Georgia Performance Standards Grades 3 - 5 Mathematics Days 3 and 4: Classroom Implementation

Carmen H. Smith Massie McAdoo, Ph.D. (404) 463-1746 csmith@doe.k12.ga.us Massie McAdoo, Ph.D. (404) 463-6924 mmcadoo@doe.k12.ga.us Georgia Department of Education 1754 Twin Towers East, Atlanta, Georgia 30334

Getting Acquainted Name Card: Name or nickname Contact Information: If you have not been receiving the e-mails please write your name, grade(s) you work with, and e-mail address

Group Norms and Housekeeping Ask questions Work toward solutions Honor confidentiality Meet commitments or let others know if you are struggling Housekeeping: Parking Lot Phone calls Rest rooms Breaks Lunch

Plan to Attend! The National Council of Teachers of Mathematics Annual Conference will be in Atlanta March 21-24, 2007. http://www.nctm.org/meetings/atlanta/ Member cost: $205 Non-member cost: $281

GCTM Annual Conference at Rock Eagle: October 17-19, 2007 Apply to be a speaker and/or plan to attend!

Other Announcements?

Redelivery Reflections At your table, discuss the following 3 items and list them on your chart paper. Successes Questions Concerns

Standards Based Education Model GPS Stage 1 Identify Desired Results (Big Ideas) Enduring Understandings  Essential Questions  Skills and Knowledge (one or more) Standards Elements Stage 2 Determine Acceptable Evidence (Design Balanced Assessments) (To assess student progress toward desired results) All above, plus Tasks Student Work Teacher Commentary Participant’s Guide, page 8 Stage 3 Plan Learning Experiences and Instruction (to support student success on assessments, leading to desired results) All above

Overview of Days 3 and 4 Describing the Standards-Based Classroom Facilitating the Standards-Based Classroom Designing Lessons to Support the Standards-Based Classroom

standards-based mathematics classroom look like? Essential Question1 What does a standards-based mathematics classroom look like?

Math Lab Lesson What did you hear in the news bulletin? Why are some of those things still regarded as controversial?

DOG WASH Four girls offered to wash the neighbor's dog for $5.00. They didn't know how to divide the money. The dog owner said: "I will pay 4/5 of the total amount equally to the four of you. The first one to tell me how much money each child should receive will get 1/2 of the other 1/5 of the cost in addition to their portion of the original 4/5". If someone gave the dog owner the right answer, how did the money get divided up between the children? Did the dog owner pay the full price that the children asked? Why or why not? Write to help explain your best thinking using words, numbers, or pictures.

Birthday Cookout Be able to explain and describe what you see happening during this lesson and task. Think about what needs to take place before children would be able to perform this task.

How many people asked for chicken? How many people asked for steak? Bob turned 60 this year! His family celebrated by having a cookout. Marcy took orders and found one fifth as many people wanted chicken as wanted steaks, one fourth as many people wanted steaks as wanted hot dogs, and one half as many people wanted hot dogs as wanted hamburgers. She gave her son-in-law, the chef, an order for 80 hamburgers. How many people asked for chicken? How many people asked for steak? How many asked for hot-dogs? **Extension: What percent of the guests ordered each type of entrée? Write to help explain your best thinking using words, numbers, or pictures. Be prepared to share!

The Standards What are the……. Key content standards Related content standards Process standards Concepts and skills to maintain

What did you see in this lesson?

What should we see? Warm-up Mini lesson, opening, setting the stage Work period, activity period Summary, closing

Ticket Out of the Room (for AM break) Reflection: One thing I have learned this morning… I am feeling… How I plan to use this new knowledge? Participant’s Guide, page 35

Role of the teacher: Plan authentic learning experiences. Provide solid foundations in math to promote application of skills and knowledge Talk less, listen more.

Role of the teacher: Circulate through the classroom, facilitating math discussions. Provide clarification when necessary. Ask questions that encourage reasoning and making connections.

Role of the teacher: Establish classroom procedures to promote effective management of small groups of differentiated learners. Participate in ongoing assessments of all learners.

Role of the students: Work individually, in pairs, or small groups to complete a task. Gather data, share ideas, look for patterns, make conjectures, and utilize problem-solving strategies.

Role of the students: look for solutions. Explore mathematical relationships and make connections to real life experiences. Ask questions and look for solutions.

