National Singapore Math Summer Institute, Denver
-
Upload
jimmy-keng -
Category
Education
-
view
2.699 -
download
2
Transcript of National Singapore Math Summer Institute, Denver
![Page 1: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/1.jpg)
Opening Keynote
The Foundations of Singapore Mathematics
Dr Yeap Ban HarMarshall Cavendish InstituteSingapore
www.marshallcavendish.com/education/mci
![Page 2: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/2.jpg)
“Mathematics is an excellent vehicle
for the development and improvement of a person’s intellectual competence ...”
Singapore Ministry of Education 2006
![Page 3: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/3.jpg)
Source: Mathematics Syllabus Primary
Singapore Ministry of Education 2006
![Page 4: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/4.jpg)
The Bar Model Method
In a basket, 5/9 of the fruits are apples and the rest are oranges. 3/10 of the apples are green in colour. There are 15 green apples. How many fruits are there in the basket?
Source: Primary School Leaving Examination 2006 – 2010
![Page 5: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/5.jpg)
The Bar Model Method
In a basket, 5/9 of the fruits are apples and the rest are oranges. 3/10 of the apples are green in colour. There are 15 green apples. How many fruits are there in the basket?
Source: Primary School Leaving Examination 2006 – 2010
15
3 units = 15
1 units = 5
18 units = 18 x 5 = 90
There are 90 fruits in the basket.
![Page 6: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/6.jpg)
Emphasis on Problem Solving
Some children shared a sum of money. When each child tried to take $11, the last child received only $6. When each child received $8, there was $25 left over.
Find the amount each child received if the sum of money is shared equally among them.
![Page 7: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/7.jpg)
Emphasis on Problem SolvingSome children shared a sum of money. When each child tried to take $11, the last child received only $6. When each child received $8, there was $25 left over.
Find the amount each child receives if the sum of money is shared equally among them.
Method 1
$25 + $2 = $27
$27 ÷ $3 = 9
There are 9 children who returned $3.There are 10 children in all.
Total = $8 x 10 + $25 = $105
Each child receives $105 ÷ 10 = $10.50
Method 2
Children $11 $8
3 $22+$6 $24+$25
4 $33+$6 $32+$25
5 $44+$6 $40+$25
…
10 $99+$6 $80+$25
![Page 8: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/8.jpg)
Emphasis on Problem SolvingSome children shared a sum of money. When each child tried to take $11, the last child received only $6. When each child received $8, there was $25 left over.
Find the amount each child receives if the sum of money is shared equally among them.
Method 3
Let there be x children.
$11(x – 1) + $6 = $8x + $25
The sum of money was 10 x $8 + $25 = $105Each child receives $105 ÷ 10 = $10.50
$11x – $11 + $6 = $8x + $25
3x = 30 or x = 10
![Page 9: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/9.jpg)
The CPA Approach: The Importance of Initial Concrete Experience
![Page 10: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/10.jpg)
www.marshallcavendish.com/education/mci
![Page 11: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/11.jpg)
www.marshallcavendish.com/education/mci
![Page 12: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/12.jpg)
www.marshallcavendish.com/education/mci
![Page 13: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/13.jpg)
www.marshallcavendish.com/education/mci
![Page 14: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/14.jpg)
www.marshallcavendish.com/education/mci
Use the base ten materials to show 23. Use it to find the value of 23 – 11.
23 = 20 + 3
![Page 15: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/15.jpg)
www.marshallcavendish.com/education/mci
Use the base ten materials to show 23. Use it to find the value of 23 – 15.
23 = 10 + 13
2 31 5
11
![Page 16: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/16.jpg)
www.marshallcavendish.com/education/mci
51 + 12 51 – 17 51 ÷ 3
![Page 17: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/17.jpg)
www.marshallcavendish.com/education/mci
51 + 12 51 – 17 51 ÷ 3
![Page 18: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/18.jpg)
www.marshallcavendish.com/education/mci
51 + 12 51 – 17 51 ÷ 3
![Page 19: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/19.jpg)
www.marshallcavendish.com/education/mci
51 + 12 51 – 17 51 ÷ 3
![Page 20: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/20.jpg)
www.marshallcavendish.com/education/mci
51 + 12 51 – 17 51 ÷ 3
![Page 21: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/21.jpg)
www.marshallcavendish.com/education/mci
Using sticks to learn division by grouping.King Solomon Academy, London
![Page 22: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/22.jpg)
Emphasis on Visualization
![Page 23: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/23.jpg)
Emphasis on Visualization
![Page 24: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/24.jpg)
Emphasis on Visualization
![Page 25: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/25.jpg)
Emphasis on Visualization
![Page 26: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/26.jpg)
www.marshallcavendish.com/education/mci
Emphasis on visualization and generalization in problem solving.High School Attached to Tsukuba University, Japan
![Page 27: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/27.jpg)
“A curriculum as it develops should revisit this basic ideas repeatedly, building upon them until the student has grasped the full formal apparatus that goes with them.”
Jerome Bruner 1960 The Process of Education
![Page 28: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/28.jpg)
Emphasis on Spiral Approach
Grade 1 Multiplication using drawing
Math in Focus
Singapore Math by Marshall Cavendish
![Page 29: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/29.jpg)
Emphasis on Spiral Approach
Grade 2 Multiplication of 2, 5, 10 and 3, 4
Math in Focus
Singapore Math by Marshall Cavendish
![Page 30: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/30.jpg)
Pensar sin Limites
Matematica Metodo Singapur
![Page 31: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/31.jpg)
Daqiao Primary School
Singapore
![Page 32: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/32.jpg)
Emphasis on Spiral Approach
Grade 3 Multiplication of 6, 7, 8, 9 2-digit x 1 digit, 3-digit x 1-digit
6 6 66
Math in Focus
Singapore Math by Marshall Cavendish
Escuela No. 1577 Teniente Dagoberto Godoy Chile
![Page 33: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/33.jpg)
Emphasis on Spiral Approach
Grade 3 Multiplication of 2-digit x 1 digit3-digit x 1-digit
National Institute of EducationSingapore
![Page 34: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/34.jpg)
Emphasis on Spiral Approach
Grade 4 Multiplication of 4-digit x 1 digit, 2-digit x 2-digit
42
30
4
![Page 35: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/35.jpg)
National Institute of EducationSingapore
![Page 36: National Singapore Math Summer Institute, Denver](https://reader035.fdocuments.us/reader035/viewer/2022081401/5583e52ad8b42ab0278b497c/html5/thumbnails/36.jpg)
Emphasis on Systematic Variation