Henrico County Public Schools New Mathematics Teachers General Math Session How to make your horse thirsty and other stuff you might want to know

Henrico County Public Schools New Mathematics Teachers General Math Session How to make your horse thirsty and other stuff you might want to know

Henrico County Public SchoolsNew Mathematics TeachersGeneral Math Session

How to make your horse thirsty and other stuff you might want to knowAugust 20, 20131:30 p.m. 4:30 p.m.Glen Allen High SchoolIntroductionsNameSchoolTeaching ExperienceObjectivesTo familiarize you with curriculum expectationsTo introduce you to the materials, places, people and processes that can help you do your bestTo teach you how to get what you wantTodays ScheduleIts pretty simpleGeneral InformationCollaborative Teaching/DifferentiationBreakBreakout SessionsMiddle SchoolHigh School

PlanningVDOE Website: http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/review.shtml Curriculum Framework SOL Test BlueprintsKeep in mind, SOLs are the MINIMUM standard.Our textbooks are outdated and do not reflect the new rigor! They should not be your first resource!5PlanningHCPS Math Website: http://blogs.henrico.k12.va.us/math/

Here is the info!6HCPS Secondary Math CoursesOne stop shopping for all your course needs!

Course websitesNew website updates!Well explore more laterCurriculum GuidesPacingVertical ArticulationVDOE Enhanced Scope and Sequence LessonsSOL and Curriculum FrameworkTeacher Notes and Elaboration

Benchmark BlueprintBreakdown of winter benchmark testEach SOL course containsPacing guidesSOL trackerLink to VDOE SOLLink to VDOE mathematics website

2009 Mathematics Standards of LearningRigor has been increasedRepetition has been decreasedRetention and application of content from previous years requiredVertical alignment has been improvedAgain, the textbooks are a resource and should not be relied upon for instruction.

Pay attention to details!

http://teachers.henrico.k12.va.us/math/Teacher/Downloads/NTA/DANCING_BEAR_MOONWALKING_BEAR_CYCLIST_AWARE.wmv SOL TrackerSOL are broken down into a teacher checklistShaded rows are SOL bulletsNon-shaded rows are broken down SOL paragraphs

If you teach to the SOL test

Instructional FocusTo address the increased rigor of the SOL, Henrico Countys instructional focus will be the centered around the NCTM Process Standards.Problem SolvingReasoningRepresentationsCommunicationConnections

The observational focus will be rigor and engagement.

What if cupcakes are the discipline?15Cupcakes are the discipline instead of math!One is not good or bad. They all have a time and place. You want it to be balanced.You dont have to know a lot. Open a box of cupcakes, pull out ingredients and follow instructions. Old multiple choice assessments have been cupcake problems in the pastCook book - More application need to identify food, ingredients, measure, etc. and difficult to do without a cookbookCupcake Wars - four of the countrys top cupcake bakers face off in three elimination challenges until only one decorator remains.with crazy ingredients and they have to make cupcakes not very applicableIron chef In each episode, chefs have one hour to cook and improvise a multi-course meal around a theme ingredient that must be present in each dish. Ex. Today the ingredient is cantelope

16One key question when assessing level of assessment who is doing the work and/or the thinking?Effective QuestioningIs 15 a prime number?Students can answer with a simple Yes or No.What does the students response inform the teacher about the pupils knowledge about prime numbers?Why is 7 an example of a prime number?Not a one-word answer.This requires a student to recall prior knowledge to explain and justify their reasoning.17It provides an opportunity to make an assessment without necessarily asking supplementary questions. The question, Is 15 a prime number? requires follow-up questions to get a full response on which to make an assessment.

The question Why is 7 an example of a prime number? is an example of the general question Why is x an example of y? This is one type of question that is effective in providing assessment opportunities.Course websitesSpend some time in the breakout session and look through the materials and links.

