This session focuses on the use of the bar model to solve a range of problems. The presenter modelled a range of teacher behaviour to help students acquire the competencies that they are supposed to by engaging in word problems. It was presented at the Indianapolis conference. We hope not too many people were not able to get a seat at the session. If you were not able to gain entry to the session, please accept our apologies.
This seminar was for parents of primary six students in a all-girls' school in Singapore. PSLE is the national examination in Singapore taken at the end of Grade 6.
This document discusses Vedic mathematics and methods for addition, subtraction, and multiplication based on ancient Indian techniques. Some key points:
- Vedic mathematics uses direct, mental approaches to solve problems in one line.
- Addition is done by adding the place values from right to left and carrying over if needed.
- Multiplication involves multiplying the place values and carrying over similar to standard algorithms.
- Subtraction borrows from the next place value when the top number is smaller, working from right to left.
- Special methods are described for multiplying near a base of 10 or 100 by subtracting/adding the amounts above or below the base.
This document contains a math lesson on addition and subtraction for grade 1 students. It includes word problems about adding numbers of objects and taking away quantities. Students are instructed to solve addition and subtraction problems by counting up or back on a number line. The lesson encourages practicing these skills in an Excel math workbook.
This week's maths lesson involves solving logic and correspondence puzzles. The document provides 12 puzzles for students to solve throughout the week, with the answers to each puzzle provided on subsequent slides. Students are encouraged to think logically and systematically to solve the puzzles, and can skip puzzles and return to them later in the week. Times table practice is also recommended during the week.
St. Vincent de Paul Home Learning W1 5.1.21NICOLEWHITE118
This document contains the daily schedule and tasks for a student's remote learning on Tuesday 5th January 2021. It includes subjects like Prayer, PSHE, Maths, Grammar & Spelling, Reading, Geography, PE and Reading. For each subject, learning objectives and activities are outlined. For Maths, examples of multiplication calculations and using the grid method are provided. Reading comprehension involves a chapter from the book Matilda. Students are instructed to complete tasks, take breaks, and check their work. They are reminded to focus on each task and do their best.
The document teaches the 12 multiplication and 6 division facts for the number 12 by listing each fact and its answer, with the multiplication facts going up to 12 x 12 = 144 and the division facts including 12 / 1 = 12 down to 12 / 6 = 2. It was presented as a math quiz by Payton and Skye to teach these basic number facts.
This session focuses on the use of the bar model to solve a range of problems. The presenter modelled a range of teacher behaviour to help students acquire the competencies that they are supposed to by engaging in word problems. It was presented at the Indianapolis conference. We hope not too many people were not able to get a seat at the session. If you were not able to gain entry to the session, please accept our apologies.
This seminar was for parents of primary six students in a all-girls' school in Singapore. PSLE is the national examination in Singapore taken at the end of Grade 6.
This document discusses Vedic mathematics and methods for addition, subtraction, and multiplication based on ancient Indian techniques. Some key points:
- Vedic mathematics uses direct, mental approaches to solve problems in one line.
- Addition is done by adding the place values from right to left and carrying over if needed.
- Multiplication involves multiplying the place values and carrying over similar to standard algorithms.
- Subtraction borrows from the next place value when the top number is smaller, working from right to left.
- Special methods are described for multiplying near a base of 10 or 100 by subtracting/adding the amounts above or below the base.
This document contains a math lesson on addition and subtraction for grade 1 students. It includes word problems about adding numbers of objects and taking away quantities. Students are instructed to solve addition and subtraction problems by counting up or back on a number line. The lesson encourages practicing these skills in an Excel math workbook.
This week's maths lesson involves solving logic and correspondence puzzles. The document provides 12 puzzles for students to solve throughout the week, with the answers to each puzzle provided on subsequent slides. Students are encouraged to think logically and systematically to solve the puzzles, and can skip puzzles and return to them later in the week. Times table practice is also recommended during the week.
