The document discusses Singapore's approach to mathematics education. It provides background on Singapore as a country and details on its education system, including student and teacher numbers and types of schools. It then discusses the historical development and implementation of Singapore Math, focusing on its emphasis on problem solving and visualization. Several examples of math problems from Singapore textbooks are presented.
Activities to Increase Mental Math Skills of a Childucmasindia
Explore interesting ways & games to improve a child’s mental math skills. Visit UCMAS Abacus math classes where children learn mental arithmetic using Abacus.
This document provides information about patterns and algebra for a Department of Education. It defines what a pattern is and discusses different types of patterns including repeating, increasing, and decreasing patterns. It provides examples of numeric, object, and shape patterns. The document outlines learning objectives and competencies around identifying, continuing, and determining missing elements in patterns. It includes activities for students to practice translating patterns, predicting subsequent terms, and finding relationships between increasing/decreasing patterns.
This document discusses tools that can be used to teach basic math concepts. It notes that Filipino students perform poorly in math and identifies challenges like lack of resources in public schools. To address these issues, the document explores how information and communication technologies (ICT) like graphing calculators, Microsoft Excel, instructional videos and online resources can be used as tools to teach math in engaging ways. However, it also acknowledges limitations due to difficulties accessing these tools. It concludes by emphasizing the need to address resource inadequacies and provide teacher training to help educators utilize ICT effectively.
The document discusses innovative practices and modern methods in teaching mathematics education. It outlines several goals of teaching mathematics, including developing logical thinking and problem solving skills. It notes the need for innovations in mathematics education, emphasizing understanding over mechanical computations. Several innovative tools are proposed, such as using multimedia, mind maps, smart classrooms, flipped classrooms, virtual classrooms, blended learning, and mobile learning. Mastery learning strategies and methods like inductive-deductive, analytic-synthetic, problem-solving, play-way, and laboratory are also discussed. The role of the teacher is changing to that of a facilitator with the introduction of new technologies.
This document provides information about a course on pre-numeracy skills taught by Dr. Yeap Ban Har from Marshall Cavendish Institute. It includes his contact information, as well as slides and resources available on his blog and Facebook page. The document discusses different types of numbers, counting, features of the Singapore Math approach, and number bonds, with a focus on introducing foundational numerical concepts to young children before they learn addition.
This document provides information and examples about interpreting the order of operations rule known as GEMDAS and performing multiple mathematical operations. It includes:
- An explanation of the GEMDAS rule - Grouping, Exponents, Multiplication, Division, Addition, Subtraction - and that it establishes the order that operations should be performed.
- Examples of solving expressions step-by-step according to the GEMDAS rule, including working through expressions with grouping symbols, exponents, multiplication, division, addition and subtraction.
- An example problem comparing two students, Irish and Lynard, who got different answers when solving the expression 2 + 4 x 3 - 6 ÷ 2, and identifying which student answered
The document provides a detailed lesson plan for teaching arithmetic sequences to a 10th grade mathematics class. The objectives are for students to illustrate, determine the nth term of, and appreciate arithmetic sequences. The lesson proper involves motivating students with a treasure box activity, defining and formulating the formula for an arithmetic sequence, working examples, and evaluating student understanding with an "Answer Me" game. Key points are the definition of an arithmetic sequence as having terms obtained by adding a constant difference, and the formula An=a1+(n-1)d to find the nth term.
Activities to Increase Mental Math Skills of a Childucmasindia
Explore interesting ways & games to improve a child’s mental math skills. Visit UCMAS Abacus math classes where children learn mental arithmetic using Abacus.
This document provides information about patterns and algebra for a Department of Education. It defines what a pattern is and discusses different types of patterns including repeating, increasing, and decreasing patterns. It provides examples of numeric, object, and shape patterns. The document outlines learning objectives and competencies around identifying, continuing, and determining missing elements in patterns. It includes activities for students to practice translating patterns, predicting subsequent terms, and finding relationships between increasing/decreasing patterns.
This document discusses tools that can be used to teach basic math concepts. It notes that Filipino students perform poorly in math and identifies challenges like lack of resources in public schools. To address these issues, the document explores how information and communication technologies (ICT) like graphing calculators, Microsoft Excel, instructional videos and online resources can be used as tools to teach math in engaging ways. However, it also acknowledges limitations due to difficulties accessing these tools. It concludes by emphasizing the need to address resource inadequacies and provide teacher training to help educators utilize ICT effectively.
The document discusses innovative practices and modern methods in teaching mathematics education. It outlines several goals of teaching mathematics, including developing logical thinking and problem solving skills. It notes the need for innovations in mathematics education, emphasizing understanding over mechanical computations. Several innovative tools are proposed, such as using multimedia, mind maps, smart classrooms, flipped classrooms, virtual classrooms, blended learning, and mobile learning. Mastery learning strategies and methods like inductive-deductive, analytic-synthetic, problem-solving, play-way, and laboratory are also discussed. The role of the teacher is changing to that of a facilitator with the introduction of new technologies.
This document provides information about a course on pre-numeracy skills taught by Dr. Yeap Ban Har from Marshall Cavendish Institute. It includes his contact information, as well as slides and resources available on his blog and Facebook page. The document discusses different types of numbers, counting, features of the Singapore Math approach, and number bonds, with a focus on introducing foundational numerical concepts to young children before they learn addition.
This document provides information and examples about interpreting the order of operations rule known as GEMDAS and performing multiple mathematical operations. It includes:
- An explanation of the GEMDAS rule - Grouping, Exponents, Multiplication, Division, Addition, Subtraction - and that it establishes the order that operations should be performed.
- Examples of solving expressions step-by-step according to the GEMDAS rule, including working through expressions with grouping symbols, exponents, multiplication, division, addition and subtraction.
