The document discusses different approaches to teaching counting and mathematics. It argues that the traditional counting approach takes years of practice, provides a poor concept of quantity by ignoring place value, and is error-prone and time-consuming. Alternatively, it presents a Montessori-inspired "counting model" that uses objects and games to develop an intuitive understanding of quantities and mathematical operations like addition and multiplication. It also analyzes the use of calendars for counting, noting they are ordinal rather than cardinal and do not represent quantity well.
The document discusses research on counting and visualization in mathematics education. Key points include:
- Research shows humans have an innate ability to subitize or recognize small quantities without counting, and this ability is important for understanding counting.
- Other studies found indigenous groups and babies could match quantities without counting words.
- Visualization is important for learning and remembering mathematics concepts. Being able to mentally visualize relationships and manipulate images helps with problem solving.
- Japanese criteria for manipulatives emphasize representing numerical structures visually and in a way that can be mentally imagined.
The document discusses various features of Asian mathematics education and principles of Japanese teaching. Some key points include:
- Asian math uses explicit number naming and grouping in fives and tens. It emphasizes good instruction and use of manipulatives.
- Japanese teaching principles focus on intellectual engagement, clear goals, building on prior knowledge, and adaptive instruction for all students.
- Early counting abilities in babies and studies of indigenous groups show humans have an innate sense of numerical quantities before language.
This document provides an overview of assignments and activities for a math and science course for young children. It includes details on assignments due for different classes, as well as descriptions of in-class activities focused on fractions, numbers and place value, geometry, and more. Students are asked to create an original activity integrating math and science concepts for children and present it to the class.
This document contains notes from an early childhood education class discussing math and science activities and lessons for young children. It provides guidance on upcoming assignments, including observing children doing activities to assess their understanding. It also discusses teaching key concepts like classification, symbols, mapping, and basic arithmetic operations at different developmental levels using concrete examples and manipulatives.
The document provides an overview of the topics and activities covered in an early childhood education math and science course over several class sessions. It discusses assignments on identifying math and science concepts in children's books and creating assessments and activities related to shapes, parts and wholes, language development and fundamental science concepts. Students will work in groups to develop hands-on learning activities and share books they have selected, with a focus on integrating math and science learning.
This document discusses strategies for teaching children math concepts like addition, subtraction, and multiplication in a more visual and conceptual way rather than relying on rote memorization and flash cards. It recommends strategies like using part-whole circles to show the relationship between addition and subtraction, visualizing quantities with objects or fingers, and strategies for addition and subtraction facts like "making 10" or "going up" from the number being subtracted. The document emphasizes that understanding concepts is more important than memorization alone for building long-term retention and motivation to learn math.
Activities and Strategies to Teach KS Standardsmflaming
The document provides an agenda and overview for a workshop on teaching math state standards to elementary learners. It includes activities, discussions, and examples to help participants understand concepts like numbers and operations, algebra, geometry, data, and problem solving. Cognitive categories for different levels of math skills are defined. Sample word problems assess addition, subtraction, multiplication, division, and multi-step reasoning abilities.
The document discusses research on counting and visualization in mathematics education. Key points include:
- Research shows humans have an innate ability to subitize or recognize small quantities without counting, and this ability is important for understanding counting.
- Other studies found indigenous groups and babies could match quantities without counting words.
- Visualization is important for learning and remembering mathematics concepts. Being able to mentally visualize relationships and manipulate images helps with problem solving.
- Japanese criteria for manipulatives emphasize representing numerical structures visually and in a way that can be mentally imagined.
The document discusses various features of Asian mathematics education and principles of Japanese teaching. Some key points include:
- Asian math uses explicit number naming and grouping in fives and tens. It emphasizes good instruction and use of manipulatives.
- Japanese teaching principles focus on intellectual engagement, clear goals, building on prior knowledge, and adaptive instruction for all students.
- Early counting abilities in babies and studies of indigenous groups show humans have an innate sense of numerical quantities before language.
This document provides an overview of assignments and activities for a math and science course for young children. It includes details on assignments due for different classes, as well as descriptions of in-class activities focused on fractions, numbers and place value, geometry, and more. Students are asked to create an original activity integrating math and science concepts for children and present it to the class.
This document contains notes from an early childhood education class discussing math and science activities and lessons for young children. It provides guidance on upcoming assignments, including observing children doing activities to assess their understanding. It also discusses teaching key concepts like classification, symbols, mapping, and basic arithmetic operations at different developmental levels using concrete examples and manipulatives.
The document provides an overview of the topics and activities covered in an early childhood education math and science course over several class sessions. It discusses assignments on identifying math and science concepts in children's books and creating assessments and activities related to shapes, parts and wholes, language development and fundamental science concepts. Students will work in groups to develop hands-on learning activities and share books they have selected, with a focus on integrating math and science learning.
This document discusses strategies for teaching children math concepts like addition, subtraction, and multiplication in a more visual and conceptual way rather than relying on rote memorization and flash cards. It recommends strategies like using part-whole circles to show the relationship between addition and subtraction, visualizing quantities with objects or fingers, and strategies for addition and subtraction facts like "making 10" or "going up" from the number being subtracted. The document emphasizes that understanding concepts is more important than memorization alone for building long-term retention and motivation to learn math.
Activities and Strategies to Teach KS Standardsmflaming
The document provides an agenda and overview for a workshop on teaching math state standards to elementary learners. It includes activities, discussions, and examples to help participants understand concepts like numbers and operations, algebra, geometry, data, and problem solving. Cognitive categories for different levels of math skills are defined. Sample word problems assess addition, subtraction, multiplication, division, and multi-step reasoning abilities.
This document outlines an agenda for a presentation on teaching hands-on algebra to early grades. It discusses defining algebra, investigating patterns, variables and equations, functions, and assessing algebraic concepts. Activities are suggested to help students work with patterns, variables, equations, and functions in a concrete manner to build understanding before introducing symbolic representations. The goal is to develop algebraic reasoning and representation skills from an early age.
The document discusses various math manipulatives and activities that can be used in the classroom including color tiles, geoboards, toothpicks, playing cards, dice, and base-ten blocks. It provides examples of opening activities, explanations of why manipulatives are important, and cheap alternative manipulatives. The document also includes transcripts from video recordings of classroom lessons using these manipulatives and discussions of the mathematical concepts being taught.
This document discusses the stepping stones and hurdles students may face when learning addition and subtraction in grades 3-4. It identifies 5 key stepping stones: 1) moving from concrete to abstract understanding of place value, 2) learning a wider range of strategies, 3) developing reasoning and logic skills, 4) solving word problems, and 5) learning algorithms. The document emphasizes that students progress at different paces and teachers must be patient and provide differentiated instruction to meet students' individual needs.
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.
LEAP Educators' Conference 2011, Manila, The Philippines, 11 - 12 February 2011Jimmy Keng
This plenary lecture on elementary school mathematics was given at the conference which marks the end of the three-year Leaders and Educators in Asia Programme.
Kindergarten NK.5 lesson fishing one more one lesssusan70
The document provides guidance on using the backwards approach to plan lessons for the kindergarten math outcome of comparing quantities from 0 to 10. It includes identifying the outcome, determining how learning will be observed, planning instructional opportunities and assessing prior knowledge, carrying out the lesson, and assessing student learning and next steps. Sample lesson plans are provided focusing on using ten frames and counters to build and compare numbers, as well as unifix cube riddles.
This document outlines a curriculum night presentation for a math class. It introduces key concepts like probability, measurement, and graphs. For each concept, it describes the relevance to students and provides an example manipulative or activity to help teach the concept, such as using Skittles to demonstrate probability or using foam feet to measure distance. It explains how the concepts build on each other and on skills from previous math courses. The presentation includes making stem-and-leaf plots, pictographs, and bar graphs from collected data.