St. Vincent de Paul Home Learning W1 5.1.21NICOLEWHITE118
This document contains the daily schedule and tasks for a student's remote learning on Tuesday 5th January 2021. It includes subjects like Prayer, PSHE, Maths, Grammar & Spelling, Reading, Geography, PE and Reading. For each subject, learning objectives and activities are outlined. For Maths, examples of multiplication calculations and using the grid method are provided. Reading comprehension involves a chapter from the book Matilda. Students are instructed to complete tasks, take breaks, and check their work. They are reminded to focus on each task and do their best.
The document teaches the 12 multiplication and 6 division facts for the number 12 by listing each fact and its answer, with the multiplication facts going up to 12 x 12 = 144 and the division facts including 12 / 1 = 12 down to 12 / 6 = 2. It was presented as a math quiz by Payton and Skye to teach these basic number facts.
This seminar for parents discussed the five key competencies in mathematical problem solving. Parental involvement is an important aspect of helping kids do well in school.
This document provides math lessons and activities for students in Year 4. It includes multiplication tables to practice, word problems to solve using addition and subtraction, and lessons on doubling and halving two-digit numbers. Students are encouraged to contact their teacher if they have any questions.
The document provides practice problems for calculating averages. It includes examples of finding the average of sets of numbers, word problems involving averages, problems where part of the data is excluded, finding missing values, averages of algebraic expressions, and problems involving how averages change when values are added or subtracted from numbers in the set. Students are to show their work and solutions on paper and view the document as a full screen slideshow.
This document provides information about revision grids for level 4 math topics. It includes a welcome message and instructions on how the grids can be used for revision and assessment. Suggestions are given for using the grids in class individually, as a game, or to promote collaboration. The source of inspiration for the grids is cited. Users are encouraged to provide feedback on how the grids are used.
Dinesh S introduces himself as a magician who has performed over 1000 shows in the past 12 years. He mentions riding a motorcycle blindfolded for 30 km to promote road safety. He uses magic to educate people and reduce superstitions. Photos are provided of him performing magic shows in various places for different occasions and audiences. Certificates of recognition for his work are also attached.
Division involves grouping quantities into equal sets. Examples shown include dividing 12 balls equally into boxes, with 3 balls in each box, dividing 18 faces into groups of 3, with 6 groups, and dividing 9 oranges equally into 3 bags, with 3 oranges in each bag. The document introduces division and solving one-step word problems using division to determine how quantities are divided equally among groups.
The document discusses factors and multiples of numbers. It explains that a factor is an exact divisor of a number that leaves no remainder, while a multiple is the result of multiplying a number by its factors. Some key points covered include:
- 1 is a factor of every number
- The number of factors of a given number is finite, while the number of multiples is infinite
- A number is both a factor and multiple of itself
- Examples are given of writing numbers as products of factors and identifying factors and multiples of various numbers.
The document discusses factors and multiples, defining factors as whole numbers that can divide another number with the resulting quotient being a whole number, and multiples as the product of multiplying two counting numbers. It provides examples of identifying factors and multiples, such as the factors of 8 being 1, 2, 4, 8 and the first four multiples of 2 being 2, 4, 6, 8. The warm-up problem identifies the factors of 50 as 5 and 10 and its multiple as 50.
Enhance your children's division skills with our incredible teaching, activity and display resource pack! Includes a comprehensive guide to the topic, printable activity resources for independent and group work, as well as handy display and reference materials.
Available from http://www.teachingpacks.co.uk/the-division-pack/
The document discusses factors and multiples of numbers. It provides examples of arranging objects like stars and footballs in different ways to get the same total, with the number of objects in each arrangement being the factors of the total. Factors are defined as exact divisors that leave no remainder. Multiples are numbers that a factor divides into with no remainder. Every number is a factor of itself and has an infinite number of multiples.
Here are some tips for improving problem solving skills in PSLE Mathematics:
- Take time to understand the question fully before attempting to solve it. Re-read if needed.
- Look for key information like numbers, operations, shapes etc and think about how they might be related.
- Draw diagrams or make lists when working with multiple steps, relationships or parts. This helps organize your thinking.
- Estimate answers before calculating to check if your working makes sense.
- Check your work - go back and ensure steps are correct and you have not made computational errors.
