole numbers. Secure the ones digit with zero (0) to emphasize that the number is less than one. This also proves that any proper fraction is always less than one Notice that the digits in the quotient are repeating and seems to be endless when divided continuously. This is an example of a repeating and nonterminating decimal.

3 Activity Sheet No. 3 TYPE OF ACTIVITY: Mathematical Investigation : Changing Fraction to Decimals LEARNING OBJECTIVES : Hypothesize how a fraction is changed to decimal with denominators 9, 99, Decimals are classified into 4 kinds: Non-repeating and Terminating Decimal the digits do not repeat or occur in a pattern and has a definite number of place value. Example: 0.129, , Repeating and Terminating Decimal the digits are repeated and has a definite number of place values. Example: 0.555, , Non-repeating and Non-Terminating Decimal the digits do not repeat and has infinite number of place values. Example: the value of pi (π) = Repeating and Non-Terminating Decimal the digits do not repeat and has infinite number of place values. Example: = = 0.84 (the bar on top of the digit signifies that the digits under it are being repeated in a pattern)

4 Activity Sheet No. 4 : Decimals to Fractions LEARNING OBJECTIVES : Rename decimals as fractions in its simplest form. REFERENCE : Math for Life 5 Revised Edition, p AUTHOR/S : Adelaida Celeridad-Wright & Adela C. Villamayor Since a fraction can be changed to a decimal, then a decimal can be changed back to fraction. To change a decimal to fraction, write the fraction the way you read its decimal equivalent. Whenever possible, reduce the fraction to its simplest form. Example: 1.) 0.45 (read as forty-five hundredths similar to!"!"" ) 0.45 = Simplify the fraction if necessary by dividing the numerator and denominator by their GCF;!"! =! 9. Therefore, 0.45 =!""!!" ) (read as four and fifty-six thousandths similar to ) = Simplify the fraction if necessary by dividing the numerator and denominator by their GCF;!"! =! 7. Therefore, = 4!"""!!"# 125.

5 Activity Sheet No. 5 : Rounding Off Decimals LEARNING OBJECTIVES : Round off decimals to the indicated palce value. REFERENCE : Math for Life 5 Revised Edition, pp Adelaida Celeridad-Wright & Adela C. Villamayor To round off decimals, Find your digit, Look right next door, Five or more, add one more, Four or less, just ignore. (locate the digit being rounded) (look at the digit to the right of the place being rounded to.) (if the digit is 5 or more, add 1 to the digit being rounded remove the digits to its right) (if the digit is 4 or less, let the digit remain as it is and remove the digits to its right.) Example: Round off to the nearest hundredths 6 is the digit to be rounded. Since the digit to its right is greater than 4, then we add 1 to

6 Activity Sheet No. 6 : Comparing and Ordering Decimals LEARNING OBJECTIVES : Compare and arrange decimals in descending and ascending order. REFERENCE : Soaring 21 st Century Mathematics 5, p. 99 Mauel T. Kotah, et al. Math for Life 5 Revised Edition, pp Adelaida Celeridad-Wright & Adela C. Villamayor To compare decimals, compare the digits in the same place value beginning at the left until you find a difference. The number with a greater digit in the same place value is the greater number, otherwise, the lesser number. Example: a. Compare the whole numbers same value b. Compare the digits in the tenths place same value c. Compare the digits in the hundredths place is less than 9 Therefore, 8.43 < 8.49 In arranging decimals, compare all the decimals in a given set. To arrange in ascending order means to start with least to greatest. To arrange in descending order means to start with greatest to least. Example: 0.845, 0.019, 0.892, 0.91 Tip: Arrange the numbers horizontally to easily compare each digit with the same place value rd th nd st st descending order: 0.91, 0.892, 0.845, ascending order: 0.019, 0.845, 0.892, 0.91

7 Activity Sheet No. 8 : Addition and Subtraction of Decimals LEARNING OBJECTIVES : Perform addition and subtraction of decimals. REFERENCE : Soaring 21 st Century Mathematics 5, p. 99 Mauel T. Kotah, et al. Math for Life 5 Revised Edition, pp Adelaida Celeridad-Wright & Adela C. Villamayor When adding or subtracting decimals, the alignment of the digits according to its place value must be observed. To do this, simply align the decimal points and the place values will follow. Annex zeroes to the right as place holders if needed. Then, add or subtract in the same way as whole numbers. Example What is the sum of and 7.95? < What is subtracted form 9.8?

