Primary 3/4 Mathematics Workshop For Parents. 14 April 2012. Workshop Outline. Introduction to Problem-Solving Model Method 3 Different types of Models 4 different Heuristics Format of assessment. Problem-solving Approach. Understand the Problem (Understand) Devise a Plan (Plan)
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Primary 3/4 Mathematics WorkshopFor Parents
14 April 2012
Endeavour Primary School
Mathematics Department 2012
Model Method
Draw a diagram
Concrete-Pictorial-Abstract Approach
Concrete – Manipulatives:
Base-Ten Blocks
Pictorial - Models:
100
30
?
Abstract – Symbols:
100 – 30 = 70
Concrete-Pictorial-Abstract Approach
4 + 2 = 6
a) Whole Numbers
b) Fractions
2. Comparison Model
a) Comparing 2 items
b) Comparing 3 items
c) Other Comparison Models
a) Total unchanged
b) Total changed
1. Part-whole Model
Find value of unknown part
Find value of whole
Calvin earns $2000 every month. He pays
$300 for food. He also spends $200 on his car, $500 on housing and saves the rest. How much does he save every month?
Calvin earns $2000 every month. He pays
$300 for food. He also spends $200 on his car, $500 on housing and saves the rest. How much does he save every month?
$2000
$300
$200
$500
?
food
savings
car
housing
Calvinearns $2000 every month. He pays
$300 for food.Healsospends $200 on his car,$500 on housingandsaves the rest.. How much does he saveevery month?
$2000
$300
$200
$500
?
food
car
housing
saving
Used
$300 + $200 + $500
= $1000
Savings
$2000 - $1000
= $1000
He saves $1000 every month.
How can we check if $1000 is a reasonable answer?
What is another way to solve this problem?
Qi Ying bought some sweets. She ate half of them and gave 5 sweets to Joy. She had 7 sweets left. How many sweets did Qi Ying buy?
Ate
5 (Joy)
7 (Left)
1 unit (half)
1 unit (half)
Qi Ying bought some sweets. She ate halfof them and gave 5 sweetsto Joy. She had7 sweets left.How many sweets did Qi Ying buy?
?
Ate
5 (Joy)
7 (Left)
1 unit
1 unit
?
1 unit
5 + 7
= 12
2 units
2 × 12
= 24
Qi Ying bought 24 sweets.
How can we check if ‘24 sweets’ is a reasonable answer?
What is another way of representing this problem?
÷ 2
?
5 + 7
× 2
? girls
24 boys
24
2 units
24 ÷ 2
1 unit
= 12
There are 12 girls.
How can we check if the answer is reasonable?
¼ of the fish in an aquarium are goldfish. There are 4 more guppies than goldfish in the aquarium. The remaining 16 fish are carps. How many fish are there in the aquarium?
?
goldfish
¼ of the fishin an aquarium are goldfish.There are 4 more guppies than goldfish in the aquarium. The remaining 16fish are carps. How many fishare there in the aquarium?
2 units
4 + 16
= 20
¼
¼
¼
¼
4
4 units
2 × 20
guppies
= 40
16 carps
There are 40 fish.
How can we check if the answer is reasonable?
2. Comparison Model
Find total sum given between difference and value of an item
Find value of an item given difference and sum
Sven collected 3426 stamps. He
collected 841 fewer stamps than Jerome.
How many stamps did they collect?
?
Svencollected3426 stamps. He
collected 841 fewer stampsthanJerome.
How many stampsdidtheycollect?
Who has more?
Sven
3426
Whose bar should be longer?
fewer
Jerome
841
?
?
Sven
3426
fewer
Jerome
841
?
Jerome
3426 + 841
= 4267
Total
3426 + 4267
= 7693
They collected 7693 stamps.
How can we check if ‘7693 stamps’ is a reasonable answer?
What is another way to solve this problem?
?
Smaller
Larger
¼
?
Smaller
Larger
¼
2 units
1 unit
How can we check if the answer is reasonable?
Kyle, Siti and Alice have a total of 290 stickers. Kyle has twice as many stickers as Siti. Alice has 50 stickers more than Siti. How many stickers does Alice have?
Kyle, Siti and Alice have a total of 290 stickers. Kyle has twiceas manystickers asSiti. Alicehas 50 stickersmorethanSiti. How many stickersdoes Alicehave?
Kyle
290
Siti
Alice
50
Note how ‘50’ is represented.
Kyle
290
Siti
Alice
50
4 units
290 – 50
= 240
1 unit
Alice
240 ÷ 4
60 + 50
= 60
= 110
Let Siti have x stickers.
