1. Welcome Sign in sheet Handouts Cell phones on vibrate Please Sit in Grade Level Groups

2. Math Cadre November 2011

3. Helpful Hints for Distance Learning What a great opportunity to bring us closer together. DL people sit close and zoom in Please turn microphone on and jump in for questions Microphones on for whole group sharing and listening Microphones off for small group work All groups including DL please report out If sound goes down make a sign and show it on camera If connection goes down, phone or text If we do something silly, please do it with us

4. Agenda Name game, and Number Pyramid Activity Dropout rate – read and discuss Analyze student work – read, discuss, analyze What is understanding – read, discuss, math “rules” The Big Five NeSA practice test – take test identify concepts and vocabulary Vocabulary – videos, why, strategies, work session, S.O.M. Writing in math – strategies, websites, student work Lunch and Sharing – websites, writing # song, doubles song (Stephanie), card game for adding polynomials (Julia), Saxon math meeting Subtraction a common thread – 1 st grade Brain Pop (Andrea), 3 rd grade P,P,T (Nan), subtracting using money (Valerie & Jody), integers (Kathy), polynomials (Tanya & Kathy) Split Geogebra or Manipulatives Closure

5. Warm-up Name Game – say name and a favorite math word Pyramid Activity Cut out the triangle Discuss patterns in the chart Use the triangle to create a fact family Make multiplication pyramid Use triangle to create fact family Explore Algebra pyramid

6. Dropout Prevention National High School Center betterhighschools.org More than half of 6 th graders with these 3 criteria eventually left school 1. Attend school less than 80% of the time 2. Receive a low behavior grade 3. Fail either math or English Suggestions: 1. Establish a data system that tracks attendance, grades, promotion status, engagement, and behavior as early as fourth grade 2. Determine criteria for who is off-track and establish a continuum of appropriate interventions

7. Dropout Prevention National High School Center betterhighschools.org Eighth graders who miss 5 weeks of school and fail math or English have a 75% chance of dropping out. There is a window of opportunity in reaching middle grade students who show poor behavior but are not yet failing academic subjects 30% of students who enter High School will not graduate Future dropouts can be identified in the first year of high school Track ninth graders who miss more than 10 days of school Monitor first quarter freshman grades, paying particular attention to core academic subjects

8. Dropout Prevention National High School Center betterhighschools.org Raising high school academic rigor and keeping students in school need not be mutually exclusive Schools that offer fewer courses below Algebra 1 reduce the odds of dropping out by 28% A balance between relevance and rigor will result in more students staying in school Provide: support, extended learning time, catch-up courses, and transitions into high school

9. Student Mistakes Handout – answer the problems, make mistakes you think students would make Read and discuss student miscues Marilyn Burns – About Teaching Mathematics

10. Activity – Looking at Student Work Sort student work into A papers, B papers, and so on Chart and discuss in your groups: a. good things students are doing b. misunderstandings/mistakes c. how students are showing work Determine the ratio of “naked” problems to “real-life / discovering patterns” problems

11. Report Out What did you notice? What did you learn?

12. About Teaching Mathematics Marilyn Burns 1992 When examining student miscues, one often notices that children rely on following recipes rather than reasoning about what is sensible to do. Following recipes results from learning arithmetic as a collection of specific methods / rules / procedures used to arrive at answers, rather than students making sense of the mathematics. Why, in school, is it implied that there is one right way to do arithmetic? And why is the symbolic method used to produce arithmetic results so often separated from the meaning in the situation?