This document provides instructions for a learning task to teach students about addition through number stories using the number 5. The task uses strips of paper, number cards, and clips to demonstrate that 5 + 0 is the same as 0 + 5. Students are asked to arrange the clips on the strips to show number stories like 5 + 0 = 5. Extensions include asking students to write number equations and designing electronic addition activities. The goal is for students to understand addition concepts like conservation of number and see patterns in number stories up to 8.
This document discusses various tools and techniques for teaching mathematics creatively and joyfully. It emphasizes the need to use blended strategies to engage different types of learners and develop higher-order thinking skills. Some recommended approaches include using different types of papers, foldables, games like sudoku and puzzles, interactive applets, collaborative projects, blogs, appreciating math in everyday examples, origami, peer teaching and more. The goal is to make math accessible and encourage passion for learning through independent and creative environments.
Today's agenda includes a math lesson covering personal strategies for addition, subtraction, multiplication, and division. The schedule also includes a nutrition break, looking at virtual manipulatives and resources, lunch, and an assessment period. The document discusses teaching math concepts conceptually rather than procedurally and the importance of understanding operations rather than just memorizing computations. It provides examples of story problems and strategies adults use to solve math problems informally in everyday life.
This document discusses principles of counting in early mathematics education, including stable order, order irrelevance, conservation, abstraction, one-to-one correspondence, cardinality, movement is magnitude, and unitizing. It provides definitions and examples for each principle. The document also lists resources for finding ideas for intentional play-based learning in mathematics, including the Kindergarten Program document and a video on the topic.
This document provides an overview and agenda for a professional development session on the 1st Grade Math Expressions curriculum. It outlines the daily routines, materials, assessments, pacing guide, and teaching strategies for Units 1-8. Key concepts are highlighted for each unit, which focus on number sense, addition, subtraction, place value, measurement, and time. Non-essential lessons and quick quizzes are also noted. Contact information is provided for questions.
The document discusses mathematics topics for grade 5/6 students, including addition and subtraction with 4 or more digits, place value with numbers over 1 million, and real-life problem solving activities involving estimation. It also mentions teaching multiplication using multiplicative thinking rather than repeated addition, and covers addition/subtraction of fractions and decimals. Place value, efficient mental math strategies, and mathematical modeling are important concepts addressed.
This document contains information presented at a curriculum night for parents. It discusses key math concepts like probability, measurement, and graphs. For probability, examples are given how it is used in everyday life and careers. A lesson is proposed using Skittles to teach probability to students. Measurement is defined and the relevance discussed. A lesson using foam feet and student feet to measure distance is suggested. Finally, graphing is addressed with a lesson where students will create stem-and-leaf plots, pictographs, and bar graphs using age data from parents and amounts of buttons in a bag.
The document provides early math lesson plans for teaching preschoolers numbers and counting, left/right orientation, and geometry. It includes books, objectives, vocabulary, and activities for each topic. For example, one lesson teaches counting to 5 by using colored tiles and another has children grouping toy bugs into cages numbered 6-10. The reflection notes that the preschoolers needed more scaffolding than expected to use materials mathematically. Slowly introducing concepts over multiple days in different contexts helps children connect topics to play.
Learning & Teaching GCSE MathematicsColleen Young
This document provides teaching resources and ideas for GCSE Mathematics. It includes information on specification changes, assessment objectives, teaching guidance from exam boards, and problem solving strategies. Sample exam questions, topic tests, and diagnostic questions are provided. Additional resources on areas like extension materials, revision activities, and developing recall are also referenced.
The document discusses hands-on math activities for kindergarten students focusing on number sense, patterns, and algebraic thinking. It describes activities using manipulatives to help students represent, compare, and order numbers. Other activities address identifying, duplicating, and extending patterns using objects. The document emphasizes building foundations for algebraic concepts like functions through concrete experiences with patterns, relationships between numbers, and using math language.
Chine.
Le Petit Lin Yi va tout seul au marché faire les courses pour sa mère.
S'il se débrouille bien et il lui reste de l'argent, il pourra même s'acheter le lampion rouge dont il rêve pour la Fête de la Lune.
Mais... il ne faut pas oublier les cacahuètes pour l'Oncle Hui !
C'est lui qui dit à la fin : « Pendant la période de la Fête de la Lune, beaucoup de choses spéciales peuvent arriver, surtout si tu passes sous la Porte de Lune. Il ne faut pas se poser de questions, juste être heureux. »
This document outlines an agenda for a presentation on teaching hands-on algebra to early grades. It discusses defining algebra, investigating patterns, variables and equations, functions, and assessing algebraic concepts. Activities are suggested to help students work with patterns, variables, equations, and functions in a concrete manner to build understanding before introducing symbolic representations. The goal is to develop algebraic reasoning and representation skills from an early age.
The document discusses various math manipulatives and activities that can be used in the classroom including color tiles, geoboards, toothpicks, playing cards, dice, and base-ten blocks. It provides examples of opening activities, explanations of why manipulatives are important, and cheap alternative manipulatives. The document also includes transcripts from video recordings of classroom lessons using these manipulatives and discussions of the mathematical concepts being taught.
This document discusses the stepping stones and hurdles students may face when learning addition and subtraction in grades 3-4. It identifies 5 key stepping stones: 1) moving from concrete to abstract understanding of place value, 2) learning a wider range of strategies, 3) developing reasoning and logic skills, 4) solving word problems, and 5) learning algorithms. The document emphasizes that students progress at different paces and teachers must be patient and provide differentiated instruction to meet students' individual needs.
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.
LEAP Educators' Conference 2011, Manila, The Philippines, 11 - 12 February 2011Jimmy Keng
This plenary lecture on elementary school mathematics was given at the conference which marks the end of the three-year Leaders and Educators in Asia Programme.
Kindergarten NK.5 lesson fishing one more one lesssusan70
The document provides guidance on using the backwards approach to plan lessons for the kindergarten math outcome of comparing quantities from 0 to 10. It includes identifying the outcome, determining how learning will be observed, planning instructional opportunities and assessing prior knowledge, carrying out the lesson, and assessing student learning and next steps. Sample lesson plans are provided focusing on using ten frames and counters to build and compare numbers, as well as unifix cube riddles.
This document outlines a curriculum night presentation for a math class. It introduces key concepts like probability, measurement, and graphs. For each concept, it describes the relevance to students and provides an example manipulative or activity to help teach the concept, such as using Skittles to demonstrate probability or using foam feet to measure distance. It explains how the concepts build on each other and on skills from previous math courses. The presentation includes making stem-and-leaf plots, pictographs, and bar graphs from collected data.
This document provides instructions for a learning task to teach students about addition through number stories using the number 5. The task uses strips of paper, number cards, and clips to demonstrate that 5 + 0 is the same as 0 + 5. Students are asked to arrange the clips on the strips to show number stories like 5 + 0 = 5. Extensions include asking students to write number equations and designing electronic addition activities. The goal is for students to understand addition concepts like conservation of number and see patterns in number stories up to 8.
This document discusses various tools and techniques for teaching mathematics creatively and joyfully. It emphasizes the need to use blended strategies to engage different types of learners and develop higher-order thinking skills. Some recommended approaches include using different types of papers, foldables, games like sudoku and puzzles, interactive applets, collaborative projects, blogs, appreciating math in everyday examples, origami, peer teaching and more. The goal is to make math accessible and encourage passion for learning through independent and creative environments.
