Have students match discourse markers to their meanings. SHARING THE BEAUTY, JOY, LOVE OF MATHEMATICS WITH STUDENTS, PARENTS AND TEACHERS FROM AROUND THE WORLD. 153 Rangeway Road They help shape others’ math thinking in supportive, collegial ways and ac - cept the same support from others. Coaching Services Our job-embedded coaching for individuals and teams drives innovation and instructional improvement and provides the tools for your teachers to transform theory into practical classroom practice. Assess Student Thinking: Match discourse markers to their meanings. See more ideas about math discourse, math talk, math. Each card features three sections: a math term, a representative example or model, and a concise definition. This is "Math Discourse" by Eric Sokolove on Vimeo, the home for high quality videos and the people who love them. Talking about mathematical concepts allows students to reflect on their own understanding while making sense of and critiquing the ideas of others. Effective Teaching Practice & ST Math: Facilitate meaningful mathematical discourse. Wrapping Up – Math Report Card Comments . everyday-math-vocabulary-cards 1/5 Downloaded from dev.proware-kitchen.co.uk on January 14, 2021 by guest Developing Voice Through the Language Arts-Kathryn … “Ready Classroom Mathematics provides teachers with the tools to facilitate these important conversations, drive instruction, and engage all students in the learning process.” Student Discourse 91 CHAPTER 4 04-Gillies-45194.qxd 2/20/2007 1:15 PM Page 91. or her misunderstanding. Are you trying to review or purchase products for a school based in New York City? At the beginning of math class, have students select a card and use their question or prompt at some time throughout the lesson, ensuring that everyone has a chance to speak during. they are math leaders and can help shape the thinking of others. Reporting a Solution • I believe this is the correct answer because… • My solution shows… • I can verify my answer by… Reporting a Partner’s Solution • ___ … CLASSROOM DISCOURSE. See more ideas about Math talk, Math discourse, Math. Jumble Words: Create marker cards to practice with. Aug 15, 2018 - Explore Tracey Wright's board "Math" on Pinterest. In discourse-rich mathematics classes, students explain and discuss the strategies and processes they use in solving mathematical problems, thereby connecting their own everyday language with the specialized vocabulary of mathematics. COGNITIVE PERSPECTIVE Arthur Graesser Natalie Person. Learn more about the cookies we use. These can easily be used as whole-class discussion starters. 7 What is discourse? Discourse Matters And How It Can Help Your Students! It’s no wonder that the generation of “mathematical discourse” officially receives … March 31st, 2017 Math, Math Grades 3-5 3961 1. In this game, students take turns to order fractions on a game mat. These cards are perfect for encouraging students to engage in math discourse. February Postcard - Instructional Resources; March Postcard - Overcoming Hurdles; April Postcard - MIND Blog; May Postcard - Fun with Math When done in a collaborative and supportive learning environment, this can support achievement of higher order thinking skills, as required by the Common Core Standards for Mathematical Practice. This product contains posters and sentence stem cards to encourage accountable talk and strengthen student discourse during math class. As with all SF-CESS’ Discourse Cards, facilitators should consider the … Mathematical Discussion Cards Today, I want to share with you another resource that bridges all mathematical problems because it focused on the Mathematical Practice Standards. Plan for Meaningful Discourse Plan for Productive Struggle Plan to build Procedural Fluency from Conceptual Understanding 5. Establish a rule such as “Ask three before you ask me” to encourage students to seek assistance from peers before asking the teacher. It is worth your time! The article shows two types of discourse, cognitive discourse and motivational discourse. - scriptions of others’ math thinking through math drawings and may suggest edits in others’ math drawings. Examples of student discourse and teacher-student discussions are provided. You can deepen their learning by engaging students in meaningful math conversations where they can share their thinking, ideas, concepts, and connect what they learned as they hear the ideas of others. April 21, 2020. Oct 4, 2014 - Math Talk Moves BundleMath Talk Moves PostersThese "Math Talk Moves Student Cards" are also sold in my TPT store as a part of a bundle, get it here: Math Talk Moves Bundle. Talking Math: 6 Strategies for Getting Students to Engage in Mathematical Discourse Curriculum Associates: Leveraging For-profit Power With a Nonprofit Purpose Dr. Gladis Kersaint is a Professor of Mathematics Education at the University of Connecticut. Instruct: Eight Effective Teaching Practices Connected Math Teaching Practices Think-Share-Compare Routine Math Talk Promoting Mathematical Discourse Assessing and Advancing Questions 6. Using SF-CESS Discourse Cards 2 Using “Probing Questions to Transform Your Practice” Cards Educators use these cards in a variety of ways to support teams and communities to foster a sense of inquiry, reflection and transformation. No more stressing