ORANGE UNIFIED SCHOOL DISTRICT ELEMENTARY MILD-MODERATE SDC MATH TRAINING MARCH 16, 2014 KATHY LLOYD EANINGFUL PPLICATIONS RANSFORMING ABITS M EANINGFUL A PPLICATIONS T RANSFORMING H ABITS

OUTCOMES ALIGNING MULTIPLE GRADE LEVEL “BIG IDEAS” ALIGNING MULTIPLE GRADE LEVEL “BIG IDEAS” CONCEPTUAL UNDERSTANDING/STEP 2 CONCEPTUAL UNDERSTANDING/STEP 2 STRATEGIES TO HELP STUDENTS DEVELOP NUMBER SENSE STRATEGIES TO HELP STUDENTS DEVELOP NUMBER SENSE MATH ROTATION LAYOUT OPTIONS MATH ROTATION LAYOUT OPTIONS

ACCORDING TO THE NCTM STANDARDS N ATIONAL C OUNCIL OF T EACHERS OF M ATHEMATICS : STUDENTS ARE MORE SUCCESSFUL IN MATH WHEN… STUDENTS ARE MORE SUCCESSFUL IN MATH WHEN… UNDERSTAND THE SIZE OF NUMBERS, UNDERSTAND THE SIZE OF NUMBERS, DEVELOP MULTIPLE WAYS OF THINKING ABOUT AND REPRESENTING NUMBERS, DEVELOP MULTIPLE WAYS OF THINKING ABOUT AND REPRESENTING NUMBERS, USE NUMBERS AS REFERENTS, USE NUMBERS AS REFERENTS, AND DEVELOP ACCURATE PERCEPTIONS ABOUT THE EFFECTS OF OPERATIONS ON NUMBERS.” (P. 80) AND DEVELOP ACCURATE PERCEPTIONS ABOUT THE EFFECTS OF OPERATIONS ON NUMBERS.” (P. 80)

NUMBER SENSE

DOMAINS CONNECTED TO NUMBER SENSE COUNTING AND CARDINALITY COUNTING AND CARDINALITY OPERATIONS AND ALGEBRAIC THINKING OPERATIONS AND ALGEBRAIC THINKING NUMBER AND OPERATIONS IN BASE TEN NUMBER AND OPERATIONS IN BASE TEN NUMBER AND OPERATIONS - FRACTIONS NUMBER AND OPERATIONS - FRACTIONS

ENVISION CONTENT FOCUS & COHERENCE: BIG IDEAS NUMBER USES, CLASSIFICATION, AND REPRESENTATION NUMBERS CAN BE USED FOR DIFFERENT PURPOSES, AND NUMBERS CAN BE CLASSIFIED AND REPRESENTED IN DIFFERENT WAYS NUMBERS CAN BE USED FOR DIFFERENT PURPOSES, AND NUMBERS CAN BE CLASSIFIED AND REPRESENTED IN DIFFERENT WAYS BASIC FACTS AND ALGORITHMS THERE IS MORE THAN ONE ALGORITHM FOR EACH OF THE OPERATIONS WITH RATIONAL NUMBERS. SOME STRATEGIES FOR BASIC FACTS AND MOST ALGORITHMS FOR OPERATIONS WITH RATIONAL NUMBERS, BOTH MENTAL AND PAPER PENCIL, USE EQUIVALENCE TO TRANSFORM CALCULATIONS INTO SIMPLER ONES THERE IS MORE THAN ONE ALGORITHM FOR EACH OF THE OPERATIONS WITH RATIONAL NUMBERS. SOME STRATEGIES FOR BASIC FACTS AND MOST ALGORITHMS FOR OPERATIONS WITH RATIONAL NUMBERS, BOTH MENTAL AND PAPER PENCIL, USE EQUIVALENCE TO TRANSFORM CALCULATIONS INTO SIMPLER ONES

NUMBER USES, CLASSIFICATION, AND REPRESENTATION ALIGNMENT GradeTopics K1, 2, 3, 5,6 1 st 3, 7, 8 2 nd 5, 10 GradeTopics 3 rd 1 4 th 11 5 th 1, 3, 9 6 th 1, 6