- An example problem comparing two students, Irish and Lynard, who got different answers when solving the expression 2 + 4 x 3 - 6 ÷ 2, and identifying which student answered
The document provides a detailed lesson plan for teaching arithmetic sequences to a 10th grade mathematics class. The objectives are for students to illustrate, determine the nth term of, and appreciate arithmetic sequences. The lesson proper involves motivating students with a treasure box activity, defining and formulating the formula for an arithmetic sequence, working examples, and evaluating student understanding with an "Answer Me" game. Key points are the definition of an arithmetic sequence as having terms obtained by adding a constant difference, and the formula An=a1+(n-1)d to find the nth term.
This document provides instructions for adding whole numbers using the column addition method. It explains that the digits should be positioned with the tens over the tens and units over the units. When adding the units, if they total 10 or more a ten needs to be carried over to the tens column. Then the tens are added, including any tens carried over from the units. Examples of 57 + 76, 69 + 58, and 37 + 85 are shown step-by-step using this method.
M6_Q2_W8B_Performing Basic Operations on Integers.pptxElmerpascual4
This document provides a lesson on performing basic operations (multiplication and division) with integers. It defines the rules for multiplying and dividing integers, such as the product of two integers with the same sign is positive and the product of integers with opposite signs is negative. Examples and practice exercises are provided to illustrate multiplying and dividing integers. The lesson concludes by summarizing the rules for multiplying and dividing integers.
The Mathematics Club of La Suerte Integrated School has prepared an action plan for the 2022-2023 school year with the following objectives:
1. Elect new officers for the Mathematics Club and provide them an orientation on their duties and responsibilities.
2. Conduct recreational mathematics activities and tutorials to showcase students' abilities and help low-performing learners.
3. Recognize deserving club officers and members with certificates and submit an accomplishment report at the end of the school year.
Integrating Higher-Order Thinking Skills into MathClif Mims
This document discusses integrating higher-order thinking skills into middle and high school math classes. It provides examples of how students can demonstrate conceptual understanding through creating their own math problems and solutions using digital tools like videos, posters, and animations. The document advises that teachers allow students to struggle productively, explore concepts, and create multiple representations of their understanding in order to develop higher-order thinking skills beyond just memorizing steps. Special thanks are given to a teacher who has implemented these strategies in their classroom.
Multiplying 3-digit numbers by 2-digit numbers gemmajoaquin
This document provides a lesson on multiplying 3-digit numbers by 2-digit numbers. It begins with a review of multiplication and then demonstrates multiplying without and with regrouping using short methods and lattice methods. Examples and exercises are provided for students to practice. Key skills learned are multiplying 3-digit and 2-digit numbers in various ways including short and lattice methods.
The document summarizes the education systems and mathematics teaching strategies of Australia, Canada, Denmark, Taiwan, and discusses potential applications in the Philippines. The key points are:
1. It provides an overview of the education systems of each country, including curriculum goals focused on student development and engagement.
2. It examines PISA test results in mathematics, science, and reading for each country.
3. It outlines different teaching strategies used in each country, such as constructivism in Australia, repetition and games in Canada, differentiation in Denmark, and spontaneity/interaction in Taiwan.
4. It suggests the best approaches from each country, like constructivism and authentic learning, could be applied to
The document lists various locations found in schools including the Guidance Office, I.T. Computer Room, School Playground, School Canteen, School Gymnasium, Library, Classroom, and Office of the Principal.
This document provides instruction on subtracting 2-3 digit numbers with and without regrouping. It begins by reviewing subtraction concepts like the minuend, subtrahend, difference, and the regrouping rhyme. Examples are provided of subtracting without regrouping like 320-10=310 and with regrouping like 634-455=179. Practice problems are included for students to visualize, write number sentences for, and solve 2-3 digit subtraction problems both with and without regrouping. An assignment is given for students to complete additional similar practice problems on their own.
The K to 12 program in the Philippines reforms the basic education system from 10 to 12 years. It aims to provide students with sufficient time to master concepts and skills, develop lifelong learning abilities, and adequately prepare graduates for employment, entrepreneurship or higher education. The key aspects of the K to 12 program include enhancing the curriculum, implementing a senior high school phase, ensuring quality teaching through teacher training, and facilitating students' transition to employment through partnerships with industry.
The educational system of Taiwan is overseen by the Ministry of Education and follows a 6-3-3-4 structure comprising preschool, elementary school, junior high school, senior high school/vocational school, university, and graduate studies. Education is highly valued in Taiwan and enrollment rates are over 90% across all levels of compulsory education. The government places emphasis on reforming the educational system to promote lifelong learning, internationalization, and improving accessibility and quality of education.
This document discusses the integration of technology and manipulatives in mathematics teaching. It outlines topics like virtual manipulatives, dynamic geometry software, computer algebra systems, and other technologies. Virtual manipulatives allow students to interact with visual representations of dynamic objects to build mathematical understanding. Effective use requires teachers to understand representations and lesson structure. Sample websites for virtual manipulatives on measurement, conversions, and volume are provided. Integrating technology can keep students engaged by empowering them in today's technological world.
The document discusses patterns and relations including increasing and decreasing patterns. It describes demonstrating understanding of patterns through observing, describing, extending, comparing and creating patterns using manipulatives, pictures, sounds and actions. It also discusses representing and explaining pattern rules as well as strategies for solving problems involving patterns.
The American curriculum established in Philippine public schools after the 1900s was aimed at conquering Filipinos intellectually as well as physically. The curriculum and teaching materials focused on American culture, ideals, and values. English was the primary language of instruction. During the Commonwealth period from 1935-1946, the curriculum expanded to include subjects like farming, trade, and domestic science. The 1940 Educational Act reorganized elementary schools and established collegiate normal schools for teacher training.
The document summarizes operations on integers using the real number line. It discusses addition, multiplication, division, and subtraction of integers. For addition, it explains that adding numbers with the same sign yields a sum with that common sign, while adding numbers with different signs involves subtracting the absolute values. For multiplication and division, it notes that operations between integers with the same sign produce a positive result, while operations between integers with different signs yield a negative result. For subtraction, it describes how subtraction can be rewritten as addition by changing the subtractend to its opposite.