- Practice explaining your reasoning and showing your working, as this helps develop logical thinking skills.
- Review incorrect or challenging questions again later
The document defines average and provides formulas for calculating average. It discusses how to calculate the average of consecutive even/odd numbers, what happens when quantities are added to or replaced in a group, and how to calculate averages of specific data sets like positive integers. It then provides 10 problems calculating averages based on the information and formulas provided in the definitions section. The problems include calculating averages of data sets, determining values based on changes to averages, and identifying values that would produce a given average.
This document provides examples and explanations of calculating averages. It defines average as the total of quantities divided by the number of quantities. Various methods for finding averages are presented, including using the standard formula, accounting for excess or deficiency, and handling arithmetic progressions. Examples include finding averages of data sets with different numbers of items and values, as well as word problems involving changes to averages when new data is included or removed.
The document provides a series of maths practice questions and lessons for students over 5 days. It includes mixed times tables questions to practice, speed tests, word problems involving money and decimals, short multiplication, and reading/writing Roman numerals. Lessons cover adding/subtracting involving money, decimals, and fractions. Daily quizzes provide additional math problems to solve.
This document contains a math lesson on Roman numerals, addition, subtraction, multiplication and division of whole numbers and decimals. It includes word problems, examples worked out step-by-step and answers for students to check their work. The lesson recaps working with negative numbers and compares ordering numbers in ascending and descending order.
This document discusses fractions and decimal practice problems. It introduces fractions using examples like 5/6. It provides fraction identification questions about shapes divided into different fractions. It also gives word problems about fractions of objects like glasses and pencils. Finally, it includes decimal addition and subtraction practice problems.
The document discusses the order of operations and word problems. It explains that the order of operations (PEMDAS - Please Excuse My Dear Aunt Sally) determines the order that math operations should be performed. It provides an example of working through an order of operations problem step-by-step. It also discusses how to set up and solve word problems by identifying key words that indicate the appropriate math operation and translating the word problem into a numeric equation. Sample word problems are provided along with their step-by-step solutions.
The document contains multiple questions related to average, percentage, and profit. It discusses concepts like:
- Calculating average when new data is added
- Finding percentages when parts of a whole change
- Solving word problems involving averages, percentages, and profit/loss calculations
- Multiple choice and short answer questions test understanding of basic mathematical concepts
2016 05-25- HPEDSB Making Math Contextual, Visual and ConcreteKyle Pearce
Making Math Contextual, Visual and Concrete Full Day Workshop with Hastings Prince Edward District School Board in Belleville, Ontario. Presentation took place in May 2016.
The document outlines the 2010 PSLE examination time table in Singapore, including oral exams on August 19-20, a listening comprehension exam on September 17, and written exams from October 6-12 covering subjects like English, Math, Science. It also provides information about arranging home tutors to help prepare for the PSLE exams through an online tuition agency.
PSLE Mathematics Seminar
Association of Mathematics Educators
Dr. Yeap Ban Har
National Institute of Education
Nanyang Technological University
This seminar was conducted at Singapore Polytechnic.
The document provides information about preparing for and taking the PSLE Mathematics exam in Singapore. It discusses the structure of the exam, which consists of two papers, and outlines the curriculum focus on problem solving. It also provides examples of different types of math problems students may encounter on the exam. At the end, it discusses a news article where parents complained that this year's PSLE math exam was unusually difficult, possibly because it was the first year calculators were allowed.
This seminar for parents discussed the five key competencies in mathematical problem solving. Parental involvement is an important aspect of helping kids do well in school.
This document provides math lessons and activities for students in Year 4. It includes multiplication tables to practice, word problems to solve using addition and subtraction, and lessons on doubling and halving two-digit numbers. Students are encouraged to contact their teacher if they have any questions.
The document provides practice problems for calculating averages. It includes examples of finding the average of sets of numbers, word problems involving averages, problems where part of the data is excluded, finding missing values, averages of algebraic expressions, and problems involving how averages change when values are added or subtracted from numbers in the set. Students are to show their work and solutions on paper and view the document as a full screen slideshow.
