Lesson 4 Using Look up Cubes

UNIT4 Microteaching Lesson Plan一、Class Description该班级为初二年级学生，对于出二第一学期的学生来说，他们在经过初一一年的英语学习后，已具有了相当的英语基础，同时也具备一些使用的语言知识的水平。

在这样的基础上，学生对于讨论跟他们生活息息相关的内容很容易产生兴趣，另外，该班的学习风一般，英语水平处于中等。

二、Teaching Materials and Teaching Content人民教育出版社Go for it! 八年级上册, UNIT4 SECTIONB 3a——3c.三、unit target1.Teaching aims（1）. Words and Phrases：1.at the subway station2.around the world =all over the world=the whole world3.3、in North America north adj./n. 北部的，北方（的）--northernadj.4.South adj./n. 南部的，南方（的）--southern adj.5.East adj./n. 东部的，东方（的）--eastern adj.6.west adj./n. 西部的，西方（的）-- western adj.7.Southeast 东南northeast 东北（先南北后东西）8.North China 华北in the north of China 在中国北部9. 4. in other parts of the world10.5. depend on11.6. in big cities12.7 must be13.8. be different from14.9. a lot more fun15.10. a small number of students a number of16.11 .more…than（2）. Sentence Structures：1.-How do you get to school?-I walk to school.-I get to school on foot.2. -How far is it (from your/his/her home to school)?-It’s three miles.-It’s nine kilometers.3. -How long does it take (you/him/her to get from home to school)?-It takes (about) 25 minutes.-It takes (about) one and a half hours.4. That must be a lot more fun than taking a bus.（3）.Learn some reading skills2. Cognitive aimsWith the studying strategies of imitating and drilling，get the students to do reading task，and learn to describe the transportation.3. Emotional：This unit is mainly let the students to know the different kinds of transportation, improve their traffic consciousness. At the same time, enrich the students' study life; know the differences between Chinese culture and foreign culture.四、Difficulties and Key Points1.Reading skills2. Some new words、structures and phrases.五、Teaching ProceduresStep1：.Greeting. (__1__mins)T：Good morning，everyone.S：Good morning，Mr.---.T：How are you?S：I’m fine, Thank you, and you?T：I’m fine, too.（强化交际水平，检查复习学过知识)Step2：lead-in(__3__mins)1. T：How’s the weather today?S：It is rainy and coldT：So，How do you get to school？S1：I go to school by busS2：I go to school by a bike…(对学习过的内容实行复习，为新课埋下伏笔)T：Ok, this is our ways, Do you want to how the students around the world get to school?S：YesT：Ok，today we’ll study how the students around the world get to school?Step3：While-teaching (__35__mins)1. 3a ReadingA. Pre-readingT：Turn to page 23, look at this picture, what can you see?S：A bus and some studentsT：Yes, there’re some students, what are they doing?S：They’re getting off the bus and walk to school.T：Right, very good. Now it’s time to read this passage, before you read it, I have some questions.a. How many countries appeared in this passage?What about them?b. Read the statements about the article and write“T”or “F”Now, you have several minutes to do it!( 给学生提出问题，让学生独立完成阅读篇章，训练学生的阅读水平)B. Post-readingThis part mainly check the answers，can ask some students answer it and then teach the article, give the explanation of some words and sentences，train the ability of practice.T：Times up，Have you finished it？S：YesT：Firstly，how to read a passage？S：…..T：Ok, when you read a passage you should read the questions first and understand them，and when you look at the questions you should circle the“Key words”and then take the questions to read the article.(将阅读技巧渗透,训练学生的阅读技能)C. check the answersT 1. In． North．．． all．．． students take the bus to school.．．．．． America．．．．．．．, notT 2. Other parts of the world are different．．．．．．．．． from the United States.F 3.In Japan．．．．．．．ways of getting to school are bus, train and bike.．．．．．, the three most．．．．popular(Students take trains, or walk, or ride bikes)F 4. In China．．．．．．． means of transportation. (It depends on．．．． popular．．．．．, bikes and buses are the mostwhere you are)T 5. Students in Hongshanhu．．．．．．．．．． and．．．．．．．．．． have to take a boat to get to school.．．． Kaishandao2. 3b Reading and writingLet students look at the chart. Then read the article and fill in the blanks individually..3. 3c WritingJust now we filled in an article about how students get to Garden High School. What about you? How do students in our class get to school? Let’s make a survey and list your ideas on the board. You can use the words and numbers to write a passage about how students in our class get to school.Sample passage：In my class, most students ride their bikes to school. Many students go to school on foot. Some students live far from school, so they go to school by bus. A few students take their parents' car to school.At Guiyang, most students live at school. They just walk to their classroom. So they don’t ride their bikes to school. Many students play on the playground in the early morning. Some students play football. Some read aloud their English texts. But at the same time, other students in other schools have to take the bus, ride the bike, to hurry to their schools.五、Assignment(__1__mins)Write a newspaper article，Tell how students get to your school.六、Blackboard Writing design。