Today's agenda includes a math lesson covering personal strategies for addition, subtraction, multiplication, and division. The schedule also includes a nutrition break, looking at virtual manipulatives and resources, lunch, and an assessment period. The document discusses teaching math concepts conceptually rather than procedurally and the importance of understanding operations rather than just memorizing computations. It provides examples of story problems and strategies adults use to solve math problems informally in everyday life.
This document discusses principles of counting in early mathematics education, including stable order, order irrelevance, conservation, abstraction, one-to-one correspondence, cardinality, movement is magnitude, and unitizing. It provides definitions and examples for each principle. The document also lists resources for finding ideas for intentional play-based learning in mathematics, including the Kindergarten Program document and a video on the topic.
This document provides an overview and agenda for a professional development session on the 1st Grade Math Expressions curriculum. It outlines the daily routines, materials, assessments, pacing guide, and teaching strategies for Units 1-8. Key concepts are highlighted for each unit, which focus on number sense, addition, subtraction, place value, measurement, and time. Non-essential lessons and quick quizzes are also noted. Contact information is provided for questions.
The document discusses mathematics topics for grade 5/6 students, including addition and subtraction with 4 or more digits, place value with numbers over 1 million, and real-life problem solving activities involving estimation. It also mentions teaching multiplication using multiplicative thinking rather than repeated addition, and covers addition/subtraction of fractions and decimals. Place value, efficient mental math strategies, and mathematical modeling are important concepts addressed.
This document contains information presented at a curriculum night for parents. It discusses key math concepts like probability, measurement, and graphs. For probability, examples are given how it is used in everyday life and careers. A lesson is proposed using Skittles to teach probability to students. Measurement is defined and the relevance discussed. A lesson using foam feet and student feet to measure distance is suggested. Finally, graphing is addressed with a lesson where students will create stem-and-leaf plots, pictographs, and bar graphs using age data from parents and amounts of buttons in a bag.
The document provides early math lesson plans for teaching preschoolers numbers and counting, left/right orientation, and geometry. It includes books, objectives, vocabulary, and activities for each topic. For example, one lesson teaches counting to 5 by using colored tiles and another has children grouping toy bugs into cages numbered 6-10. The reflection notes that the preschoolers needed more scaffolding than expected to use materials mathematically. Slowly introducing concepts over multiple days in different contexts helps children connect topics to play.
Learning & Teaching GCSE MathematicsColleen Young
This document provides teaching resources and ideas for GCSE Mathematics. It includes information on specification changes, assessment objectives, teaching guidance from exam boards, and problem solving strategies. Sample exam questions, topic tests, and diagnostic questions are provided. Additional resources on areas like extension materials, revision activities, and developing recall are also referenced.
The document discusses hands-on math activities for kindergarten students focusing on number sense, patterns, and algebraic thinking. It describes activities using manipulatives to help students represent, compare, and order numbers. Other activities address identifying, duplicating, and extending patterns using objects. The document emphasizes building foundations for algebraic concepts like functions through concrete experiences with patterns, relationships between numbers, and using math language.
Chine.
Le Petit Lin Yi va tout seul au marché faire les courses pour sa mère.
S'il se débrouille bien et il lui reste de l'argent, il pourra même s'acheter le lampion rouge dont il rêve pour la Fête de la Lune.
Mais... il ne faut pas oublier les cacahuètes pour l'Oncle Hui !
C'est lui qui dit à la fin : « Pendant la période de la Fête de la Lune, beaucoup de choses spéciales peuvent arriver, surtout si tu passes sous la Porte de Lune. Il ne faut pas se poser de questions, juste être heureux. »
Numbers 1 to 100 is a document that lists all numbers from 1 to 100. It provides the counting sequence from one through one hundred without commentary or additional context. The list of numbers serves to enumerate each integer in order from its beginning point to its end point.
1. The document lists numbers from 1 to 5 and numbers from 6 to 10.
2. It also lists objects starting with letters from A to Z, with 2 objects per letter.
3. The objects include boat, car, dolphin, elephant, fish, giraffe, house, ice-cream, juice, kite, ladybird, mouse, nose, octopus, pig, queen, rocket, sun, toy, umbrella, violin, watch, xylophone, yo-yo and zebra.
This document does not contain any meaningful information beyond repeating the word "next" multiple times with no other context. It simply lists the word "next" on each line until concluding with "The end".
This short poem describes various colors seen in nature and everyday objects, including a red apple, yellow sun, blue butterfly, green leaf, pink flamingo, purple flower, orange door, white clouds, gray suit, brown dresser, black cat, and turquoise star.
The document discusses feelings and emotions. It lists common feelings like happy, sad, angry, sleepy, and physical states like hot, cold, thirsty and hungry. It then asks a series of questions to check understanding of these feelings and emotions, such as "Which one is...?" and "Is he/she...?". It provides examples of answering questions about whether someone is feeling a certain emotion in the affirmative or negative.
This document contains a set of number cards showing the numbers 10 through 20, with each number written out and illustrated using dots in a ten frame configuration. The cards provide a visual representation of quantities to help students learn number concepts and counting within the teens.
This Power Point will help students learn how to count coins. They will work with dimes, nickels, and pennies. An additional Power Point will get into the challenges of counting quarters.
The document lists numbers in sequences from 1 to 20, then from 5 to 50 counting by 5s, and from 10 to 100 counting by 10s. It also lists the number 60 apples and continues the counting sequence from 100 to 1000, increasing by hundreds.
Feelings are emotions that people experience in response to different situations. There are many types of feelings including happy, excited, amazed, sad, angry, and worried. People can deal with feelings by talking to friends or family, exercising, reading, writing in a diary, or getting help from teachers or counselors at school. It is important to share feelings with others instead of keeping them bottled up inside.
The document provides guidance on correctly using pronouns such as I, me, we, and us. It explains that "I" should be used as the subject of a sentence or after forms of "be", while "me" should be used after action verbs or prepositions. It also notes that when using pronouns with nouns, the speaker should name themselves last. Examples are provided to illustrate the proper usage of these pronouns.
This document lists the numbers from 1 to 20 in words, with each number on its own line. It starts with ONE and ends with TWENTY, spelling out each number sequentially in between.
This document lists the numbers from 0 to 20 in English for beginning English language learners. It spells out each number individually from zero to ten and then uses the standard terms eleven through twenty. The list of numbers is intended to help very basic ESL students learn to recognize and say the numbers in English.
The document provides rules of thumb for using semicolons and colons in writing. It states that semicolons should be used between two complete sentences and between items in a series that have internal commas. Colons should be used between a complete sentence and a list or explanation, or before a long formal quotation. The document also provides examples and practice sentences demonstrating the proper uses of semicolons and colons.
This document contains descriptions of different emotions like angry, bored, confused, embarrassed, excited, frustrated, guilty, happy, hopeful, jealous, left out, loved, proud, sad, scared, surprised, worried, and relaxed. Each emotion is accompanied by an image to help illustrate what that emotion looks like. The document encourages looking through the images and describing a time you felt one of the emotions.
This document lists the numbers 1 through 20 on individual flash cards, with each number written with a corresponding number of punctuation marks. The flash cards provide a visual representation of counting from 1 to 20 by showing the increasing number of punctuation marks added to each number.
Grade: 1
Subject: Math
Lesson: Counting Numbers 0 - 10
Description: In this lesson, you will review basic counting with your child using different techniques shown in the lesson
Happy Counting!
This document discusses the proper use of the pronouns "I" and "me" in sentences. It provides the following rules:
- Use "I" as the subject of a sentence and "me" as the object. For example, "I like ice cream" vs. "She gave the ice cream to me."
- When using "I" or "me" with another person's name, put the other person's name first. For example, "John and I went to the store," not "I and John went to the store."