13. What is Understanding? Why don’t students remember math? Why do we end up re-teaching?

14. Reading Understanding by John Van de Walle

15. Continuum of Understanding – Richard Skemp Understanding is a measure of the quantity and quality of connections an idea has with existing ideas. The greater the number of connections to a network of ideas, the better the understanding. Rich interconnected web of ideas Ideas that are isolated and Wow thus without meaning

16. Knowledge learned by rote and/or rules is at the isolated end of the continuum and thus, essentially without meaning. List some math “rules” we teach

17. Report Out What rules did you put on your list?

18. The Big Five Reading Math Procedural Fluency Conceptual Understanding Problem Solving Reasoning Justification Proof Math is Sensible And Worthwhile

19. Conceptual understanding - Comprehension of math concepts, operations and relations Procedural fluency - Knowledge of procedures and skill in performing them flexibly, accurately, and efficiently Strategic competence - Ability to formulate, solve, and represent math problems Adaptive reasoning - Capacity for logical thought, reflection, explanation, and justification Productive disposition - Habitual inclination to see math as sensible, useful, and worthwhile; a belief in one’s own efficacy Rope Model The Big 5

20. The Big Five Do any learning proficiencies match up? Discuss in your groups. Math Conceptual Understanding Problem Solving Reasoning, Justification, and Proof Procedural Fluency Productive Disposition (math is sensible and worthwhile) Reading 1 2 3 4 5

21. Concepts, Problem Solving, Procedures, Vocabulary Take the practice test Note the concepts assessed Circle the Vocabulary

22. Break Restrooms by front door Drinks and treats in the hall Back in 10 minutes please Video Vocab and Goal of the Day http://www.youtube.com/watch?v=S Xwh0A3YP5s&feature=related Video Sentence Frame for Vocab http://mathsentenceframes.wikispac es.com/Sentence+Frames+in+Action

23. Why Vocabulary Instruction? 12 percentile gain with any direct instruction 33 percentile gain with systematic direct instruction of words in passage Marzano et. al. (2001.) Classroom Instruction That Works. Alexandria, VA: McREL.

24. Building Academic Vocabulary A Six-Step Process Mass Practice weekly 1 to 5 new words Learning Words Distributive Practice periodically all previous words Practicing Words 4.Engage students in word activities 5.Discuss words--develop depth 6.Engage student “play” with words-games 1.Introduce word  Student friendly descriptions, examples, explanations, images, etc.  Must connect to students’ prior knowledge 2.Students own words-check for understanding 3.Students create nonlinguistic representation

25. Vocabulary Do’s and Don’ts Do feature a word most days Do intro vocab with daily objective Do define the word, give examples, non-examples, use visuals, synonyms, antonyms Do expect students to use, say, write, and illustrate the word Do hold students accountable – sentence frames, quizzes, draw a picture quiz Do use actions, chants, rhymes, or stories Don’t pass out a long list of words at the beginning of a unit and expect students to memorize them Don’t have students copy definitions out of a dictionary or glossary Don’t “dummy” down the language i.e. Top number instead of numerator Switch around instead of commutative

26. Deliberate Vocabulary Instruction Kids Must Use the Words Actions = 2 years growth Word of the Day Word Wall Vocabulary Cards Personal Dictionary Personal Word Wall Who Has, I Have Game ( play game) Chants, Rhymes, Stories, Songs Sentence Frames & Quizzes, Picture Quizzes Drawings, Photos, Illustrations Foldables

27. Learning Occurs with Engagement Many students are only involved a tiny fraction of their day Actions Stand up - Hands up - Match up Thumbs up, Thumbs down Show on your hand 1 - 5 Think, write, pair, share Yes, no, because Choral responses Chants, rhymes, raps Signaling White boards - sheet protector with white paper inside Ring of Cards Follow with your finger Sky writing Partner share Choose sides and move

28. Saxon Vocabulary Where to find: Page 8 in Test Taking Strategies Guide complete list “Math Language Box” at beginning of every lesson Student reference chart has illustrations and terms

29. Work Session Make some vocabulary activities

30. Stand Out Math Chants Demo Sum means to add repeat Difference means to subtract repeat Product means to multiply repeat Quotient means to divide repeat Fraction means to divide repeat 37 + 24 = _________ 37 – 24 = _________ 37 x 4 = __________ 37 4 = __________ 37 = ___________ 4