Kyle 2x
Alice x + 50
4x + 50 = 290
4x = 240
x = 60
60 + 50 = 110
Alice has 110 stickers.
Kyle, Siti and Alice have a total of 270 stickers. Kyle has thrice as many stickers as Siti. Alice has half as many stickers as Siti. How many stickers does Siti have?
Kyle, Siti and Alicehaveatotal of 270stickers. Kyle hasthrice as manystickersas Siti. Alicehashalf as manystickersas Siti. How many stickersdoesSitihave?
Kyle
Siti
270
Alice
9 units
270
Kyle
Siti
Alice
270
270 ÷ 9
1 unit
= 30
2 units
30 x 2
= 60
Siti has 60 stickers.
How can we check if the answer is reasonable?
Other Comparison Models
2 files and 3 pens cost $18 altogether. A file costs 3 times as much as a pen. Find the cost of 1 file.
Other Comparison Models
2 files and 3 pens cost $18 altogether. A file costs 3 times as much as a pen. Find the cost of 1 file.
Files
Pens
Other Comparison Models
2 files and 3 pens cost $18 altogether. A file costs 3 times as much as a pen. Find the cost of 1 file.
Files
$18
?
Pens
Files
$18
?
Pens
9 units
$18
= $2
1 unit
$18 ÷ 9
3 units
$2 x 3
= $6
1 file costs $6.
Other Comparison Models
2 crystal vases and 3 plates cost $161. The cost of 1 plate is half the cost of 1 vase.
What is the cost of 1 vase?
Other Comparison Models
2 crystal vases and 3 plates cost $161. The cost of 1 plate is half the cost of 1 vase.
What is the cost of 1 vase?
Vases
Plates
Other Comparison Models
2 crystal vases and 3 plates cost $161. The cost of 1 plate is half the cost of 1 vase.
What is the cost of 1 vase?
Vases
$161
?
Plates
Vases
$161
?
Plates
7 units
$161
1 unit
$161 ÷ 7
= $23
2 units
$23 x 2
= $46
1 vase costs $46.
3. Before and After Model
Total unchanged
Total changed
Alan
558
Ben
Alan and Ben had 558 cards altogether. Alan gave of his cards to Ben. After that, Ben had twice the number of cards as Alan.
How many cards did Ben have at first?
Alan
558
Ben
?
9 units
558
1 unit
558 ÷ 9
= 62
5 units
62 x 5
= 310
Ben had 310 cards at first.
Alice
Betty
Alice and Betty had the same amount of money each. After Alice spent $120 and Betty spent $45, Betty had twice as much money as Alice.
How much money did each girl have at first?
Alice and Betty had the same amount of money each. After Alice spent $120 and Betty spent $45, Betty had twice as much money as Alice.
How much money did each girl have at first?
Alice
1 unit
$120
$45
1 unit
1 unit
Betty
Alice and Betty had the same amount of money each.
After Alice spent $120 and Betty spent $45, Betty had twice as much money as Alice.
How much money did each girl have at first?
Alice
1 unit
$120
?
$45
1 unit
1 unit
Betty
1 unit
$120 - $45
= $75
$75 + $120
= $195
Each girl had $195 at first.
Alice and Betty had the same amount of money each.
After Alice spent $120 and Betty spent $45, Betty had twice as much money as Alice.
How much money did each girl have at first?
Alice
1 unit
$120
$45
1 unit
1 unit
Betty
?
1 unit
$120 - $45
= $75
2 units
$75 x 2
= $150
$150 + $45
= $195
Each girl had $195 at first.
Male
Female
There was an equal number of male and female passengers in a train at first. After 193 male passengers and 46 female passengers alighted, there were 4 times as many female passengers as male passengers left in the train. How many male passengers were in the train at first?
Male
1 unit
193
1 unit
1 unit
1 unit
1 unit
46
Female
There was an equal number of male and female passengers in a train at first. After 193 male passengers and 46 female passengers alighted, there were 4 times as many female passengers as male passengers left in the train. How many male passengers were in the train at first?
Male
1 unit
193
?
1 unit
1 unit
1 unit
1 unit
46
Female
There was an equal number of male and female passengers in a train at first. After 193 male passengers and 46 female passengers alighted, there were 4 times as many female passengers as male passengers left in the train. How many male passengers were in the train at first?
There was an equal number of male and female passengers in a train at first. After 193 male passengers and 46 female passengers alighted, there were 4 times as many female passengers as male passengers left in the train.
How many male passengers were in the train at first?
Male
1 unit
193
?