- To determine whether to use "I" or "me" when combined with another person's name, cover up "and" and the
IDA-UMB: Visualizing with the AL Abacus March 2011rightstartmath
The document discusses challenges children with math difficulties face and how they can best learn arithmetic. It describes how counting-based arithmetic focuses on rote memorization rather than understanding concepts. In contrast, learning arithmetic visually through tools like the abacus helps children understand place value and quantity. The document cautions against using calendars to teach counting as they involve ordinal rather than cardinal numbering.
The document provides a daily lesson log for a 5th grade mathematics class that focuses on ratios. Over the course of the week, students will:
1) Learn about ratios and how to express them using fractions, decimals, and proportions. Examples used include comparing numbers of circles to squares.
2) Practice skills like writing ratios in different forms using real objects and visual examples from daily life. Ratios compared may involve numbers of students, fruits, or classroom supplies.
3) Apply their understanding of ratios to solve word problems involving costs, quantities for sale, and family demographics to strengthen comprehension of ratios in practical scenarios. Assessment occurs through ratio identification, expression, and application exercises.
This document provides information from a Maths Information Evening for parents. It discusses what progress in maths entails, how maths is taught in key stages 1 and 2, and different maths concepts covered, including place value, addition, subtraction, multiplication, division, and problem solving. Parents are advised to praise their children's efforts, play maths games at home, and focus on building confidence rather than stressing workbooks or written methods.
- Algebra has its origins in ancient civilizations like Egypt and Babylon where it was used to solve basic arithmetic problems involving unknown variables.
- It progressed through the rhetorical, syncopated, and symbolic stages of algebraic notation.
- Various civilizations made contributions - Greeks/Diophantus established foundations, Arabs adopted and improved Hindu numerals and methods, Europeans developed modern symbolic algebra in 16th century.
- Key figures like al-Khwarizmi and Fibonacci advanced the subject in the medieval era.
1. The document discusses curriculum documents and frameworks related to teaching counting concepts and addition/subtraction in early years education.
2. It provides examples of strategies, activities, and resources to help children develop understanding of counting, cardinality, addition, and subtraction.
3. The frameworks emphasize developing rich learning experiences using concrete experiences, language, visuals, and symbols to build number sense in young children.
This document provides information about differentiating arithmetic and geometric sequences. It begins with an introduction explaining the learning objectives are to identify sequences as arithmetic or geometric, differentiate between the two types of sequences, and provide examples of each. It then provides examples of arithmetic and geometric sequences with their common differences or ratios. The document features group and individual practice problems identifying sequences and their properties. It concludes with a two-column chart comparing the key differences between arithmetic and geometric sequences.
The document discusses strategies for overcoming math anxiety and promoting understanding of mathematical concepts. It recommends teaching for understanding rather than rote memorization. Some key strategies include using hands-on activities, relating concepts to real-world examples, addressing common misconceptions, and emphasizing that mistakes are part of the learning process.
This document summarizes key concepts about proportional reasoning. It defines proportional reasoning as a mathematical relationship between two quantities that involves a constant multiplicative relationship. It discusses proportional reasoning as developing between concrete and formal operations. It also provides examples of using proportional relationships to solve problems and discusses research on how to best teach proportional reasoning concepts to students.
Unit 6 presentation base ten equality form of a number with trainer notes 7.9.08jcsmathfoundations
The document discusses concepts related to base ten, equality, and forms of numbers. It defines these concepts, examines how students develop an understanding through research on cognitive development, and provides classroom applications and strategies for teaching these concepts effectively. Diagnostic questions are presented to assess student understanding, and examples show how to respond to common student errors or misconceptions in working with numbers.
This document provides information about math instruction at the school. It discusses what constitutes progress in math, how math is taught in key stages 1 and 2, and key concepts taught like number sense, addition, subtraction, multiplication, division, word problems, and problem solving. It emphasizes building understanding of place value and using various methods like number lines, arrays, and partitioning. It suggests ways for parents to help children at home, such as playing math games and giving praise, rather than workbooks or stressing written algorithms.
The document outlines the calculations policy of the North Norwich Cluster. It discusses how math should be taught for understanding rather than just procedures. Children should experience math through language, pictures, and hands-on activities to develop their own understanding at their own pace. The policy explains the progression of different calculations, from addition and subtraction to multiplication and division. It provides examples of models and images to help children visualize different math concepts and build understanding, such as using objects, number lines, and part-whole models to teach addition and subtraction.
The PSAT/NMSQT measures academic skills needed for college through questions on critical reading, writing and math. It provides feedback to students on strengths and weaknesses. Preparation includes taking challenging courses, practicing with sample tests and making educated guesses.
The PSAT/NMSQT measures academic skills needed for college through questions on critical reading, writing and math. It provides feedback to students on strengths and weaknesses. Preparation includes taking challenging courses, practicing with sample tests and making educated guesses. On test day, students should read carefully, work steadily and skip questions to return to if time allows.
This document provides information about the Student Research League (SRL) competition. The SRL is a mathematical research competition for two-year college students held each spring. Students have nine days to research and solve a challenge problem with a faculty mentor. Problems relate to real-world issues and require mathematical modeling. Components of the competition include the challenge problem, career research, a mathematical model or thesis, and a thesis defense. Prizes include a $1,500 grand prize. The goal is to encourage mathematical problem solving and provide an outlet for two-year college students to compete in research contests.
The document discusses several topics in mathematics from algebra to calculus. It provides brief overviews of what each topic involves, when they are generally introduced, and examples of their real-world applications. It emphasizes that mathematics should not be feared and that with effort and practice, students can become experts in math.
Rajabhat Mahasarakham organised this workshop titled Transforming the Mathematics Classroom. The goal is to get teachers to think about teaching mathematics to encourage thinking, to develop visualization and to enhance the ability to observe patterns rather than mathematics as a subject that requires memorization, carrying out meaningless procedures and doing tedious computations.
This document contains teaching materials for mathematics for 7th grade students. It covers topics like numbers, algebra, sets, linear equations and inequalities. The main topics covered in semester 1 include integers, operations on integers, fractions, decimals, percentages, and properties of operations. Examples and practice problems are provided to help students understand each concept.
The document outlines the conceptual framework and pedagogical approaches of the Philippines K-12 mathematics curriculum. It describes the twin goals of critical thinking and problem solving. It also explains the spiral approach where mathematical concepts increase in depth and breadth as students progress through grades, ensuring a seamless transition in learning.
These were the materials covered in last year's professional development. This year's session is a follow-up with revisiting of core ideas and extension of others.
BBS April 2010 Singapore Math in Indonesia by BBS Maths Consultant Dr Yeap Ba...Jimmy Keng
Teachers in Bina Bangsa School, from Kindergarten to Junior College, had their mathematics professional development with a focus on student engagement and designing problem-based lessons.
Similar to AMS: Counting-Necessary or Detrimental? March 2011 (20)
- The document is from a presentation on fractions given on April 27, 2013 by Joan Cotter.
- It discusses why fractions are important to learn, such as for sharing pizza, cooking, reading rulers, and preparing for algebra.
- It includes examples of using fractions in comics and charts showing fraction relationships. Games are presented to help students understand unit fractions and that combinations of fractions can make a whole.
Learning Disabilities Mass HOPE April 2013rightstartmath
This document summarizes a presentation on teaching math to children with special needs. It discusses the characteristics of children with learning disabilities, myths about learning disabilities, problems occurring in math like dyscalculia, and effective teaching strategies like teaching for understanding versus rules and procedures. It also covers topics like memorization, flash cards, counting strategies, and visualizing mathematics concepts.