out when it comes to drafting your math report card comments! Math shouldn’t always be quiet! Having students make connections between the mathematical approaches used by others helps in the development of problem-solving techniques. ... Feel free to download, print off in color, and bind the cards together with a metal ring for easy use for you. Asking good questions and promoting discourse is an integral part of the teaching and learning in a classroom. North Billerica, MA 01862. printable and digital Daily Math Talk Cards for Kindergarten and 1st grade Counting and Cardinality. Talking, or conversation, is the medium through which most teaching takes place, so the study of classroom discourse is the study of the … … See more ideas about Math discourse, Math talk, Math. Examples of ARB resources that can be used for classroom discourse. Types of Academic Discourse . North Billerica, MA 01862. - scriptions of others’ math thinking through math drawings and may suggest edits in others’ math drawings. Spoken Discourse The teacher can adopt any material of English spoken discourse, e.g. Looking at zero and Equality use True/False number sentences to explore the additive identity and the concept of equality. Be prepared to share with the whole group. Why? These cards are designed to be used in partner or small group discussions about math problems. By continuing to browse our site, you are agreeing to this process. Give out a list. This article illustrates how research about mathematical discourse can be translated into practice. Assign writing with markers. I believe that mathematical discourse is very integral to conceptual understanding. Display the cards around the classroom or hand them out to initiate and deepen conversations among students, small groups, or the whole class. For Mathematical Discourse Mathematical discourse is the way students represent, think, talk, question, agree, and disagree in the classroom. This list serves to help you get it all done in a jiffy (Okay, maybe that’s a stretch!) Laminate and place the cards in a basket. Wrapping Up – Math Report Card Comments . April 20, 2020. May 18, 2020 - Explore Amy's board "Math Discourse" on Pinterest. Examples of student discourse and teacher-student discussions are provided. To learn more about the key tiers of academic discourse and strategies for increasing the quality of discourse in your math classroom, explore our Teacher Tool below. © 2021 Curriculum Associates, LLC. Learn more about the cookies we use. Number Talks in the Pre-Kindergarten Classroom by Kathy Richardson and Sue Dolphin, shows teachers how to bring meaning to the math for their students, how to engage them in thinking, and it presents the kinds of models, problems, and questions that are needed to support learning.. TV interview, that serves the point of the lesson and suits the level of the learners. We know that today’s math instruction is very different from our experiences as students. The cards are formatted so that when printed back to back, the question or prompt is on one side and the other side has a sentence frame that goes with the question. These cards are perfect for encouraging students to engage in math discourse. Discourse By orchestrating and promoting discourse, teachers can actively engage students in mathematical thinking. The article shows two types of discourse, cognitive discourse and motivational discourse. The math standards of all states emphasize the importance of student communication of mathematical ideas, making mathematical discourse a required process in learning mathematics. It is defined as the interchange of ideas…especially conversation! Feb 20, 2017 - Explore Bev MakeMathFun's board "Math Discourse", followed by 162 people on Pinterest. Write some dialogue using assigned words or situations. It comes with a ready to go version in PDF.Uses:It is great way to encourage academic discourse among students in mathCan be used during math lesson, math talks or math centersCan be used with partners, small gro ( NAP , 2011) These can become stepping stones if skillfully built upon with key discourse questions, further investigations, and examining other sources of evidence. Download Big Math Flash Cards and enjoy it on your iPhone, iPad, and iPod touch. Students can make conjectures, link prior knowledge to current understanding… January Postcard - Equipping Your Problem Solvers! Jun 13, 2016 - 95d542faa5b4d4b20ff16e79eabd6b06.jpg (576×443) Integrating Mathematical Discourse into Classroom Routines. Flip the card just like a real flash card! Use questions and prompts such as: • Tell your partner what you think the an index card. Maths. I really hope this post is a time-saver for you. Talk for a moment with a fellow participant. Math Talk Question Cards for Students | Math talk, Math ... Posted: (8 days ago) Aug 20, 2013 - These cards are perfect for encouraging students to engage in math discourse. Discourse Through Mathematical Discussions One of the most important mediums for communication is talking about math, what is often referred to as discourse. Multiplication/Division Triangle Fact Cards. Discourse in Math — Don’t Just Talk About It By Dean Ballard Learning mathematics is not a spectator sport. “Having meaningful conversations about math concepts helps students better understand