第1篇---Introduction:Starting an English language class with a lively and engaging warm-up activity can set the tone for an entire session. It's a chance to energize your students, break the ice, and get everyone prepared for the learning ahead. This warm-up extravaganza is designed to be fun, interactive, and thought-provoking, ensuring that both teachers and students are ready to dive into the English language with enthusiasm.---Activity 1: "English Charades"Objective: To improve vocabulary and acting skills while fostering teamwork.Materials: Whiteboard or blackboard, markers, and a list of English words related to the upcoming lesson theme.Instructions:1. Divide the class into small teams.2. Write a list of English words on the board that are relevant to the lesson topic.3. Each team takes turns acting out a word without speaking while the other teams guess.4. The first team to guess correctly earns a point.5. Continue until all words have been acted out.---Activity 2: "Word Scramble"Objective: To reinforce spelling and vocabulary skills.Materials: Prepared word scrambles, pens, and paper.Instructions:1. Distribute the word scrambles to the students.2. Each student must unscramble the letters to find the correct word.3. After unscrambling, students can check their answers with a partner or the teacher.4. Discuss the words and their meanings, and use them in sentences.---Activity 3: "The English Alphabet Challenge"Objective: To review the alphabet and encourage creative thinking.Materials: A list of random objects or pictures, one for each letter of the alphabet.Instructions:1. Prepare a list of random objects or pictures, one for each letter of the alphabet.2. Have students stand in a circle.3. The teacher calls out a letter, and the first student to find an object or picture starting with that letter shows it to the class.4. The student then describes the object or picture in English, and the next student must find something starting with the next letter of the alphabet.5. Continue around the circle until the alphabet is complete.---Activity 4: "Role Reversal"Objective: To build confidence and improve speaking skills.Instructions:1. Choose a topic related to the lesson.2. Divide the class into two groups.3. Each group takes turns in a "role reversal" activity.4. One group acts as the teachers, and the other acts as the students.5. The teachers ask questions about the topic, and the students must answer in English.6. After a few rounds, the roles are reversed.---Activity 5: "The English Language Scavenger Hunt"Objective: To encourage teamwork and reinforce vocabulary.Materials: A list of vocabulary words, clues, and a map of the classroom.Instructions:1. Create a map of the classroom with various "clues" leading to different locations.2. Each clue is a piece of vocabulary related to the lesson.3. Students must find the clues, decode them, and use the words in a sentence to reach the next location.4. The first team to reach the end of the scavenger hunt wins a prize.---Conclusion:By incorporating these fun and interactive warm-up activities into your English language classes, you can create an engaging and supportive learning environment. Not only will these activities help to energize your students, but they will also reinforce key language skills and make the learning process enjoyable for everyone involved. Remember, a warm-up is not just about starting the lesson; it's about setting the stage for a successful and memorable learning experience.第2篇---Introduction:Welcome to our English Language Odyssey, a fun and engaging warm-up activity designed to ignite the passion for learning English and foster a positive, interactive atmosphere in our English教研活动. As we embark on this journey, let's get to know each other and our fellow educators, while also warming up our minds and bodies. Get ready to explore, laugh, and learn together!---Activity 1: "The Language Carousel"Objective: To introduce ourselves and learn about each other's language backgrounds.Materials: Large pieces of paper, markers, and a timer.Instructions:1. Divide the participants into small groups of four to six people.2. Give each group a large piece of paper and markers.3. Set a timer for 2 minutes.4. Each person in the group will write a fact about themselves in English on the paper, focusing on their language background, such as the languages they speak, where they are from, or how they learned English.5. After 2 minutes, pass the paper to the next person in the group, who will add another fact.6. Continue this process until the timer goes off.7. Once the timer is up, each group will share their paper with the rest of the participants, and everyone will have a chance to ask questions and learn more about each other.---Activity 2: "Word Bingo"Objective: To review and practice common English vocabulary in a fun, competitive way.Materials: Bingo cards with common English words, a timer, and bingo markers.Instructions:1. Prepare Bingo cards with a grid of squares, each containing a common English word.2. Hand out a Bingo card to each participant.3. Explain the rules: When a word is read aloud by the facilitator, participants must find the word on their card and mark it with a bingo marker.4. The first participant to mark a full line (or a designated pattern) wins a small prize.5. Play multiple rounds, increasing the difficulty by introducing new words or using a mix of English and another language for clues.---Activity 3: "The Language Charades"Objective: To practice speaking and listening skills while having fun.Materials: A list of English phrases or sentences related to common activities, a timer, and a whiteboard or blackboard.Instructions:1. Divide the participants into two teams.2. Write a list of English phrases or sentences on the whiteboard, such as "I'm hungry," "I need a break," or "I can't find my keys."3. Each team takes turns sending a member to the front of the room.4. The member must act out the phrase or sentence without speaking, and their teammates must guess what it is.5. The first team to correctly guess three phrases wins a point.6. Continue playing until one team reaches a predetermined number of points or a set time limit.---Activity 4: "The Story Circle"Objective: To enhance creativity and storytelling skills in English.Materials: A ball or soft object, pens, and paper.Instructions:1. Sit in a circle with the participants.2. Start by throwing the ball to a participant, who must think of a word or phrase in English and write it down.3. Pass the ball to the next person, who must add to the story by thinking of a new word or phrase that connects to the previous one.4. Continue passing the ball around the circle, building a story together.5. Once the ball has been passed around a few times, discuss the story and how it was created.---Conclusion:As our English Language Odyssey comes to an end, we hope that these warm-up activities have not only entertained but also prepared us for aproductive and enjoyable English教研活动. Remember, language learningis a journey filled with laughter, challenges, and discoveries. Let's continue to explore and grow together!第3篇---Introduction:Starting the day with a burst of energy and creativity is essential for any English language teacher. A well-crafted warm-up activity can not only set a positive tone for the class but also help students engage more actively in the learning process. This warm-up extravaganza is designed to be both fun and educational, ensuring that both teachers and students look forward to the English language learning journey.---I. Icebreaker Games (10 minutes)1. "Two Truths and a Lie"- Objective: To build rapport and encourage communication.- How to Play: Each participant writes down three statements about themselves, two of which are true and one that is a lie. The group goes around, sharing their statements, and others must guess which one is false. The person who guesses correctly gets a point.2. "English Scavenger Hunt"- Objective: To introduce new vocabulary and reinforce basic grammar.- How to Play: Divide the class into small teams. Create a list of vocabulary words and grammar concepts related to the upcoming lesson. Teams must find these words or examples around the classroom or school grounds and present them to the teacher.---II. Interactive Warm-Ups (15 minutes)1. "Word Search Challenge"- Objective: To enhance vocabulary and problem-solving skills.- How to Play: Create a word search puzzle with words related to the topic of the day. Students must find and circle the words. As a twist, include some anagrams or hidden phrases to add an extra challenge.2. "Story Starters"- Objective: To improve creative writing and listening skills.- How to Play: Write a sentence on the board and invite students to add their own sentences to create a story. After a few minutes, read the story aloud, and discuss how the story evolved.---III. Group Activities (20 minutes)1. "Role-Playing Scenarios"- Objective: To practice real-life conversations and enhance fluency.- How to Play: Prepare a series of role-playing scenarios based on common situations (e.g., ordering food in a restaurant, asking for directions). Assign different roles to students and let them act out the scenes. Encourage the use of complete sentences and appropriate vocabulary.2. "Grammar Relay"- Objective: To reinforce grammar rules through teamwork and competition.- How to Play: Divide the class into teams. Each team must complete a series of grammar exercises within a time limit. Points are awarded for correct answers. The team with the most points wins.---IV. Collaborative Writing (15 minutes)"Story Cubes"- Objective: To stimulate creativity and collaborative writing skills.- How to Play: Provide each student with a set of Story Cubes. These are dice with pictures on each face. Students must create a story using the images rolled on their cubes. After a few minutes, they can share their stories with the class.---V. Reflective and Closing Activity (10 minutes)"What I Learned Today"- Objective: To encourage self-reflection and share learning experiences.- How to Play: At the end of the warm-up, ask students to write down one thing they learned or found interesting today. They can share these insights with a partner or the whole class.---Conclusion:This warm-up extravaganza for English language teachers is designed to be a dynamic and engaging way to start the learning process. By incorporating a variety of activities that cater to different learning styles and interests, teachers can create an inclusive and enjoyable environment that sets the stage for a successful day of English language instruction. Remember, a warm-up is not just about getting ready for the lesson; it's about sparking curiosity, fostering collaboration, and building a sense of community within the classroom.。

可编辑修改精选全文完整版重大版小学英语四年级下册全册教案重大版小学英语四年级下册全册教案目录Unit1 Where Is My Pencil Box《Lesson1》 (3)Unit1 Where Is My Pencil Box《Lesson2》 (7)Unit1 Where Is My Pencil Box《Lesson3》 (12)Unit2 Welcome to Our Farm《Lesson1》 (16)Unit2 Welcome to Our Farm《Lesson2》 (22)Unit2 Welcome to Our Farm《Lesson3》 (27)Unit2 Welcome to Our Farm《Story corner》 (31)Unit3 There Is a Cake on the Table《Lesson 1》 (37) Unit3 There Is a Cake on the Table《Lesson2》 (42) Unit3 There Is a Cake on the Table《Lesson3》 (45) Unit3 There Is a Cake on the Table《Story corner》 (48) 《Review 1》 (52)Unit4 Whose Cap Is This《Lesson1》 (55)Unit4 Whose Cap Is This《Lesson2》 (61)Unit4 Whose Cap Is This《Lesson3》 (66)Unit5 When Is the Tiger Show《Lesson1》 (69)Unit5 When Is the Tiger Show《Lesson2》 (75)Unit5 When Is the Tiger Show《Story corner》 (78) Unit6 How's the Weather Today《Lesson 1》 (85)Unit6 How's the Weather Today《Lesson2》 (89) 《Review 2》 (95)Unit1 Where Is My Pencil Box?《Lesson1》1新设计Unit1 Where Is My Pencil Box?(Lesson 1 第1课时)2教学目标知识与技能目标:1.能听、说、读、写in on under near desk chair p encil box 词汇。