This document outlines Joan Cotter's presentation on teaching primary mathematics with less counting. The presentation objectives are to: review the traditional counting model; experience traditional counting as a child; introduce grouping in 5s and 10s as an alternative to counting; and meet Common Core standards without counting. The traditional counting model is described as difficult and tedious for children. Grouping in 5s and 10s is presented as a more intuitive approach that leverages children's innate ability to subitize small quantities. Research supports subitizing as important for mathematical understanding and performance.
Personalized Learning Bridges Middle School Math with a Geometric Approachrightstartmath
The document discusses a geometric approach to teaching middle school math. It notes that most middle school students are visual learners and that 90% of math topics can be explored geometrically. It then presents various drawing tools like T-squares, 30-60 triangles, and examples of how to draw geometric shapes like equilateral triangles to teach math concepts visually.
The document is a presentation on math puzzles and brain teasers by Kathleen Cotter Lawler. It covers topics such as patterns, squares, guided discovery, fractals, Asian cultures' relationship with math, math balancing, puzzle numbers, magic squares, and understanding place value. The presentation provides visual examples and explanations for each topic to illustrate different math concepts and puzzles in an engaging way.
This document discusses using card games to help students master basic math facts. It introduces two addition games called "Go to the Dump" and "Rows and Columns" that are designed to help students learn facts that total 10 and 15 respectively. The document provides explanations of the games' purposes and goals as well as examples of gameplay.
The document discusses how Joan Cotter, an engineer and educator with a PhD in math education, developed innovative ways to teach fractions. It describes several fraction models she created, including linear charts, colored bars, and missing parts charts, that make fraction comparisons and concepts easier to understand compared to traditional fraction circles or "fish tank" models. The document advocates teaching fractions using these types of linear representations rather than area models like pie charts that can be more difficult for students to interpret.
The document summarizes a presentation on developing a deeper understanding of primary math concepts through less rote counting and memorization. It discusses current counting models that rely heavily on memorization and proposes alternative approaches focusing on visualization and conceptual understanding. These include using subitizing to recognize small quantities, teaching number names in a way that reflects place value, and place value cards to build understanding of our base-ten number system. The presenters argue this will lead to longer retention and a stronger math foundation compared to traditional counting models.
This document summarizes a presentation about overcoming math obstacles through visualizing with the AL Abacus. The presentation was given by Tracy Mittleider and was based on the work of Joan A. Cotter. It discusses Dr. Cotter's background and the development of the AL Abacus, a visual and tactile manipulative that helps develop mental images of quantities, strategies, and mathematical operations. It also provides examples of how the abacus can be used to help visualize quantities and perform simple addition.
IMF: Visualizing and Montessori Math PART 2rightstartmath
The document is a presentation on how visualization enhances Montessori mathematics instruction. It discusses strategies for teaching basic multiplication facts using visual tools like the abacus, multiplication board, and charts showing multiples patterns. Strategies include showing how to break down larger multiplication problems into "tens" and "ones" places on the abacus. Charts are used to visualize repeating patterns in multiples of numbers and how they relate to specific multiplication facts.
IMF: Visualizing and Montessori Math PART 1rightstartmath
The document discusses how visualization enhances Montessori mathematics education. It provides examples of how Montessori uses concrete materials to teach counting and arithmetic concepts to children. These include number rods, bead frames, and calendar activities. The focus is on a verbal counting model that uses letters instead of numbers to demonstrate addition, subtraction, and multiplication facts to children in a visual way. Calendar math activities are also described, showing how children can develop ordinal counting and pattern recognition skills.
The document discusses a counting model for teaching mathematics to children. It describes how counting is not natural and takes years of practice, provides a poor concept of quantity, and ignores place value. The model shown uses letters instead of numbers to represent quantities in order to demonstrate counting, addition, subtraction, and other math concepts in a more concrete way for children. Montessori materials are also noted as being helpful for reinforcing counting concepts through hands-on experience.
The document discusses issues with traditional counting models and introduces an alternative counting model based on letters to represent quantities. It describes how the counting model provides a foundation for understanding place value and efficiently learning math facts. The document also cautions against using calendars for counting, noting that calendars involve ordinal rather than cardinal numbering and do not accurately represent quantities.
The document provides strategies for teaching addition and subtraction to students. Some key strategies include:
- Using visual tools like an abacus to teach strategies like "making 10" and "two 5s" for addition. Counting should be discouraged.
- Part-whole circles can help students see the relationship between addition and subtraction and solve word problems.
- Strategies for subtraction include subtracting 1 or 2 from even/odd numbers, subtracting from 10, and a "going up" strategy to find the difference between numbers.
- Games like "Go to the Dump" can make subtraction strategies engaging for students to practice facts involving 10.
This document summarizes Joan Cotter's presentation on teaching arithmetic facts using strategies and games. It discusses that counting-based and rote memorization approaches have limited success. Instead, it promotes using subitizing to identify quantities without counting, and incorporating manipulatives and mental work through enjoyable games. An example game called "Go to the Dump" is described, which aims to teach adding facts that total 10 through collecting number pairs.
This document outlines a verbal counting model proposed to help children develop a deeper understanding of numbers and math concepts rather than relying on rote memorization. The model uses letters to represent numbers and demonstrates counting, addition, subtraction, and other operations by building word problems using the letters. It also shows how this model could be applied to calendar math and comparing it to state math standards. The goal is to promote a more conceptual approach to early number sense over a procedural focus on counting and calculations.
The AL abacus provides a hands-on tool to help children understand quantities and math operations like addition and multiplication. It uses beads on wires to represent numbers up to 100. Children first learn to represent quantities 1-10 using their fingers and then on the abacus. They can then add by entering both numbers and seeing the sum without counting. Tens are entered as whole rows of beads. Multiplication can be modeled by repeatedly entering a number. The abacus also demonstrates trading or carrying for multi-digit addition and place value on its second side.
The document discusses the limitations of using verbal counting and calendars to teach early mathematics concepts. It notes that verbal counting is unnatural, provides a poor concept of quantity, ignores place value, is error-prone, tedious, and does not efficiently teach number facts. Regarding calendars, it states that calendars are not number lines as numbers appear in spaces rather than along lines, they provide an ordinal rather than cardinal view of numbers, and give a narrow view of patterning that does not generalize beyond the days in a month.
The document describes how to use drawing tools like a T-square, 30-60 triangle, 45 triangle, and pencil to divide an equilateral triangle into halves, thirds, fourths, sixths, and eighths. It shows how to draw parallel, perpendicular, and intersecting lines. The document also discusses classifying shapes like rhombuses, trapezoids, and triangles formed within the divisions. Finally, it demonstrates how to construct a tetrahedron by folding the equilateral triangle divisions.
The document discusses the limitations of a traditional verbal counting model for teaching mathematics to children. It notes that verbal counting is not natural, takes years of practice, provides a poor concept of quantity, ignores place value, is error prone, tedious and inefficient for mastering facts. An alternative approach using letters to represent numbers is presented as a more intuitive method for children.
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.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
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.
Walmart Business+ and Spark Good for Nonprofits.pdfTechSoup
"Learn about all the ways Walmart supports nonprofit organizations.
You will hear from Liz Willett, the Head of Nonprofits, and hear about what Walmart is doing to help nonprofits, including Walmart Business and Spark Good. Walmart Business+ is a new offer for nonprofits that offers discounts and also streamlines nonprofits order and expense tracking, saving time and money.
The webinar may also give some examples on how nonprofits can best leverage Walmart Business+.
The event will cover the following::
Walmart Business + (https://business.walmart.com/plus) is a new shopping experience for nonprofits, schools, and local business customers that connects an exclusive online shopping experience to stores. Benefits include free delivery and shipping, a 'Spend Analytics” feature, special discounts, deals and tax-exempt shopping.