This document provides information about revision grids for level 4 math topics. It includes a welcome message and instructions on how the grids can be used for revision and assessment. Suggestions are given for using the grids in class individually, as a game, or to promote collaboration. The source of inspiration for the grids is cited. Users are encouraged to provide feedback on how the grids are used.
Dinesh S introduces himself as a magician who has performed over 1000 shows in the past 12 years. He mentions riding a motorcycle blindfolded for 30 km to promote road safety. He uses magic to educate people and reduce superstitions. Photos are provided of him performing magic shows in various places for different occasions and audiences. Certificates of recognition for his work are also attached.
Division involves grouping quantities into equal sets. Examples shown include dividing 12 balls equally into boxes, with 3 balls in each box, dividing 18 faces into groups of 3, with 6 groups, and dividing 9 oranges equally into 3 bags, with 3 oranges in each bag. The document introduces division and solving one-step word problems using division to determine how quantities are divided equally among groups.
The document discusses factors and multiples of numbers. It explains that a factor is an exact divisor of a number that leaves no remainder, while a multiple is the result of multiplying a number by its factors. Some key points covered include:
- 1 is a factor of every number
- The number of factors of a given number is finite, while the number of multiples is infinite
- A number is both a factor and multiple of itself
- Examples are given of writing numbers as products of factors and identifying factors and multiples of various numbers.
The document discusses factors and multiples, defining factors as whole numbers that can divide another number with the resulting quotient being a whole number, and multiples as the product of multiplying two counting numbers. It provides examples of identifying factors and multiples, such as the factors of 8 being 1, 2, 4, 8 and the first four multiples of 2 being 2, 4, 6, 8. The warm-up problem identifies the factors of 50 as 5 and 10 and its multiple as 50.
Enhance your children's division skills with our incredible teaching, activity and display resource pack! Includes a comprehensive guide to the topic, printable activity resources for independent and group work, as well as handy display and reference materials.
Available from http://www.teachingpacks.co.uk/the-division-pack/
The document discusses factors and multiples of numbers. It provides examples of arranging objects like stars and footballs in different ways to get the same total, with the number of objects in each arrangement being the factors of the total. Factors are defined as exact divisors that leave no remainder. Multiples are numbers that a factor divides into with no remainder. Every number is a factor of itself and has an infinite number of multiples.
Here are some tips for improving problem solving skills in PSLE Mathematics:
- Take time to understand the question fully before attempting to solve it. Re-read if needed.
- Look for key information like numbers, operations, shapes etc and think about how they might be related.
- Draw diagrams or make lists when working with multiple steps, relationships or parts. This helps organize your thinking.
- Estimate answers before calculating to check if your working makes sense.
- Check your work - go back and ensure steps are correct and you have not made computational errors.
- Practice explaining your reasoning and showing your working, as this helps develop logical thinking skills.
- Review incorrect or challenging questions again later
The document defines average and provides formulas for calculating average. It discusses how to calculate the average of consecutive even/odd numbers, what happens when quantities are added to or replaced in a group, and how to calculate averages of specific data sets like positive integers. It then provides 10 problems calculating averages based on the information and formulas provided in the definitions section. The problems include calculating averages of data sets, determining values based on changes to averages, and identifying values that would produce a given average.
This document provides examples and explanations of calculating averages. It defines average as the total of quantities divided by the number of quantities. Various methods for finding averages are presented, including using the standard formula, accounting for excess or deficiency, and handling arithmetic progressions. Examples include finding averages of data sets with different numbers of items and values, as well as word problems involving changes to averages when new data is included or removed.
The document provides a series of maths practice questions and lessons for students over 5 days. It includes mixed times tables questions to practice, speed tests, word problems involving money and decimals, short multiplication, and reading/writing Roman numerals. Lessons cover adding/subtracting involving money, decimals, and fractions. Daily quizzes provide additional math problems to solve.
This document contains a math lesson on Roman numerals, addition, subtraction, multiplication and division of whole numbers and decimals. It includes word problems, examples worked out step-by-step and answers for students to check their work. The lesson recaps working with negative numbers and compares ordering numbers in ascending and descending order.
