pearl city hawaii lower grades 12 august

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Professional Development for Singapore Math (Lower Grades)

Yeap Ban Har

banhar@sg.marshallcavendish.com

Pearl City, Hawaii12 August 2011

Photo: Nanakuli Elementary School

Professional Development for Singapore Math (Lower Grades)

Day 2 Session 1Video Study

Focus on ThinkingPatterning & Generalization

Photo: Princess Elizabeth Primary School

Students have learnt to add three one-digit numbers prior to this lesson. These are grade one students towards the end of the school year.

Lesson Segment Observation

Practice in speaking • How do the students

respond?

• Are there evidence of engagement or thinking?

• What are the teacher actions?

• What are the questions that I have?

Problem Presentation

Problem Solution (whole class)Observing

Problem Solution (whole class)Using Table

Conclusion

Consolidation Not in the video

The problem-solving lesson in the video follows the lesson we studied yesterday in the Open Lesson.

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www.marshallcavendish.com/education/mci

www.marshallcavendish.com/education/mci

www.marshallcavendish.com/education/mci

Professional Development for Singapore Math (Lower Grades)

Day 2 Session 2Number Bonds

Photo: Princess Elizabeth Primary School

www.marshallcavendish.com/education/mci

Number bonds is taught before addition and subtraction.

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Number Bonds is emphasized prior to the learning of addition.

Children are given, say, 5 unifix cubes and guided to see that 1 and 4 make 5, for example. Others may say that 3 and 2 make 5 or 4 and 1 make 5. Yet others may say that 5 and 0 make 5.

Earlybird Kindergarten Mathematics (Standards Edition)

Number Bonds

Photo: PCF Telok Blangah Kindergarten

One duck is big. Six ducklings are small.

Photo: PCF Telok Blangah Kindergarten

Photo: PCF Telok Blangah Kindergarten

Photo: PCF Telok Blangah Kindergarten

Photo: PCF Telok Blangah Kindergarten

Photo: PCF Telok Blangah Kindergarten

Number Bonds continues to receive attention in Grade 1.

My Pals Are Here! Mathematics 1

Addition Facts are given emphasis in the first six months of grade one.

The children learn it in stages as the textbooks distinguished between Numbers to 10 and Numbers to 20.

Count On and Count All are used in Numbers to 10.

Addition Facts

Earlybird Kindergarten Mathematics (Standards Edition)

While Count On and Count All are used in Numbers to 10, Make Ten is given emphasis in Numbers to 20.

Addition Facts & Number Sense

Photo: Princess Elizabeth Primary School

27 – 3

27 – 13

27 – 18

10

17

27 ÷ 324

3

Applications of Number Bonds

Professional Development for Singapore Math (Lower Grades)

Day 2 Session 3Emphasis on Visualization,

Connections and Number Sense

Photo: Princess Elizabeth Primary School

Articulating one’s thoughts orally, at first, and in written forms using words, pictures, diagrams and symbols is important.

Communication

Maris Stella H

igh (Primary) School

Looking for Patterns is introduced through exploration with Shapes. Subsequently, this is done using numbers – in a more abstract context.

Connections

Make Connections to Generalize

Photo: Princess Elizabeth Primary School

Connections

Photo: Princess Elizabeth Primary School

Visualization is, among other things, the ability to manipulate visual images without the benefit of concrete objects.

In the Japanese lessons, we saw children engaged in three-dimensional visualization (bean-container task) and two-dimensional visualization (pattern-block task).

Visualization

Photo: A Japanese Public School

This is the rationale stated in Singapore Mathematics curriculum document.

“an excellent vehiclefor the developmentand improvement

of a person’sintellectual competence”

Professional Development for Singapore Math (Lower Grades)

Day 2 Session 3Regrouping & Place Value

Photo: Princess Elizabeth Primary School

Professional Development for Singapore Math (Lower Grades)

Day 2 Session 3Addition

Theory of Variations

Photo: Princess Elizabeth Primary School

12 + 9

What are the different ways to add 12 and 9?

Students first add by counting all …

And then counting on and making ten.

For large number addition, students can add the tens and ones separately – regrouping may be necessary.

100 Chart helps counting on for larger numbers.

Study the variations over several lessons.

“A curriculum as it develops should revisit these 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

One feature of Singapore Math is the spiral approach.

Professional Development for Singapore Math (Lower Grades)

Day 2 Session 3Subtraction

Spiral Approach

Photo: Princess Elizabeth Primary School

Ready for Maths Series

Shaping Maths 1

Shaping Maths 1

“A curriculum as it develops should revisit these 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

Students have many opportunities to learn subtraction but each time building upon the strategies learnt previously.

My Pals Are Here! Mathematics 2

Drill-and-practice and thinking are not exclusive.

Professional Development for Singapore Math (Lower Grades)

Day 2 Session 4Bar Model Method

Photo: Princess Elizabeth Primary School

Modeling using real objects, pictures of real objects and more abstract model drawings.

Bar models are used to represent quantities – discrete and continuous ones.

58

12

Observe how this problem is different from the last one even though numbers used are the same.

Observe how this problem is different from the last one even though numbers used are the same.

12Natalie

Peter

58

58 – 12 = 46

46 ÷ 2 = 23

Natalie’s bag is 35 kg.Peter’s bag is 23 kg.