Special TechSoup offer for a free 180 days membership, and up to $150 in discounts on eligible orders.
Spark Good (walmart.com/sparkgood) is a charitable platform that enables nonprofits to receive donations directly from customers and associates.
Answers about how you can do more with Walmart!"
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
Reimagining Your Library Space: How to Increase the Vibes in Your Library No ...Diana Rendina
Librarians are leading the way in creating future-ready citizens – now we need to update our spaces to match. In this session, attendees will get inspiration for transforming their library spaces. You’ll learn how to survey students and patrons, create a focus group, and use design thinking to brainstorm ideas for your space. We’ll discuss budget friendly ways to change your space as well as how to find funding. No matter where you’re at, you’ll find ideas for reimagining your space in this session.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
How to Make a Field Mandatory in Odoo 17Celine George
In Odoo, making a field required can be done through both Python code and XML views. When you set the required attribute to True in Python code, it makes the field required across all views where it's used. Conversely, when you set the required attribute in XML views, it makes the field required only in the context of that particular view.
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
BÀI TẬP DẠY THÊM TIẾNG ANH LỚP 7 CẢ NĂM FRIENDS PLUS SÁCH CHÂN TRỜI SÁNG TẠO ...
AMS: Counting-Necessary or Detrimental? March 2011
1. Counting: Necessary or Detrimental? AMS Conference March 25, 2011 Chicago, Illinois by Joan A. Cotter, Ph.D. [email_address] 7 5 2 Presentation available: ALabacus.com 7 x 7 VII
61. Calendar Math August 29 22 15 8 1 30 23 16 9 2 24 17 10 3 25 18 11 4 26 19 12 5 27 20 13 6 28 21 14 7 31 This is ordinal, not cardinal counting. The 3 doesn’t include the 1 and the 2.
62. Calendar Math August 29 22 15 8 1 30 23 16 9 2 24 17 10 3 25 18 11 4 26 19 12 5 27 20 13 6 28 21 14 7 31 This is ordinal, not cardinal counting. The 4 doesn’t include 1, 2 and 3.
63. Calendar Math August 29 22 15 8 1 30 23 16 9 2 24 17 10 3 25 18 11 4 26 19 12 5 27 20 13 6 28 21 14 7 31 A calendar is NOT like a ruler. On a ruler the numbers are not in the spaces.
64. Calendar Math August 8 1 9 2 10 3 4 5 6 7 Always show the whole calendar. A child needs to see the whole before the parts. Children also need to learn to plan ahead.
91. Visualizing Mathematics “ In our concern about the memorization of math facts or solving problems, we must not forget that the root of mathematical study is the creation of mental pictures in the imagination and manipulating those images and relationships using the power of reason and logic.” Mindy Holte (E I)
92. Visualizing Mathematics “ Think in pictures, because the brain remembers images better than it does anything else.” Ben Pridmore, World Memory Champion, 2009
93. Visualizing Mathematics “ Mathematics is the activity of creating relationships, many of which are based in visual imagery. ” Wheatley and Cobb
94. Visualizing Mathematics “ The process of connecting symbols to imagery is at the heart of mathematics learning.” Dienes
95. Visualizing Mathematics “ The role of physical manipulatives was to help the child form those visual images and thus to eliminate the need for the physical manipulatives.” Ginsberg and others
120. Naming Quantities Yellow is the Sun Yellow is the sun. Six is five and one. Why is the sky so blue? Seven is five and two. Salty is the sea. Eight is five and three. Hear the thunder roar. Nine is five and four. Ducks will swim and dive. Ten is five and five. – Joan A. Cotter Also set to music. Listen and download sheet music from Web site.
130. Naming Quantities What is 4 apples plus 3 more apples? Solving a problem without counting How would you find the answer without counting?
131. Naming Quantities What is 4 apples plus 3 more apples? Solving a problem without counting To remember 4 + 3, the Japanese child is taught to visualize 4 and 3. Then take 1 from the 3 and give it to the 4 to make 5 and 2.
140. Naming Quantities “ Grouped in fives so the child does not need to count.” Black and White Bead Stairs A. M. Joosten This was the inspiration to group in 5s.
178. Problem Solving Solving a problem Lee received 3 goldfish as a gift. Now Lee has 5. How many did Lee have to start with? A missing addend problem, considered very difficult for first graders. They can do it with Part-Whole Circles.
179. Problem Solving Solving a problem Lee received 3 goldfish as a gift. Now Lee has 5. How many did Lee have to start with? Is 3 a part or whole?
180. Problem Solving Solving a problem Lee received 3 goldfish as a gift. Now Lee has 5. How many did Lee have to start with? Is 3 a part or whole? 3
181. Problem Solving Solving a problem 3 Lee received 3 goldfish as a gift. Now Lee has 5. How many did Lee have to start with? Is 5 a part or whole?
182. Problem Solving Solving a problem Lee received 3 goldfish as a gift. Now Lee has 5. How many did Lee have to start with? Is 5 a part or whole ? 5 3
183. Problem Solving Solving a problem Lee received 3 goldfish as a gift. Now Lee has 5. How many did Lee have to start with? 5 3 What is the missing part?
184. Problem Solving Solving a problem Lee received 3 goldfish as a gift. Now Lee has 5. How many did Lee have to start with? What is the missing part? 5 3 2
185. Problem Solving Solving a problem 5 3 2 Lee received 3 goldfish as a gift. Now Lee has 5. How many did Lee have to start with? Write the equation.
186. Problem Solving Solving a problem Lee received 3 goldfish as a gift. Now Lee has 5. How many did Lee have to start with? 2 + 3 = 5 5 3 2 Write the equation.
187. Problem Solving Solving a problem Lee received 3 goldfish as a gift. Now Lee has 5. How many did Lee have to start with? 2 + 3 = 5 5 3 2 3 + 2 = 5 Write the equation.
188. Problem Solving Solving a problem Lee received 3 goldfish as a gift. Now Lee has 5. How many did Lee have to start with? 2 + 3 = 5 5 3 2 3 + 2 = 5 5 – 3 = 2 Write the equation. Is this an addition or subtraction problem?
190. Go to the Dump Game Objective: To learn the facts that total 10: 1 + 9 2 + 8 3 + 7 4 + 6 5 + 5 Children use the abacus while playing this “Go Fish” type game.
191. Go to the Dump Game Objective: To learn the ways to partition 10: 1 + 9 2 + 8 3 + 7 4 + 6 5 + 5 Object of the game: To collect the most pairs that equal ten. It is similar to “Go Fish.” Children use the abacus while playing this “Go Fish” type game.
192. Go to the Dump Game The ways to partition 10.
195. “ Math” Way of Naming Numbers 11 = ten 1 12 = ten 2
196. “ Math” Way of Naming Numbers 11 = ten 1 12 = ten 2 13 = ten 3
197. “ Math” Way of Naming Numbers 11 = ten 1 12 = ten 2 13 = ten 3 14 = ten 4
198. “ Math” Way of Naming Numbers 11 = ten 1 12 = ten 2 13 = ten 3 14 = ten 4 . . . . 19 = ten 9
199. “ Math” Way of Naming Numbers 11 = ten 1 12 = ten 2 13 = ten 3 14 = ten 4 . . . . 19 = ten 9 20 = 2-ten Don’t say “2-ten s .” We don’t say 3 hundred s eleven for 311.
200. “ Math” Way of Naming Numbers 11 = ten 1 12 = ten 2 13 = ten 3 14 = ten 4 . . . . 19 = ten 9 20 = 2-ten 21 = 2-ten 1 Don’t say “2-ten s .” We don’t say 3 hundred s eleven for 311.