Explore Section Resources8.4Game LibraryWith the Game Library , students can:• Play a digital version of the games found in the Student Edition, with English and Spanish audio • Have fun practicing math concepts • Choose games by grade band and categoryTEACHAnswer Presentation Tool Digital Examples • Spanish audio ELLDynamic Classroom • Spanish audio ELLEnglish Language Learner Support ELL Game Library • Spanish audio ELLInteractive Tools ELLMulti-Language Glossary ELLNewton & Descartes’s Math Musicals ELL • Differentiated Rich Math Tasks Resources by Chapter • Warm-Up• Extra Practice ELL • Reteach ELL• Enrichment and Extension Skills Trainer ELLVocabulary Flash Cards ELLKey: = emerging = proficient = advancedELL = English Language LearnersASSESSDynamic Assessment System • Practice • Assessments• Point-of-use Remediation ELL • Reports Formative Check Homework App Practice Workbook• Review & Refresh• Evidence-Based Scale Worksheets Self-AssessmentPLANGraphic Organizers ELL Lesson PlansMath Tool Paper ELL Pacing Guide441ALesson 8.48.4Florida BenchmarksNumber Sense and OperationsMA.K.NSO.1.1: Given a group of up to 20 objects, count the number of objects in that group and represent the number of objects with a written numeral. State the number of objects in a rearrangement of that group without recounting.MA.K.NSO.1.2: Given a number from 0 to 20, count out that many objects.Also MA.K.NSO.2.1Count and Write 13 and 14Laurie’s NotesMath OverviewIn this lesson, students count groups of 13 or 14 objects and are introduced to writing13 and 14. You want students to understand they are still counting ones. Each number name is associated with one object as they count. Like the number 10, they need to write two digits to represent 13 and 14.The theme for this lesson is growing vegetables.Materials• linking cubes• Our Vegetable Garden **Found in the Instructional ResourcesDig InGoal: Introduce the numbers 13 and 14.• Show 12 linking cubes. Add one and then two more cubes to introduce the numbers 13 and 14.Hold up the linking cube train for 12. Ask, “How many cubes do you think there are? Why? Tell your neighbor.” Listen for 10 plus 2 more is 12.• Have a student hold the train. “[name], point to each cube as the class choral counts to see whether there are 12 cubes.”Make it obvious that you are placing another cube on the train. “Now how many do you have?” Some students may know the number name 13. “Let’s count together.” Connection: “What is the next number after 12?” 13 “So, 13 is 10 ones and 3 more ones. You have 13 ones.”Distribute the booklet Our Vegetable Garden and ask, “Do you know how vegetables grow?” Discuss growing seeds and what vegetable gardens look like. Read the booklet. Students count aloud the vegetables. Discuss what it means to pull carrots and dig potatoes.• Extension: “Do you cook all vegetables before you eat them?”• Extension: Discuss the rhyming words cook and look and grew and new.• Students bring their booklet from the circle to their seat.FOCUS on Major WorkStudents count 13 or 14 objects in a group and represent the number of objects with the matching written numeral.RIGOR in the Lesson• Conceptual UnderstandingStudents model counting 13 and 14 objects using linking cubes.• Procedural FluencyStudents become fluent in counting objects in a group of 13 or 14 and writing the matching numeral.• Application Selected Examples:°Conceptual applicationExercise 4, page 443 °Real-life applicationExercise 5, page 446Learning Target:Count and write the numbers 13 and 14.Success Criteria:• Count one object for each number to 14.• Write the numbers 13 and 14.441B Chapter 8Where Are We In Our Learning?“You have counted 13 objects.” Discuss that the ten frame is full and there are 3 more onesLaurie’s NotesExplore OverviewGoal: Count to 13.• Distribute linking cubes. “You went to the garden to pull carrots. Place a cube on each carrot.” Pause and then say, “Count aloud the carrots pulled.” Students point and count, “1, 2, 3,” and so on to 13.“Slide your cubes to the ten frame. Where do the extra cubes go?”“So, you have 10 carrots plus how many more?” 3 more carrotsNameExploreGO DIGITALLearning Target: Count and write thenumbers 13 and 14.Count and Write 13 and 148.4Chapter 8 Lesson 4four hundred forty-one441Directions: Place a linking cube on each carrot. Slide cubes to the top frame. Slide the extra cubes to the bottom frame.Number Sense and OperationsMA.K.NSO.1.1: Given a group of up to 20 objects, count the number of objects in that group and represent the number of objects with a written numeral. State the number of objects in a rearrangement of that group without recounting. MA.K.NSO.1.2: Given a number from 0 to 20, count out that many objects. Also MA.K.NSO.2.1© B i g I d e a s L e a r n i n g , L L Cfl_gk_se_0804.indd 44124/02/21 6:55 PMExtensionAdd another cube for one more carrot. Repeat the counting.441Lesson 8.48.4Laurie’s NotesTeaching Notes• Note that the cabbage and beets are arranged in a rectangular array resembling a ten frame, plus some more. Probe to see if students are using this visual support as they count the vegetables.• Model: Together as a class, count the group of 13 heads of cabbage and 14 beets. Finger trace the numbers 13 and 14. Students should be familiar with the verbal pathways for 1, 3, and 4.• Remind students to leave a small space between the digits.Summarize and connect the examples to the learning for today. “You have counted to 13 and 14. You have written the numbers 13 and 14. Tell your partner what you know about these two numbers.” Listen for a group of ten plus 3 or 4 more. You have to write two parts for each number.Preparing to Teach• Introduce the vocabulary cards for thirteen and fourteen and discuss your anchor chart.• 5MTRStructure: “What do you notice aboutyour new numbers?” Listen for the same endings, -teen . Students may ask why threeteen is not used if there is a fourteen. In the English-speaking world, the names for the teen numbers do not make their base-ten meanings evident. Moreover, saying the names fourteen to nineteen reverse the order the digits are written in. Saying the numbers, ten three and ten four as they do in East Asia, makes more sense.Build Understanding13thirteen fourteen14Page 442 in the Student Edition442Chapter 8Where Are We In Our Learning?Review each success criteria and have students use their thumb signals.English Language Learner Support ELL Vocabulary Review Tell students they will be counting to fourteen. Review counting from one to twelve, then add the numbers thirteen and fourteen. It is common for students to pronounce numbers from the teens in ways that sound like multiples of ten. For example, they may pronounce thirteen and thirty similarly. Say the word thirteen and have students repeat. Then say the word thirty and have students repeat. Do the same with the words fourteen and forty .Leveled Proficiency ComprehensionPoint to the cabbage, beets, green beans, and peppers as you say the name of each. Have students repeat. Explain that they are all types of vegetables. You may want to teach them that cabbage is often referred to as a head, such as, “two heads of cabbage.” Have students practice language in pairs. Have one student ask the other a question, such as, “How many green beans are there?” Then have students switch roles asking and answering questions for the other exercises.Beginner: Students may state the answer and the item counted.Intermediate and Advanced: Students may answer using simple sentences, such as, “There are thirteen green beans.”Laurie’s NotesTurn and Talk: “Are there fewer green beans or red peppers? How do you know?” Answers will vary. Listen for understanding 13 and 14 both have 10 plus some more. Do students recall that 3 is fewer than 4? Do students say, “13 comes before 14 when you count”?Write the numbers 13 and 14. “How do you read these numbers?” You want to make sure students are not saying one three and one four.• Supporting Learners: Have students circle a group of ten. Now students can focus on how many more than 10 they have.GO DIGITALDirections: • C ount the vegetables. Say the number. Trace and write the number.• Count the vegetables. Say the number. Write the number.442 four hundred forty-twofourteen14© B i g I d e a s L e a r n i n g , L L Cfl_gk_se_0804.indd 44224/02/21 6:55 PMTeaching TipThe green beans are in a linear arrangement where counting them is more challenging. Students can cross out each bean as they count.442ALesson 8.48.4Scaffolding for All Learners Scaffold instruction to support all students in their learning. Learning is individualized and students may move in and out of these levels with each skill and concept. Student self-assessment and feedback help guide your instructional decisions about how to layer support.ELL R efer to the Explore Section Resources for moreresources available to support all students.EMERGINGStudents are not confident in the counting sequence to 14 and may need objects to touch or manipulate as they count. Prompting of a verbal pathway may be necessary for writing one or more numbers.• Exercise 4: The circular arrangement is challenging. Remind studentsto mark where they are starting so they know what objects remain to be counted.Resources Available:• Resources by Chapter°Extra Practice, pp. 395–396 °Reteach, p. 397Laurie’s NotesScaffolding Instruction: Students have added two number names to their vocabulary. Continue to refer to the anchor chart and vocabulary cards so students associate the words and visual models. Given a collection of 13 objects, can students count them?When students count to 13, can they write the amount? Listen for how students are reading 13 and if they are writing 13 with only a small amount of space between the digits.Chapter 8 Lesson 4NameIn-Class PracticeGO DIGITAL – Count the objects. Say the number. Write the number.four hundred forty-three 443© B i g I d e a s L e a r n i n g , L L Cfl_gk_se_0804.indd 44324/02/21 6:56 PMPage 443 in the Student EditionThe array of broccoli is not in a ten frame arrangement. Students at a glance may assume it is in a ten frame and thus have a wrong count. Be sure students are pointing and counting each vegetable in one-to-one correspondence.443Chapter 8Where Are We In Our Learning?Have students work with a partner and build a linking cube tower of 13 by alternatingcounting while adding a cube to the train. Have them repeat the exercise, building a tower of 14 cubes with the other partner starting the tower.PROFICIENTStudents are able to count one object for each number to 14 and write the corresponding amount.• Exercises 1–4: Pair students. Each decides the object they will begin their count with. They compare the total when they finish.• Exercises 1–4: Listen for correct number names and number sequence.Resources Available:• Resources by Chapter°Extra Practice, pp. 395–396ADVANCEDStudents can count to 14 without difficulty and are fluent in their writing.• Extension: Have students walk around the classroom and identify objects that have the numbers 13 or 14 on them, such as a calendar, room numbers, math wall, or poster. Have them discuss with their partner where they found the numbers.Resources Available:• Resources by Chapter°Enrichment and Extension, p. 398Laurie’s NotesExtensions: Use Number Cards 1–14Instructional Resource. Shuffle and place face down. One student selects a card. Their partner uses this number as the starting number and counts on to 14. Reverse roles.Chapter 8 Lesson 4GO DIGITALDirections: – Count the objects. Say the number. Write the number.four hundred forty-three443© B i g I d e a s L e a r n i n g , L L Cfl_gk_se_0804.indd 44324/02/21 6:56 PMSupporting LearnersThe circular arrangement in exercise 4 can be hard for students to count. Encourage students to mark their starting point, or cross off pumpkins as they count them. Providing linking cubes to place on the pumpkins will also help more concrete learners count.443ALesson 8.48.4Laurie’s NotesModel Real Life OverviewThis application allows students to show their understanding of drawing a model and counting to 14.Supporting Learners: Encourage students to draw the vegetables in an array instead of randomly in the bins. They could draw them as if they were in a ten frame and a five frame. This will help students keep track of the number of cucumbers and corn they have drawn.Model Real LifeDirections: Draw and color 14 cucumbers and 13 ears of corn in the bins. Then write the numbers.GO DIGITAL444 four hundred forty-four© B i g I d e a s L e a r n i n g , L L Cfl_gk_se_0804.indd 44424/02/21 6:56 PMTeaching Tip2MTRModel a Problem: “Exchange drawings with a partner. How many cucumbers did your partner draw? Was the amount easy to count? Explain.” Use this time to display various models. Some are easier to count than others. “When you draw, you are communicating your thoughts. You want others to understand what you are thinking.”Which model is easier to count?Extension“Are there more cucumbers or corn in the bin? How do you know? How many more?”444Chapter 8Solving the Model Real Life ExampleClosure• Draw or display a group of 14 objects. Select a volunteer to count the objects, using a pointer to associate each number with an object. Remaining students clap or tap softly as they hear each number.• “Use a finger to air write the number 14. Pull down . There is your 1. Now pull down a little , across and stop , pull down . There is your 4.”• Repeat for a group of 13 objects. The number path for 3 is pull around and in , around and stop .Where Are We In Our Learning?“You have counted to 14 today. How comfortable are you with your learning? Can you tell your partner how to write the numbers 13 and 14?”Laurie’s NotesProblem Solving for All LearnersStudents may benefit from trying the exercises independently and then working with peers to refine their work. It is important to provide time in class for problem solving, so that students become comfortable with the problem-solving plan.• Plan and Solve: The following notes will help you discuss this problem with students. Preview: “What do you think is happening in the picture? Have you seen a large bin of vegetables sold at a market? Talk to your partner about what you see.”“What shape can you draw for a cucumber or an ear of corn?” Remind students this is not art class. “Draw the vegetables just so someone else would be able to count them.”• Read the directions. Students can draw the vegetables with a pencil or you may choose to have students use crayons or colored pencils to start.Students have drawn a model for 13 and 14. Did they draw one vegetable for each number to 14? Did you notice students drawing a few vegetables and then going back to count how many they had? How did they know when to stop drawing? You want students to talk about their counting and how they know they have 13 or 14.444ALesson 8.48.4Connect and Extend LearningCheck out theDynamic AssessmentSystem at .ExerciseEmerging Proficient Advanced DOK 1DOK 2DOK 31••••2•••3•••4•••5•• Use the results from the exercises to provide differentiated support for all learners.Practice Notes• Remind students to begin with making a group of ten.• Provide students with linking cubes for additional support, if needed.Assignment GuideLearning Target:Count and write the numbers 13 and 14.Success Criteria:• Count one object for each number to 14.• Write the numbers 13 and 14.445A Chapter 8Extend Student LearningVisual-SpatialExplain the term “baker’s dozen.” Tellstudents when bakers need 12 muffins, they often make 13 in case they drop one or one does not turn out well. Give students clay and tell them to make a baker’s dozen, or 13, muffins. Have them count as they make each one and then again after they have finished.Cross-Curricular ConnectionsArtProvide students with a piece of construction paper. Ask them to draw the head of acaterpillar using a tracer or allowing them to free draw. Then, have students create the body of the caterpillar by finger painting 13 dots. Ask students to count each dot aloud as they complete their art project.NameExample8.4PracticeGO DIGITALDirections: and Count the vegetables. Say the number. Write the number.Learning Target: Count and write thenumbers 13 and 14.Directions: Count the linking cubes. Say the number. Write the number.thirteen fourteenChapter 8 Lesson 4four hundred forty- ve445© B i g I d e a s L e a r n i n g , L L Cfl_gk_se_0804.indd 44524/02/21 6:56 PM445Lesson 8.48.4Use the results from the selected problems to provide differentiated support for all learners.ASSESS and DIFFERENTIATEDynamic Assessment System• Practice• Assessments• Point-of-use Remediation ELL • ReportsDynamic Classroom• Spanish audio ELL Formative CheckHomework App Interactive Tools ELLMulti-Language Glossary ELLNewton & Descartes’s Math Musicals ELL• Differentiated Rich Math TasksPractice Workbook• Review & Refresh• Evidence-Based ScaleWorksheetsResources by Chapter• Extra Practice ELL• Reteach ELL• Enrichment and ExtensionSelf-AssessmentSkills Trainer ELLVocabulary Flash Cards ELLKey: = emerging = proficient = advanced ELL = English Language Learners Directions: and Count the vegetables. Say the number. Write the number.Draw 14 heads of lettuce in the dirt. Write the number.GO DIGITAL446four hundred forty-six©BigIdeasLearning,LLC fl_gk_se_0804.indd 44624/02/21 6:56 PM446Chapter 8。

