Samples of Comparison Samples of Comparison Model 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 P 8 P24 P48 P48 P24 P24 model model
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. - PowerPoint PPT Presentation
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Samples of Comparison Samples of Comparison ModelModel
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
P 8
P24
P48
P48
P24P24
modelmodel
Sample of Comparison Sample of Comparison ModelModel
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?
pencilpad of papereraser
P42 - =3 units cost =1 unit cost =
Therefore, the pencil costs , the pad of paper costs , and the eraser costs .
?? P5P5
P5P5????
P2P2
P12P12
P10P10
P30P30
P10P10P17P17 P15P15
P30
P42P42
Your TurnYour Turn
An apple, an orange and a pear costs An apple, an orange and a pear costs P40. A pear costs P5 more than the P40. A pear costs P5 more than the apple, while an orange costs P3 less apple, while an orange costs P3 less than a pear. How much is the cost of than a pear. How much is the cost of each fruit?each fruit? Click for answer
Eureka!!!Eureka!!!
orange orange we subtract 5 & 3 = P13 we subtract 5 & 3 = P13
pearpear = P 16 = P 16
appleapple = P 11 = P 11
P40 – P7 = P33P40 – P7 = P33
3 units cost = P333 units cost = P33
1 unit cost = P111 unit cost = P11
??
??
?? P5P5
P2P2
P40P40
modelmodel
Sample of Sharing ModelSample 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.
a. How many marbles does Sammy have in the end? b. How many marbles does Sammy give Tony?
SammyTony
124 / 2 = 62198 – 62 = 136 marbles were left to Sam orSammy = 74 + 62 = 136. Sammy has 136 marbles at the end.Tony was given 62 marbles.
modelmodel
7474
62
62
124124198198
Your TurnYour 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.
a. How many sweets does Sammy have in the end?
b. How many sweets does Sammy give Tony?
modelmodel
Click for answer
Eureka!!!Eureka!!!
SammyTony
198 – 74 = 124124 – 12 = 112112/2 = 56Sammy has 198-56 = 142 sweets.Sammy gave 56 sweets.
modelmodel
7474
7474
5656 56561212
5656
Sample of Constant Value ModelSample of Constant Value Model
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?
42Wenieson
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.
modelmodel
1010 22
2222
2222
2222
2020
6464 3232
2222
22 is the constant value
that we add on both
quantities
Your TurnYour 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?
modelmodel
Click for answer
EurekaEureka
modelmodel
RacquelAna
42
26
1052
If years ago, Ana was 26, what must Racquel’s age be during that time?26 x 2 = 52
What’s the difference between the projected age and the present age? 52 – 42 = 10
We want to know the number of years ago. Subtract 10 from each.42 -10 = 3226 - 10 = 16
Ten years ago, Ana’s age was half of Racquel’s age.
26-10=16
42-10 = 32 10
10
Go For Gold!Go For Gold!
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YESNO
Learn More ExamplesLearn More Examples““Practice makes perfect.”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?
Learn More ExamplesLearn More Examples““Practice makes perfect.”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?
55AllanAllan
JessicaJessica
32 pupils32 pupils
87 – 55 = 3287 – 55 = 32
32/2 = 1632/2 = 16
Jessica must give 16 marbles to Allan.Jessica must give 16 marbles to Allan.
Learn More ExamplesLearn More Examples““Practice makes perfect.”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?
Learn More ExamplesLearn More Examples““Practice makes perfect.”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 juiceCans of juice
hamburgerhamburgerP121P121
11 units = 121;11 units = 121; 1 unit = 111 unit = 11
3 units = 333 units = 33
Each can of juice is P22more than the hamburgerEach can of juice is P22more than the hamburger
A difference between each item cost is P33-P11= P22.A difference between each item cost is P33-P11= P22.
Learn More ExamplesLearn More Examples““Practice makes perfect.”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?
Learn More ExamplesLearn More Examples““Practice makes perfect.”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?
JohnJohn
WilliamWilliam
P120P120
120- (2x45) = 30; 120- (2x45) = 30;
Mr. Enriquez gave P30 to each. Altogether, he gave P60.Mr. Enriquez gave P30 to each. Altogether, he gave P60.
4545
4545 4545 3030 3030
3030
45 is half of 90; 45 is half of 90; 30 is the excess; the constant value 30 is the excess; the constant value
Add 30 to both quantities to satisfy the condition. Add 30 to both quantities to satisfy the condition.
Learn More ExamplesLearn More Examples““Practice makes perfect.”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.
Learn More ExamplesLearn More Examples““Practice makes perfect.”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.
TomasTomas
RonaldRonald 345345
4 units + 25 = 3454 units + 25 = 345
Tomas is 160 cm tallTomas is 160 cm tall
4 units = 3204 units = 320
ArmandArmand
2525
1 unit = 801 unit = 80
Stretch Your Mind 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?
81 109765432
GoldGold
Stretch Your Mind 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?
81 109765432
GoldGold
Stretch Your Mind Stretch Your Mind
6. The sum of two numbers is 31 and their difference is 5. What are the two numbers?
81 109765432
GoldGold
Stretch Your Mind 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?
81 109765432
GoldGold
Count Your TreasuresCount Your Treasures
These are the answers to the given exercises.
3.3. Daryl is 14 years old. Benson is 42 years old. Ed is 22 years old.Daryl is 14 years old. Benson is 42 years old. Ed is 22 years old.
BensonBenson
5 units + 8 years = 78 years5 units + 8 years = 78 years
5 units = P705 units = P70
1 unit = 70 /51 unit = 70 /5
DarylDaryl
8EdEd
78 years
1 unit = 14 years1 unit = 14 years
81 109765432
Count Your TreasuresCount Your Treasures
These are the answers to the given exercises.
4.4. ABC School has 4 070 students and XYZ School has 1370 students.ABC School has 4 070 students and XYZ School has 1370 students.
ABCABC
4 units - 40 students = 5440 students4 units - 40 students = 5440 students
4 units = 5 4804 units = 5 480
1 unit = 1 370 1 unit = 1 370
XYZXYZ
40
5 440 years
81 109765432
Count Your TreasuresCount Your Treasures
These are the answers to the given exercises.
6.6. The two numbers are 13 and 18.The two numbers are 13 and 18.
31 - 5 = 2631 - 5 = 26
2 units = 622 units = 62
1 unit = 131 unit = 13
3131First numberFirst number
Second numberSecond number
55
81 109765432
Count Your TreasuresCount Your Treasures
These are the answers to the given exercises.
7.7.Joseph will have 126 cards and Manny will have 136.Joseph will have 126 cards and Manny will have 136.
164 - 98 = 66164 - 98 = 66
66 - 10 = 5666 - 10 = 56
56/2 = 2856/2 = 28
9898MannyManny
JosephJoseph
6666
282810102828
28 + 10 will be added to Manny.28 + 10 will be added to Manny.