This document provides classroom materials on exponents including guide cards, activity cards, assessment cards, enrichment cards, and a reference card. The cards introduce exponents, ask students to identify bases and exponents, rewrite expressions without zero or negative exponents, simplify expressions using laws of exponents, and evaluate exponential expressions. The reference card reviews the general form of exponential expressions and laws for multiplying, dividing, and taking powers of exponential expressions.
The document discusses strategies for teaching mathematics, including discovery approach, inquiry teaching, demonstration approach, math-lab approach, practical work approach, individualized instruction using modules, brainstorming, problem-solving, cooperative learning, and integrative technique. It provides details on each approach, such as the discovery approach aiming to develop higher-order thinking skills and both teachers and learners playing active roles. It also lists 10 creative ways to teach math using dramatizations, children's bodies, play, toys, stories, creativity, and problem-solving abilities.
This document provides instruction on adding integers. It begins with objectives and essential questions about how adding integers differs from adding whole numbers and how the sign of integers affects their sum. It then presents two rules for adding integers: 1) if integers have the same sign, add the numbers and keep that sign, and 2) if integers have different signs, subtract the numbers disregarding sign and keep the sign of the integer farther from zero. Examples demonstrate applying each rule. The document concludes by providing practice problems for students to solve.
The document summarizes the Secondary Education Development Program (SEDP) and the New Secondary Education Curriculum (NSEC) implemented in the Philippines in 1989. It provides background on the objectives of replacing the 1973 curriculum, key features of the SEDP and NSEC such as its student-centered and multidisciplinary approach. It also compares the 1989 curriculum to the current K to 12 Basic Education Curriculum, highlighting differences in approach, medium of instruction, and textbook ratios.
Singapore Math Seminar at Minneapolis MNJimmy Keng
This seminar for about 400 teachers was held at Elk River High School. It is based on MAP101 Fundamentals of Singapore Math. A similar session was held in Chicago the next day. This is part of the Experiencing Singapore Math Program designed for administrators and teachers who are new to Singapore Math.
The document discusses Singapore Math and its spiral curriculum approach. It provides examples of how fractions are taught over multiple grades, with concepts being revisited and built upon each year. It also discusses enrichment lessons, and gives an example of a lesson where students explore different methods for dividing fractions by whole numbers.
This document provides instructions for adding whole numbers using the column addition method. It explains that the digits should be positioned with the tens over the tens and units over the units. When adding the units, if they total 10 or more a ten needs to be carried over to the tens column. Then the tens are added, including any tens carried over from the units. Examples of 57 + 76, 69 + 58, and 37 + 85 are shown step-by-step using this method.
M6_Q2_W8B_Performing Basic Operations on Integers.pptxElmerpascual4
This document provides a lesson on performing basic operations (multiplication and division) with integers. It defines the rules for multiplying and dividing integers, such as the product of two integers with the same sign is positive and the product of integers with opposite signs is negative. Examples and practice exercises are provided to illustrate multiplying and dividing integers. The lesson concludes by summarizing the rules for multiplying and dividing integers.
The Mathematics Club of La Suerte Integrated School has prepared an action plan for the 2022-2023 school year with the following objectives:
1. Elect new officers for the Mathematics Club and provide them an orientation on their duties and responsibilities.
2. Conduct recreational mathematics activities and tutorials to showcase students' abilities and help low-performing learners.
3. Recognize deserving club officers and members with certificates and submit an accomplishment report at the end of the school year.
Integrating Higher-Order Thinking Skills into MathClif Mims
This document discusses integrating higher-order thinking skills into middle and high school math classes. It provides examples of how students can demonstrate conceptual understanding through creating their own math problems and solutions using digital tools like videos, posters, and animations. The document advises that teachers allow students to struggle productively, explore concepts, and create multiple representations of their understanding in order to develop higher-order thinking skills beyond just memorizing steps. Special thanks are given to a teacher who has implemented these strategies in their classroom.
Multiplying 3-digit numbers by 2-digit numbers gemmajoaquin
This document provides a lesson on multiplying 3-digit numbers by 2-digit numbers. It begins with a review of multiplication and then demonstrates multiplying without and with regrouping using short methods and lattice methods. Examples and exercises are provided for students to practice. Key skills learned are multiplying 3-digit and 2-digit numbers in various ways including short and lattice methods.
The document summarizes the education systems and mathematics teaching strategies of Australia, Canada, Denmark, Taiwan, and discusses potential applications in the Philippines. The key points are:
1. It provides an overview of the education systems of each country, including curriculum goals focused on student development and engagement.
2. It examines PISA test results in mathematics, science, and reading for each country.
3. It outlines different teaching strategies used in each country, such as constructivism in Australia, repetition and games in Canada, differentiation in Denmark, and spontaneity/interaction in Taiwan.
4. It suggests the best approaches from each country, like constructivism and authentic learning, could be applied to
The document lists various locations found in schools including the Guidance Office, I.T. Computer Room, School Playground, School Canteen, School Gymnasium, Library, Classroom, and Office of the Principal.
This document provides instruction on subtracting 2-3 digit numbers with and without regrouping. It begins by reviewing subtraction concepts like the minuend, subtrahend, difference, and the regrouping rhyme. Examples are provided of subtracting without regrouping like 320-10=310 and with regrouping like 634-455=179. Practice problems are included for students to visualize, write number sentences for, and solve 2-3 digit subtraction problems both with and without regrouping. An assignment is given for students to complete additional similar practice problems on their own.
The K to 12 program in the Philippines reforms the basic education system from 10 to 12 years. It aims to provide students with sufficient time to master concepts and skills, develop lifelong learning abilities, and adequately prepare graduates for employment, entrepreneurship or higher education. The key aspects of the K to 12 program include enhancing the curriculum, implementing a senior high school phase, ensuring quality teaching through teacher training, and facilitating students' transition to employment through partnerships with industry.
The educational system of Taiwan is overseen by the Ministry of Education and follows a 6-3-3-4 structure comprising preschool, elementary school, junior high school, senior high school/vocational school, university, and graduate studies. Education is highly valued in Taiwan and enrollment rates are over 90% across all levels of compulsory education. The government places emphasis on reforming the educational system to promote lifelong learning, internationalization, and improving accessibility and quality of education.