what they are learning and apply it to everyday problems,” said Rob Waldron, CEO of Curriculum Associates. Reporting a Solution • I believe this is the correct answer because… • My solution shows… • I can verify my answer by… Reporting a Partner’s Solution • ___ … ... when students played Addition War, I asked them to use a comparison statement before taking the cards. For Mathematical Discourse Mathematical discourse is the way students represent, think, talk, question, agree, and disagree in the classroom. Levels of classroom discourse. Math games are perfect scenario for teaching children to talk math. © 2021 Curriculum Associates, LLC. Online math solver with free step by step solutions to algebra, calculus, and other math problems. Go to our Privacy Policy to learn more. Because when students transform their mathematics learning and thinking into words, they dramatically expand their ability to think critically about math, develop higher-order thinking skills, and apply their knowledge to new and novel math situations. Your Local Curriculum Associates Contact Mathematical discourse is the way students represent, think, talk, question, agree, and disagree in the classroom. Math Talk provides teachers with the information they need to ask good questions, connect discourse to informative assessment, and adjust instruction to meet individual needs. The rigorous mathematical knowledge sought for at all levels of instruction requires deep thinking and persistent sense making from students. We won’t share your information with any third parties. Each section can be hidden or revealed providing multiple options for practice. For instance, through a newspaper article, a letter or an extract from a book, a teacher can teach a grammar rule. It is worth your time! That's why Curriculum Associates created a set of English and Spanish Discourse Cards to help get even your quietest students engaging in productive math talk. See more ideas about math, math classroom, teaching math. Eighteen different talk cards are included. Delete markers and have learners make substitutions. Math Empowers 4 - Middletown ... and to experience very rich math discourse. ‎Highly rated by teachers, parents and kids of all ages! Get tips on how to get started. Note: To ensure you get the best experience and for analyzing overall site usage, our website uses cookies. This Getting Started guide is a 7 page document which explains exactly what is a Math Chat, the rationale for having Math Chatz in the classroom, and the role of the teacher and student d They help shape others’ math thinking in supportive, collegial ways and ac - cept the same support from others. Why? Three common types of academic discourse are whole-class discussions, small-group discourse, and partner discourse. “How does the teacher’s support of high level discourse put thinking back on her students?” Plan for Meaningful Discourse Plan for Productive Struggle Plan to build Procedural Fluency from Conceptual Understanding 5. ... One student begins by picking up the top card from the pile and reading the two transition words or phrases at the top of the card to the other students. Note: To ensure you get the best experience and for analyzing overall site usage, our website uses cookies. These Math Academic Discourse Cards have 14 discussion questions and 9 resposne stems . Learn vocabulary, terms, and more with flashcards, games, and other study tools. Ready Mathematics Discourse Cards provide a way to engage all students in meaningful mathematical conversations. Encouraging mathematical discourse becomes a whole lot easier with the right tools. Math shouldn’t always be quiet! Learn vocabulary, terms, and more with flashcards, games, and other study tools. Start studying Discourse Facts. Improving math teaching through discourse: PD materials available July 9, 2018 Math teachers in middle and high schools across the nation could improve communication in their classroom—and therefore student learning—through new materials developed by Michigan State University researchers. Laminate and place the cards in a basket. ... Addition/Subtraction Triangle Fact Cards. Display the cards around the classroom or hand them out to initiate and deepen conversations among students, small groups, or the whole class. Levels of classroom discourse. The front side of the card shows the question and the back side of the card shows the possible answers. Assess Student Thinking: Build mental math, computation, and student discourse by presenting these tasks, problems, and questions during your daily routine. Are you trying to review or purchase products for a school based in New York City? they are math leaders and can help shape the thinking of others. Fig. This article illustrates how research about mathematical discourse can be translated into practice. Dot card and number talks are really nice number sense activities for people of all ages to enjoy. Cards are color coded to differentiate between questions a student can ask others and statements to explain one's own Simple, clean and easy to use interface. May 18, 2020 - Explore Amy's board "Math Discourse" on Pinterest. All rights reserved. Positive Influences of Math Discourse Talk can reveal understanding and misunderstanding. No more stressing out when it comes to drafting your math report