8 < < PASIG CATHOLIC COLLEGE Activity Sheet No. 9 : Multiplication of Decimals LEARNING OBJECTIVES : Multiply decimals by a whole number or another decimal. REFERENCE : Soaring 21 st Century Mathematics 5, pp Mauel T. Kotah, et al. Math for Life 5 Revised Edition, p Adelaida Celeridad-Wright & Adela C. Villamayor To find the product of decimals, multiply the numbers in the same way as we multiply whole numbers. The number of decimal places must be equal to the total number of decimals places in the factors. Example: What is the product of and 3.5? What is the product of and 3.12? There is a total of 3 decimal places in the factors. Therefore, same number of decimal places there must be in the product There is a total of 5 decimal places in the factors. Therefore, same number of decimal places there must be in the product.

9 Activity Sheet No. 10 LEARNING OBJECTIVES : Division of Decimals : Divide decimals by whole numbers and vice versa. Divide decimals by another decimal. REFERENCE : Soaring 21 st Century Mathematics 5, pp Mauel T. Kotah, et al. Math for Life 5 Revised Edition, pp Adelaida Celeridad-Wright & Adela C. Villamayor To divide decimals; a. Change the divisor to a whole number by moving the decimal point to the right as many places needed to make it a whole number. (If the divisor is a whole number, there is no need to move the decimal point.) b. Do likewise with the decimal point in the dividend. Move the decimal point as many places as you moved in the divisor. c. Secure the place of the decimal point in the quotient directly above the decimal point in the dividend. d. Divide the numbers in the same way we divide whole numbers. Example: 1.) Divide: ) Divide: The decimal point in a whole number is placed after the ones digit The decimal point is not necessary if the number does not include a decimal, thus, if it is a whole number.

10 LEARNING OBJECTIVES Activity Sheet No. 11 TYPE OF ACTIVITY: Problem Solving : Solving Word Problems involving Decimals : Analyze and solve word problems involving fundamental operations on decimals. REFERENCE : Math for Life 5 Revised Edition, p. 178 AUTHOR/S : Adelaida Celeridad-Wright & Adela C. Villamayor In solving word problems, one must carefully understand what the problem is asking. Some word problems includes hidden questions that the problem solver must figure out in order to answer what is asked. Example: Francis takes a 12-month loan for a motorcycle that costs Php75, He paid a down payment of Php30, 000. How much should he still pay monthly? Understand a. What are the given information in the problem? Php75, cost of the motorcycle Php30, down payment b. What is asked in the problem? How much is his monthly payment? Plan c. What operations will you use to answer the problem? subtraction, multiplication and division Solve d. What is the solution to the problem? Php30, ? Php75, To know the amount of the remaining balance, subtract the amount of down payment from the actual price of the motorcycle: Php75, Php30, Php45, To know the amount of the monthly payment, divide the remaining balance by 12 months: Php45, months = Php3, Look Back: Php3, months = Php45,

11 Activity Sheet No. 13 TYPE OF ACTIVITY: Concept Development / Computational Skills LEARNING OBJECTIVES REFERENCE : Ratio : Compare two quantities in the form of ratio. Express ratios in several forms and in simplest terms. : Soaring 21 st Century Mathematics 2 nd Edition, pp Manuel T. Kotah, et al. Math for Life 5 Revised Edition, p Adelaida Celeridad-Wright & Adela C. Villamayor Ratio is a comparison of quantities. The ratio of a to b is commonly written as a : b. It may also be written as a fraction!! however, it should be read as a ratio and not as a fraction (e.g. 2:3 or!! is read as 2 is to 3 and not two-thirds. Example: In a Catholic bible, there are 27 books in the New Testament and 46 books in the Old Testament. What is the ratio of books in the New Testament to the books in the Old Testament.? The ratio is 27 : 46 or!"!". Ratios may also be written in simplest form by dividing both terms by their GCF. These ratios, the higher term and its lowest term are called equivalent ratios. Example: 21 : 14 = 3 : 2 24 : 30 = 4 : 5 35 : 65 = 7 : 13