新人教版七年级上册英语教案Unit 4 Where’s my schoolbag?授课班级授课日期授课类型对话课学时数The 2nd period (Section A 2a – 2c)教学目标1. Learn to ask and answer questions about where things are.2. Learn the names of some furniture and some personal things of students.教学内容New words: keys, baseball, computer gameSentences: Is the baseball on the sofa? No, it isn’t. It’s under the chair.重点难点New words: keys, baseball, computer gameSentences: Is the baseball on the sofa? No, it isn’t. It’s under the chair.学情分析教学方法任务型教学、分级评价法、直观教学法、模仿示范法、情景教学和合作学习法学习方法课前预习、课堂内外练习、听说读写结合教学过程设计备注课题引入I. Warming-up and revision.2.Divide the class into Group A and B. Draw two fishes on the blackboard astheir symbols, tell the students that each time they answer questions right, they can get one or more points for their group and draw one or more bubbles around their fish, at the end of the class, the group which gets more bubbles will be the winner today. Say, “One, two, three!” Get the whole class sit straight, thus announce the beginning of the competition.3.Do some exercises: Choose the correct answers.4.Look at some furniture and a flashing backpack, and review the sentencepattern: Where’s…? It’s…5.Look at some furniture and a set of flashing keys, and review the sentencepattern: Where are…? They’re…教学步骤及主要内容II. New sentences:1. Look at the pictures of the balls and learn the new sentence pattern: Is it onthe …? Yes, it is./ No, it isn’t. It’s…2. Practice the new conversations with some pictures.3. Look at more pictures with things in plural forms and learn the new sentencepattern: Are the keys in…? Yes, they are. / No, they aren’t.4. Guessing game:5. Make up your conversations with some pictures: first in parts, then in pairs.III. Listeningthe new words on the first page of Unit 4.game: Show the pictures on the screen with no words. Get student to speak out their names.and do 2a.IV. Conversationsthe students to look at the balls on the screen. Learn the new sentences. Where is the ball? It’s on the is the ball? It’s under the box..Where is the ball? It’s in the box.at the cats and read the conversations.: Look at some pictures and practice the similar conversations.at more pictures and learn new conversations:Where are the…? They are …5. Practice with a picture with many things in both singular and plural forms.课堂练习V. Listeningand do 1b..the answers.for the last time and repeat.VI. Game: Find the differenceat the pictures on Page 21 and Page 19, get students to find the difference.2 pictures of rooms with some furniture: They look similar. Get students to find the difference.小结与作业课堂小结本课作业VII. Homeworkand read after the tape for thirty minutes.the conversation of Section A,3a.down the Chinese meaning of the new words and key sentences, then translate them into English.本课教学后记（课堂设计理念，实际教学效果及改进设想）Unit 4 Where’s my schoolbag?授课班级授课日期授课类型巩固课学时数The 3rd period (Section B 1a –2b)教学目标1. Grasp the prepositions: on, under, in.2. Learn to write a note of taking or bringing things.教学内容✧New words: video tape, alarm clock, math book, hat ✧Sentences: The math book is on the dresser.重点难点video tape, alarm clock, math book, hat The math book is on the dresser.学情分析教学方法任务型教学、分级评价法、直观教学法、模仿示范法、情景教学和合作学习法学习方法课前预习、课堂内外练习、听说读写结合教学过程设计备注课题引入I. Warming-up and revision.the class into Group A and B. Draw two fishes on the blackboard as their symbols, tell the students that each time they answer questions right, they can get one or more points for their group and draw one or more bubbles around their fish, at the end of the class, the group which gets more bubbles will be the winner today. Say, “One, two, three!” Get the whole class sit straight, thus announce the beginning of the competition.1.Look at some pictures and review the sentence pattern: Where’s…? It’s…教学步骤及主要内容II. New words:a)Look at the pictures of Tommy’s room and learn the new words:math book, video tape, alarm clock, hat. And also review somewords.b)Do 1a.c)Close your books and see: How many things can youremember?III. PracticeStudent A: ask questions. Student B: Keep your books closed.A: Wher e’s the notebook?B: It’s on the bed.课堂练习IV. Listeningand do 2a.the answers.and do 2b: Write sentences like this: The math book is on the dresser. Call attention to: The keys are… (plural form)for the last time and repeat.小结与作业课堂小结本课作业VI. Homeworkand read after the tape for thirty minutes.the 6 sentences of 2b.down the Chinese meaning of the new words and key sentences, then translate them into English.本课教学后记（课堂设计理念，实际教学效果及改进设想）Unit 4 Where’s my schoolbag?授课班级授课日期授课类型复习课学时数4th period (SectionB3a—4)教学目标1. Grasp the prepositions: on, under, in.2. Learn to write a note of taking or bringing things.教学内容✧New words: take, bring, need✧Sentences: Please take these things to your sister. Can you bring some things to school? I need my hat,…重点难点Please take these things to your sister. Can you bring some things to school?I need my hat.学情分析教学方法任务型教学、分级评价法、直观教学法、模仿示范法、情景教学和合作学习法学习方法课前预习、课堂内外练习、听说读写结合教学过程设计备注课题引入I. Warming-up and revision.the class into Group A and B. Draw two fishes on the blackboard as their symbols, tell the students that each time they answer questions right, they can get one or more points for their group and draw one or more bubbles around their fish, at the end of the class, the group which gets more bubbles will be the winner today. Say, “One, two, three!” Get the whole class sit straight, thus announce the beginning of the competition.some new words.教学步骤及主要内容II. Presentation:a picture of Lily, a worried girl, and some pictures of her sister and grandma:T explains: Lily is unhappy. She needs some things at school, but they are at home. She calls grandma. But she’s going shopping. Her sister is playing in the park and she’s coming soon. So grandma leaves a note for her sister and asks her to take the things to Lily. Let’s read the note.课堂练习III. Notesa)Read the note of 3a and draw the missing things in the picture.b)Check the answer.c)Language points : take & bring First T explains their differenceand show some examples, then get Ss to make some sentences.d)How to write a note: Explain and show a sample.e)Read 3a again.f)Do 3b: Read and complete the note.g)Check the answer.h)Read the note of 3b.i)Write your own note: Get the Ss who do it quickly to read theirnotes. The others can do it as homework.小结与作业课堂小结本课作业IV. Homeworkand read after the tape for thirty minutes.the note of 3a.down the Chinese meaning of the new words and key sentences, then translate them into English.本课教学后记（课堂设计理念，实际教学效果及改进设想）。