HCPS Teacher Resource PageA lot of links to important documents! http://teachers.henrico.k12.va.us/math/teacher.html

ExamView test banksOnline textbooksCarnegie Learning filesGraphing calculator instructions

Speaking of calculatorsMake sure that the calculator is a TOOL used for instruction!It has become a crutch for many students and teachers.Be accountable for them and have a system for storing and collecting them.Observations/EvaluationsTeacher Evaluation Process focus on process skillsSnapshot observationsTeacher requested observationsTeacher Evaluation Process

STEM Teacher Recruitment and Retention Incentive AwardsHold an active five-year Virginia teaching license (Collegiate Professional or Postgraduate Professional License) with an endorsement in Middle Education 6-8: Mathematics; Mathematics: Algebra I; Mathematics; and be assigned to a teaching position in a corresponding subject area.

Teachers Reassigned from a Fully Accredited School to a Hard-to-Staff School or School Not Fully AccreditedRegardless of teaching experience, be a teacher who is reassigned from a fully accredited school in a Virginia school division to a hard-to-staff school or a school that is not fully accredited in the 2013-2014 school year.

Teachers New to the Profession or Teachers With Up to Three Years Teaching Experience [Applicants must have less than three years teaching experience.]Be a teacher new to the profession (no teaching experience) or a teacher with up to three years of teaching experience (less than three years teaching experience);

Successful teachers selected to participate in the pilot program under this criteria will be eligible to receive a $5,000 initial incentive award after the completion of the first, second, or third year of teaching with a satisfactory performance evaluation and a signed contract in the same school division for the following school year.MEMO #169-13 - Science, Technology, Engineering, and Mathematics (STEM) Teacher Recruitment and Retention Incentive Awards10 Rookie Mistakes to AvoidASCD articlePeople who can help you!You can lead a horse to water, but you cant make him drink

In the past, an acceptable philosophy for educators was:If you lead a horse to water and he doesnt want to drink, its your job to make him thirsty.

The present philosophy for educators goes something like this:Collaborative Teaching/Differentiated LearningMs. Ashley Reyher Collaborative Math Classrooms: Co-teaching Tips and StrategiesCollaborative Math flipchart

Questions?Please contact me about anything!Skip [email protected] sessionsHigh school stays here in room 203Middle school goes to room 205

Breakout optionsChanging Instruction Video Dan Meyer (slide 31) What Can You Do With This (WCYDWT) Video (slide 32)Problem Based Learning Video (slides 33-35)Wordle Activity wordle.net copy/paste standards to create a graphic (slides 36-42)Examine curriculum guide, websites, teacher resource page (slide 43)Four scenarios (slides 44-48)Tasks discussion (slides 49-53)NCTM process standards & Blooms Taxonomy (slides 54-63)Vertical articulation (slide 64)Breaking down the standards wordle (slides 64-73)Teacher Evaluation complete a skills problem and grade on a rubricOther options?

Changing InstructionDan Meyer Math class needs a makeover Today's math curriculum is teaching students to expect -- and excel at -- paint-by-numbers classwork, robbing kids of a skill more important than solving problems: formulating them. At TEDxNYED, Dan Meyer shows classroom-tested math exercises that prompt students to stop and think.http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html

WCYDWT Video(What Can You Do With This)The best motivator of all is connecting math to the real world.

http://teachers.henrico.k12.va.us/math/Teacher/downloads/nta/ESPN_RichEisen.mov The Die Hard with a Vengeance version of teaching Polya's four-step problem solving process

Problem Based Learninghttp://teachers.henrico.k12.va.us/math/Teacher/downloads/nta/die_hard_jugs.mov.wmv 33Was this a worthwhile task?Does the problem challenge students to use higher-level critical thinking skills?Are there multiple ways to solve this problem? Is it accessible to all students?

What process standards were utilized?A critical pointa teacher of mathematics has a great opportunity. If he fills his allotted time with drilling his students in routine operations he kills their interest, hampers their intellectual development, and misuses his opportunity. But if he challenges the curiosity of his students by setting them problems proportionate to their knowledge, and helps them to solve their problems with stimulating questions, he may give them a task for, and some means of, independent thinking.Polya, 1973/194535Lets Wordle the standards!Course 1 Standards37Grade 6

Course 2 Standards38Grade 7

Course 3 Standards39Grade 8

Algebra 1 Standards40

Geometry Standards41

Algebra 2 Standards42

Examine the HCPS Curriculum Guides43http://blogs.henrico.k12.va.us/mathExamine the HCPS online courseshttp://blogs.henrico.k12.va.us/math/courses/Examine the HCPS teacher resource page.http://teachers.henrico.k12.va.us/math/teacher.html

Four Scenarios!!!Read the scenario presentedThink through and jot down answersShare ideas/Ask Questions44Scenario #1You want to experiment with a new teaching method and would like to incorporate manipulatives into your lessons, but you are unsure if it will go over well with your students.

