The document discusses alternative algorithms for teaching multiplication and division to students. It emphasizes developing conceptual understanding over rote memorization and encourages using invented strategies before standard algorithms. Teachers should focus on building meaning, efficiency, accuracy, and flexibility through rich problems and modeling of thinking with tools. Students' work should be analyzed to identify strategies like partitioning, repeated addition, and compensate to guide further instruction.
This is the course or teachers in Indonesia on number sense for Primary 4 to 6. It covers place values, regrouping, large number multiplication and division and some ideas on estimation and multiples.
This is the course or teachers in Indonesia on number sense for Primary 4 to 6. It covers place values, regrouping, large number multiplication and division and some ideas on estimation and multiples.
Beyond the Algorithm: Multiplication and Division Strategies that Make Sense! (Grades 4-6) Presented By Kimberly Rimbey at the MEAD Conference, Tucson, AZ, on 1-20-18
Making sense of multi-digit division requires strong connections with multiplication and place value. Join us as we explore multiplication and division using concrete and visual models, connected to written work, and grounded in problem solving. Formative assessment strategies will be included.
These are the unpacking documents to better help you understand the expectations for Third gradestudents under the Common Core State Standards for Math. The examples should be very helpful.
Multiplication -- More Than Repeated Addition and Times Tables.pdfChris Hunter
Multiplication is repeated addition... but it also means so much more than that! In this workshop, you will explore several fundamental meanings of this operation (e.g., equal groups, arrays and areas, how a quantity is “stretched,” etc.) through rich tasks that address each of these meanings. Also, you will explore and discuss relationships between the “basic facts.” More importantly, you will learn how to help your students see that these relationships extend to other types of numbers that they come across in BC’s intermediate and middle years mathematics curriculum (e.g., two-digit whole numbers, fractions, decimals, integers, etc.).
Beyond the Algorithm: Multiplication and Division Strategies that Make Sense! (Grades 4-6) Presented By Kimberly Rimbey at the MEAD Conference, Tucson, AZ, on 1-20-18
Making sense of multi-digit division requires strong connections with multiplication and place value. Join us as we explore multiplication and division using concrete and visual models, connected to written work, and grounded in problem solving. Formative assessment strategies will be included.
These are the unpacking documents to better help you understand the expectations for Third gradestudents under the Common Core State Standards for Math. The examples should be very helpful.
Multiplication -- More Than Repeated Addition and Times Tables.pdfChris Hunter
Multiplication is repeated addition... but it also means so much more than that! In this workshop, you will explore several fundamental meanings of this operation (e.g., equal groups, arrays and areas, how a quantity is “stretched,” etc.) through rich tasks that address each of these meanings. Also, you will explore and discuss relationships between the “basic facts.” More importantly, you will learn how to help your students see that these relationships extend to other types of numbers that they come across in BC’s intermediate and middle years mathematics curriculum (e.g., two-digit whole numbers, fractions, decimals, integers, etc.).
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
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.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
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 Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
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.
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Alt Algrthm Mult Div
1. Alternative Algorithms for Multiplication and Division If we don’t teach them the standard way, how will they learn to compute? Kathy Cheval and Kathy Bowers, Salem-Keizer Public Schools, Salem, OR http://is.salkeiz.k12.or.us
2. If we can convince students that mathematics is figure-out-able, that it is more than memorization, then we can increase student buy-in and confidence. If we can get students to think in class, instead of just trying to memorize series after series of steps, we can save time and decrease frustration because by building on understanding, we will have fewer misapplied and mixed-up rules. Why Numeracy for Secondary Students Harris & Pope, 2005
3. How has this student misapplied the rules for multiplying? Based upon the work above, what understandings and misunderstandings does this student have?