Visual Computer manuscript No.(will be inserted by the editor)Convex Contouring of Volumetric Data Tao Ju1,Scott Schaefer1,Joe Warren1Department of Computer Science,Rice UniversityThe date of receipt and acceptance will be inserted by the editorAbstract In this paper we present a fast,table-driven isosurface extraction technique on volumetric data.Un-like Marching Cubes or other cell-based algorithms,the proposed polygonization generates convex negative space inside individual cells,enabling fast collision detection on the triangulated isosurface.In our implementation, we are able to perform over2million point classifica-tions per second.The algorithm is driven by an auto-matically constructed look-up table that stores compact decision trees by sign configurations.The decision trees determine triangulations dynamically by values at cell ing the same technique,we can perform fast, crack-free multi-resolution contouring on nested grids of volumetric data.The method can also be extended to ex-tract isosurfaces on arbitrary convex,space-filling poly-hedra.Keyword:contour,polygonization,implicit modeling 1IntroductionRecent advances in hardware technology of3D scanning and sensoring has brought about the generation of large-scale volumetric data such as MRI scans,CT scans and geological images.A common approach to visualize these volume datasets is to represent the data as implicit func-tions and construct polygonal approximations of isosur-faces,i.e.locus of points with some given function value. This process is often referred to as contouring.The con-toured surface partitions the whole volume into negative space(locus of points with lower function values)and positive space(locus of points with higher function val-ues).In many interactive applications,such as computer gaming and real-world simulations,navigation is con-fined to the negative space,therefore fast operations for checking the side of the main subject(e.g.the navigator) with respect to the contoured surface becomes critical.These operations are often referred to as collision detec-tions.Traditionally,contouring algorithms consider the data volume in uniform cubical cells and polygonize isosur-faces in each non-empty cell,i.e.,cells that are inter-sected by the isosurface.By doing so,the entire nega-tive space is decomposed into sub-spaces within individ-ual cells.Assuming that the negative space models free space,checking whether a point lies inside the free space can be greatly accelerated if the negative sub-space is convex within the enclosing cell.Note that this point-classification is the fundamental operation for computing collision detection with other convex objects.For exam-ple,an edge lies in the free space if for each cell it passes through,both endpoints of the line segment within that cell lie in the cell’s negative space(figure1left).This observation is not true if the negative space within the cell is non-convex(figure1right).Fig.1Edge classification in a signed square with two dif-ferent contours.The dashed lines indicate the contours,the gray areas represent negative space,and the dark gray lineis the edge to be checked.The most widely used cell-based algorithm is the March-ing Cubes(MC)algorithm introduced by Lorensen and Cline[7].MC generates triangles on isosurfaces within each cell based on a pre-computed table of positive/negative patterns(referred to as sign configurations hereafter)2Tao Ju etal.Fig.2Triangulations from theof cell corners.MC became popular for its fast polygo-nization and easy implementation due to its table-drivenmechanism.However,for some sign configurations,MCdoes not produce polygonizations that are consistentin topology with neighboring cells,and thus result insurface discontinuities[4].This drawback has sparkledextensive research on dis-ambiguation solutions[1],[4],[5],[10]and strategies to generate topologically correctpolygonizations[9].Although these solutions generatetopologically consistent isosurfaces,the resulting nega-tive space inside each cell is sometimes disconnected,andthus not convex.In this paper,we propose a fast table-driven cell-basedcontouring method that generate topologically consis-tent contours,while preserving convexity of the nega-tive space within each cell.The algorithm depends on acomposite look-up table that associates each sign con-figuration with a compact decision tree for dynamic tri-angulation of isosurface patches.The reason for the useof a decision tree is that the actual triangulation de-pends not only on the signs,but also on the magnitudeof corner values.The decision trees are pre-computed toensure a minimal number of tests in determining eachtriangulation.This technique can be extended without difficulty tomulti-resolution contouring.In most multi-resolutionapproaches,direct application of the cell-based contour-ing algorithm to a grid of non-uniform cells can resultin surface cracks,i.e.discontinuity between iso-surfacesgenerated from neighboring cells at different resolutions.Various multi-resolution frameworks have been proposedfor contouring on non-uniform grids[3],[8],[11],[12],[14],yet they involve special crack-patching strategies.Bloomenthal[2]proposes an adaptive contouring methodwhich requires run-time face tracing to maintain con-sistent contours for neighboring cells.We show that byconstructing look-up tables for transition cells using theabove algorithms,the same table-driven contouring methodcan be applied to non-uniform data to generate crack-free isosurfaces.The remainder of this paper is organized as follows.Afterreviewing the table-driven Marching Cubes algrorithm,we present the convex contouring algorithm on uniformgrids.Then we explain the automatic construction oflook-up tables in more detail.Next we extend the pro-posed technique to non-uniform grids to produce crack-free contour surfaces.We conclude by discussing otherpossible extensions and applications.2Marching Cubes and Look-up TablesMarching Cubes is a popular algorithm for extractinga polygonal contour from volumetric data sampled ona uniform3D grid.For each cell on the grid,the edgesintersected with the iso-surface are detected from signsat cell corners.The algorithm then forms triangles byconnecting intersections on those edges(referred to asedge intersections hereafter).To speed up the process,ituses a look-up table that establishes triangulations foreach sign configuration.Since there are8corners in acell,the look-up table contains256entries,four of whichare shown infigure2.Using the look-up table,the Marching Cubes algorithmcontours a cell in two steps:1.Look up the triangulation in the table by the signconfiguration,2.For each triangle,compute the exact location of eachvertex(edge intersection)from values at the cell cor-ners by linear interpolation.The Marching Cubes algorithm is fast because it uses ta-ble look-up to build polygonal contours.Unfortunately,the contoured surface generated by the original look-uptable in[7]may contain holes,since the triangular con-tour within each cell is not always consistent with thatof the neighboring cells(figure3).Although this problem wasfixed in later work,it re-veals another drawback of manually created tables.Theentries in the Marching Cubes’look-up table are con-structed by identifying15topologically distinct sign con-figurations and triangulating each case by hand.The lackof automation makes it susceptible to errors and diffi-cult to adapt to other polyhedrons.As we shall see,thelook-up tables used in convex contouring are constructedalgorithmically based on the topology and geometry ofgiven polyhedrons,and therefore minimizes possible er-rors.Convex3Fig.3Two the Marching Cubes topology.3Convex Contouring Using Look-up Tables The goal of convex contouring is to extract polygonal contours that enclose convex negative spaces within each cell.In this section,we will introduce the concept of con-vex contours and describe the proposed polygonization technique based on a pre-computed look-up table.Ex-amples of convex contouring will be presented together with performance comparison with the Marching Cubes algorithm.3.1Convex contourAssuming that the underlying implicit function is trilin-ear inside each cell,the convex hull of the negative space in a cell is the convex hull of all negative cell corners and edge intersections.The convex contour is the part of this convex hull that lies interior to the cell.In 2D,for exam-ple,the convex contour consists of interior line segments connecting edge intersections (i.e.,dashed lines in fig-ure 1left).In 3D,the convex contour consists of interior triangles whose vertices are edge intersections (figure 4left).Together with the triangles that fill the negative regions on cell faces (figure 4right),they constitute the convex hull of the negative space inside thecell.Fig.4Convex contour on the convex hull of the negative space.Note that the convex contour in a cell is outlined by linear convex contours on the faces of the cell (high-lighted in figure 4).Since the linear convex contour in a2D square is uniquely determined given the signs at the 4corners (allowing movement of the edge intersections along the edges),the polygonal convex contours from neighboring 3D cells always share the same linear con-tour on the common face.Hence convex contours always form topologically consistent isosurfaces.In figure 5,we show the convex contours for the same cells from figure 2.In comparison,we observe that the convex contour always encloses a connected,convex neg-ative space within the cell,whereas the contour from the Marching Cubes algorithm does not.Note that a convex contour is sometimes composed of multiple connected components,as shown in the rightmost cell of figure 5.Each of these connected piece of the contour