What can you do?What are some possible solutions?Who can assist you with this situation?Scenario #2As a new mathematics teacher, you are assigned a mentor/buddy and are somewhat nervous about your teaching assignment. You are surprised to learn that your mentor, though very nice, does not teach your content. You also learn that the only other teacher who teaches your content is an old grouch who does nothing but complain.

What can you do?What are some possible solutions?Who can assist you with this situation?Scenario #3You and your collaborative partner are not seeing eye-to-eye on classroom management and instruction. The kids are beginning to notice that the two of you are not working as a team.

What can you do?What are some possible solutions?Who can assist you with this situation?Scenario #4Several students are bored with your lesson on solving two-step equations. They start to ask the age old question, Why do we have to learn this?

What can you do?What are some possible solutions?Who can assist you with this situation?

Instruction: Why focus on tasks?Classroom instruction is generally organized and orchestrated around mathematical tasksThe tasks with which students engage determines what they learn about mathematics and how they learn itThere is no decision that teachers make that has a greater impact on students opportunities to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages students in studying mathematics. Lappan & Briars, 199549Rich Mathematical Tasks: The Cornerstone of Rigorous InstructionInstruction: Two tasks.Marthas Carpeting TaskMartha was re-carpeting her bedroom which was 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase?Fencing TaskMs. Browns class will raise rabbits fortheir spring science fair. They have 24feet of fencing with which to build arectangular rabbit pen in which to keepthe rabbits.If Ms. Brown's students want their rabbits to have as much room as possible, how long would each of the sides of the pen be?How long would each of the sides of the pen be if they had only 16 feet of fencing? How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it. 50Rich Mathematical Tasks:Fencing TaskBuild pens with physical materials (linear and area pieces)Draw pens on grid paper (grid paper)Make a table of the dimensions of possible pensMake a graph that shows the relationship between one linear dimension and the area (graph paper or graphing calculator)Set up an algebraic equation and solveInstruction: Tasks - ComparisonSimilaritiesBoth require prior knowledge of areaArea problemsDifferencesWay in which the area formula is used The need to generalizeThe amount of thinking and reasoning required The number of ways the problem can be solvedThe range of ways to enter the problem51Way in which area formula is used -Marthas Carpeting can be solved by knowing and using the area formula but this formula alone is not sufficient to solve the Fencing Task- Marthas carpeting does not lead to a generalization but the Fencing Task doesThe amount of thinking and reasoning required - Marthas Carpeting requires limit thinking and reasoning while the Fencing Task cant be solved without itFencing task might be considered a more equitable task -- for several reasonsBuild pens with physical materials (linear and area pieces)Draw pens on grid paper (grid paper)Make a table of the dimensions of possible pensMake a graph that shows the relationship between one linear dimension and the area (graph paper or graphing calculator)Set up an algebraic equation and solveInstruction: TasksNot all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.Stein, Smith, Henningsen, & Silver, 2000

The level and kind of thinking in which students engage determines what they will learn.Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Oliver, & Human, 1997