This document discusses fractions and decimal practice problems. It introduces fractions using examples like 5/6. It provides fraction identification questions about shapes divided into different fractions. It also gives word problems about fractions of objects like glasses and pencils. Finally, it includes decimal addition and subtraction practice problems.
The document discusses the order of operations and word problems. It explains that the order of operations (PEMDAS - Please Excuse My Dear Aunt Sally) determines the order that math operations should be performed. It provides an example of working through an order of operations problem step-by-step. It also discusses how to set up and solve word problems by identifying key words that indicate the appropriate math operation and translating the word problem into a numeric equation. Sample word problems are provided along with their step-by-step solutions.
The document contains multiple questions related to average, percentage, and profit. It discusses concepts like:
- Calculating average when new data is added
- Finding percentages when parts of a whole change
- Solving word problems involving averages, percentages, and profit/loss calculations
- Multiple choice and short answer questions test understanding of basic mathematical concepts
2016 05-25- HPEDSB Making Math Contextual, Visual and ConcreteKyle Pearce
Making Math Contextual, Visual and Concrete Full Day Workshop with Hastings Prince Edward District School Board in Belleville, Ontario. Presentation took place in May 2016.
The document outlines the 2010 PSLE examination time table in Singapore, including oral exams on August 19-20, a listening comprehension exam on September 17, and written exams from October 6-12 covering subjects like English, Math, Science. It also provides information about arranging home tutors to help prepare for the PSLE exams through an online tuition agency.
PSLE Mathematics Seminar
Association of Mathematics Educators
Dr. Yeap Ban Har
National Institute of Education
Nanyang Technological University
This seminar was conducted at Singapore Polytechnic.
The document provides information about preparing for and taking the PSLE Mathematics exam in Singapore. It discusses the structure of the exam, which consists of two papers, and outlines the curriculum focus on problem solving. It also provides examples of different types of math problems students may encounter on the exam. At the end, it discusses a news article where parents complained that this year's PSLE math exam was unusually difficult, possibly because it was the first year calculators were allowed.
This document summarizes the insights of Lee Kuan Yew on China, US-China relations, and geopolitics. It describes Lee Kuan Yew as a strategist's strategist and leader's leader. Regarding China, it notes China's strategy of peaceful rise but also obstacles to continued growth like governance issues. It states China will not become a liberal democracy. On US-China relations, it notes the relationship will be both cooperative and competitive, and that the US sometimes takes a confrontational approach by not considering cultural differences. Finally, it asserts that global integration is necessary to avoid conflicts between regional blocs, and the US cannot come and go from Asia if it wants to affect Asia's strategic evolution.
This document provides information about coaching children in primary mathematics for the PSLE:
1) It discusses 3 things about problem solving in the PSLE and 2 sections that assess challenging problem solving.
2) It outlines a 5-step process to help children with challenging problems and provides 2 examples demonstrating the steps.
3) Marshall Cavendish Institute is offering a 4-session workshop for parents/tutors to understand the primary math curriculum and coach topics like fractions, geometry, word problems, and algebra.
The Great State of Design with CSS Grid Layout and FriendsStacy Kvernmo
This document discusses the importance of doing work that you love and believe is great. It includes a quote from Steve Jobs about finding truly satisfying work by doing what you believe is great work and loving what you do. The rest of the document provides examples of challenges, questions, and discussions that commonly come up for designers in their work.
Bendermeer Primary School Seminar for ParentsJimmy Keng
This document provides an overview of a presentation on helping children with primary mathematics. It discusses how mathematics can develop intellectual competence and reflects on shifts in test questions to require more conceptual understanding and real-world problem solving over rote algorithms. Examples of math questions and lessons from various primary grades in Singapore, the US, UK, Netherlands and Japan are presented, covering topics like number sense, patterns, problem solving and visual models. Key competencies and strategies for problem solving are discussed.