is called a patch ,which may contain multiple holes (such as the center left cell in figure 5).Each hole on the patch is surrounded by a ring of linear convex contours that can be detected by the signs at the corners.Hence a look-up table for patch boundaries can be constructed automat-ically for each sign configuration.3.2Triangulation and Decision treesUnfortunately,although the boundary of the patches on the convex contour is unique for each sign configuration,the actual polygonization is not.In fact,different scalar values at cell corners,which determine the location of edge intersections,may modify the shape of the convex hull and result in different triangulation of the convex contour.As illustrated in figure 6,two cells that share the same sign configuration,but with different scalars at cell corners,result in different triangulated convexcontours.Fig.6Triangulation in cells with different scalar values at corners.Edge intersections are indicted by gray dots.To determine the correct triangulation based on the lo-cation of edge intersections,one could apply a full-scale convex-hull algorithm to compute the convex hull of the negative space.However,such algorithms are too gen-eral for our purposes,since we want only the part of this convex hull that lies interior to the cell.Instead,we can take advantage of the fact that the topology of the boundary is known for each patch on the convex contour.In fact,we can construct a set S of all possible triangu-lations for each patch.For example,figure 6shows the4Tao Ju etal.Fig.5Convex contours in cells withonly two possible triangulations for the convex contour ofthat sign configuration,since the contour contains a sin-gle4-sided patch.According to Euler’s polygon divisionproblem[6],there are(2n−4)!(n−1)!(n−2)!ways to triangulate an−sided patch into n−2triangles.In fact,this size ofS can be further reduced if we realize that the verticesof these triangles are restricted tofixed cell edges,hencesome triangulations will never appear on the convex hullof negative space.We will discuss this process in detailwhen we describe how the look-up table is constructed.Now we can think of the triangulation problem as thefollowing:given the exact locations of the edge inter-sections,choose an appropriate triangulation from S sothat the triangles satisfy the convex hull property(i.e.,all edge intersections and negative corners lie on one sideof the triangle).Hence we need a fast method to differ-entiate the correct triangulation from others by lookingat the edge intersections.Assuming that triangles on theconvex contour face inside the convex hull of the nega-tive space,we can do this by the following4-point test:given four distinct edge intersections V1,V2,V3,V4,if V4lies on the front-facing side of the triangle(V1,V2,V3),then the inverted triangle(V1,V3,V2)does not belongto the convex contour(figure7left).Similarly,triangles(V1,V2,V4),(V2,V3,V4)and(V3,V1,V4)do not satisfythe convex hull property.Otherwise,by symmetry,weclaim that triangles(V1,V2,V3),(V1,V4,V2),(V2,V4,V3)and(V1,V3,V4)do not lie on the convex contour(figure7right).Note that if all vertices lie on the same plane,either choice can be made.V1V2V3V4V1V2V3V4Fig.7Four-point test with vertices V1,V2,V3,V4.Each4-point test on the edge intersections rules outthose from the set S of all possible triangulations thatcontain any of the four back-facing triangles.Since anytwo triangulations differ at least in the triangles sharedby one of the boundary edge,the correct triangulationcan be distinguished from every other triangulation in Sthrough appropriate4-point tests.For best performance,a decision tree can be built to distinguish each triangula-tion through a minimal set of tests.An example of sucha decision tree is shown infigure8for a5-sided patch.At each node,the remaining triangulations are shownand the4-point test is represented by indices of the fourvertices(the order is shown at the top left corner).If thefourth vertex lies on the front-facing side of the triangleformed by thefirst three vertices(in order),we take theleft branch.Otherwise,we follow the right branch.Theprocess stops at a leaf node,where a single triangulationisleft.2,4,5,13,4,5,12,3,4,52,3,5,11,2,3,412345Fig.8A decision tree using4-point test for5-sided patches.Since the construction of decision trees is based on theoriginal set S,they can be pre-computed and optimizedfor every patch in each sign configuration.As we shallsee,the maximum depth of all these decision trees is5and the average tree depth is1.88.In other words,thecorrect triangulation of the convex contour in a cubic cellcan be determined by performing a maximum of5point-face trials on the edge intersections,and on average nomore than2trials.3.3The look-up tableThe look-up table contains256entries,one for each signconfiguration of a cubic cell.In each entry,the look-uptable stores the decision trees computed for each patchConvex Contouring of Volumetric Data5 Fig.9Two screen shots of a real-time navigation application using a convexly contoured terrain.by traversing the nodes in the decision trees in pre-order. Each non-leaf node contains a4-point test,and each leaf node stores a triangulation.The edge intersections in4-point tests and triangulations are represented by indices of the edges on which they lie.Two example entries in this table are shown in table1,with their correspond-ing sign configurations and edge indexing drawn on the right.3.4Contouring by table look-upsIn comparison with the Marching Cubes algorithm,con-vex contouring extracts the polygonal contour in a cell in two steps:1.Look up the decision trees(one for each patch)in thetable by the signs at the cell corners,2.For each decision tree,perform4-point tests on spec-ified edge intersections until arriving at a single tri-angulation.Fig.10Convex contouring on volumetric data.Infigure10,two sets of volumetric data generated by scan-conversion of polygonal models are contoured us-ing the new method.Observe that the edges on the sur-face are manifold and the contour is crack-less.Since the negative space inside each non-empty cell is convex, collision detection can be localized into cells and there-fore become independent of the grid size.Figure9shows two screen shots of a real-time navigation program in which the movement of the viewer is confined within the negative space.The terrain is an iso-surface constructed using convex contouring on a256cubic grid.On a con-sumer level PC machine(dual1.5GHz processors with 2.5G memory),we achieved over2million point classifi-cations per second.As we mentioned before,the average number of tests used to determine triangulation for each patch is less than2.Hence we can perform convex contouring on vol-umetric data with speed comparable to the Marching Cubes algorithm.In table2,the performance of con-vex contouring is compared with that of the Marching Cubes for contouring the terrain infigure9on differ-ent grid sizes.We also compared the average number of triangles generated in each cell in both methods.Notice that convex contouring generates on average only about 2%more triangles than the Marching Cubes algorithm. These extra triangles are needed to preserve the convex-ity of the negative space.Grid Size Marching Cubes Convex Contouring 1283125ms141ms2563781ms907ms51232109ms2437msAvg.Triangles 3.181 3.257Table2Comparison of total contouring time and average number of triangles per cell in convex contouring and the Marching Cubes.6Tao Ju et al.Index Table Entry Cell Configuration171{1,9,12,7}→4-point test{{1,9,7},{9,12,7}}→Triangulation{{1,9,12},{1,12,7}}123456789101112125{1,3,6,12}→4-point test in parent node{1,12,10,2}→4-point test in left child{{1,3,12},{1,12,2},{3,6,12},{12,10,2}}{{1,3,12},{1,12,10},{1,10,2},{3,6,12}}{1,12,10,2}→4-point test in right child{{1,3,6},{1,6,12},{1,12,2},{12,10,2}}{{1,3,6},{1,6,12},{1,12,10},{1,10,2}}123456789101112Table1Two example entries in the look-up table.Each entry is a list of triangulations(each stored as a list of triangles) and4-point tests(each stored by the indices of the vertices)traversed from the decision tree in pre-roder.4Automatic Construction of Look-up TablesIn this section,we will review the table construction pro-cess in more detail.For a given sign configuration,we first detect the patch boundaries as a group of rings of linear contours.Then,for each patch,we construct the set of all possible triangulations that could take place on the convex hull of the negative space.Finally,an opti-mal decision tree is built for every patch detected on the contour.The look-up table can be found on the web at /jutao/research/contour tables/.4.1Detection of patch boundariesA patch on the convex contour in a cubic cell is bounded by linear convex contours on cell faces.These linear con-tours form single or multiple rings that surround the ”holes”of the patch.Since the linear convex contours are unique on each cell face for a given sign configura-tion,a single ring can be constructed using the following tracing strategy:starting from a cell edge that exhibits a sign change(where an edge intersection is expected) and facing the positive end,look for the next edge with a sign change by turning counter-clockwise on the face boundary.Repeat the search process until it returns to the starting edge,when a closed ring is formed(seefigure 11).Notice that face-tracing produces oriented linear convex contours on each cell face.Each linear contour on the cell face is directed so that the negative region on that face lies to its left when looking from outside.There-fore the triangles on the convex contour of the cell that share these linear contours will face towards the nega-tive space.The orientation of the rings are importantfor linear contours already built,and