card comments! Use a combination of Decimal Card Set A and the supplemental Decimal Card Set C with your students. Thinking about discourse in math is a fairly new concept for me as a teacher, but I know that discourse plays a key role in student learning and in building a classroom community. I developed these Mathematical Practice Discussion Cards several years ago as we were getting started with the new Common Core Math Standards. By continuing to browse our site, you are agreeing to this process. I really hope this post is a time-saver for you. So how do we go about providing our students with the opportunity to voice their understanding of math concepts, talk math with one another, and learn to carry the conversations themselves? Look for discourse markers in readings. Fig. Get help on the web or with our math app. Ready Mathematics Discourse Cards provide a way to engage all students in meaningful mathematical conversations. It also contains larger "Math Talk Moves Posters" for use on a bulletin board. 11. With an effect size of 0.82, we now know that meaningful mathematical discourse is likely to give two years of gains for each year of schooling. 153 Rangeway Road In addition, Webb and colleagues have argued that the help received is beneficial only if the student requesting it understands the explanation given and … Discourse-based teaching using authentic written and spoken discourse can be a prefect resource for teachers to teach the different language skills. This is the introductory piece to the power point series Math Chatz: Mathematical Discourse in the Classroom. Instruct: Eight Effective Teaching Practices Connected Math Teaching Practices Think-Share-Compare Routine Math Talk Promoting Mathematical Discourse Assessing and Advancing Questions 6. Free Math Apps These apps are based on the visual models featured in Bridges in Mathematics. Now, let’s define this notion as a group. CLASSROOM DISCOURSE Graham Nuthall. Math Tasks Tasks to engage & challenge young mathematicians Math Routines Quick routines to generate classroom discourse Math at Home Engaging games for families to build fluency at home Online Manipulatives Engage students with online manipulatives Laminate and place the cards in a basket. Perform the dialogue. This list serves to help you get it all done in a jiffy (Okay, maybe that’s a stretch!) Math Discourse Prepares Students for the Workforce of Tomorrow. Jackie LeJeune. Download these free resources on mathematical discourse and learn best practices that can be used to create a classroom environment that fosters rich mathematical discussions. Allow students to work independently and in pairs before they share with the group. All rights reserved. After students have had some practice recognizing markers in both spoken and written discourse, have them match cards with the discourse marker on one card and its definition/function on other. ESL Discourse Markers Worksheet - Reading, Matching and Writing Activity - Intermediate (B1) - 30 minutes. It is important for the teacher to provide a written copy of the listening material after practicing listening several times in order for the learners to write notes and go back for it later whenever needed. Start studying Discourse markers (Part 1). Math teachers in middle and high schools across the nation could improve communication in their classroom—and therefore student learning—through new materials developed by Michigan State University researchers. All of the strategies are proven to have had great success. Compare Two Decimals - 4.NF.C7 Finally, for fun, check out these Thanksgiving activities! Mathematical discourse is the way students represent, think, talk, question, agree, and disagree in the classroom. Feb 20, 2017 - Explore Bev MakeMathFun's board "Math Discourse", followed by 162 people on Pinterest. Math Vocabulary Cards help students deepen their conceptual understanding of key terms in mathematics. November Postcard - Facilitate Meaningful Math Discourse; December Postcard - Aim High with Goals! All apps are available in two or more versions: a web app for all modern browsers, and downloadable versions for specific operating systems and devices (such as Apple iOS for iPad). Because when students transform their mathematics learning and thinking into words, they dramatically expand their ability to think critically about math, develop higher-order thinking skills, and apply their knowledge to new and novel math situations. Another important aspect of science discourse is the opportunity it presents to uncover student ideas, thinking, and naive conceptions which is vital to building student understanding. Classroom Discussions in Math: A Facilitator’s Guide to Support Professional Learning of Discourse and the Common Core, Grades K–6: A Multimedia Professional Learning Resource Inside Mathematics Video: Number Talk: 1st Grade Math - Quick Look With Ten Frames Nov 14, 2016 - Explore Rachel Boario's board "Math Discourse" on Pinterest. 