This document provides a summary of a presentation on surviving math given by Dr. Yeap Ban Har from the Marshall Cavendish Institute in Singapore. The presentation included slides available on Facebook and discussed shifts in math test questions over time towards requiring more conceptual understanding. It also showed sample math problems and performance data from Primary 4 students in Singapore on TIMSS tests. The document lists the speaker, location, contact information and source of additional slides.
Bukit Panjang Primary School Parents' SeminarJimmy Keng
The document contains sample math word problems and their solutions from past PSLE exams in Singapore. It includes problems about units and pricing, collecting seashells, spacing of poles, and lists of numbers. The problems cover a range of topics like fractions, percentages, equations, and word problems.
The document provides examples of finding the greatest common factor (GCF) and least common multiple (LCM) of pairs of numbers. It then presents word problems involving finding the GCF or LCM of amounts in order to determine the maximum or minimum number of items that can be grouped in sets of equal size. Sample problems are provided along with step-by-step solutions showing different methods for calculating the GCF and LCM. Teachers are encouraged to provide additional practice problems for students to solve.
The document discusses various problem solving heuristics for lower primary mathematics. It provides 14 examples of word problems demonstrating different heuristics students can use to solve problems, such as using tables, looking for patterns, guess and check, and breaking problems into steps. The heuristics allow students to systematically solve problems even if they are initially unfamiliar.
This document contains examples of solving one-step equations with decimal and fraction coefficients. It provides step-by-step explanations for solving equations such as 16 = 0.25n, x = 1/5, -d = 5, and n = 3/4x. It demonstrates using the division property of equality to isolate the variable and check the solution by substituting it back into the original equation. Understanding how to solve these one-step equations lays the foundation for solving more complex multi-step equations.
This document provides an overview of grade 4 math topics including mental math, order of operations, word problems, and relevant Massachusetts frameworks. It contains examples of multiplication and division problems to solve mentally as well as multi-step word problems involving the four basic operations. The frameworks reference standards related to selecting the appropriate operation to solve problems, accurately performing multi-digit calculations, and using the four operations to solve word problems involving comparison or multiple steps.
This document contains a mathematics practice test for 4th grade students with multiple choice, true/false, word problems, and challenge questions. It covers topics like arithmetic operations, order of operations, word problems involving money, factors, and properties of numbers. The document tests students on their ability to perform calculations, translate between word sentences and mathematical expressions, solve multi-step word problems, and reason about number patterns.
Subtraction is the process of taking away a number from another. The minuend is the first number and the subtrahend is the second number being subtracted. The difference is the resulting number. To subtract, start with the ones place and work left to right borrowing from the place to the left as needed. Estimation means having a rough calculation and can be used to quickly estimate differences mentally. Key action words for subtraction include subtract, deduct, decrease, difference, minus, take away, diminish, reduce, and remove.
Subtraction is the process of taking away a number from another. The minuend is the first number and the subtrahend is the second number being subtracted. The difference is the resulting number. To subtract, start with the ones place and work left to right borrowing from the place to the left as needed. Estimation means having a rough calculation and is used to make mental calculations quicker when an approximate answer is acceptable. Key words in subtraction include subtract, deduct, decrease, difference, minus, take away, diminish, reduce, and how many left.
This document provides an overview of the bar model method for teaching mathematics. It discusses using bar models to develop visualization, number sense, and problem-solving abilities. It provides examples of using part-whole and comparison bar models to represent word problems involving fractions, percentages, multi-step word problems, algebra, and real-world scenarios. It also discusses how bar models can be used to differentiate instruction for different levels of learners.
The document provides examples and step-by-step solutions to mathematical word problems involving functions, equations, and algebraic modeling. It includes 8 sample word problems, showing the work to determine an appropriate equation or function to model each problem and solve to find the unknown values. The overall goal is to help students analyze problems, determine solution strategies using algebra, and evaluate whether solutions make sense in context.
The document provides examples and step-by-step solutions to mathematical word problems involving functions, equations, and algebraic modeling. It includes 8 sample word problems, showing the process of setting up and solving equations to determine unknown values. The overall goal is to help students analyze problems, determine appropriate solution strategies using algebraic notations, and evaluate solutions in context.