This document discusses the integration of technology and manipulatives in mathematics teaching. It outlines topics like virtual manipulatives, dynamic geometry software, computer algebra systems, and other technologies. Virtual manipulatives allow students to interact with visual representations of dynamic objects to build mathematical understanding. Effective use requires teachers to understand representations and lesson structure. Sample websites for virtual manipulatives on measurement, conversions, and volume are provided. Integrating technology can keep students engaged by empowering them in today's technological world.
The document discusses patterns and relations including increasing and decreasing patterns. It describes demonstrating understanding of patterns through observing, describing, extending, comparing and creating patterns using manipulatives, pictures, sounds and actions. It also discusses representing and explaining pattern rules as well as strategies for solving problems involving patterns.
The American curriculum established in Philippine public schools after the 1900s was aimed at conquering Filipinos intellectually as well as physically. The curriculum and teaching materials focused on American culture, ideals, and values. English was the primary language of instruction. During the Commonwealth period from 1935-1946, the curriculum expanded to include subjects like farming, trade, and domestic science. The 1940 Educational Act reorganized elementary schools and established collegiate normal schools for teacher training.
The document summarizes operations on integers using the real number line. It discusses addition, multiplication, division, and subtraction of integers. For addition, it explains that adding numbers with the same sign yields a sum with that common sign, while adding numbers with different signs involves subtracting the absolute values. For multiplication and division, it notes that operations between integers with the same sign produce a positive result, while operations between integers with different signs yield a negative result. For subtraction, it describes how subtraction can be rewritten as addition by changing the subtractend to its opposite.
This document provides classroom materials on exponents including guide cards, activity cards, assessment cards, enrichment cards, and a reference card. The cards introduce exponents, ask students to identify bases and exponents, rewrite expressions without zero or negative exponents, simplify expressions using laws of exponents, and evaluate exponential expressions. The reference card reviews the general form of exponential expressions and laws for multiplying, dividing, and taking powers of exponential expressions.
The document discusses strategies for teaching mathematics, including discovery approach, inquiry teaching, demonstration approach, math-lab approach, practical work approach, individualized instruction using modules, brainstorming, problem-solving, cooperative learning, and integrative technique. It provides details on each approach, such as the discovery approach aiming to develop higher-order thinking skills and both teachers and learners playing active roles. It also lists 10 creative ways to teach math using dramatizations, children's bodies, play, toys, stories, creativity, and problem-solving abilities.
This document provides instruction on adding integers. It begins with objectives and essential questions about how adding integers differs from adding whole numbers and how the sign of integers affects their sum. It then presents two rules for adding integers: 1) if integers have the same sign, add the numbers and keep that sign, and 2) if integers have different signs, subtract the numbers disregarding sign and keep the sign of the integer farther from zero. Examples demonstrate applying each rule. The document concludes by providing practice problems for students to solve.
The document summarizes the Secondary Education Development Program (SEDP) and the New Secondary Education Curriculum (NSEC) implemented in the Philippines in 1989. It provides background on the objectives of replacing the 1973 curriculum, key features of the SEDP and NSEC such as its student-centered and multidisciplinary approach. It also compares the 1989 curriculum to the current K to 12 Basic Education Curriculum, highlighting differences in approach, medium of instruction, and textbook ratios.
Singapore Math Seminar at Minneapolis MNJimmy Keng
This seminar for about 400 teachers was held at Elk River High School. It is based on MAP101 Fundamentals of Singapore Math. A similar session was held in Chicago the next day. This is part of the Experiencing Singapore Math Program designed for administrators and teachers who are new to Singapore Math.
The document discusses Singapore Math and its spiral curriculum approach. It provides examples of how fractions are taught over multiple grades, with concepts being revisited and built upon each year. It also discusses enrichment lessons, and gives an example of a lesson where students explore different methods for dividing fractions by whole numbers.
The document discusses the need to reform the Philippines' K-12 education system to better prepare students for the 21st century. It notes that the world is changing rapidly due to technology and globalization. However, Philippine students are performing poorly on international assessments in math and science. It also has one of the shortest pre-university programs in Asia. The K-12 reform aims to enhance the basic education curriculum by extending it to 12 years, focusing on competency-based learning, and improving math and science education based on models like Singapore Math. This is to allow Filipino students to better deal with rapid change and solve complex problems.
Singapore Math Strategies for U.S. SchoolsJimmy Keng
The document provides an overview of Singapore Math strategies that could be used in U.S. schools. It discusses the fundamentals of Singapore Math which include a focus on problem solving, thinking, managing information, visualization, generalization, and number sense. It also discusses how Singapore students have demonstrated high achievement in international math assessments like TIMSS. The pedagogical approach of Singapore Math focuses on understanding over procedural skills. Differentiated instruction and assessment are also emphasized.
This document provides an introduction to Singapore Math. It notes that Singapore students placed top three in international math tests in recent years. It then discusses what the TIMSS test is and provides sample results showing Singapore and other countries' scores. It outlines five factors for Singapore's math success: a sound curriculum, high expectations, subject banding, well-managed schools, and qualified teachers. It also gives overviews of Singapore Math philosophy and methods, including an emphasis on mental math, moving from concrete to abstract understanding, and requiring mastery of basic facts. Sample word problems are presented at the end.
This document provides an overview of the Common Core standards for 5th grade math. It outlines the main topic areas covered, including operations and algebraic thinking, number and operations in base ten, number and operations with fractions, measurement and data, and geometry. For each topic area, it lists the relevant standards and provides an example illustration or question to demonstrate how the standards are applied. The document is intended to give teachers and students an overview of what is covered in 5th grade math based on the Common Core requirements.
This document discusses Singapore Math and teacher preparation. It focuses on the approach of Singapore Math, which emphasizes problem solving, conceptual understanding, and thinking. It outlines the framework for preparing teachers to teach mathematics in this way, which includes having teachers learn content conceptually and the corresponding pedagogical knowledge. Courses in Singapore help teachers develop as learners and observers by giving opportunities to study math lessons.