31. Chants and Gestures to Remember Math Vocabulary and Concepts http://ww w.standout math.com/ mathlangu age.html http://ww w.standout math.com/ mathlangu age.html Math Language Tab Click for a demonstration

32. Writing to Learn Math - Shana Student understanding will be enhanced with writing prompts that occur before, during, and after an activity. Have students write about their understanding Have students write about their thinking Entrance/exit tickets, journals, explaining, justifying, proving Sentence starters I understand ______, but I am still confused about ______ The two most important things about today are _____ and ______ I know my solution is correct because _______ Today I learned ___, what you do is ______, something tricky is ______

33. Writing to Learn Math Define parallel and perpendicular in your own words How would your describe an improper fraction? Write a paragraph about the graph How do you know 1/4 is larger than 1/5 What properties do triangles have? Links to Writing Activities http://wvde.state.wv.us/strate gybank/WritinginMathematics.html http://wvde.state.wv.us/strate gybank/WritinginMathematics.html http://futureofmath.mistertea cher.com/Writing%20Prompts. pdf http://futureofmath.mistertea cher.com/Writing%20Prompts. pdf Share student examples Student examples

34. Work Session Design a writing activity you could do tomorrow or sometime in the next week.

35. Lunch and Sharing Lunch 20 minute Sharing – websites, writing # song, doubles song (Stephanie), card game for adding polynomials (Julia), Saxon math meeting (Alliance and Garden County) etc. Thanks to our food service staff

36. Websites aplusmath http://www.aplusmath.com/ Cool Math Try Number Games Math Line X Factor http://www.coolmath.com/ Multiplication.com http://multiplication.com/ Counton http://counton.org/ Oswego math http://oswego.org/ocsd- web/games/mathmagician/cathymath.html http://oswego.org/ocsd- web/games/mathmagician/cathymath.html

37. Websites Geogebra Tutorials http://www.screencast.com/users/LFS/folders/GeoGebra%20Lessons Geogebra Lessons http://geogebramath.org/lms/nav/index.jsp Khan Academy (use second link for Khan on PBS) http://www.khanacademy.org/ http://www.khanacademy.org/video/pbs-newshour-on-the-khan- academy?playlist=Khan%20Academy- Related%20Talks%20and%20Interviews http://www.khanacademy.org/video/pbs-newshour-on-the-khan- academy?playlist=Khan%20Academy- Related%20Talks%20and%20Interviews Math is Fun http://www.mathsisfun.com/ KUTA Pre-Al, Algebra, Geometry http://www.kutasoftware.com/free.html

38. Subtraction - Common Thread Subtraction in 1 st grade Andrea LH shows Brain Pop and other activities Subtraction in 3 rd grade Nan LH shows P,P,T Subtraction in 4 th / 5 th Jody & Valerie GC Saxon Math 5 th Grade Book Lesson 9 page 51 Subtraction of integers in 7 th / 8 th grades using 2 color counters Promethean and Smart Board Addition and subtraction of polynomials in 9 th /10 th grades using algebra tiles

39. Subtracting Integers Use of manipulatives Adding is joining Subtracting is removing Promethean Lesson on Integers

40. Adding and Subtracting Positive and Negative Rational Numbers 4 + 3 = -4 + 3 = -4 + - 3 = 4 + -3 = 99 9 9 9 9 9 9 3 - 2 = -3 - - 2 = 3 - - 2 = -3 - -2 = 4 3 4 3 4.2 + 3.1 =-4.2 + 3.1 =-4.2 + -3.1 =4.2 + -3.1 = 6.7 - 2.5 =-6.7 - 2.5 =-6.7 - -2.5 =6.7 - -2.5 =

41. Adding and Subtracting Polynomials Using Algebra Tiles This Lesson is designed for an Algebra Class This is a one day lesson planned for an hour. Materials needed: A class set of Algebra Tiles Overhead Algebra Tiles An Overhead Overhead Markers http://math.buffalostate.edu/~it/ Movies/ddestino.pdf http://math.buffalostate.edu/~it/ Movies/ddestino.pdf