12 Activity Sheet No. 14 TYPE OF ACTIVITY: Concept Development / Computational Skills : Rate LEARNING OBJECTIVES : Compute for the unit rate of a given comparison. REFERENCE : Soaring 21 st Century Mathematics 2 nd Edition, pp. 246 AUTHOR : Manuel T. Kotah, et al. Rate is a comparison of two quantities of different units. Example: The car travels at 60 kilometers per hour while the motorcycle travels at 40 kilometers per hour. Kilometer is a unit of distance while hour is a unit of time. Since two different units were used to compare the two quantities, the rate is being describe in the situation. The rate of distance over time is called speed. Rate can be written as 60km per hour or 60km/hour. A rate that is simplified to a per-unit form is called unit rate. Unit rate is easily identified if the denominator is 1 Example: Luke can type 90 words in 3 minutes. On an average, how many words can he type every minute? Rate à 90 words per 3 minutes or 90 words/3 minutes To compute for the unite rate, divide the numerator by the denominator then copy the units of each term respectively. Unit rate à 30 words/minute

13 Activity Sheet No. 15 LEARNING OBJECTIVES REFERENCE : Proportion : Determine if two ratios make a proportion. Find the missing term in a proportion. : Soaring 21 st Century Mathematics 2 nd Edition, pp : Manuel T. Kotah, et al. AUTHOR Proportion is a statement of two equal ratios. a : b = c : d Example a.) 1 : 2 = 12 : 24 b.) 21 : 14 = 6 : 4 In a proportion, the inner terms are called the means and the outer terms are called the extremes. extremes a : b = c : d means The law of proportion states that the product of the means is equal to the product of the extremes. a x d = b x c a.) 24 b.) 84 1 : 2 = 12 : : 14 = 6 : If the product of the means is not equal to the product of the extremes, then the two ratios do not make a proportion.

14 Activity Sheet No. 16 TYPE OF ACTIVITY: Problem Solving : Solving Word Problems Involving Proportion LEARNING OBJECTIVES : Analyze and solve word problems that involve proportion. REFERENCE : Soaring 21 st Century Mathematics 2 nd Edition, p. 254, Manuel T. Kotah, et al. Math for Life 5 Revised Edition, p Adelaida Celeridad-Wright & Adela C. Villamayor In solving problems involving proportion, the terms must correspond accordingly. Identify what object is being described by each quantity so as not to interchange the means by the extremes and vice versa. Using an approach can make the given problem clearer and easier to solve. Here are some examples of word problems that involve proportion. Example #1 In a library, there are 25 books for every two rows in the shelf. How many books are there if there are 8 rows in a shelf? Write a proportion based on the problem. 25 : 2 = N : 8 books : rows books : rows 25 8 = : 2 = N : 8 2 N = 200 What should be the value of N to make 2 N = 200? 2 N = 200 N = N = 100 Therefore, there are 100 books in a shelf of 8 rows.

15 FOURTH QUARTER Activity Sheet No. 17 TYPE OF ACTIVITY: Concept Development : Percent Changing Percent to Fraction and vice versa LEARNING OBJECTIVES : Define percent in relation to fraction. Express fractions as percents and vice versa. REFERENCE : Soaring 21 st Century Mathematics Kotah, Manuel T., et al. Percent means per hundred or hundredths. ( per means for every and cent means hundred ). The symbol used for percent is %. Example In a 10 by 10 grid, there are 100 boxes. 30% of the grid is shaded with blue, 34% of the grid is shaded with red, 30% of the grid is shaded with yellow, 6% of the grid is unshaded. 1.) In a group of 100 students, 24 of them like strawberries, 18 students like blueberries and 39 like raspberries. That means; 24% of the group likes strawberries, 18% of the group likes blueberries and 39% of the group likes raspberries. Take note that in the first example, the shaded region can be expressed as fractions. Thus, a fraction can be expressed as percent and vice versa. To change a percent to fraction, drop the percent symbol (%) and put 100 as the denominator. Reduce if necessary. 30% =!"!"" =!!", 34% =!"!"" =!",!" 6% =!!"" =!!" 24% =!"!"" =!!", 39% =!"!"", 18% =!"!"" =!!", To change a fraction to percent, divide the numerator by the denominator. Multiply the quotient by 100 and put the percent symbol (%). 24 = = = 24 à 24%