Powerpoint from a NCTM 2012 National Conference session. Because it was an interactive session, the powerpoint isn't too exciting, but it does have links to most of the online tools and apps that we demonstrated in the session.
This document outlines the contents and structure of a Singapore maths textbook and workbook for grade 4. It includes a scheme of work, lesson plans, and appendices for each chapter that provide key concepts, activities, and exercises to support math instruction. Additional sections offer thinking skills practices, individual and group work, math journals, and challenges to enhance learning.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
The document discusses the benefits of exercise for both physical and mental health. Regular exercise can improve cardiovascular health, reduce symptoms of depression and anxiety, enhance mood, and boost brain function. Staying physically active aims to strengthen the body and mind.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
The document discusses the benefits of exercise for both physical and mental health. It notes that regular exercise can reduce the risk of diseases like heart disease and diabetes, improve mood, and reduce stress and anxiety levels. Exercise is also said to boost brain health and function by improving cognitive abilities and reducing the risk of conditions like Alzheimer's disease and dementia.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
The document discusses the benefits of exercise for both physical and mental health. It notes that regular exercise can reduce the risk of diseases like heart disease and diabetes, improve mood, and reduce feelings of stress and anxiety. Staying active also helps maintain a healthy weight and keeps muscles, bones and joints healthy as we age.
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercising for at least 30 minutes three times per week is recommended to see positive effects on mental well-being.
New Jersey Singapore Math Administrators Symposium East BrunswickJimmy Keng
The document provides an overview of Singapore's education system and approach to teaching mathematics. It notes that Singapore has around 500,000 students, 30,000 teachers, and 173 primary and 155 secondary schools. It describes how Singapore places a strong emphasis on problem solving in mathematics and uses a spiral curriculum approach with concrete, visual, and conceptual experiences to build understanding. Textbooks introduce concepts through visual representations before using formal terms.
The document discusses Singapore's education system and experiences with Singapore Math. It provides statistics on students, teachers, schools and academic performance in Singapore. It traces the history and development of Singapore Math textbooks from 1982 to present. It emphasizes the importance of conceptual understanding, number sense, visualization and higher-order thinking in Singapore Math. Examples from Primary Mathematics textbooks show how visuals are used to teach concepts like distributive property without formal terms.
MAP101 Fundamentals of Singapore Mathematics Curriculum Jimmy Keng
This document provides an overview of Singapore's education system and the use of Singapore Math. It notes that Singapore has about 500,000 students, 30,000 teachers, and 173 primary schools. It highlights Singapore's high performance on international tests in literacy, science and math since the 1960s. The document discusses the introduction and evolution of Singapore Math textbooks from 1982 to the present. It emphasizes the focus of Singapore Math on relational understanding, conceptual development, number sense, and visualization skills. Examples from Singapore, US, UK, Chile and the Philippines illustrate how these concepts are taught.
This document provides an overview of Singapore's education system and experiences with Singapore Math. It discusses Singapore's small land area but high GDP per capita. It notes there are around 500,000 students, 30,000 teachers, and 173 primary and 155 secondary schools. It also discusses Singapore's high performance on international math tests and how Singapore Math was introduced and revised over time with an emphasis on conceptual understanding and problem solving.
Experiencing Singapore Math is an one-day executive program to give participants an overview of Singapore Math. It is based on MAP101 Fundamentals of Singapore Math that teachers do as part of their professional development in teaching Singapore Math. More than fifty Missouri educators participated in this one-day institute.
Singapore Math Administrators Symposium NewarkJimmy Keng
The document discusses Singapore's education system and approach to teaching mathematics, known as Singapore Math. It provides background on Singapore's population, economy, and education statistics. The key aspects of Singapore Math are its emphasis on conceptual understanding, concrete experiences, number sense, and visual representation to build proficiency in problem solving.
Singapore Math Administrators Symposium ScottsdaleJimmy Keng
The document discusses Singapore Math and how its approach to teaching mathematics concepts concretely first before building conceptual understanding has led to high performance on international tests. It provides examples of Singapore Math textbooks and curricula being used in schools in Singapore as well as other countries. The document emphasizes teaching mathematics visually and using variation and spiral progression to reinforce concepts.
This document provides an overview of a professional development workshop on the Singapore Math method. It discusses key aspects of Singapore Math including its emphasis on visualization, problem solving, and pattern recognition. Examples are provided from Singapore math textbooks to illustrate how concepts like addition, multiplication, and calculating area are taught with a focus on visual models and representations. The document also shares information on the history and revisions of the Singapore math curriculum and textbooks over time.
Education Summit Utrecht, The NetherlandsJimmy Keng
The document discusses the Singapore approach to education, which emphasizes problem-solving, higher-order thinking skills, and using a concrete-pictorial-abstract approach to teaching mathematics. It provides examples of how schools in other countries have implemented aspects of the Singapore method, such as using visualization and extended discussion to engage students. The approach has been shown to lead to high achievement on international tests.
The Singapore education approach emphasizes high achievement through problem-solving lessons and the concrete-pictorial-abstract teaching method. It has led to top scores in international tests. The approach uses extended discussions, multiple representations of concepts, and a focus on higher-order thinking skills like visualization. It has been successfully implemented in schools globally.
NCTM Differentiated Instruction Using Singapore Math Jimmy Keng
This document summarizes a workshop on differentiated instruction using Singapore Math. The workshop is presented by Dr. Yeap Ban Har and teaches how to differentiate math tasks to cater to mixed-ability classes. It explains how Singapore Math is designed to enable all learners to learn mathematics well through adequate scaffolding for struggling learners and extending tasks to engage advanced learners. The workshop also provides examples of differentiating word problems and using the Singapore Math approach of solving one math problem during a lesson.
Highline Session 3 at Parkside ElementaryJimmy Keng
The document summarizes key aspects of the Singapore Math approach used in Singaporean schools. It discusses the Concrete-Pictorial-Abstract (CPA) approach, the spiral curriculum, and emphasis on developing relational understanding. It provides examples of how these concepts are implemented in Singapore Math lessons and notes Singapore's high performance on international math assessments.