42. Break Restrooms by front door Drinks and treats in the hall Back in 10 minutes please

43. Split into Groups Geogebra with Craig Manipulatives with Kathy

44. Using Manipulatives Keep manipulatives in baggies for quick passing out (poke a hole and the air will go out) Have clear rules – if a student can’t handle it, they lose the opportunity Walk around and watch what they are doing Have a set of overhead or virtual manipulatives so teacher and students can demonstrate Dice in a cup keeps them controlled

45. Saxon Visuals and Manipulatives Embedded in K-3 Alternate Approach in teacher’s guide for 4-6 Adaptations has good written strategies for making connections and showing work Virtual Manipulatives

46. Supplies Needed Play money Two Color Counters Algebra Tiles 1 inch Tiles Small craft sticks, tongue depressors, 4in x 4in paper squares Unifix Cubes 22 circles, 5 different colors, random amount

47. Basic Operations Visual Mathematics Course 1 – Math Learning Center, Salem Oregon One Inch Tiles Show 3 times 4 Dimensions Groups of Commutative property Dimensions first 4 x 6 Show 15 divided by 3 Equal groups, sharing, subtracting Area and 1 dimension 32, 4 Show 9 + 5 Commutative property Show 9 – 5 Take away Difference Count up Count down

48. Averaging Visual Mathematics Course 1 – Math Learning Center, Salem Oregon Unifix Cubes Make 5 columns 4,7,2,9,3 Move cubes to make columns level Make 3 columns of 10,2,7 Make 4 columns 12,6,8,0 Model your GPA Five columns have an average of 8. The smallest column is 4, the largest is 18 Four numbers have an average of 9. Three of the numbers are: 7,11,5 The average of three numbers is 14. One of the numbers is six. Six numbers have an average of 8, but none of the numbers is 8.

49. Doggie Bag and No Left Overs Promethean and Smart Board Put circles into columns of matching colors Record Put circles into even, leveled off towers You should have left overs; what will you do to make the columns even? Record Write 3 math problems for what you did.

50. Place Value Activities Place value chart and money Pre-write, what do you know? Take ten and build it up to 1,000,000 Biggest, smallest digit game Long Division and The Banker Choose a banker Share out the money Write and discuss on worksheet Long division is a perfect way to review place value

51. Modeling Regrouping Use cups and sticks 23 + 8 = 47 + 75 = 329 + 174 = 25 - 8 = 43 - 7 = 84 - 59 = 362 - 175 = 200 - 8 =

52. Closure What is something you will take away from today? It was wonderful to spend the day with caring, math educators. Thank you so much for coming. Evaluations

56. Patient Problem Solving dan@mrmeyer.com blog.mrmeyer.com dan@mrmeyer.com Write, what do you think patient problem solving is? Patient problem solving http://www.youtube.com/watch?v=BlvKWEvKSi8 Algebra problem with video clip http://www.youtube.com/watch?v=k-1_a5rX5P0&feature=related I liked, I would change Stand up - hands up - match up Another idea for problem solving - handout with two problems

57. Use Bar Models Visualize Problems http://www.thinkingblocks.com/ Thinking Blocks.com Li Ping Ma Singapore Math

58. Begin With the End In Mind Backward Design Planning Template McTighe Unit GoalsState Indicators Understandings Vocabulary Essential Questions What students will know and be able to do Informal Assessment Formal Assessment & Tasks Learning Activities

59. Saxon Assessments Cumulative Test – after 5 lessons Power Up Test – after 5 lessons Test Taking Strategies after 5 lessons Test Day Activity Performance Task (these alternate every 5 lessons) Investigations – after 10 lessons Recording forms: Whole class and raw score Individual student item analysis Student facts practice (Need whole class item analysis form) (Need weekly reporting form similar to R.M.)

60. Stopwatch Partners Get up and find a partner Write their name at 15, 30, 45, and 60