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