What does the teacher do? TRADITIONAL STANDARDS-BASED textbook guides instruction standards and curriculum map guide instruction spends most of the time telling – whole group spends most of the time facilitating – small group seeks the “ONE” right answer from students asks more open-ended / application questions

What does the teacher do? TRADITIONAL STANDARDS-BASED teaches only specific procedures encourages students to use problem solving strategies encourages students’ questions, explanations, and discussions discourages student interaction/discussion asks mostly knowledge-level questions asks more high-level questions

What do the students do? TRADITIONAL STANDARDS-BASED work alone work in flexible groups or pairs focus on only getting the right answer use reasoning to justify their answers and solutions memorize facts for tests understand and apply concepts, as well as, facts Let’s compare the traditional classroom to the standards-based classroom. Remember that these are generalizations!! solve problems and look for real life connections practice procedures

What do the students do? TRADITIONAL STANDARDS-BASED use pencil, paper, and worksheets use manipulatives, graphic organizers, and games show knowledge by writing down numbers show knowledge both orally and written one way to show an answer use multiple representations for solutions (pictures, models, diagrams, words, etc.

What does a standards-based elementary school math classroom look like? Flexible cooperative groups of children Hands-on learning experiences “Productive” noise Differentiated student tasks and products Student work with teacher commentary Multiple representations of solutions Manipulatives, graphic organizers, charts, and graphs Minimal number of worksheets / skill and drill

More and Less LESS whole-class teacher-directed instruction LESS student passivity, sitting, listening, receiving LESS attempts by teachers to cover large amounts of material LESS rote memorization of facts and details LESS stress on competition and grades MORE experiential, inductive, hands-on learning MORE active learning with all the attendant noise of students doing, talking, collaborating MORE deep study of a smaller number of topics MORE responsibility transferred to students for their work: goal-setting, record-keeping, monitoring, evaluation MORE choice for students; e.g., picking their own books, etc. MORE attention to affective needs and varying cognitive styles of students MORE cooperative, collaborative activity. E. D. Hirsch Jr, 1986

Questioning Strategies Questions should play an important role in creating an active learning environment in every classroom. Questioning strategies may be tailored to fit the needs of different subjects, various types of information, and different levels of competence. Questions and questioning techniques influence learners' achievement, attitudes, and thinking skills. Achievement can improve if high levels of questions are accompanied by wait-time, redirection, and probing techniques.

Teacher Questions Plan some questions as you prepare Ask clear, specific questions Use vocabulary students can understand Ask questions from all levels of Bloom's Taxonomy of Educational Objectives Use questions to help students connect important concepts Use questions to give you feedback Allow sufficient time for students to answer Rephrase questions as needed

Student Questions Make it easy for students to ask questions Ask other students to answer Wait for students to formulate their questions Make time for questions Have students formulate questions prior to class

Essential Question 2 What does a well facilitated standards-based mathematics classroom look like?

BASEBALL PIZZA PARTY Your table is going to Mellow Mushroom restaurant to celebrate your baseball team’s big win. You order food for your entire table. The restaurant charges a 6% tax for all food items, and since everyone loved the service, you decide to tip the recommended 20% to your waiter / waitress. Remember to write out your table’s order and to show all of your work. Calculate the total amount for the check (be sure to include tax and tip!) Write all of your work on a poster and be prepared to share.

Baseball Pizza Party Example: Two large all-meat pizzas for $9.99 each = $19.98 Two medium veggie pizzas for $7.88 each = $15.76 Four large waffle fries for $1.79 each = $7.16 Four large drinks = $3.96 Huge ice cream cake = $12.88 Subtotal = $59.74 6% tax = 0.06 X $59.74 = + $3.58 Total (with tax) = $63.32 20% tip = 0.20 X $63.32 = + $12.66 Total Cost (with 20% tip and 6% tax) = $75.98

Well Facilitated Classrooms Teachers must: foster student involvement and cooperation in all classroom activities; establish a productive working environment.

Table Talk What needs to be done in order to foster student involvement and cooperation in all classroom activities? Be prepared to share.

“It takes just as much energy to achieve positive results as it does to achieve negative results. So why waste your energy on failing when that same amount of energy…

… can help you and your students SUCCEED.” Harry K. Wong 1998

“Parents are sending us the best kids they have “Parents are sending us the best kids they have. They are not keeping the good ones at home.” - Larry Lezotte

Routines These are things that students automatically do without the teacher needing to prompt or supervise.

Procedures These must be explained in a clear and concise manner. These must be rehearsed, practiced, done over and over and over again until they become routines! These must be reinforced by reminding the students of the expectation and experiencing it.

“We are what we repeatedly do “We are what we repeatedly do. Excellence, therefore, is not an act but a habit.” ---Aristotle

What is important when developing a lesson plan? Essential Question 3 What is important when developing a lesson plan?