4. Multi-digit Multiplication and DivisionWhat are the goals for students? Develop conceptual understanding Develop computational fluency
5. What is Computational Fluency? Fluency demands more of students than does memorizing a procedure. Fluency rests on a well-build mathematical foundation that involves: Understandingimplies that the student brings meaning to the operation being carried out. The student can explain the “why” of each step taken to solve the problem. Efficiencyimplies that the student does not get bogged down in the steps or lose track of the logic of the strategy. An efficient strategy is one that the student can carry out easily. Accuracy depends on careful recording, knowledge of basic number combinations and other important number relationships, as well as verifying the results. Flexibility requires the knowledge of more than one approach to solving a problem. Students need to be flexible to choose an appropriate strategy for a specific problem.
7. Multiplicative Thinking Multiplication is more complex than addition because the two numbers (factors) in the problem take different roles. 12 cars with 4 wheels each. How many wheels? 12 x 4 = 48 cars wheels/car wheels (groups) (items per group) (total number of items) (multiplier) (multiplicand) (product)
8. Multi-digit Multiplication Strategies12 cars with 4 wheels each. How many wheels? Additive Strategies Direct Modeling Repeated Addition Doubling Multiplicative Strategies
9. Multi-digit Multiplication Strategies52 cards per deck. 18 decks of cards. How many cards? Multiplicative Strategies Single Number Partitioning Both Number Partitioning Compensating
10. Multi-digit Multiplication StrategiesAs you look at student work, try to identify the kinds of strategies you see students using. While this list is not comprehensive, it will give you a place to begin. Often you will see evidence of more than one strategy being used. Multiplicative Strategies Single Number Partitioning Both Number Partitioning Compensating Additive Strategies Direct Modeling Repeated Addition Doubling
11. There are 18 ants with 6 legs each. How many legs altogether? Sample 1 Sample 2
12. Students collected cans to recycle. Each box holds 12 cans. They filled 38 boxes with cans. How many cans did they collect? Sample 3 Sample 4
13. There are 62 fifth graders. It costs $38 per student for outdoor school. How much do the fifth graders need to earn so everyone can go? Sample 5 Sample 6
14. There are 62 fifth graders. It costs $38 per student for outdoor school. How much do the fifth graders need to earn so everyone can go? Sample 6 Sample 7
15. Teacher’s Role Provide rich problems to build understanding Encourage the use of “thinking tools” (manipulatives like snap cubes or 300 charts) when needed Guide student thinking Provide multiple opportunities for students to share strategies Help students complete their approximations Model ways of recording strategies Press students toward more efficient strategies
16. Two Contexts for Division Measurement Division (number of groups unknown) There are 54 children on a full bus. Each seat can hold 3 children. How many seats are there on the bus? Partition Division (size of groups unknown) There are 54 children on a full bus. There are 18 seats. How many children are sitting on each seat?
17. Multi-digit Division StrategiesThe strategies students use for division will be very similar to those they used for multiplication. As you look at student work, try to identify the kinds of strategies you see students using. This is not a comprehensive list, and often you will see evidence of more than one strategy being used. Multiplicative Strategies Single Number Partitioning Both Number Partitioning Compensating Additive Strategies Direct Modeling Repeated Addition/Subtraction Doubling
18. There are 54 children on a full bus. Each seat can hold 3 children. How many seats are there on the bus? Sample 1 Sample 2
19. There are 54 children on a full bus. There are 18 seats. How many children are sitting on each seat? Sample 3 Sample 4
22. Teaching a “standard” way? Delay! Delay! Delay! Spend most of your time on invented strategies. The understanding students gain from working with invented strategies will make it much easier for them to understand a standard algorithm. For most students, this means delaying the teaching of a standard way of multiplying and dividing until 5th grade. Students who don’t clearly understand the way should be allow to use a way that make sense to them.
23. Which “standard” way? Partial Products for 52 x 18 (modeled by an open array) 52 52 x 18x 18 16 16 400 400 20 416 500 . 20 936 436 500 936 50 2 500 20 10 8 400 18
24. Which “standard” way? Partial Products for 936 18 18 936 18 936 100 x 18 = 1800 180 10 x 18 900 50 756 36 360 20 x 18 36 2 396 0 52 360 20 x 18 36 36 2 x 18 0 52 x 18