16 FOURTH QUARTER Activity Sheet No. 18 : Changing Percent to Decimal and vice versa LEARNING OBJECTIVES : Express decimals as percent and vice versa REFERENCE : Soaring 21 st Century Mathematics Kotah, Manuel T., et al. Math for Life 5 Revised Edition Wright, Amelia C. and Villamayor, Adelia C. CONCEPT NOTES : To change a percent to a decimal, drop the % symbol and move the decimal point two places to the left. 35% = 0.35 Example: 1.) 45% = ) 37% = ) 99% = ) 100% = ) 125% = 1.25 To change a decimal to a percent, move the decimal point two places to the right then affix the % symbol = 98% Example: 1.) 0.33 = 33% 2.) 0.52 = 52% 3.) 0.07 = 7% 4.) 0.7 = 70% 5.) = 9.3%

17 FOURTH QUARTER Activity Sheet No. 19 TYPE OF ACTIVITY: Concept Development : Percentage, Base and Rate LEARNING OBJECTIVE : Identify the elements of percent in a give problem. REFERENCE : Soaring 21 st Century Mathematics Kotah, Manuel T., et al. Math for Life 5 Revised Edition Wright, Amelia C. and Villamayor, Adelia C. Percentage is part of the base determined by the rate. Base is the whole on which the rate operates. Rate is the number of hundredths part taken and is written with percent symbol (%).

18 FOURTH QUARTER Activity Sheet No. 20 : Finding Percentage LEARNING OBJECTIVES : Solve for the percentage in a worded problem. REFERENCE : Math for Life 5 Revised Edition, Wright, Amelia C. and Villamayor, Adelia C. In finding the percentage, base or rate from a given problem, we use the PBR Triangle in obtaining the formula for each situation. P B R To find the percentage, multiply the base and the rate. P = B R. Example 1 What is 30% of 500? R = 30% B = 500 P =? P = % (change percent to decimal) P = P = 150 Example 2 15% of the fruits in the basket are apples. If there are 60 fruits in the basket, how many are apples? R = 15% B = 60 P =? P = 60 15% (change percent to decimal) P = P = 9, therefore, there are 9 apples in the basket.

19 FOURTH QUARTER Activity Sheet No. 21 LEARNING OBJECTIVES : Finding the Base : Solve for the base in a worded problem. REFERENCE : Math for Life 5 Revised Edition, Wright, Amelia C. and Villamayor, Adelia C. To find the base, divide the percentage by the rate. B = P R Example 1: 24 is 60% of what number? P P = 24 R = 60% B =? B = P R B R B = 24 60% (change percent to decimal) B = B = 40 Example 2: 20% of the class are non-catholics. If there are 7 non-catholics, how many students are there in the class? P = 7 R = 20% B =? B = P R B = 7 20% (change percent to decimal) B = B = 35, therefore there are 35 students in the class.

20 FOURTH QUARTER Activity Sheet No. 22 : Finding the Rate LEARNING OBJECTIVES : Solve for the rate in a worded problem. REFERENCE : Math for Life 5 Revised Edition, Wright, Amelia C. and Villamayor, Adelia C. To find the rate, divide the given percentage by the base or rewrite the number as a fraction. R = P B B P R Example 1: 56 is what percent of 80? P = 56 B = 80 B =? R = P B R = R = 0.7 (change decimal to percent) R = 70% Example 2: Czarina s score in her exam is 38. If there are 40 items in the exam, what is the rate of her score? P = 38 B = 40 B =? R = P B R = R = 0.95 (change decimal to percent) R = 95%