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1. Samples of Comparison Model Ex. 1: A sandwich and a soft drink cost P56. If the sandwich costs P8 more than the soft drink, what is the cost of the sandwich? P8 sandwich P56 soft drink P56 - = 2 units = 1 unit = Therefore, the sandwich costs ? ? P48 P 8 P48 P24 P24 model

2. Sample of Comparison Model Ex.2: A pencil, pad paper, and eraser cost p42. The paper costs P5 more than the eraser, while the pencil costs P2 more than the paper. Find the cost of each item? pencil pad of paper eraser P42 - = 3 units cost = 1 unit cost = Therefore, the pencil costs , the pad of paper costs , and the eraser costs . ? P5 P2 P42 ? P5 ? P30 P12 P30 P10 P17 P15 P10

3. Your Turn An apple, an orange and a pear costs P40. A pear costs P5 more than the apple, while an orange costs P3 less than a pear. How much is the cost of each fruit? Click for answer

4. Eureka!!! orange we subtract 5 & 3 = P13 pear = P 16 apple = P 11 P40 – P7 = P33 3 units cost = P33 1 unit cost = P11 ? P2 P40 ? P5 ? model

5. Sample of Sharing Model Sammy has 198 marbles and Tony has 74 marbles. Sammy gives some marbles to Tony so that both have the same number of marbles. • How many marbles does Sammy have in the end? • How many marbles does Sammy give Tony? Sammy Tony 124 / 2 = 62 198 – 62 = 136 marbles were left to Sam or Sammy = 74 + 62 = 136. Sammy has 136 marbles at the end. Tony was given 62 marbles. 124 198 62 74 62 model

6. Your Turn Sammy has 198 sweets and Tony has 74 sweets. Sammy gives some sweets so that he has 12 more sweets than Tony in the end. • How many sweets does Sammy have in the end? • How many sweets does Sammy give Tony? Click for answer model

7. Eureka!!! Sammy Tony 198 – 74 = 124 124 – 12 = 112 112/2 = 56 Sammy has 198-56 = 142 sweets. Sammy gave 56 sweets. 74 56 12 56 74 56 model

8. Sample of Constant Value Model 22 is the constant value that we add on both quantities Wenie’s age is 42 and her son’s age is 10. In how many years time will Wenie’s age be twice the age of her son? 42 Wenie son What is double the son’s age today? How many years in excess of the mother’s age is twice the age of the son? In how many years more will Wenie’s age be twice as that of her son? In 22 years, how old is the mother? the son? In years, Winie’s age is twice her son’s age. 22 22 10 22 20 22 22 64 32 model 22

9. Your Turn Racquel’s age is 42 and Anna’s age is 26. How many years ago was Anna’s age half of Racquel’s age? Click for answer model

10. Eureka Racquel 42-10 = 32 42 10 10 52 Ana 26-10=16 26 10 If years ago, Ana was 26, what must Racquel’s age be during that time? 26 x 2 = 52 52 – 42 = 10 What’s the difference between the projected age and the present age? We want to know the number of years ago. Subtract 10 from each. 42 -10 = 32 26 - 10 = 16 Ten years ago, Ana’s age was half of Racquel’s age. model

12. Learn More Examples“Practice makes perfect.” 2. Allan has 55 marbles and Jessica has 87 marbles. How many marbles must Jessica give to Allan so that they will have the same number of marbles?

13. Learn More Examples“Practice makes perfect.” 2. Allan has 55 marbles and Jessica has 87 marbles. How many marbles must Jessica give to Allan so that they will have the same number of marbles? Allan 55 32 pupils Jessica 87 – 55 = 32 32/2 = 16 Jessica must give 16 marbles to Allan.

14. Learn More Examples“Practice makes perfect.” 3. Anthony buys two hamburgers and 3 cans of juice for P121. Each can of juice costs three times as much as one hamburger. How much more does each can of juice cost than each hamburger?

15. Learn More Examples“Practice makes perfect.” 3. Anthony buys two hamburgers and 3 cans of juice for P121. Each can of juice costs three times as much as one hamburger. How much more does each can of juice cost than each hamburger? Cans of juice P121 hamburger 11 units = 121; 1 unit = 11 3 units = 33 A difference between each item cost is P33-P11= P22. Each can of juice is P22more than the hamburger

16. Learn More Examples“Practice makes perfect.” 4. John had P45 and William had P120. One day Mr. Enriquez gave John and William an equal amount of money. After that, John had half the amount of money as William. How much money did Mr. Enriquez give them altogether?

17. 30 45 45 45 30 30 Learn More Examples“Practice makes perfect.” 4. John had P45 and William had P120. One day Mr. Enriquez gave John and William an equal amount of money. After that, John had half the amount of money as William. How much money did Mr. Enriquez give them altogether? John William P120 120- (2x45) = 30; 45 is half of 90; 30 is the excess; the constant value Add 30 to both quantities to satisfy the condition. Mr. Enriquez gave P30 to each. Altogether, he gave P60.

18. Learn More Examples“Practice makes perfect.” 5. Tomas is twice as tall as Ronald. Ronald is 25 cm shorter than Armand. Their total height is 345 cm. Find the height of Tomas.

19. Learn More Examples“Practice makes perfect.” 5. Tomas is twice as tall as Ronald. Ronald is 25 cm shorter than Armand. Their total height is 345 cm. Find the height of Tomas. Tomas Ronald 345 25 Armand 4 units + 25 = 345 4 units = 320 1 unit = 80 Tomas is 160 cm tall

20. 1 2 3 4 5 6 7 8 9 10 Stretch Your Mind 3. Benson is three times as old as Daryl. Ed is 8 years older than Daryl. The sum of their ages is 78 years. How old is each? Gold

21. 1 2 3 4 5 6 7 8 9 10 Gold Stretch Your Mind 4. The number of students in ABC National High School is 40 less than thrice the number of students XYZ National High School. The total number of students in both schools is 5440. How many students does each school have?

22. 1 2 3 4 5 6 7 8 9 10 Gold Stretch Your Mind 6. The sum of two numbers is 31 and their difference is 5. What are the two numbers?

23. 1 2 3 4 5 6 7 8 9 10 Gold Stretch Your Mind 7. Manny and Joseph have 98 cards and 164 respectively. Joseph gives some cards to Manny. If Manny has 10 more cards than Joseph in the end, find the number of cards each of them have in the end?

24. 1 2 3 4 5 6 7 8 9 10 Count Your Treasures These are the answers to the given exercises. 3. Daryl is 14 years old. Benson is 42 years old. Ed is 22 years old. Benson 78 years Daryl 8 Ed 5 units + 8 years = 78 years 1 unit = 70 /5 5 units = P70 1 unit = 14 years

25. 1 2 3 4 5 6 7 8 9 10 Count Your Treasures These are the answers to the given exercises. 4. ABC School has 4 070 students and XYZ School has 1370 students. 40 ABC 5 440 years XYZ 4 units - 40 students = 5440 students 4 units = 5 480 1 unit = 1 370

26. 1 2 3 4 5 6 7 8 9 10 Count Your Treasures These are the answers to the given exercises. 6. The two numbers are 13 and 18. 5 First number 31 Second number 31 - 5 = 26 2 units = 62 1 unit = 13

27. 1 2 3 4 5 6 7 8 9 10 Count Your Treasures These are the answers to the given exercises. 7. Joseph will have 126 cards and Manny will have 136. 98 Manny Joseph 28 10 28 66 164 - 98 = 66 66 - 10 = 56 56/2 = 28 28 + 10 will be added to Manny.