Professional Development for Singapore Math (Upper Grades)
Day 2 Session 1Open Lesson
Visualization & Generalization
Emphasis on Visualization & Generalization
Draw a polygon with a total of 4 dots on the sides.
Other than visualization, the ability to see patterns and to make generalization is another core intellectual competency.
Nanakuli Elementary School, Hawaii
Nanakuli Elementary School, Hawaii
Nanakuli Elementary School, Hawaii
Nanakuli Elementary School, Hawaii
Professional Development for Singapore Math (Upper Grades)
Day 2 Session 2Focus on
Visualization
Focus on Thinking: Visualization
The area of the trapezoid.
In Singapore Math, visualization is one of the core thinking skills.
Focus on Thinking: Visualization
Focus on Thinking: Visualization
In Singapore Math, bar model method is a key strategy and it emphasizes visualization.
110g
Focus on Thinking: Visualization
In Singapore Math, bar model method is a key strategy and it emphasizes visualization.
110g
290g
Focus on Thinking: Visualization
In Singapore Math, bar model method is a key strategy and it emphasizes visualization.
110g
290g
Focus on Thinking: Visualization
In Singapore Math, bar model method is a key strategy and it emphasizes visualization.
110g
? ?
290g
Focus on Thinking: Visualization
In Singapore Math, bar model method is a key strategy and it emphasizes visualization.
110g
? ?
290g
290 g – 110 g = 180 g
180 g ÷ 2 = 90 g
3 x 90 g = 270 g
Bella puts 270 g of sugar on the dish.
Professional Development for Singapore Math (Upper Grades)
Day 2 Session 3Focus on
Generalization
Focus on Thinking: Generalization
In Singapore Math, patterning and generalization is an core intellectual competency.
1 2 3 4 5 6
10 9 8 711
12 13 14 15 16
21 20 19 18 17
22 23 24 25 2631 30 29 28 27
32 33 34 35 36
Focus on Thinking: Generalization
In Singapore Math, patterning and generalization is an core intellectual competency.
1 2 3 4 5
8 7 69
10 11 12 13
17 16 15 14
18 19 20 2125 24 23 22
26 27 28 29
6 is shared equally between 2.6 ÷ 2 = 3
In 6, how many 2s are there?6 ÷ 2 = 3
1÷12=2
2÷12=22
3÷12=32
4÷12=4 2
𝑛÷12=𝑛2
1÷34=1
13
2÷34=21
13
3÷34=31
13
Skemp
Understanding in mathematics • relational (conceptual) • instrumental (procedural)• conventional
Teaching for conceptual understanding is given emphasis in Singapore Math.
Primary Mathematics Standards Edition Grade 6
Primary Mathematics Standards Edition Grade 6
Primary Mathematics Standards Edition Grade 6
Professional Development for Singapore Math (Upper Grades)
Day 2 Session 4Focus on
Number Sense
We use five consecutive
numbers starting with n
Sum, s Middle, m
1, 2, 3, 4, 5 89
10
135
2, 3, 4, 5, 6 111213
246
6, 7, 8, 9, 10 ???
???
72, 72, 74, 75, 76 ???
???
There were several ways the value of m was established• First, last and
middle of the numbers used
• If there are more odd numbers in the list then m are odd
Contributions from course participants
The value of s was established in different ways• First + last + middle of the numbers used to get the middle s• Three times the middle number to get the middle s• The middle three consecutive numbers which is essentially the same as three
times the middle number to get the middle s• The first + second + last of the numbers used to get the smallest s
For 72, 73, 74, 75 and 76, we can use the values of s for 2, 3, 4, 5, 6 – just add 210.
Contributions from course participants