A3_B3_Lets Model the Way 1
Transcript of A3_B3_Lets Model the Way 1
LET’S STAR THE WAY! 1 P2/P3/P4 YU NENG PRIMARY SCHOOL
MDM SITI NURAISHAH & MR SHAWN YEO
To better support our children in the
Learning of Mathematics
FOCUS How the model method is used to develop pupils’
understanding of mathematical concepts and proficiency in solving word problems.
We will begin with basic model drawing concepts and progress to more advanced problem solving
techniques to solve higher-order problems at P3 and
P4 using the STAR approach.
Model Drawing A problem – solving TOOL
• Helps students visualize the situations involved so that they are able to construct relevant equations
• Helps students gain a deeper understanding of the operations they may use to solve problems
• Instead of relying on keywords and superficial features, it helps students see the relationship
between and among the variables in the problem
Choose the strategies suited to your child’s level of understanding.
Concrete-Pictorial-Abstract
The Model Approach
(1) 33 more than 12 is ____________.
12
?
33
33+12 = 45
33 more than 12 is 45.
3 3
+ 1 2 -----------
_ 4 5___
Step 1 Study the question carefully
Step 2 Think of a plan
Step 3 Act on my plan
Step 4 Reflect and check
STAR Math
Classification
• Part-Whole Model • Comparison Model
Gradual progression in difficulty
(2) Sammy had 68 marbles. He won 15 marbles in a game. How many marbles did he have after the game?
1. Study the
problem
- Sammy had 68 marbles
- He won 15 marbles in a game
(2) Sammy had 68 marbles. He won 15 marbles in a game. How many marbles did he have after the game?
2. Think of a plan to solve the problem
- How many marbles does Sammy have at first?
- What happened next? What does winning 15 marbles mean?
- What is the ‘focus’ of the question?
- What can you do to solve the question?
?
68 + 15
= 83
(2) Sammy had 68 marbles. He won 15 marbles in a game. How many marbles did he have after the game?
He had marbles after the game.
68 had
15 won
83
3. Act on your plan
83 - 15 = 68
(2) Sammy had 68 marbles. He won 15 marbles in a game. How many marbles did he have after the game?
4. Reflect on your answer
(3) There are 62 pink flowers and 98 yellow flowers in a garden. Farmer Yap puts 109 white flowers into the garden. How many flowers are there in the garden now?
1. Study the
problem
- There are 62 pink flowers and 98 yellow flowers
- Farmer Yap puts 109 white flowers into the vase
(3) There are 62 pink flowers and 98 yellow flowers in a garden. Farmer Yap puts 109 white flowers into the garden. How many flowers are there in the garden now?
2. Think of a plan to solve the problem
- How many types of flowers are there at first?
- What happened next?
- How many types of flowers are there now?
- What can you do to solve the question?
- How can you show your thinking by drawing model?
(3) There are 62 pink flowers and 98 yellow flowers in a garden. Farmer Yap puts 109 white flowers into the garden. How many flowers are there in the vase now?
?
= 269
98 + 109 62 +
62
pink
98
yellow
109
white
There are flowers. 269
3. Act on your plan
(3) There are 62 pink flowers and 98 yellow flowers in a garden. Farmer Yap puts 109 white flowers into the vase. How many flowers are there in the vase now?
= 109
4. Reflect on your answer
269 - 62 - 98
36 - 20 = 16
(4) Dan had 36 marbles. He gave 20 marbles to his friend. How many marbles had he left?
36
20 ?
He had left. 16 marbles
gave left
35 + 21
= 56
35
?
21
left
(5) Mother gave John some money. John spent $35 on a dictionary and had $21 left. How much money did Mother give John?
Dictionary
Mother gave John $56.
(6) Danial has 100 stamps. Siti has 20 more stamps than Danial. How many stamps does Siti have?
100 + 20
Danial
Siti
100 100 20
?
= 120
Siti has 120 stamps.
(7) Ethan has 100 stamps. He has 20 more stamps than Sally. How many stamps does Sally have?
100 - 20
Ethan
Sally
20
?
= 80
Sally has 80 stamps.
100
(8) Fred has 128 stamps. Gloria has 10 more stamps than Fred. How many stamps do they have altogether?
Fred
Gloria
128 128 10
?
They have 266 stamps altogether.