1 unit
1 unit
1 unit
1 unit
46
Female
3 units
193 - 46
= 147
1 unit
147 ÷ 3
= 49
49 + 193
= 242
There were 242 male passengers at first.
Is model drawing the only method?
No!
2. Guess and Check
- 4
x 3
÷ 2
50
?
54
108
+ 4
x 2
÷ 3
50 + 4 = 54
54 x 2 = 108
108 ÷ 3 = 36
The missing number is 36.
Find the missing number.
C
B
D
A
+ 7
÷2
- 8
28
?
A train carrying some passengers left Station A.
At Station B, 7 passengers boarded.
At Station C, half of the passengers alighted.
At Station D, 8 passengers alighted.
As the train left Station D, there were 28 passengers on the train.
How many passengers were on the train when it left Station A?
A train carrying some passengers left Station A.
At Station B, 7 passengers boarded.
At Station C, half of the passengers alighted.
At Station D, 8 passengers alighted.
As the train left Station D, there were 28 passengers on the train.
How many passengers were on the train when it left Station A?
C
B
D
A
+ 7
÷2
- 8
28
?
36
72
- 7
+ 8
x 2
28 + 8 = 36
36 x 2 = 72
72 – 7 = 65
65 passengers were on the train when it left Station A.
+ 1h 40 min
+ 50 min
2pm
John took 50 minutes to wash his car and another 1 h 40 min to polish it. He finished washing and polishing his car at 2 pm. At what time did he start washing his car?
John took 50 minutes to wash his car and another 1 h 40 min to polish it. He finished washing and polishing his car at 2 pm. At what time did he start washing his car?
+ 1h 40 min
+ 50 min
?
12.20pm
2pm
- 1h 40 min
- 50 min
- 40 min
- 1 h
2 pm 1 pm 12.20 pm
- 50 min
12.20 pm 11.30 am
He started washing his car at 11.30 am.
At a park, there are 25 bicycles and tricycles. These vehicles have a total of 55 wheels. If there are more bicycles than tricycles, how many bicycles are there at the park?
At a park, there are 25 bicycles and tricycles. These vehicles have a total of 55 wheels. If there are more bicycles than tricycles, how many bicycles are there at the park?
At a park, there are 25 bicycles and tricycles. These vehicles have a total of 55 wheels. If there are more bicycles than tricycles, how many bicycles are there at the park?
At a park, there are 25 bicycles and tricycles. These vehicles have a total of 55 wheels. If there are more bicycles than tricycle, how many bicycles are there at the park?
At a park, there are 25 bicycles and tricycles. These vehicles have a total of 55 wheels. If there are more bicycles than tricycle, how many bicycles are there at the park?
At a park, there are 25 bicycles and tricycles. These vehicles have a total of 55 wheels. If there are more bicycles than tricycle, how many bicycles are there at the park?
At a park, there are 25 bicycles and tricycles. These vehicles have a total of 55 wheels. If there are more bicycles than tricycle, how many bicycles are there at the park?
There are 20 bicycles at the park.
At a park, there are 25 bicycles and tricycles. These vehicles have a total of 55 wheels. If there are more bicycles than tricycle, how many bicycles are there at the park?
Method 1: Guess and Check
Method 2: Supposition
Suppose all the vehicles are bicycles, the number of wheels
But there are 55 wheels altogether.
55 ‒ 50 = 5 extra wheels
Each tricycle has 1 wheel more than a bicycle, 5 ÷ 1 = 5
There are 5 tricycles.
25 ‒ 5 = 20
2 x 25 = 50
There are 20 bicycles at the park.
Sue has 23 coins. Some are 10¢ coins and the others are 20¢ coins. She has more 10¢ coins than 20¢ coins. The total value of the coins is $3.40. How many 20¢ coins are there?
Sue has 23 coins. Some are 10¢ coins and the others are 20¢ coins. She has more 10¢ coins than 20¢ coins. The total value of the coins is $3.40. How many 20¢ coins are there?
Sue has 23 coins. Some are 10¢ coins and the others are 20¢ coins. She has more 10¢ coins than 20¢ coins. The total value of the coins is $3.40. How many 20¢ coins are there?
Sue has 23 coins. Some are 10¢ coins and the others are 20¢ coins. She has more 10¢ coins than 20¢ coins. The total value of the coins is $3.40. How many 20¢ coins are there?
Sue has 23 coins. Some are 10¢ coins and the others are 20¢ coins. She has more 10¢ coins than 20¢ coins. The total value of the coins is $3.40. How many 20¢ coins are there?
Sue has 23 coins. Some are 10¢ coins and the others are 20¢ coins. She has more 10¢ coins than 20¢ coins. The total value of the coins is $3.40. How many 20¢ coins are there?