What is important? A focus on learning, rather than teaching Bringing the “big ideas” to life A focus on learning, rather than teaching Helping students to understand, not just remember the understanding of others Incorporating a variety of different teaching strategies

Instructional Planning Be extremely familiar with grade-level standards Lessons Identify standards Determine acceptable evidence Plan instruction

Criteria for Good Tasks Involves significant mathematics Can be solved in a variety of ways Elicits a range of responses Requires communication Stimulates best performance Lends itself to a scoring rubric

Making Instructional Decisions How will we hook and hold student interest? Where are we going? Why? What is expected? How will we equip students to explore and experience? Consider How will we organize and sequence the learning? How will we help students rethink, rehearse, revise, and refine? How will we tailor learning to varied needs, interests, styles? How will students self-evaluate and reflect on their learning?

Multiple Representations Pictures Tables Words Symbols Graphs Demonstrate activities that can be used to support the given standard: Arrays (Pictures) Collections (Words) Repeated Addition (Symbols) Multiplication Table (Tables) Function/ Input-Output Chart (Graphs)

As you work this task, keep in mind what needs to be done to Polygon Percent Task! As you work this task, keep in mind what needs to be done to foster student involvement and cooperation in all classroom activities; and establish a productive working environment.

Polygon Percent Task Cut out the hexagons, triangles, rhombuses, and trapezoids to make your designs. Use polygons to make designs that cover part of the pattern (there are 60 triangles in the design). Make designs that cover at least three of these percentages of the pattern: 20%, 25%, 40%, 50%, 75%, 80%. Activity from : http://www.thefutureschannel.com/pdf/math/polygon_percent_patterns.pdf

“Mighty is geometry; joined with art, resistless.” -Euripides

UNITS ARE JUST BIG PICTURES

My Perfect Saturday Dog Wash Birthday Cookout Baseball Pizza Party Polygon Percents My Perfect Saturday

Pick a Unit Work with a partner or a small group. Decide on a unit for your lesson. Use a task from any previous day of training, one that you currently use in your own class, or is in one of the resources you brought today as your desired result or assessment. Use the four parts of a good lesson to design a lesson.

1st 9 weeks 2nd 9 weeks 3rd 9 weeks 4th 9 weeks Georgia Performance Standards: 3rd Grade Curriculum Map 1st 9 weeks 2nd 9 weeks 3rd 9 weeks 4th 9 weeks Unit 1 2 3 4 5 6 7 weeks 9 Whole Numbers: Addition & Sub-traction Multiplication & Division Geometry Measurement Fractions Decimals Data Analysis Algebra: The Study Of Patterns Putting It All Together All units will include skills to maintain, the Process Standards, and the Algebra strand. Routine topics such as math facts, ordering numbers, calendars, time, money, and patterns should be addressed on an ongoing basis.

All units will include skills to maintain and the Process Standards. Georgia Performance Standards: 4th Grade Curriculum Map 1st 9 weeks 2nd 9 weeks 3rd 9 weeks 4th 9 weeks Unit 1 2 3 4 5 6 7 weeks Place Value, Numeration, & Rounding Multiplication Division Angle Weight Measurement Plane Coordinates, Geometric Figures, Graphs Fractions Decimals Algebra Putting it All Together All units will include skills to maintain and the Process Standards. Routine topics such as estimation, mental computation, basic computation facts, number patterns and rules, and problem solving should be addressed on an ongoing basis.

Georgia Performance Standards: 5th Grade Curriculum Map 1st 9 Weeks 2nd 9 Weeks 3rd 9 Weeks 4th 9 Weeks Unit 1 2 3 4 5 6 weeks 7 Groovy Graphing Divine Decimals Funky Fractions Positively Perfect Plane Figures (2-D) Super Solid Figures (3-D) Putting It All Together All units will include Skills to Maintain, Process Standards, and the Algebra Strand. Routine topics such as add/subtract decimals and fractions with like denominators, whole number computation, angle measurement, length/area/weight, number sense, data usage and representations, characteristics of 2D and 3D shapes and order of operations should be addressed on an ongoing basis.

Sharing Our Lessons Jigsaw Groups

Wrapping Up What have you learned over the past two days? What do you need next? How will you redeliver this module on classroom implementation?

Discussion of Redelivery Action Plan Determine your goal for redelivery. Determine time allotted. Develop timeline of activities. List resources and ideas.

Days of Training Implementation Year One Implementation Year Two Day One: Standards, Content, and Curriculum Mapping Day Two:  Assessment Days Three and Four: Classroom Implementation Implementation Year Two Day Five: Differentiation Day Six: Examining Student Work Day Seven: On-line Survey We don’t have to do it all today!

Assignment Bring student work for the tasks worked today or your own personal tasks along with completed permission forms. Bring four copies of another task from the 3-5 Framework and four copies of student work for that task along with permission forms.

Student Work Sample

Contact Information Carmen H. Smith (404) 463-1746 csmith@doe.k12.ga.us Massie McAdoo, Ph.D. (404) 463-6924 mmcadoo@doe.k12.ga.us Georgia Department of Education 1754 Twin Towers East Atlanta, Georgia 30334

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