128 + 10 = 138
Number of stamps Gloria had =
138 + 128 = 266
I
If our child can understand the concepts, he will be able to work out the answer using the
correct strategy
1. Equal concept 2. Comparison concept 3. Difference concept 4. Multiple concept 5. Difference & Multiple concepts 6. Making-A-Whole concept 7. Before-After concept 8. Parts-&-Units concept 9. Comparison Fractions concept 10.Use Model Approach & make inferences 11.Use Model Approach & Part-Whole concept 12.Use Model Approach & changing Ratio concept 13.Use Model Approach & Guess & Check strategy 14.Use Model Approach & Replacement Concept
P2 to P4
Parts-&-Units concept Comparison Fractions concept Use Model Approach & make inferences Use Model Approach & Part-Whole concept Use Model Approach & changing Ratio concept Use Model Approach & Guess & Check strategy Use Model Approach & Replacement Concept
Equal Concept
(9) 14 + ______ = 29
14 ?
29
Equal Concept
(10) 29 - ______ = 16
29
?
29 – 16 = 13
16
?
Comparison Concept (11) In a fund-raising project, Responsibility 3-1 collected $516 more than Responsibility 3-2. Responsibility 3-1 collected $1 874. How much money did Responsibility 3-2 collect?
Re 3-1
Re 3-2
1 874
516 ?
Responsibility 3-2 collected $1 358.
1874-516
= 1358
Difference Concept (12) Mrs Lim bought a bag and two similar books for $40. The bag cost $16 more than the book.
Find the cost of the book.
1 bag
1 book
1 book
16
40
40 – 16 = 24
1 unit = 24 3 = 8 The book cost $8.
3 units = 24
Multiple Concept (13) Ann is twice as old as Bill. Carol is three times as old as he is. If their total age is 30 years old, how old is Bill?
Bill
Ann
Carol
30
1 unit = 30 6 = 5 Bill is 5 years old.
6 units = 30
Difference & Multiple Concepts
(14) Joseph sold twice as many oranges as Larry. Peter sold 25 more oranges than Larry. If they sold 45 oranges altogether, how many oranges did Peter sell?
1. Study the
problem
- Joseph sold twice as many oranges as Larry - Peter sold 25 more oranges than Larry - They sold 85 oranges altogether
Difference & Multiple Concepts
(14) Joseph sold twice as many oranges as Larry. Peter sold 25 more oranges than Larry. If they sold 45 oranges altogether, how many oranges did Peter sell?
2. Think of a plan to solve the problem
- Who has twice? How many units does Larry have?
- Did Peter sell 25 oranges? How many oranges did Peter sell?
- What does ‘sold 85 oranges’ mean?
- What is the ‘focus’ of the question?
Difference & Multiple Concepts
(14) Joseph sold twice as many oranges as Larry. Peter sold 25 more oranges than Larry. If they sold 45 oranges altogether, how many oranges did Peter sell?
Larry
Joseph
Peter
45
1 unit = 20 4 = 5
25
45 – 25 = 20
Peter sold 30 oranges. 5 + 25 = 30
3. Act on your plan
Difference & Multiple Concepts
(14) Joseph sold twice as many oranges as Larry. Peter sold 25 more oranges than Larry. If they sold 45 oranges altogether, how many oranges did Peter sell?
Larry
Joseph
Peter
45
25
30 – 25 = 5 (L)
5 x 2 = 10 (J)
5 + 10 + 30 = 45
4. Reflect on your answer
Making-A-Whole Concept (15) Jane collected three times as many stickers as Karen. Gina collected 21 stickers less than Jane. The three girls collected 112 stickers altogether. How many stickers did Karen collect?
Karen
Jane
Gina
112
1 unit = 133 7 = 19
21
7 units = 112 + 21 = 133
Karen collected 19 stickers.
+ 21
Before-After Concept (16) Ali had 3 times as many books as Eva. After Eva had bought another 60 books, she had twice as many books as Ali. How many books did Ali have?
1. Study the
problem
- Ali had 3 times as many books as Eva - After Eva had bought another 60 books, she had twice as many books
as Ali
Before-After Concept (16) Ali had 3 times as many books as Eva. After Eva had bought another 60 books, she had twice as many books as Ali. How many books did Ali have?
2. Think of a plan to solve the problem
- Who has 3 times? How many units does Eva have?
- What did Eva do? What happened after she bought additional
books? Did Ali buy additional books?
- Who has more books now? How do you know?
- What is the ‘focus’ of the question?
Before-After Concept (16) Ali had 3 times as many books as Eva. After Eva had bought another 60 books, she had twice as many books as Ali. How many books did Ali have?
Ali
Eva
Before
Ali
Eva
After
60 5 units = 60
1 unit = 60 5 = 12 3 units = 12 x 3 = 36 Ali had 36 books.
3. Act on your plan
Before-After Concept (16) Ali had 3 times as many books as Eva. After Eva had bought another 60 books, she had twice as many books as Ali. How many books did Ali have?
Ali
Eva
Before
Ali
Eva
After
60
4. Reflect on your answer
36 ÷ 3 = 12 12 + 60 = 72 36 x 2 = 72
KNOWLEDGE IS THE KEY TO
SUCCESS
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