BASIC FACTS AND ALGORITHMS ALIGNMENT GradeTopics K 1 st 4, 5, 10, 11 2 nd 2, 3, 6, 7, 8, 9, 10, 11, 14 GradeTopics 3 rd 2, 3, 6 4 th 1, 4, 5, 6, 7, 8,10,12 5 th 2, 3, 4, 5, 6, 7, 9, 11 6 th 4, 5

STEP 2: DEVELOP THE CONCEPT: INTERACTIVE STEP 2: DEVELOP THE CONCEPT: INTERACTIVE 1. Purpose & Connect = Engage & APK 2. Problem = Student Directed Critical Thinking 3. Model = Discussion to Make Explicit. 4. Extend = Deepen Understanding This step is Problem-Based Interactive Learning to engage students in explorations of the key concepts of the lesson. It is broken in 4 parts. Observe Mathematical Practices during PBL Supports conceptual understanding, problem solving, procedural fluency and math discourse (rigor called for in CCSS ) that will help students be more successful

FOR EACH INQUIRY, GIVE STUDENTS TIME TO DISCUSS WITH PARTNER. MONITOR AND FACILITATE STUDENT DISCUSSIONS. THIS IS A GREAT PLACE TO USE RESPONSE FRAMES. FOR EACH INQUIRY, GIVE STUDENTS TIME TO DISCUSS WITH PARTNER. MONITOR AND FACILITATE STUDENT DISCUSSIONS. THIS IS A GREAT PLACE TO USE RESPONSE FRAMES. THERE ARE _____ BIRDS IN THE NEST. EACH ____ STANDS FOR _______ SO ______________. I CAN CHECK BY __________ (YOU CAN MAKE THESE RESPONSE FRAMES FROM THE EXAMPLE ANSWERS) ACADEMIC VOCABULARY & MODEL/DISCUSS TO MAKE EXPLICIT ACADEMIC VOCABULARY & MODEL/DISCUSS TO MAKE EXPLICIT Supports student ability to reason and explain understanding by engaging in math discourse using academic language

ONE WAY TO HELP STUDENTS DEVELOP NUMBER SENSE IS THROUGH NUMBER TALKS. ents A ten minute classroom conversation around purposefully crafted computation problems that students solve mentally By sharing and defending their solutions and strategies, students are provided with opportunities to collectively reason about numbers while building connections to key conceptual ideas in mathematics.

GOALS FOR NUMBER TALKS GOALS FOR NUMBER TALKS 1.DEVELOPING NUMBER SENSE 2.DEVELOPING FLUENCY WITH SMALL NUMBERS 3.SUBITIZING 4.MAKING TENS

OBSERVATION QUESTIONS FOR THE KINDER CLIP How does the teacher build student fluency with small numbers? What questions does the teacher pose to build understanding?

LET’S ENGAGE TENS-FRAME ADDITION PROBLEM: TENS-FRAME ADDITION PROBLEM: 8 + 6

OBSERVATION QUESTIONS FOR THE 2 ND GRADE CLIP What questions does the teacher use to build understanding about decomposing and composing numbers? What strategies are the students using to build meaning of the numbers?

NUMBER TALKS WHAT I CAN USE: DOT IMAGES DOT IMAGES DOUBLES/NEAR DOUBLES DOUBLES/NEAR DOUBLES MAKING TENS MAKING TENS NUMBER SENTENCES NUMBER SENTENCES QUESTIONS I MAY HAVE: APPENDIX B: QUESTIONS AND ANSWERS APPENDIX B: QUESTIONS AND ANSWERS

HOW CAN WE USE THESE MATERIALS FOR STUDENT CENTERED LEARNING?

SDC BALANCED INSTRUCTIONAL DESIGN Teacher Directed Explicit Direct Instruction Student Directed Hands/Interactive Center Step 2 Interactive Learning Number Talks Number sense

KATHY LLOYD K-6 MATH INSTRUCTIONAL SPECIALIST ~ ORANGE UNIFIED SCHOOL DISTRICT EANINGFUL PPLICATIONS RANSFORMING ABITS K-6 MATH INSTRUCTIONAL SPECIALIST ~ ORANGE UNIFIED SCHOOL DISTRICT M EANINGFUL A PPLICATIONS T RANSFORMING H