If we want students to develop the capacity to think, reason, and problem solve then we need to start with high-level, cognitively complex tasks. Stein & Lane, 199652Task CharacteristicsHigh cognitive demand Significant content (i.e., they have the potential to leave behind important residue)Require justification or explanationMake connections between two or more representationsOpen-endedAllow entry to students with a range of skills and abilitiesMultiple ways to show competence53These last two characteristics can help make a task EQUITABLE -- That is, level the playing field so that students with a wide range of abilities can ENTER a TASK.CommunicationConnectionsProblem SolvingReasoning and ProofRepresentationNCTM Process Standards54NCTM Process StandardsCommunicationUse the language of mathematics to express mathematical ideas precisely. Writing about mathematics.Discussing mathematical ideas.You have eleven fruits in your basket, some are one kind of fruit, and the rest are another kind. How many of each could you have?55NCTM Process StandardsConnectionsBetween different mathematical areasBetween mathematics and scienceBetween mathematics and other subject areas (such as history, literature, and art)Between mathematics and the real worldExampleMr. Goodlock drives to and from Hermitage almost every day. Along the way the posted speed limits range from 30 mph to 65 mph. Mr. Goodlock has logged his daily commute. 56NCTM Process StandardsConnectionsThese are the posted speed limits and the odometer reading at the beginning of each drive segment Mr. Goodlock encounters:Odometer ReadingPosted MPH0602.7557.84511.83518.26524.33027.3Parking LotCalculate the amount of time Mr. Goodlock spends in each speed zone. Make a graph showing your results. Mr. Goodlock usually drives at the posted speed limit. If we assume a trip with no traffic and we ignore time spent at stop signs and traffic lights -- what is the total driving time for Mr. Goodlock's trip?57NCTM Process StandardsProblem SolvingBuild new mathematical knowledge through problem solvingSolve problems that arise in mathematics and in other contexts Apply and adapt a variety of appropriate strategies to solve problems Monitor and reflect on the process of mathematical problem solving

Translation: include one and two-step story problems typically found in textbooks. A school auditorium can seat 648 people in 18 equal rows. How many seats are there in each row?Process: requires solution processes other than computational procedures. Application: computation is generally the solution process used to solve application problems.How many soda cans would it take to fill the school gym?58New Door Problem - Rearrange the 7 letters in New Door to form one word

Process - At an air show, 8 skydivers were released from a plane. Each skydiver was connected to each of the other skydivers with a separate piece of ribbon. How many pieces of ribbon were used in the skydiving act?NCTM Process StandardsReasoningLook at the set shown below. {15, 23, 39, 42}Which number is prime? ReasoningLook at the set shown below. {2a, 3a, 4a, 5a}If a is a prime number, how many members of the set are also prime?Reasoning & ProofRecognize reasoning and proof as fundamental aspects of mathematics Make and investigate mathematical conjectures Develop and evaluate mathematical arguments and proofs Select and use various types of reasoning and methods of proof 59From 2004 Grade 8 SOL testNCTM Process StandardsMathematical RepresentationsCreate and use representations to organize, record, and communicate mathematical ideas Select, apply, and translate among mathematical representations to solve problems Use representations to model and interpret physical, social, and mathematical phenomena

Sam went to a store and spent half of his money. Then he gave one-fifth of what he had left to his sister. Of the amount he had left, he lost half of it. When Sam got home, he had $0.50. How much money did he have before entering the store?

60Sam went to a store and spent half of his money. Then he gave one-fifth of what he had left to his sister. Of the amount he had left, he lost half of it. When Sam got home, he had $0.50. How much money did he have before entering the store?

Blooms Taxonomy

61Blooms Taxonomy76, 79, 75, 77, 74 For the data listed, the value 76.2 represents the

A. Median B. Mode C. Range D. MeanWhat is the mathematics assessed in the item on the right?

Which cognitive level does the question address? 62Grade 6 2006 SOL test, AnalysisAns. DBlooms TaxonomyThe difference in cost between a largebag of chips and a small bag of chipswas $.90. Alicia bought 5 large bags and3 small bags of chips for her party andspent $17.22. What was the cost of asmall bag of chips?F $5.74G $2.49H $2.15J $1.59What is the mathematics assessed in the item on the right?

Which cognitive level does the question address?632006 SOL Algebra 1 test, systemsAns. JExamine the 5-8 Vertical Articulation64Identify the similarities and differences between the grade levelsWhat are the key verbs?Was there anything that surprised you?Breaking Down the 6-8 StandardsList the 5 most important concepts you see in Grades 6 and 7Can you draw a representation of the topics?Number and Number Sense & Computation and Estimation65Grade 6

Number and Number Sense & Computation and Estimation66Grade 7

Number and Number Sense & Computation and Estimation67Grade 8

Measurement and Geometry68Grade 6



Probability, Statistics, Patterns, Functions, and Algebra71Grade 6



Henrico County Public Schools New Mathematics Teachers General Math Session How to make your horse thirsty and other stuff you might want to know

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