lower primary heuristics model drawing
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Lower PrimaryLower PrimaryModel Drawing Model Drawing
WorkshopWorkshopFor ParentsFor Parents
Endeavour Primary SchoolMathematics Department
Rationale for Model Rationale for Model DrawingDrawing
•Visual representation of details
•Helps children with problem solving
•Helps children logically think using visual models to determine their computations
Endeavour Primary SchoolMathematics Department
•Teaches mathematical language
•Provides foundation for algebraic understanding
•Empowers students to think systematically and master more difficult problems
Rationale for Model Rationale for Model DrawingDrawing
Endeavour Primary SchoolMathematics Department
•Makes multi-step and multi-concept problems easy to work
Rationale for Model Rationale for Model DrawingDrawing
Endeavour Primary SchoolMathematics Department
Model Drawing does Model Drawing does NOTNOT
• Work on every problem
• Specify ONE RIGHT model
• Specify ONE RIGHT operation
Endeavour Primary SchoolMathematics Department
Concrete-Pictorial-Abstract Approach
Concrete• Modeling each mathematical concept with concrete materials: base-ten blocks- Fraction bars- Geometric figures etc.
Pictorial• Transforming the concrete model into a pictorial (semiconcrete) level which involves:- Drawing pictures- Drawing models etc.
Abstract • Modeling the mathematics concept at a symbolic level using: - Numbers- Mathematical symbols etc.
Illustration of CPA
Concrete – Manipulative
s:
Base-Ten Blocks
Pictorial - Models:
100
30 ?
Abstract – Symbols:
100 – 30 = 70
1. Main Item• Read the problem.• Identify the main item.• Draw a unit bar for the main item.2. Details• Identify other key details.• Draw in other details with the unit bar as a
guide.
• Re-read the problem one sentence at a time adjusting the unit bars to match the story.
3. Strategy• Write the number sentence and the answer.
Model DrawingModel Drawing
Endeavour Primary SchoolMathematics Department
4 Types of Models4 Types of Models
1. Part-Whole Model
2. Comparison Model
3. Multiplication Model
4. Division ModelEndeavour Primary SchoolMathematics Department
Calvin spent $135 on a shirt and$75 on a blouse.
How much did he spend altogether?
Part-Whole ModelsPart-Whole Models
$135
shirt
$75
blouse
?
Endeavour Primary SchoolMathematics Department
$135
shirt
$75
blouse
?
Altogether $135 + $75= $210
Ans: He spent $210 altogether.
Endeavour Primary SchoolMathematics Department
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?
Part-Whole ModelsPart-Whole Models
$300 $200
car(c)
$500
food(f)
housing(h)
?
saving(s)
$2000
Endeavour Primary SchoolMathematics Department
$300 $200
car
$500
food housing
?
$2000
saving
Used $300 + $200 + $500= $1000
Ans: He saves $1000 every month.
Saving $2000 - $1000= $1000
Endeavour Primary SchoolMathematics Department
Aloysius collected 3426 stamps. He collected 841 fewer stamps than Ben. How many stamps did Ben collect?
Comparison ModelsComparison Models
3426A
841
fewer
?
fewer
B
Endeavour Primary SchoolMathematics Department
Who has
more?
Whose bar is
longer?
3426A
B 841
fewer
?
Ben 3426 + 841= 4267
Ans: Ben collected 4267 stamps.
Endeavour Primary SchoolMathematics Department
Same quantity so same length
Peter had 789 cards. He had 58 more cards than Sam. How many cards did they collect altogether?
Comparison ModelsComparison Models
789P
S 58 fewer?
Endeavour Primary SchoolMathematics Department
Who has
more?
Whose is
longer?
789P
S 58 fewer?
Sam 789 – 58= 731
Ans: They collected 1520 cards altogether.
Altogether 789 + 731= 1520
Endeavour Primary SchoolMathematics Department
“More” does not always
mean add
Carl has $90. David has twice as much money as Carl. How much money does David have?
Comparison ModelsComparison Models
$90C
D $90 $90
?Endeavour Primary SchoolMathematics Department
Same quantity so same length
$90C
D $90 $90
?
David 2 x $90= $180
Ans: David has $180.
Endeavour Primary SchoolMathematics Department
Ali ran 170m. Ben ran twice as far as Ali. Claire ran 20m more than Ben.How far did Claire run?
Combined ModelsCombined Models
170mA
B
?
C
20m
Endeavour Primary SchoolMathematics Department
170m 170m
Ben 2 x 170m= 340m
Ans: Claire ran 360m.
Claire 340m + 20m= 360m
Endeavour Primary SchoolMathematics Department
170mA
B
C
20m170m 170m
?
Cindy gave 10 sweets to 5 friends.How many sweets did she give in all?
Multiplication ModelsMultiplication Models
10 10 10 10 10
?
10 10
Endeavour Primary SchoolMathematics Department
10 10 10 10 10
?
10 10
No. of sweets given 5 x 10
= 50
Ans: Cindy gave away 50 sweets.
Endeavour Primary SchoolMathematics Department
Same quantity so same
sized
Jody gave 5 sweets to 20 friends.How many sweets did she give in all?
Multiplication ModelsMultiplication Models
5 5 . . . . 5
?
1st 2nd 20th
Endeavour Primary SchoolMathematics Department
5 5 . . . . 5
?
1st1st 2nd 10th
No. of sweets given 10 x 5
= 50
Ans: Jody gave away 50 sweets.
Endeavour Primary SchoolMathematics Department
Wendy has 200kg of rice. She packs the rice into bags of 5kg.How many bags of rice does she have?
Division ModelsDivision Models
5kg5kg . . . . 5kg
1st 2nd ?th
?
Endeavour Primary SchoolMathematics Department
5kg 5kg . . . . 5kg
200kg
1st1st 2nd ?th
No. of bags 200kg ÷ 5kg= 40
Ans: She has 40 bags of rice.
Endeavour Primary SchoolMathematics Department
Part-Whole ModelsPart-Whole ModelsWhat to look out for?What to look out for?
1. Draw the bar with the 1. Draw the bar with the larger value longer.larger value longer.
2. Start drawing the curly 2. Start drawing the curly bracket at the start of bar.bracket at the start of bar. ((Enclose the number with Enclose the number with 2 lines to show where it 2 lines to show where it starts and ends.)starts and ends.)
Comparison ModelsComparison ModelsWhat to look out for?What to look out for?
1.1. Alignment and thickness ofAlignment and thickness of the bars.the bars.
2. Bars which have the same 2. Bars which have the same quantity must be of same quantity must be of same length.length.
Combined ModelsCombined ModelsWhat to look out for?What to look out for?
1.1. Bars must be relatively sized. Bars must be relatively sized.
Multiplication/Division ModelsMultiplication/Division ModelsWhat to look out for?What to look out for?
1.1. Bars must be relatively sized.Bars must be relatively sized.
2. Bars of equal quantity must be2. Bars of equal quantity must be of same size.of same size.
In General:In General:
1.1. Naming of bars must match Naming of bars must match
correctly.correctly.
2. Place a question mark on the2. Place a question mark on the
part of model where answer part of model where answer
is.is.
Thank you for your attention.
The End.
Question and Answer Session
Endeavour Primary SchoolMathematics Department
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