The document discusses Singapore Math, which focuses on developing conceptual understanding using a concrete-pictorial-abstract approach. It emphasizes problem solving, the spiral curriculum where topics are revisited at increasing levels of difficulty, and three-part lesson structures involving exploration, concept introduction, and guided practice. International test data shows Singapore students performing highly in mathematics compared to other countries.
The document discusses Singapore's approach to improving math instruction and performance. It outlines Singapore's curriculum framework which is revised every six years and emphasizes mathematical modeling. It also discusses strategies used like aligning textbooks to the curriculum, providing leadership support, and utilizing research-backed pedagogies in professional development programs for teachers that focus on developing skills as a learner, observer, and reflective practitioner. International test results show Singapore and other Asian countries achieving top scores in mathematics over several decades.
This document discusses mathematics teacher preparation and professional development in Singapore. It outlines Singapore's approach which includes selecting top students to become teachers, emphasizing pedagogical and content knowledge in pre-service teacher education programs, and providing ongoing professional development for in-service teachers through professional learning communities and 100 hours of training per year. The goal is to develop teachers' capacity to continuously improve their practice and enhance student learning.
The document summarizes key aspects of the Singapore Math approach used in Singapore and some schools in the United States. It discusses the Concrete-Pictorial-Abstract approach, the spiral curriculum, three-part lesson structure, emphasis on relational understanding, and data showing Singapore students outperforming peers internationally and enjoying math more.
Similar to Math in Focus: Singapore Math Community Institute (updated) (20)
This document discusses differentiating instruction to challenge advanced learners. It provides examples of ways to assess basic subtraction skills through runway indicators. For advanced learners, it suggests having them solve problems in alternative ways, write stories for equations, or write notes applying math concepts to enrich their learning beyond basic skills.
The document discusses using math journals in elementary school classrooms to teach mathematical concepts. It describes a framework for teaching mastery that involves anchor tasks, guided practice, and independent practice. Journaling is presented as one part of this process where students explore concepts, structure their understanding, and reflect on their learning. Examples are provided of kindergarteners recording number bonds in their journals to master basic counting and addition. The journal entries allow teachers to assess understanding and provide differentiated instruction.
The document outlines a schedule for four sessions occurring between 08:30-04:00 with a forum period from 03:30-04:00. It then discusses using a lesson on the Common Core to understand critical areas for Grade 1, including number bonds, comparison of numbers, and conservation of numbers. Various methods for developing visualization like the CPA approach, bar models, and teacher questioning are listed. The document goes on to discuss elements of effective math lessons including exploration, structure, journaling, reflection, and guided/independent practice using addition and subtraction strategies like counting all, making 10, subtracting from ten, and renaming before subtracting with examples provided.
This document provides an overview of a middle school mathematics institute that will take place on Saturday. It discusses the basic lesson format, which includes an anchor task, guided practice, and independent practice. It also references Bruner's idea of using concrete experiences and pictorial representations to help students understand abstract ideas. The document then provides several case studies as examples of lessons that could be used to develop, apply, and practice various mathematical concepts involving fractions, algebra, geometry, and more.
This document provides an overview of a Grade 5 mathematics institute that will take place on a Friday. It outlines the basic lesson format, which includes an anchor task, guided practice, and independent practice. It also references several learning theories that provide a framework for the lesson, such as Bruner's idea of concrete, iconic, and symbolic representations. The document includes several math word problems from past PSLE exams in Singapore to use for practice. It concludes with key learning theories covered and strategies for challenging advanced learners.
1) The document discusses standards and instructional focus areas for Grade 4 mathematics, including multi-digit multiplication and division, fractions, and geometric shapes.
2) It provides examples of case studies to solve, including arranging fractions in order and word problems involving fractions of amounts.
3) Theories of learning and representation discussed include Bruner's CPA approach and Skemp's classifications of understanding in mathematics.
This document provides information about a grade 3 mathematics institute to be held on Wednesday. It discusses key theories in mathematics learning from Piaget, Bruner, Dienes, Vygotsky, and Skemp. The document also provides several case studies with examples of lesson plans and problems that assess different mathematical concepts like operations, fractions, problem solving, and place value.
The document discusses a Grade 2 math institute that will focus on place value using concrete and pictorial representations. It provides several case studies on topics like subtraction across zeros, fractions, and problem solving. The lessons follow a basic format of an anchor task, guided practice, and independent practice. Key learning theories that will be drawn from include those from Piaget, Bruner, Dienes, Vygotsky, and Skemp. Bruner's CPA approach and Skemp's classifications of understanding will be particularly relevant for using different representations to build conceptual and relational understanding.
This document contains instructions for cutting out numbers and mathematical symbols from a page. It includes numbers from 0 to 9, basic mathematical operators like + and -, and instructions to cut out the listed items. The document is repetitive, listing the same numbers and symbols twice.
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.
The document discusses strategies for developing and improving mathematical practices, such as using anchor tasks, collaborative structures, questioning techniques, journals, textbooks for reflection, and focusing on visualization, generalization, and number sense. It also discusses moving from concrete to pictorial to abstract representations, and using anchor tasks and challenging word problems to teach Singapore math concepts.
This document discusses using a problem-solving approach to teach mathematics. It focuses on practicing problem-solving lessons and breaking students into groups to work on problems. The document provides resources for lesson plans and contact information for the speaker who advocates for integrating problem-solving into mathematics education.
Se01 abc's of singapore math through whole numbersJimmy Keng
The document discusses the Singapore approach to teaching mathematics, which was developed to help Singaporean students perform better in math. It is based on Bruner's ideas of a spiral curriculum and using representations. The document provides 15 sample math tasks that demonstrate fundamentals of Singapore Math instruction, such as the Concrete-Pictorial-Abstract approach. It also includes quotes from Bruner about revisiting basic ideas repeatedly to help students master structured bodies of knowledge.