The document provides information about resources for revising mathematics over half term break, including social media accounts and a blog. It then gives examples of typical calculator paper questions involving ratios, averages, expanding brackets, and properties of numbers. It encourages revising everything as all topics may appear. Tips are given such as using CorbettMaths and completing five questions a day. Sample questions are worked through on ratios, averages, and trial and improvement problems.
2010 Henry Park Primary School Seminar for ParentsJimmy Keng
This document summarizes a seminar for parents about the PSLE mathematics exam. It discusses the exam format, which consists of two papers, and explains that the exam tests concepts covered in the primary school mathematics curriculum and problem-solving skills. It provides examples of different types of problems featured in the exam. The document emphasizes that mathematical problem-solving, visualization, number sense, self-monitoring of thinking, communication, and pattern recognition are important competencies tested in the exam. Textbooks and lessons in primary school aim to develop these skills in students.
This document provides an overview of the 8-step model drawing strategy used in Singapore Math to help students solve word problems. It explains that model drawing is a key strategy that uses bars or diagrams to represent quantities in word problems visually. It then demonstrates how to set up and solve a variety of word problems using the 8-step model drawing approach through worked examples. The examples cover topics like addition, subtraction, fractions, ratios, percentages and more.
The document provides information about various mathematical concepts including the mean, median, mode, and range. It defines the mean as the average, which is calculated by adding all numbers in a data set and dividing by the total count. The median is defined as the middle value when the data is arranged in order. The mode is the value that occurs most frequently. The range is the difference between the highest and lowest values. Examples are given for calculating the mean of a data set.
The document provides a lesson on evaluating numerical expressions using the order of operations. It includes examples of simplifying expressions with addition, subtraction, multiplication, division and exponents. It also has examples of word problems involving amounts of money spent on items. The lesson concludes with a quiz to assess understanding of simplifying expressions and applying the order of operations.
Similar to Association of Mathematics Educators Seminar on PSLE Mathematics (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.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
Thinking of getting a dog? Be aware that breeds like Pit Bulls, Rottweilers, and German Shepherds can be loyal and dangerous. Proper training and socialization are crucial to preventing aggressive behaviors. Ensure safety by understanding their needs and always supervising interactions. Stay safe, and enjoy your furry friends!
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.
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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.
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Liberal Approach to the Study of Indian Politics.pdf
Association of Mathematics Educators Seminar on PSLE Mathematics
1. mathematics Yeap Ban Har Marshall Cavendish Institute, Singapore & Pathlight School, Singapore banhar.yeap@pathlight.org.sg www.banhar.blogspot.com 12 March 2011 @ Raffles Institution ORGANIZED BY
12. Which of the following numbers is the largest? 6.59 6.95 6.509 6.905 See Examples on Page 1 The Really Basic Stuff
13. Mental Strategies A movie started at 11.55 p.m. and ended at 1.30 a.m. How long was the movie in hours and minutes? 12.00 1.00 1.30 There are 10 such MCQs in PSLE Mathematics. See Specimen Paper 1 Questions 1 – 10. The Really Basic Stuff