dashed arrows indicate the tracing route.determining the set of possible triangulations that share the same patch boundary.Similar tracing techniques have been described by nu-merous authors in[2],[9],[13],in which convexity of the negative region on each cell face is preserved.These algo-rithms construct a single ring for each patch boundary. However,the problem remains on how to group multiple rings to form the boundary of a multiple-genus patch (such as the center left cell infigure5).Although such patches arise in only4cases among256sign configura-tions,they may appear much more often in other non-cubic cells(such as transition cells in multi-resolution grids,see Section6).We need to be able to identify these cases automatically from the sign configuration and group the rings appropriately.By definition,a patch is a continuous piece on the con-vex hull of negative space.Hence it also projects onto a continuous piece of regions on the cell faces.These regions are positive areas that surround positive cor-Convex Contouring of Volumetric Data7ners connected by cell edges.Therefore the boundary of each patch on the convex contour isolates a group of positive corners that are inter-connected by cell edges. The previous face-tracing algorithm could be modified so that rings constructed around a same edge-connected component of positive corners are grouped to form the boundary of a single patch.This rule is demonstrated in figure12.In the top left cell,two rings of linear contours form the boundary of two patches,due to the presence of two isolated positive corners.In the top right cell,where there is only one edge-connected component of positive corners,the two rings are grouped to form the bound-ary of a single cylinder-like patch.The connectivity of the positive corners in these two cells are illustrated at the bottom offigure12.In contrast,face-tracing without ring-grouping would give the same result in both cells, thus violating the convex hull property in the secondcell.Fig.lighted)to form boundaries of patches.Positive corners are colored gray.Bottom:Connectivity graph of positive corners 4.2Pre-triangulation of Convex ContourThe set of possible triangulations for a patch with an oriented boundary topology can be enumerated by re-cursive algorithms.However,this often results in redun-dant triangulations that never appear on the convex con-tour.For example,the genus-2patch in the center left cell infigure5can be triangulated in only one way on the convex hull of the negative space,regardless of the magnitudes of scalar values at the corners.In contrast, brute-force enumeration would return21possible trian-gulations for an arbitrary genus-2patch with two trian-gular holes.The key observation is that,the patches on the convex contour are not arbitrary patches,their ver-tices(edge intersections)are restricted tofixed edges on the cell.These spacial restrictions limit the number of possible triangulations that could occur on the convex contour.For fast polygonization at run-time,we hope to pre-triangulate each patch as much as possible during table construction,based only on the sign configuration. By the convex hull property,the half-space on the front-facing side of a triangle on the convex contour must con-tain(or partially contain)every other cell edge that ex-hibits a sign change.Note that the three vertices of the triangle can move only along threefixed cell edges,this half-space is always contained in the union of the half-spaces formed when the three vertices are at the ends of their cell edges.Hence we have a way to identify triangles that will not appear on the convex contour:given three cell edges(C1,C2),(C3,C4)and(C5,C6)(C i are cell cor-ners),construct border triangles,i.e.,triangles formed by one end of each edge in order(such as(C1,C3,C5)).If there is an edge on the cell exhibiting a sign change that lies completely to the back of all non-degenerate border triangles,any triangle whose vertices belong to these three edges(in order)will not lie on the convex con-tour.This idea is illustrated infigure13.The highlighted cell edge on the left exhibits a sign change,and lies to the back of all the border triangles constructed from the three dashed edges(E1,E2,E3).Hence the dashed trian-gle formed by intersections on those edges never appears on the convex contour.In contrast,the highlighted cell edge on the right lies partially to the front of at least one of the border triangles formed by the edges(E1,E2,E3), hence the dashed triangle may exist in the triangulation of the convex contour.E1E2E3E1E2E3Fig.13Identifying triangles that do not lie on the convex contour.By eliminating triangulations that contain these ineli-gible triangles,we can trim down the space of possible triangulations.For example,the number of remaining triangulations for thefirst three cells infigure5are re-spectively4,1and4.4.3Construction of decision treesEven after pre-triangulation,some patches still have many potential triangulations on the convex hull of the nega-tive space.To speed up the polygonization at run-time,8Tao Ju et al.we can pre-compute a set of4-point tests on the vertices of the patch(edge intersections)to distinguish between the remaining triangulations.These tests can be orga-nized in a decision tree structure,introduced in the last section.Different sets of tests result in differently shaped decision trees.To obtain optimal performance,we imple-ment a search algorithm that looks for the optimal set of tests that produces a decision tree with the small-est depth.Since each of the two outcomes of a single test eliminates a non-intersecting subset of the remain-ing triangulations,the minimal depth of the correspond-ing decision tree is lower bounded by log2N,where N is the total number of triangulations.For example,the depth of an optimized decision tree for a patch of length 4,5and6are1,3and5respectively.Further computa-tion reveals that the maximum length of a patch(which can not be pre-triangulated)in a cubic cell is6;hence any patch can be triangulated within5point-face trials on thefly by walking down the pre-computed decision tree.On average,however,it only takes1.88tests to de-termine the triangulation of a patch,due to infrequent occurrence of large patches and the reduced triangula-tion space as a result of pre-triangulation.5Multi-resolution Convex ContouringIn volume visualization,the number of polygons gener-ated by uniform contouring easily exceeds the capacity of modern hardware.For real-time applications,it is often advantageous to display the geometry at different lev-els of detail depending on the distance from the viewer. This technique has the advantage that it speeds up the rendering process without sacrificing much visual accu-racy.By using a view-dependent approach,the grid is contoured at different resolutions depending on the dis-tance from the navigator.In particular,we can create a series of nested bounding boxes centered at the viewer, with the grid resolution decreasing by a factor of2.A2D example of this multi-resolution framework is shown infigure14left,in which a circle is contoured using cell grid at two different resolutions.When the coarse cells at the top meet thefine cells at the bottom,the con-tour in the coarse cells need to be consistent with the contour from the neighboringfine cells on the common edges.We call these coarse cells transition cells,which are adjacent to cells at afiner resolution.A2D transition cell thus hasfive corners andfive edges,as shown in the middle offigure14.By connecting edge intersections on each cell edge,the transition cells can be contoured in a way similar to a regular4-corner cell,yielding consistent contours with the adjacentfine cells.Some of the con-toured example are shown infigure14right.Notice that the convexity of the negative region is still preserved in each transition cell.In3D,a transition cell between two resolutions is either adjacent to twofine cells on an edge,or adjacent to four fine cells on a face(seefigure15left).These two types of cells can be regarded as convex polyhedrons with9 corners(figure15center)and13corners(figure15right) respectively.Since the previous discussion on regular cells applies to any convex polyhedron,we can also build look-up ta-bles and perform convex contouring on these transition cells.In this way,crack-free surfaces can be contoured on nested grids within the same framework as uniform contouring.5.1Convex contours in transition cellsAs in a regular cell,the convex contour inside a tran-sition cell is outlined by the linear contours on the cell faces.Since the linear convex contour is unique on each face for a given sign configuration,the boundary of patches on the convex contour can be pre-computed using the proposed face-tracing algorithm.At the top offigure16, the oriented boundaries of patches in different transition cells are detected and drawn as dashed arrows.Since con-vex contours from neighboring cells in a multi-resolution grid always share the same linear contour on the com-mon face as their boundaries,topological consistency is preserved everywhere on the contouredsurface.Fig.16Patch boundaries(top)and triangulation(bottom) in three transition cells.By pre-computing optimal decision trees for each patch, the triangulation can be determined by applying succes-sive4-point tests on the edge intersections.At the bot-tom offigure16,patches detected from the cells on the top are triangulated on the convex hull of the negative space.However,due to the presence of four co-planar faces on a13-corner cell,this convex hull could degener-ate onto a plane(figure17left).To determine the correct triangulation of the convex contour on the degenerate convex hull,we introduce an outward perturbation to。