There are 1120¢ coins .
Mr John has some stickers. If he gives each child 5 stickers, he will have 5 stickers left. If he gives each child 6 stickers instead, he will have 3 stickers short. How many stickers does he have?
Mr John has some stickers. If he gives each child 5 stickers, he will have 5 stickers left. If he gives each child 6 stickers instead, he will have 3 stickers short. How many stickers does he have?
Mr John has some stickers. If he gives each child 5 stickers, he will have 5 stickers left. If he gives each child 6 stickers instead, he will have 3 stickers short. How many stickers does he have?
Mr John has some stickers. If he gives each child 5 stickers, he will have 5 stickers left. If he gives each child 6 stickers instead, he will have 3 stickers short. How many stickers does he have?
Mr John has some stickers. If he gives each child 5 stickers, he will have 5 stickers left. If he gives each child 6 stickers instead, he will have 3 stickers short. How many stickers does he have?
Mr John has some stickers. If he gives each child 5 stickers, he will have 5 stickers left. If he gives each child 6 stickers instead, he will have 3 stickers short. How many stickers does he have?
Mr John has some stickers. If he gives each child 5 stickers, he will have 5 stickers left. If he gives each child 6 stickers instead, he will have 3 stickers short. How many stickers does he have?
Mr John has some stickers. If he gives each child 5 stickers, he will have 5 stickers left. If he gives each child 6 stickers instead, he will have 3 stickers short. How many stickers does he have?
Mr John has 45 stickers.
Benny, Cindy, David and Evelyn give picture cards to one another.
Benny gives Cindy 19 cards.
Cindy gives David 15 cards.
Evelyn gives David 3 cards but David returns them to Evelyn.
David gives Benny 12 cards.
Who has fewer picture cards in the end than before?
Benny, Cindy, David and Evelyn give picture cards to one another.
Benny gives Cindy 19 cards.
Cindy gives David 15 cards.
Evelyn gives David 3 cards but David returns them to Evelyn.
David gives Benny 12 cards. Who has fewer picture cards in the end than before?
Benny, Cindy, David and Evelyn give picture cards to one another.
Benny gives Cindy 19 cards.
Cindy gives David 15 cards.
Evelyn gives David 3 cards but David returns them to Evelyn.
David gives Benny 12 cards. Who has fewer picture cards in the end than before?
Benny, Cindy, David and Evelyn give picture cards to one another.
Benny gives Cindy 19 cards.
Cindy gives David 15 cards.
Evelyn gives David 3 cards but David returns them to Evelyn.
David gives Benny 12 cards. Who has fewer picture cards in the end than before?
Benny, Cindy, David and Evelyn give picture cards to one another.
Benny gives Cindy 19 cards.
Cindy gives David 15 cards.
Evelyn gives David 3 cards but David returns them to Evelyn.
David gives Benny 12 cards. Who has fewer picture cards in the end than before?
Benny, Cindy, David and Evelyn give picture cards to one another.
Benny gives Cindy 19 cards.
Cindy gives David 15 cards.
Evelyn gives David 3 cards but David returns them to Evelyn.
David gives Benny 12 cards. Who has fewer picture cards in the end than before?
Benny, Cindy, David and Evelyn give picture cards to one another.
Benny gives Cindy 19 cards.
Cindy gives David 15 cards.
Evelyn gives David 3 cards but David returns them to Evelyn.
David gives Benny 12 cards. Who has fewer picture cards in the end than before?
Benny, Cindy, David and Evelyn give picture cards to one another.
Benny gives Cindy 19 cards.
Cindy gives David 15 cards.
Evelyn gives David 3 cards but David returns them to Evelyn.
David gives Benny 12 cards. Who has fewer picture cards in the end than before?
Benny has fewer picture cards than before.
In a game, two dice are thrown and the two numbers shown are multiplied to give a score.
What whole number less than 10 cannot be a score of this game?
In a game, two dice are thrown and the two numbers shown are multiplied to give a score.
What whole numbers less than 10 cannot be a score of this game?
In a game, two dice are thrown and the two numbers shown are multiplied to give a score.
What whole number less than 10 cannot be a score of this game?
In a game, two dice are thrown and the two numbers shown are multiplied to give a score.
What whole number less than 10 cannot be a score of this game?
In a game, two dice are thrown and the two numbers shown are multiplied to give a score.
What whole number less than 10 cannot be a score of this game?
In a game, two dice are thrown and the two numbers shown are multiplied to give a score.
What whole number less than 10 cannot be a score of this game?
The score cannot be 7.