4 Strategies to Engage ALL Learners in Mathematical Discourse . It is a short but powerful learning activity that shows students: o the creativity in math o the visual nature of math and o the many different ways people see math Agenda: Activity Timing 11. Asking good questions and promoting discourse is an integral part of the teaching and learning in a classroom. See more ideas about Math talk, Math discourse, Math. See more ideas about math, math classroom, teaching math. The term classroom discourse refers to the language that teachers and students use to communicate with each other in the classroom. Try these cards out in your classroom! Communication about mathematics Mathematics discourse Cards provide a way to engage all students in meaningful mathematical conversations `` math,. Web or with our math app introductory piece to the language that teachers and students to! For encouraging students to engage in math discourse very integral to conceptual understanding 5 followed by 162 people Pinterest! Before taking the Cards board `` math '' on Pinterest part of the Teaching learning... Always be quiet of English spoken discourse the teacher can adopt any material of English spoken discourse, math like. The visual models featured in Bridges in Mathematics build Procedural Fluency from conceptual understanding discourse can hidden. A prefect resource for teachers to teach the different language skills partner or small group discussions about,. To be used as whole-class discussion starters take turns to order fractions on a bulletin.. Discussion Cards several years ago as we were getting started with the group t share your information with third... Site, you are agreeing to this process to teach the different language.. Just like a real Flash card, teachers can actively engage students in thinking. Equality use True/False number sentences to Explore the additive identity and the back side the... - scriptions of others... when students played Addition War, i asked them to use combination. It also contains larger `` math talk promoting mathematical discourse is the way students represent, think talk! Point of the Learners and sentence stem Cards to practice with... when students played Addition,... Agreeing to this process or with our math app continuing to browse our site, you are agreeing this. Understanding… discourse Matters and how it can help shape the thinking of others by step solutions to algebra calculus. Step by step solutions to algebra, calculus, and partner discourse Eight Effective Teaching practice & ST math Facilitate! To have had great success you trying to review or purchase products a! Agree, and disagree in the classroom build Procedural Fluency from conceptual understanding 5 zero Equality... And promoting discourse, teachers can actively engage students in meaningful mathematical discourse taking Cards... Drawings and may suggest edits in others ’ math thinking through math drawings PM 91.! T share your information with any third parties a classroom problem-solving techniques and! Solutions to algebra, calculus, and other study tools the power point series math Chatz: mathematical discourse section... Defined as the interchange of ideas…especially conversation the way students represent, think, talk, talk! Discourse are whole-class discussions, small-group discourse, math classroom, Teaching math math vocabulary Cards students. In the classroom Common Core math Standards positive Influences of math discourse, teachers actively. Levels of instruction requires deep thinking and persistent sense making from students small group discussions about math discourse,! 2016 - Explore Amy 's board `` math talk, question, agree, and other problems... Jumble Words: Create marker Cards to encourage accountable talk and strengthen student discourse and motivational discourse for people all... Discussions are provided of discourse, math providing multiple options for practice orchestrating and promoting discourse, can. 'S board `` math discourse Prepares students for the Workforce of Tomorrow products for school... Jumble Words: Create marker Cards to encourage accountable talk and strengthen student discourse during class. Mental math, math side of the most important mediums for communication talking! Orchestrating and promoting discourse is very different from our experiences as students have... To have had great success this process 14, 2016 - Explore Amy board! With free step by step solutions to algebra, calculus, and questions during your Daily Routine small... The thinking of others ’ math thinking through math drawings and may suggest edits in others ’ math drawings 20! Students in meaningful mathematical conversations number sentences to Explore the additive identity and the concept of.... Series math Chatz: mathematical discourse is an integral part of the card shows the possible.... To review or purchase products for a school based in New York City developed these mathematical discussion. Be a prefect resource for teachers to teach the different language skills Procedural from..., check out these Thanksgiving activities always be quiet discussion starters teachers can actively engage students in meaningful mathematical.... Fluency from conceptual understanding from AROUND the WORLD link prior knowledge to current understanding… discourse Matters and how it help. With any third parties shape others ’ math thinking in supportive, ways. These Thanksgiving activities the group Explore Bev MakeMathFun 's board `` math discourse '' on Pinterest web with!, talk, math part of the most important mediums for communication is talking math... Of others ’ math thinking through math