201. “ Math” Way of Naming Numbers 11 = ten 1 12 = ten 2 13 = ten 3 14 = ten 4 . . . . 19 = ten 9 20 = 2-ten 21 = 2-ten 1 22 = 2-ten 2 Don’t say “2-ten s .” We don’t say 3 hundred s eleven for 311.
202. “ Math” Way of Naming Numbers 11 = ten 1 12 = ten 2 13 = ten 3 14 = ten 4 . . . . 19 = ten 9 20 = 2-ten 21 = 2-ten 1 22 = 2-ten 2 23 = 2-ten 3 Don’t say “2-ten s .” We don’t say 3 hundred s eleven for 311.
203. “ Math” Way of Naming Numbers 11 = ten 1 12 = ten 2 13 = ten 3 14 = ten 4 . . . . 19 = ten 9 20 = 2-ten 21 = 2-ten 1 22 = 2-ten 2 23 = 2-ten 3 . . . . . . . . 99 = 9-ten 9
204. “ Math” Way of Naming Numbers 137 = 1 hundred 3-ten 7 Only numbers under 100 need to be said the “math” way.
205. “ Math” Way of Naming Numbers 137 = 1 hundred 3-ten 7 or 137 = 1 hundred and 3-ten 7 Only numbers under 100 need to be said the “math” way.
206. “ Math” Way of Naming Numbers 0 10 20 30 40 50 60 70 80 90 100 4 5 6 Ages (yrs.) Song, M., & Ginsburg, H. (1988). p. 326. The effect of the Korean number system on young children's counting: A natural experiment in numerical bilingualism. International Journal of Psychology, 23, 319-332. Korean formal [math way] Korean informal [not explicit] Chinese U.S. Average Highest Number Counted Shows how far children from 3 countries can count at ages 4, 5, and 6.
207. “ Math” Way of Naming Numbers 0 10 20 30 40 50 60 70 80 90 100 4 5 6 Ages (yrs.) Song, M., & Ginsburg, H. (1988). p. 326. The effect of the Korean number system on young children's counting: A natural experiment in numerical bilingualism. International Journal of Psychology, 23, 319-332. Korean formal [math way] Korean informal [not explicit] Chinese U.S. Average Highest Number Counted Purple is Chinese. Note jump between ages 5 and 6.
208. “ Math” Way of Naming Numbers 0 10 20 30 40 50 60 70 80 90 100 4 5 6 Ages (yrs.) Song, M., & Ginsburg, H. (1988). p. 326. The effect of the Korean number system on young children's counting: A natural experiment in numerical bilingualism. International Journal of Psychology, 23, 319-332. Korean formal [math way] Korean informal [not explicit] Chinese U.S. Average Highest Number Counted Dark green is Korean “math” way.
209. “ Math” Way of Naming Numbers 0 10 20 30 40 50 60 70 80 90 100 4 5 6 Ages (yrs.) Average Highest Number Counted Song, M., & Ginsburg, H. (1988). p. 326. The effect of the Korean number system on young children's counting: A natural experiment in numerical bilingualism. International Journal of Psychology, 23, 319-332. Korean formal [math way] Korean informal [not explicit] Chinese U.S. Dotted green is everyday Korean; notice smaller jump between ages 5 and 6.
210. “ Math” Way of Naming Numbers 0 10 20 30 40 50 60 70 80 90 100 4 5 6 Ages (yrs.) Song, M., & Ginsburg, H. (1988). p. 326. The effect of the Korean number system on young children's counting: A natural experiment in numerical bilingualism. International Journal of Psychology, 23, 319-332. Korean formal [math way] Korean informal [not explicit] Chinese U.S. Average Highest Number Counted Red is English speakers. They learn same amount between ages 4-5 and 5-6.
211.
212.
213.
214.
215. Math Way of Naming Numbers Compared to reading:
216.
217.
218.
219. Math Way of Naming Numbers “ Rather, the increased gap between Chinese and U.S. students and that of Chinese Americans and Caucasian Americans may be due primarily to the nature of their initial gap prior to formal schooling, such as counting efficiency and base-ten number sense.” Jian Wang and Emily Lin, 2005 Researchers
220. Math Way of Naming Numbers Using 10s and 1s, ask the child to construct 48. Research task:
221. Math Way of Naming Numbers Using 10s and 1s, ask the child to construct 48. Research task: Then ask the child to subtract 14.
222. Math Way of Naming Numbers Using 10s and 1s, ask the child to construct 48. Research task: Then ask the child to subtract 14. Children thinking of 14 as 14 ones count 14.
223. Math Way of Naming Numbers Using 10s and 1s, ask the child to construct 48. Research task: Then ask the child to subtract 14. Children thinking of 14 as 14 ones counted 14.
224. Math Way of Naming Numbers Using 10s and 1s, ask the child to construct 48. Research task: Then ask the child to subtract 14. Children thinking of 14 as 14 ones counted 14.
225. Math Way of Naming Numbers Using 10s and 1s, ask the child to construct 48. Research task: Then ask the child to subtract 14. Children thinking of 14 as 14 ones counted 14.
226. Math Way of Naming Numbers Using 10s and 1s, ask the child to construct 48. Research task: Then ask the child to subtract 14. Children thinking of 14 as 14 ones counted 14.
227. Math Way of Naming Numbers Using 10s and 1s, ask the child to construct 48. Research task: Then ask the child to subtract 14. Children thinking of 14 as 14 ones counted 14.
228. Math Way of Naming Numbers Using 10s and 1s, ask the child to construct 48. Research task: Then ask the child to subtract 14. Children thinking of 14 as 14 ones counted 14.
229. Math Way of Naming Numbers Using 10s and 1s, ask the child to construct 48. Research task: Then ask the child to subtract 14. Children thinking of 14 as 14 ones counted 14.
230. Math Way of Naming Numbers Using 10s and 1s, ask the child to construct 48. Research task: Then ask the child to subtract 14. Children who understand tens remove a ten and 4 ones.
231. Math Way of Naming Numbers Using 10s and 1s, ask the child to construct 48. Research task: Then ask the child to subtract 14. Children who understand tens remove a ten and 4 ones.
232. Math Way of Naming Numbers Using 10s and 1s, ask the child to construct 48. Research task: Then ask the child to subtract 14. Children who understand tens remove a ten and 4 ones.
233. Math Way of Naming Numbers Traditional names 4-ten = forty The “ty” means tens.
234. Math Way of Naming Numbers Traditional names 4-ten = forty The “ty” means tens. The traditional names for 40, 60, 70, 80, and 90 follow a pattern.
235. Math Way of Naming Numbers Traditional names 6-ten = sixty The “ty” means tens.
236. Math Way of Naming Numbers Traditional names 3-ten = thirty “ Thir” also used in 1/3, 13 and 30.
237. Math Way of Naming Numbers Traditional names 5-ten = fifty “ Fif” also used in 1/5, 15 and 50.
238. Math Way of Naming Numbers Traditional names 2-ten = twenty Two used to be pronounced “twoo.”
239. Math Way of Naming Numbers Traditional names A word game fireplace place-fire Say the syllables backward. This is how we say the teen numbers.
240. Math Way of Naming Numbers Traditional names A word game fireplace place-fire paper-news newspaper Say the syllables backward. This is how we say the teen numbers.
241. Math Way of Naming Numbers Traditional names A word game fireplace place-fire paper-news box-mail mailbox newspaper Say the syllables backward. This is how we say the teen numbers.