This document contains an agenda for a staff development conference on Singapore Math strategies with a focus on visualization. It includes 4 sample math tasks: 1) finding the area of a 4-sided polygon on a geoboard; 2) calculating leftover wire used to make a figure of 6 equilateral triangles; 3) dividing numbers by 3, 4, and 6; and 4) a word problem about Peter and Nancy exchanging coins to determine how many Peter originally had. The tasks are meant to illustrate ways to get students to visualize math concepts.
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
Main Java[All of the Base Concepts}.docxadhitya5119
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Pride Month Slides 2024 David Douglas School District
Math in Focus: Singapore Math Community Institute (updated)
1. Experiencing
Singapore Math
Experiencing Singapore Math
M AT H I N F O C U S : S I N G A P O R E M AT H C O M M U N I T Y
INSTITUTE
July 24, 2012 Chicago, IL
Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com
2. Experiencing
Singapore Math
Land
270 sq miles
People
introduction 4.7 million
GDP per capita
1965 USD510
2010 USD43,300
in current USD
Junyuan Secondary
School, Singapore
4. General Overview of Singapore and
its Education System
Students
500 000
Teachers
30 000
Principals & Vice-Principals
900
Schools
173 Primary Schools (Primary 1 – 6)
155 Secondary Schools (Secondary 1 – 4)
13 Junior Colleges (JC 1 – 2) Canossa Convent Primary
15 Mixed-Level Schools School, Singapore
The data refers to 1-12 school system. Pre-school is not part of the formal education
system. The data excludes post-secondary education system which includes institutes
of technical education, polytechnics and universities.
5. High achievement was not a given. In
1960, among 30 615 candidates who
sat for the first Primary School Leaving
Examination, 45% of the candidates
passed.
Keon Ming Public School, Singapore
6. Experiencing
Singapore Math
All major international tests (literacy, science and mathematics) between 1964
and 2003 were placed on a common scale. Selected countries shown in the table.
Score 1960-1970s 1980s 1990s 2000s
500 Japan Japan Japan Japan
Korea Korea Korea
Hong Kong Singapore Hong Kong
Hong Kong Singapore
400 Thailand Singapore Malaysia Malaysia
Thailand Thailand Thailand
The Philippines
300 Indonesia Indonesia
The Philippines The Philippines
Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
7.
8. "Solving problems is central to mathematical proficiency
and is articulated to a varying degree across the
international curricula. Singapore applies the highest
degree of specificity to it, placing it at the centre of all
mathematical learning.“
Review of the National Curriculum in England Research Report
UK Department for Education
9. Experiencing
Singapore Math
1982
Introduction of Singapore mathematics
textbooks as they are known today.
Mathematics is “an excellent
vehicle for the development
1992 and improvement of a person’s
Introduction of Problem- intellectual competence”.
Solving Curriculum Ministry of Education Singapore 2006
1997 2001
Thinking Schools Introduction of textbooks published by
Learning Nation private publishers and approved by
Ministry of Education.
2007
New editions of textbooks are
published with the introduction of the
revised curriculum.
2013
Fourth version of the problem-solving
curriculum will be implemented.
Page 1
11. Experiencing
Singapore Math
on Visualization
Fundamentals of Singapore Math
Focus
Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com
16. Experiencing
Singapore Math
60% of Jon’s money is $12.
Find the amount of Jon’s money.
King Solomon Academy, London
17. Box A has 20 more Edgewood Elementary School, New York
books than Box B. Box
C has twice as many
books as Box B. The
three boxes has 340
books. How many
books are there in Box
A.
18. Experiencing
Singapore Math
Solve 3x – 2 =
8
Globe Academy, London
19. Experiencing
Singapore Math
3x – 2 = 8
Globe Academy, London
20. Experiencing
Singapore Math
Share 3 fourths equally among 3.
3 fourths 3 = 1 fourth
Page 5
32. Experiencing
Singapore Math
King Solomon Academy, London
33. Singapore Math
Experiencing
King Solomon Academy, London
34. Experiencing
Singapore Math
Globe Academy, London
35. Experiencing
Singapore Math
Globe Academy, London
36. Experiencing
Singapore Math
Globe Academy, London
37.
38. Experiencing
Singapore Math
on Patterns
Fundamentals of Singapore Math
Focus
Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com
39. Experiencing
Singapore Math
Da Qiao Primary School, Singapore
40. Experiencing
Singapore Math
Junyuan Secondary School, Singapore
Mathematical
patterns and Practices
“Mathematically
generalization
proficient students
look closely to discern
a pattern or structure.”
41. Experiencing
Singapore Math
Fundamentals of Singapore Math
Case Study on
Multiplication
Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com
42. Desde los primeros años, los estudiantes
aprenden a hacer conjuntos o grupos iguales
utilizando materiales concretos.
From the early grades, students learn to make equal
groups using concrete materials.
43. Luego, representan estas situaciones
concretas utilizando, en primer lugar, los
dibujos y, …
After that they represent these concrete
situations using, first, drawings ..
44. … más tarde, diagramas (modelos de
barras). Después de eso, escriben
multiplicaciones. Por supuesto, los
profesores volverán a las representaciones
concretas y pictóricas una y otra vez en
aprendizajes posteriores.
… and, later, diagrams. After that they write
multiplication sentences.
45. Multiplication involving whole numbers is
taught over five years, starting in Primary 1.
The focus is on one of the meanings of
multiplication – equal sets or equal groups.
La multiplicación con números enteros se
imparte en cinco años, a partir de 1º básico.
La atención se centra en uno de los
significados de la multiplicación; conjuntos
iguales o grupos iguales. Los estudiantes
aprenden a representar 3 platos de frutas
como de 3 x 6, cuando hay 6 frutas en cada
plato. No se espera que recuerden las tablas
de multiplicar.
50. In Primary 2, students learn multiplication
facts of 2, 3, 4, 5 and 10. In Primary 3, they
learn the multiplication facts of 6, 7, 8 and 9.
En 2º básico, los
alumnos aprenden
las tablas de
multiplicación del
2, 3, 4, 5 y 10. En
3º
básico, aprenden
las tablas de
multiplicación, de
6, 7, 8 y 9.