Unit 11 ShapesMy target 学习目标1.学习和掌握表示形状的词汇：circle(圆形), square(正方形), star(五角星形)。

2.会用所学的单词和句型It’s a…准确的描述生活中物品的形状。

3.会熟练运用句型How many…?来询问数量，并用There be句型准确回答。

How many squares are there? 有多少个正方形？□□There are two squares. 有两个正方形。

4.正确书写单词：picture, square, circle, star ,today, well5.复习巩固五个元音字母在单词中的发音，做到发音准确、到位。

My notebook 课堂笔记Listen and sayMiss Fang: Look at the picture. 方老师：看这幅图。

How many squares are there? 里面有多少个正方形？Joe: There are two squares. 乔：有两个正方形。

Miss Fang: How many circles are there? 方老师：有多少个圆？Peter: There are six circles. 彼得：有六个圆。

Miss Fang: How many stars are there? 方老师：有多少个五角星形？Kitty: There is one star. 基蒂：有一个五角星形。

Miss Fang: How many rectangle and triangles are there? 方老师：有多少个长方形和三角形？Alice: There are nine rectangles and one triangle. 艾丽丝：有九个长方形和一个三角形。

1.Look at the picture. 看这幅图。

Look at的意思是“看一看”，强调看的动作，后面可以直接跟名词。