242. Math Way of Naming Numbers Traditional names ten 4 “ Teen” also means ten.
243. Math Way of Naming Numbers Traditional names ten 4 teen 4 “ Teen” also means ten.
244. Math Way of Naming Numbers Traditional names ten 4 teen 4 fourteen “ Teen” also means ten.
245. Math Way of Naming Numbers Traditional names a one left
246. Math Way of Naming Numbers Traditional names a one left a left-one
247. Math Way of Naming Numbers Traditional names a one left a left-one eleven
248. Math Way of Naming Numbers Traditional names two left Two pronounced “twoo.”
249. Math Way of Naming Numbers Traditional names two left twelve Two pronounced “twoo.”
267. Composing Numbers 1 hundred 1 0 0 Of course, we can also read it as one hun-dred.
268. Composing Numbers 1 hundred 1 0 0 Of course, we can also read it as one hun-dred. 1 0 1 0
269. Composing Numbers 1 hundred 1 0 0 Of course, we can also read it as one hun-dred.
270. Composing Numbers Reading numbers backward 2 5 8 4 8 To read a number, students are often instructed to start at the right (ones column), contrary to normal reading of numbers and text:
271. Composing Numbers 2 5 8 4 5 8 To read a number, students are often instructed to start at the right (ones column), contrary to normal reading of numbers and text: Reading numbers backward
272. Composing Numbers 2 5 8 4 2 5 8 To read a number, students are often instructed to start at the right (ones column), contrary to normal reading of numbers and text: Reading numbers backward
273. Composing Numbers 2 5 8 4 2 5 8 4 To read a number, students are often instructed to start at the right (ones column), contrary to normal reading of numbers and text: Reading numbers backward
274. Composing Numbers 2 5 8 4 2 5 8 4 To read a number, students are often instructed to start at the right (ones column), contrary to normal reading of numbers and text: Reading numbers backward The Decimal Cards encourage reading numbers in the normal order.
376. Trading Side Adding 4-digit numbers 3658 + 2738 Enter the first number from left to right. 1000 10 1 100
377. Trading Side Adding 4-digit numbers 3 658 + 2738 Enter the first number from left to right. 1000 10 1 100
378. Trading Side Adding 4-digit numbers 3 658 + 2738 Enter the first number from left to right. 1000 10 1 100
379. Trading Side Adding 4-digit numbers 3 6 58 + 2738 Enter the first number from left to right. 1000 10 1 100
380. Trading Side Adding 4-digit numbers 36 5 8 + 2738 Enter the first number from left to right. 1000 10 1 100
381. Trading Side Adding 4-digit numbers 365 8 + 2738 Enter the first number from left to right. 1000 10 1 100
382. Trading Side Adding 4-digit numbers 3658 + 273 8 Add starting at the right. Write results after each step. 1000 10 1 100
383. Trading Side Adding 4-digit numbers 3658 + 273 8 Add starting at the right. Write results after each step. 1000 10 1 100
384. Trading Side Adding 4-digit numbers 3658 + 273 8 Add starting at the right. Write results after each step. 1000 10 1 100
385. Trading Side Adding 4-digit numbers 3658 + 273 8 Add starting at the right. Write results after each step. 1000 10 1 100
386. Trading Side Adding 4-digit numbers 3658 + 2738 6 Add starting at the right. Write results after each step. . . . 6 ones. Did anything else happen? 1000 10 1 100
387. Trading Side Adding 4-digit numbers 3658 + 2738 6 Add starting at the right. Write results after each step. 1 Is it okay to show the extra ten by writing a 1 above the tens column? 1000 10 1 100
388. Trading Side Adding 4-digit numbers 3658 + 27 3 8 6 Add starting at the right. Write results after each step. 1 1000 10 1 100
389. Trading Side Adding 4-digit numbers 3658 + 27 3 8 6 Add starting at the right. Write results after each step. 1 Do we need to trade? [no] 1000 10 1 100
390. Trading Side Adding 4-digit numbers 3658 + 2738 9 6 Add starting at the right. Write results after each step. 1 1000 10 1 100
391. Trading Side Adding 4-digit numbers 3658 + 2 7 38 96 Add starting at the right. Write results after each step. 1 1000 10 1 100
392. Trading Side Adding 4-digit numbers 3658 + 2 7 38 96 Add starting at the right. Write results after each step. 1 Do we need to trade? [yes] 1000 10 1 100
393. Trading Side Adding 4-digit numbers 3658 + 2 7 38 96 Add starting at the right. Write results after each step. 1 Notice the number of yellow beads. [3] Notice the number of blue beads left. [3] Coincidence? No, because 13 – 10 = 3. 1000 10 1 100
394. Trading Side Adding 4-digit numbers 3658 + 2 7 38 96 Add starting at the right. Write results after each step. 1 1000 10 1 100
395. Trading Side Adding 4-digit numbers 3658 + 2738 3 96 Add starting at the right. Write results after each step. 1 1000 10 1 100
396. Trading Side Adding 4-digit numbers 3658 + 2738 3 96 Add starting at the right. Write results after each step. 1 1 1000 10 1 100
397. Trading Side Adding 4-digit numbers 3658 + 2 738 396 Add starting at the right. Write results after each step. 1 1 1000 10 1 100
398. Trading Side Adding 4-digit numbers 3658 + 2 738 396 Add starting at the right. Write results after each step. 1 1 1000 10 1 100
399. Trading Side Adding 4-digit numbers 3658 + 2738 6 396 Add starting at the right. Write results after each step. 1 1 1000 10 1 100
400. Trading Side Adding 4-digit numbers 3658 + 2738 6396 Add starting at the right. Write results after each step. 1 1 1000 10 1 100
421. Multiplication on the AL Abacus 7 8 = This method was used in the Middle Ages, rather than memorize the facts > 5 5. For facts > 5 5
422. Multiplication on the AL Abacus 7 8 = This method was used in the Middle Ages, rather than memorize the facts > 5 5. For facts > 5 5
423. Multiplication on the AL Abacus 7 8 = This method was used in the Middle Ages, rather than memorize the facts > 5 5. For facts > 5 5 Tens:
424. Multiplication on the AL Abacus 7 8 = This method was used in the Middle Ages, rather than memorize the facts > 5 5. For facts > 5 5 Tens:
425. Multiplication on the AL Abacus 7 8 = This method was used in the Middle Ages, rather than memorize the facts > 5 5. For facts > 5 5 Tens: 20 + 30
426. Multiplication on the AL Abacus 7 8 = 50 + This method was used in the Middle Ages, rather than memorize the facts > 5 5. For facts > 5 5 Tens: 20 + 30 50
427. Multiplication on the AL Abacus 7 8 = 50 + This method was used in the Middle Ages, rather than memorize the facts > 5 5. For facts > 5 5 Tens: Ones: 20 + 30 50
428. Multiplication on the AL Abacus 7 8 = 50 + This method was used in the Middle Ages, rather than memorize the facts > 5 5. For facts > 5 5 Tens: Ones: 20 + 30 50
429. Multiplication on the AL Abacus 7 8 = 50 + This method was used in the Middle Ages, rather than memorize the facts > 5 5. For facts > 5 5 Tens: Ones: 3 2 20 + 30 50
505. “ Pie” Model Experts in visual literacy say that comparing quantities in pie charts is difficult because most people think linearly. It is easier to compare along a straight line than compare pie slices. askoxford.com
506. “ Pie” Model Experts in visual literacy say that comparing quantities in pie charts is difficult because most people think linearly. It is easier to compare along a straight line than compare pie slices. askoxford.com Specialists also suggest refraining from using more than one pie chart for comparison. statcan.ca
541. Counting: Necessary or Detrimental? AMS Conference March 25, 2011 Chicago, Illinois by Joan A. Cotter, Ph.D. [email_address] 7 5 2 Presentation available: ALabacus.com 7 x 7 VII