ORANGE UNIFIED SCHOOL DISTRICTELEMENTARY MILD-MODERATE SDC

MATH TRAINING2014-2015

MARCH 16, 2014

KATHY LLOYD

MEANINGFUL APPLICATIONS TRANSFORMING HABITS

OUTCOMES

• ALIGNING MULTIPLE GRADE LEVEL “BIG IDEAS”

• CONCEPTUAL UNDERSTANDING/STEP 2

• STRATEGIES TO HELP STUDENTS DEVELOP NUMBER SENSE

•MATH ROTATION LAYOUT OPTIONS

ACCORDING TO THE NCTM STANDARDS NATIONAL COUNCIL OF TEACHERS OF MATHEMATICS

: STUDENTS ARE MORE SUCCESSFUL IN MATH WHEN…

• UNDERSTAND THE SIZE OF NUMBERS,

• DEVELOP MULTIPLE WAYS OF THINKING ABOUT AND REPRESENTING NUMBERS,

• USE NUMBERS AS REFERENTS,

• AND DEVELOP ACCURATE PERCEPTIONS ABOUT THE EFFECTS OF OPERATIONS ON NUMBERS.” (P. 80)

NUMBER SENSE

DOMAINS CONNECTED TO NUMBER SENSE

• COUNTING AND CARDINALITY

• OPERATIONS AND ALGEBRAIC THINKING

• NUMBER AND OPERATIONS IN BASE TEN

• 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

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

NUMBER USES, CLASSIFICATION, AND REPRESENTATION ALIGNMENT

Grade TopicsK 1, 2, 3, 5 ,6

1st 3, 7, 8

2nd 5, 10

Grade Topics

3rd 1

4th 11

5th 1, 3, 9

6th 1, 6

BASIC FACTS AND ALGORITHMS ALIGNMENT

Grade Topics

K

1st 4, 5, 10, 11

2nd 2, 3, 6, 7, 8, 9, 10, 11, 14

Grade Topics3rd 2, 3, 6

4th 1, 4, 5, 6, 7, 8,10,12

5th 2, 3, 4, 5, 6, 7, 9, 11

6th 4, 5

STEP 2: DEVELOP THE CONCEPT: INTERACTIVE

1. Purpose & Connect = Engage & APK2. 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.

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

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.

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

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: 8 + 6

OBSERVATION QUESTIONS FOR THE 2ND 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

• DOUBLES/NEAR DOUBLES

• MAKING TENS

• NUMBER SENTENCES

QUESTIONS I MAY HAVE:

• APPENDIX B: QUESTIONS AND ANSWERS

HOW CAN WE USE THESE MATERIALS FOR STUDENT CENTERED LEARNING?

SDC BALANCED INSTRUCTIONAL DESIGN

Teacher DirectedExplicit Direct Instruction

Student DirectedHands/Interactive Center

Step 2 Interactive

Learning

Number Talks Number

sense

KATHY LLOYD K-6 MATH INSTRUCTIONAL SPECIALIST ~ ORANGE UNIFIED SCHOOL DISTRICT

MEANINGFUL APPLICATIONS TRANSFORMING HABITS

klloy@orangeusd.org