The document summarizes discussions from breakout sessions at the 4th Singapore Math Institute on teaching mathematics using Singapore's approach. It provides tasks and problems from Singapore classrooms related to practicing skills through problem-solving, using anchor tasks to structure lessons, and teaching geometry in grades 4-6. The goals are to emulate Singapore's emphasis on problem-solving and multi-step word problems to develop students' mathematical thinking.
This presenttaion was made to a group of parnets, business leaders, administrators, teachers, school board members and university representatives in Cache School District in Logan, Utah. This group, The High School Renewal Committee, is keen to develop a world-class high school mathematics programmed. In this presentation, some recommendations were made on how to make the average high school student perform well in mathematics.
This presenttaion was made to a group of parnets, business leaders, administrators, teachers, school board members and university representatives in Cache School District in Logan, Utah. This group, The High School Renewal Committee, is keen to develop a world-class high school mathematics programmed. In this presentation, some recommendations were made on how to make the average high school student perform well in mathematics.
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Presenters will share information and examples regarding how to implement Math Stations in elementary classrooms that help students engage in work that is aligned with the CCSS Standards for Mathematical Practices.
Implementing the Standards for Mathematical Practices through Elementary Math Work Stations
Presenters will share information and examples regarding how to implement Math Stations in elementary classrooms that help students engage in work that is aligned with the CCSS Standards for Mathematical Practices.
This presentation was made to K-12 teachers at the school district at Smithville, Missouri. It focuses on what research and theories say about mathematics teaching and learning that can result in high achievement and positive attitude and consistent with learning for the 21st century economy and society.
Seminar at Colegio Inmaculada Conception, Universidad Andres Bello &San Beni...Jimmy Keng
Pensar sin Limites Seminars
This seminar was held at various places including Colegio Inmaculada in Conception, Universidad Andres Bello in Santiago & San Benito School in Santiago. The seminar explains the pedagogy behind the Spanish edition of My Pals Are Here! Mathematics.
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This weekend course conducted at Scarsdale Teachers Institute, New York focused on the use of anchor problem to enhance the teaching and learning of mathematics.
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
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The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
Sectors of the Indian Economy - Class 10 Study Notes pdf
2014 WSU Handouts
1. 1
THE 4th
SINGAPORE MATH® INSTITUTE
AUGUST 4-6, 2014
Breakout Session: Practice Lessons Using the Problem-Solving Approach
Presenter: Yeap Ban Har
Singapore’s national mathematics curriculum is a problem-solving one. Lessons
to teach new concepts, lessons to consolidate recently learnt concepts, as well as
lessons to apply learnt concepts, can all be taught through a problem-solving
approach.
This session is on doing practice lessons using the problem-solving approach.
Task 1
Make a correct division equation. All the five digits are different.
Complete instruction.
Make a correct division equation such a two-digit number when divided by a 1-digit
number gives a two-digit quotient.
All the five digits are different.
Grade Level
What is the skill that students are practicing?
2. 2
Task 2
Start with a certain number of beans / counters / paper clips. Take turns to remove
either one or two beans / counters / paper clips. The winner is the player who
removes the last beans / counters / paper clips.
Is there a way to always win in this game?
Grade Level
What is the skill that students are practicing?
3. 3
Task 3
Use any five consecutive numbers. Arrange them such that the vertical sum equal
the horizontal sum.
Grade Level
What is the skill that students are practicing?
4. 4
THE 4th
SINGAPORE MATH® INSTITUTE
AUGUST 4-6, 2014
Breakout Session: Anchor Tasks in Singapore Math
Presenter: Yeap Ban Har
Singapore textbooks are written with the main learning task being an anchor task.
Anchor task is the single tasks used over a prolonged period of instructional time.
It embodies the idea of Teach Less, Learn More – a philosophy of the Singapore
education system.
In Primary Mathematics, anchor tasks are the one that opens the chapter (un-
numbered tasks) or the ones which follow a previous day independent Workbook
Practice. These tasks are often solved completely for the students. In Math in
Focus, anchor tasks are the boxed-up Learn tasks. Typically, a mathematics
lesson begin with about 15 minutes or so doing and discussing the anchor task,
before moving on to Guided Practice and Independent Practice (if any).
Key Questions
What is the research base for Anchor Tasks?
How does a teacher implement Anchor Tasks?
What is the purpose of Anchor Tasks?
Task 1
Find the value of 9 x 6.
5. 5
Board Plan
Journal 1 Date
Problem
9 x 8
Method 1 Method 2 Method 3
What is the learning outcome for this anchor task? Grade Level
6. 6
Task 2
3
2
2
1
What is the learning outcome for this anchor task? Grade Level
Board Plan
Journal 2 Date
Problem
Method 1 Method 2
7. 7
Task 3
Show 4 tiles. Make a shape.
Show 5 tiles. Make a shape. Make another one.
What is the learning outcome for this anchor task? Grade Level
Board Plan
Journal Date
10. 10
THE 4th
SINGAPORE MATH® INSTITUTE
AUGUST 4-6, 2014
Breakout Session: Challenging Word Problems from Singapore Classrooms
Presenter: Yeap Ban Har
Singapore schools provide significant opportunities for all students to deal with
challenging problems – problems that are more complex than (and sometimes new
/ novel compared to) textbook problems. This is because the state test includes
significant number of such problems.
Problem 1
This problem is based on one used by a Primary 3 Lesson Study done by a Professional Learning
Team in Kong Hwa School, Singapore.
Mr Lee had 3 durians more than Mr Kim.
Mr Kim then gave Mr Lee 2 durians.
Who had more durians in the end? How many more?
Primary 3
________________________________________________________________
11. 11
Problem 2
This problem is based on one given on a state test for Primary 6 students in a recent examination.
This particular problem is new to the group of Singapore students who took that test.
Han arranged 110 squares and circles in a straight line. There are at least 3 circles
between any 2 squares. What is the largest possible number of squares among
the 110 squares and circles?
Primary 5 – 6
Based on Primary 3 Content
________________________________________________________________
12. 12
Problem 3
This problem is from Catholic High School (Primary). It was given to its Primary 6 students during
a Preliminary Examination in preparing them for the national Primary School Leaving Examination,
PSLE.
A total of 325 boys and girls attended a performance in the school hall.
5
4
of the
boys and
4
3
of the girls left the hall after the performance ended. There were 29
more boys than girls who remained in the hall.
How many girls attended the performace?
Primary 5 – 6
Based on Primary 4 Content
________________________________________________________________
13. 13
Problem 4
This problem is based on one given on a state test for Primary 6 students in a recent examination.
This particular problem is new to the group of Singapore students who took that test.
Indra was packing a batch of cookies into some containers she had in her kitchen.
She tried to pack 11 cookies into each container but the last one contained only 6
cookies. When she packed 8 cookies into each container, there were 25 cookies
left over.
How many cookies were there altogether?
Primary 5 – 6
Based on Primary 4 Content
________________________________________________________________
14. 14
THE 4th
SINGAPORE MATH® INSTITUTE
AUGUST 4-6, 2014
Breakout Session: Teaching Geometry in Grades 4 – 6
Presenter: Yeap Ban Har
Students in Grade 4 are expected to be on van Hiele Level 2 of Geometric Thought.
Task 1
Cut out a triangle.
Investigate the three (interior) angles of the triangle.