14. Mental Strategies A machine can print 80 cards in 3 minutes. At this rate, how many cards can it print in 1 hour? 30 minutes 1 hour The Really Basic Stuff
17. Mental Strategies Find the value of 1000 – 724 . Find the value of 1050 – 264 . 999 – 724 724 and makes 1000 275 So, 1000 – 724 There are 10 such SAQs in PSLE Mathematics. See Examples on Page 9 The Really Basic Stuff
18. Mental Strategies Find the value of 1000 – 724 . Find the value of 1050 – 264 . 1000 + 50 990+ 60 986+ 64 786 See Examples on Page 9 The Really Basic Stuff
19. Mental Strategies Find the value of 12.2 ÷ 4 . 12 ÷ 4 2 tenths ÷ 4 20 hundredths ÷ 4 3.05 See Examples on Page 10 The Really Basic Stuff
20. Find the value of 12.2 ÷ 4 . See Examples on Page 10 The Really Basic Stuff
21. Mental Strategies Find the value of 35 ÷ 6 . See Examples on Page 9 The Really Basic Stuff
22. Visual Strategies Find the value of 35 ÷ 6 . See Examples on Page 9 The Really Basic Stuff
23. Visual Strategies Find the value of 35 ÷ 6 . See Examples on Page 9 The Really Basic Stuff
25. Pens are sold in packets of 5 pens. Each packet is sold at $7. Gopal has $30. How many pens can he buy at most? Answer: ________________ See Examples on Page 12 Basic Problem Solving
26. Pens are sold in packets of 5 pens. Each packet is sold at $7. Gopal has $30. How many pens can he buy at most? Answer: ________________ See Examples on Page 12 Basic Problem Solving
27. Foundation Mathematics Specimen Paper 2 Cup cakes are sold at 40 cents each. What is the greatest number of cup cakes that can be bought with $95? $95 ÷ 40 cents = 237 remainder 20 cents Answer: ________________ Basic Problem Solving
28. Foundation Mathematics Specimen Paper 2 Cup cakes are sold at 40 cents each. What is the greatest number of cup cakes that can be bought with $95? $95 ÷ 40 cents = 237.5 Answer: ________________ Basic Problem Solving
29. Foundation Mathematics Specimen Paper 2 Cup cakes are sold at 40 cents each. What is the greatest number of cup cakes that can be bought with $95? $95 ÷ 40 cents = 237.5 Answer: ________________ Basic Problem Solving
30. 2-marks items are typically two steps with a few requiring competencies that are required in problem solving. See Specimen Paper 1 Questions 26 – 30 Question 29 5 : 1 6 : 1 Question 29 5 : 1 = 35 : 7 6 : 1 = 36 : 6 Answer: 71 : 13 There are 5 such SAQs in each Paper. Basic Problem Solving
31. See Specimen Paper 1 Questions 26 – 30 Question 30 Basic Problem Solving
32. 2-marks items are typically two steps with a few requiring competencies that are required in problem solving. See Page 13 Problems that Requires Visualization
38. See Page 13 PSLE 2006 – 2010 Page 13 Question 46 1.2 m x 42 = 50.4 m 43 – 6 = 37 There were 36 spacing 50.4 m ÷ 36 = 1.4 m The new spacing was 1.4 m.
41. PSLE 2006 – 2010 Page 19 Question 58 3 x ? = 2 + 25 ? = 9 There were 10 girls. There were 9 x 11 + 6 = 8 x 10 + 25 = 105 sweets altogether.
42. See Page 19 PSLE 2006 – 2010 Page 19 Question 58 Guess when each tried taking 11 33 Last girl had 11 sweets 41 Last girl had 8 sweets 49 Last girl had 5 sweets 57 Last girl had 2 sweets
45. PSLE 2006 – 2010 Page 18 Question 55 See Page 18 Number of Apples Number of Oranges Number of Pears 38
46. PSLE 2006 – 2010 Page 18 Question 55 See Page 18 Number of Apples Number of Oranges Number of Pears 38
47. PSLE 2006 – 2010 Page 18 Question 55 See Page 18 Number of Apples Number of Oranges Number of Pears 23 15 15
48. PSLE 2006 – 2010 Page 18 Question 55 See Page 18 5 units = 90 + 15 = 105 Number of Apples Number of Oranges Number of Pears 105 : 5 = 21 Number of oranges used = 65 – 21 = 44 23 15 15 Number of pears = 21 + 21 + 23 =65
49. PSLE 2006 – 2010 Page 18 Question 55 See Page 18 5 units = 90 + 15 = 105 Number of Apples Number of Oranges Number of Pears 105 : 5 = 21 Number of oranges used = 65 – 21 = 44 23 15 15 Number of pears = 21 + 21 + 23 =65
60. Woodlands Primary School Go to Marshall Cavendish Institute’s Facebook for Diary of Parent Education Courses and Teacher Professional Development opportunities. banhar.yeap@pathlight.org.sg www.banhar.blogspot.com www.banhar.blogspot.com ORGANIZED BY