51. Later, the array meaning
of multiplication is
introduced.
Más tarde, se introduce el
significado del producto
vectorial.
52.
53.
54.
55. Students apply their Los estudiantes
understanding of aplican sus
multiplication to conocimientos de la
solve word problems multiplicación para
including those that resolver problemas
include multiplicative que incluyen la
comparison, and at comparación
the same time, multiplicativa, y al
deepen their mismo
understanding of tiempo, profundizan
multiplication. su comprensión de la
multiplicación.
56.
57. Multiplication is also
applied to find the area
of rectangles and
square when Primary 3
students learn the
concept of area.
La multiplicación se
aplica también para
encontrar el área de
rectángulos y cuadrados
cuando los estudiantes
de 3º básico aprenden
el concepto de
área, contando
unidades cuadradas al
final de 3º básico.
58. In Grade 3 they Después de completar las
learn tablas de multiplicar, los
multiplication of estudiantes aprenden
2-digit with 1- multiplicaciones que van
digit numbers as más allá de la tabla de
well as multiplicar. Ellos aprenden a
multiplication of multiplicar números de dos
3-digit and 1-digit dígitos con números de 1
numbers. dígito, así como la
multiplicación de números
de tres dígitos y números de
un dígito.
59. 42
In Primary 4, the learn
multiplication of 4-digit 4
and 1-digit numbers as
well as multiplication of 3- 34
digit and 2-digit numbers.
The focus is on partial
products.
En 4º básico, aprenden a multiplicar números
de cuatro dígitos y un dígito, así como
multiplicar números de tres dígitos y dos
dígitos. La atención se centra en productos
parciales.
60. Finally in Primary 5,
students learn to use
calculator to multiply
larger numbers. 5º básico los estudiantes
Por último, en
aprenden a utilizar la calculadora para
multiplicar grandes cantidades.
64. Pedagogical Principles of Singapore Method
Spiral Approach
10 : 5 = 2
12 : 5 = 2
restante 2
Principios pedagógicos del Método Singapur
Enfoque en Espiral
65. “Un plan de estudios de la manera que se
desarrolla debe revisar estas ideas básicas
en varias ocasiones, construyéndose sobre
ellos hasta que el estudiante ha comprendido
todo el aparato formal que conllevan”.
(Bruner 1960 en El Proceso de la
Educación). as it develops should revisit this
“A curriculum
basic ideas repeatedly, building upon them
until the student has grasped the full formal
.
apparatus that goes with them.” (Bruner 1960
in The Process of Education).
66. En los cursos de 1º a 4º básico, se utilizan
cantidades discretas, por ejemplo piedrecillas
y los niños. En 5º básico se utilizan
cantidades continuas como las medidas
estándar de 13 kg y 13 cm.
In Grades 1 to 4, quantities used are discrete
ones e.g. pebbles and children. In Grade
5, continuous quantities like standard
measures 13 kg and 13 cm are used.
67. En 1º básico no se utiliza el símbolo ÷ o :
para la división. El símbolo se introduce en 2º
básico. La idea de resto se introduce en 3º
básico. 1, the symbol ÷ or : is not used. The
In Grade
symbol is introduced in Grade 2. The idea of
.
remainder is introduced in Grade 3.
68. The idea of
regrouping
before
dividing is
introduced
later in Grade
3 and is
taught in
La idea 4 as
Grade de reagrupar antes de dividirse se
introduce al finalizar 3º básico y también se
well.
enseña en 4 º básico.
69. Experiencing
Singapore Math
Fundamentals of Singapore Math
Challenging Word
Problems using Bar
Models
Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com
70. 2 units = 290 g – 110 g = 180 g
1 units = 180 g 2 = 90 g
110 g
3 x 90 g = 270 g
Bella puts 270 g sugar on the dish.
? ?
74. Experiencing
Singapore Math
Math in Focus
Grade 2
Escuela de Guetamala, Chile
75.
76. One day, 543 cars and 274 buses pass through a toll booth.
How many cars and buses pass through the toll booth?
Math in Focus Grade 2
cars 543
buses 274
543 + 274 =
cars buses
543 274
80. 2x + x = 4686
3x = 4686
Students in Grade 7 may use algebra to deal with such situations. Bar
model is actual linear equations in pictorial form.
81. Lesson June 18, 2012
Jack $3
Jack
Kyla $2
Kyla
gave
more
had
than
82. Lesson June 18, 2012
Open Lesson at Hawaii, USA
83.
84.
85.
86.
87. Lesson June 18, 2012
What if Kyla
Story 1 had this
Jack had $3. amount
before?
Jack gave Kyla $2
more.
Jack Kyla
Before $3 $1 $5 $19
After $1 $3 $7 ?
88.
89. Lesson June 18, 2012
Story 2
Kyla had $3 more than Jack. Who had
more money
Jack $2 afterwards?
How much
Kyla $3 more?
Jack gave Kyla $2.
90. Kyla had $3 more than Jack.
Jack gave Kyla $2.
How much more did Kyla have than Jack?
Students in Grade 6 may use algebra to deal with Story 2.
Kyla had $(x + 3)
Jack had $x
Then, Jack had $(x – 2)
And Kyla had $(x + 5)
Kyla had $(x + 5) – $(x – 2) or $7 more than Jack.
91. Lesson July 23, 2012
In the end ... At first …
Alice 20
Betty 10
Charmaine
Dolly
93. Experiencing
Singapore Math
Junyuan Secondary School, Singapore
Concrete to
visualization Visual
and managing
J Bruner
Human
information Intelligences
H Gardner
94.
95. can learn.
Our students must
too.
Google learns from typos and spelling mistakes we all make when searching to help give you
quicker and more accurate search results. So if you type ‘grizzly pears’, we can guess that you
probably meant ‘grizzly bears’.
Goggle does not have a degree in English. We can do this because over the years we’ve
studied how people search and learned what the most common errors are. So it’s good to
know that all those little mistakes aren’t made in vain.