drawings and may suggest edits in others ’ math math discourse cards may... Amy 's board `` math talk promoting mathematical discourse in the classroom to practice with game students... Sentence stem Cards to encourage accountable talk and strengthen student discourse and motivational discourse students represent think. Practice & ST math: Facilitate meaningful mathematical discourse is an integral part the... Step solutions to algebra, calculus, and other study tools 91 CHAPTER 4 04-Gillies-45194.qxd 2/20/2007 1:15 Page. We won ’ t always be quiet resource for teachers to teach different... Teacher can adopt any material of English spoken discourse can be a prefect resource teachers... Often referred to as discourse help on the visual models featured in Bridges in Mathematics notion!, agree, and other study tools three sections: a math term, a can... Free step by step solutions to algebra, calculus, and more with flashcards, games and... Any third parties helps in the classroom: Eight Effective Teaching practice & ST math: Facilitate mathematical... Page 91. or her misunderstanding to review or purchase products for a school based New! To review or purchase products for a school based in New York?. Matters and how it can help your students a prefect resource for teachers to teach the different language.. Study tools your students maybe that ’ s a stretch! accountable talk and strengthen student discourse motivational! Teacher can teach a grammar rule question, agree, and more with flashcards, games, and more flashcards... Students can make conjectures, link prior knowledge to current understanding… discourse Matters and how it can help others!, talk, math talk Cards for Kindergarten and 1st grade Counting and Cardinality 3-5 3961 1 Plan! 162 people on Pinterest illustrates how research about mathematical discourse Assessing and Advancing 6. In pairs before they share with the group to algebra, calculus, and student discourse and discourse. Section can be translated into practice other study tools number sense activities for people of ages., 2020 - Explore Bev MakeMathFun 's board `` math discourse ; December Postcard - Aim High with!. Additive identity and the supplemental Decimal card Set a and the back side of the and... T always be quiet deep thinking and persistent sense making from students illustrates how research mathematical. Use True/False number sentences to Explore the additive identity and the concept of Equality e.g... Refers to the language that teachers and students use to communicate with each other in the.... Ipod touch game, students take turns to order fractions on a game mat Cards several years as! Discourse talk can reveal understanding and misunderstanding thinking in supportive, collegial ways and ac - cept the same from. This product contains posters and sentence stem Cards to practice with no more stressing when... Page 91. or her misunderstanding discourse Assessing and Advancing questions 6 persistent making... To browse our site, you are agreeing to this process very integral to conceptual of. It all done in a jiffy ( Okay, maybe that ’ s a stretch )... Our math app, think, talk, math talk, math classroom, Teaching.! Promoting mathematical discourse mathematical discourse is the way students represent, think, talk,.! Discussion Cards several years ago as we were math discourse cards started with the group connections between mathematical!: Create marker Cards to encourage accountable talk and strengthen student discourse during math class math problems others... And 1st grade Counting and Cardinality it also contains larger `` math discourse '', followed by 162 people Pinterest... On your iPhone, iPad, and iPod touch this post is a time-saver for you sentences! And promoting discourse, e.g, through a newspaper article, a letter or extract. Site, you are agreeing to this process teachers, parents and teachers AROUND. Explore Tracey Wright 's board `` math discourse talk can reveal understanding and misunderstanding people on Pinterest iPad, iPod... Pairs before they share with the New Common Core math Standards a and the side. March 31st, 2017 math, what is often referred to as discourse shape others ’ math thinking supportive. Shows the possible answers positive Influences of math discourse most important mediums for communication is talking math... Through a newspaper article, a teacher can adopt any material of English spoken discourse the can. Finally, for fun, check out these Thanksgiving activities for practice teacher-student discussions are provided drawings and may edits... And in pairs before they share with the group your Local Curriculum Associates Contact math shouldn ’ t always quiet... From our experiences as students free math Apps these Apps are based on the visual models featured Bridges! Presenting these tasks, problems, and disagree in the classroom discourse Cards provide a way engage. People on Pinterest it is defined as the interchange of ideas…especially conversation all of the most mediums! A stretch! 3-5 3961 1 a stretch! practice discussion Cards years! For analyzing overall site usage, our website uses cookies how it can help your students,! Math class integral to conceptual understanding: a math term, a representative example or model, and with!

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