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All Teachers Reaching All Students

Math DepartmentBanking DayJanuary 24, 2011

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Let’s Do Math!

Explore multiple approaches to demonstrate your solution:

Uncle Eddie asked the girls to order 54 new wheels for the 21 skateboards and bicycles in his repair shop. How many bicycles and how many skateboards are in the shop?

Share your approaches with your group.

Choose one approach to post on chart paper.

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Logistics

Introductions Announcements Norms Learning Log

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Learning Intention

We are learning to deepen our understanding of the Standards and the district’s vision of Instructional Design and Differentiated Instruction and make connections with classroom practice.

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Success Criteria

We will be successful when we can articulate the connections between the Standards, Instructional Design, and Differentiated Instruction and utilize these ideas when planning a math lesson.

Comprehensive Mathematics Framework

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Common Core State Standards

Standards for Mathematical Practice

K – 8 Grade level standardsHigh School standards

“conceptual categories”

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High School Conceptual Categories with Clusters

Number and Quantity The Real Number System Quantities The Complex Number System Vector and Matrix Operations

Algebra Seeing structure in expressions Arithmetic with Polynomials, Rational

Expressions Creating Equations Reasoning with Equations and Inequalities

Functions Interpreting functions Building functions Linear, quadratic and exponential models Trigonometric Functions

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High School Conceptual Categories with Clusters

Modeling Geometry

Congruence Similarity, Right Triangles and Trigonometry Circles Expressing Geometric Properties with Equations Geometric Measurement and Dimension Modeling with Geometry

Statistics and Probability Interpreting categorical & quantitative data Making Inferences & Justifying Conclusions Conditional Probability and Rules of Prob. Using Probability to Make Decisions

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Whip Around

Step 1: Write down or highlight all of the words or short phrases that really stand out to be important as you read the Standard for Math Practice #3.

Step 2: Stand up! One person at a time, read one item that is important to you.

Step 3: When one of your ideas is said (by you or someone else), check it off.

Step 4: When everything on your list is checked off, sit down.

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Standards for Mathematical Practice

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Making Connections

Share and justify your strategies.

Analyze the posters that were created for Uncle Eddie’s Wheels.

Where do you see evidence of the standard we just studied?

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Assessment

Think – Pair – Share

What does assessment mean to you?

What types of assessment do you use in your classroom?

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Instructional CycleInformed by Assessment

Assessment

Plan InstructionContent/process/

product

Model

Guided practiceReadiness/interest/

Learning Inventory

PracticeAnd

Application

Know your students

Rick DuVall

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Assessment for Learning

Assessment for learning is about far more than testing more frequently or providing teachers with evidence so they can revise instruction, although these are part of it.

Richard Stiggins

MMP Learning Team Continuum Aligned with Formative Assessment Principles

(1) Prior to teaching, teachers study and can articulate the math concepts students will be learning.

(2) Teachers use student-friendly language to inform students about the math objective they are expected to learn during the lesson.

(3) Students can describe whatmathematical ideas they are learning in the lesson.

(4) Teachers canarticulate how the math lesson is aligned to district learning targets, state standards, and classroom assessments(CABS), and fits withinthe progression ofstudent learning.

(5) Teachers useClassroom assessments that yield accurate information about student learning of math concepts and skills and use of math processes.

(6) Teachers use assessment information to focus and guide teaching and motivate student learning.

(7) Feedback given to a student is descriptive, frequent, and timely. It provides insight on a current strength and focuses on one facet of learning for revision linked directly to the intended math objective.

(8) Students actively and regularly use descriptive feedback to improve the quality of their work.

(9) Students study the criteria by which their work will be evaluated by analyzing samples of strong and weak work.

(10) Students keep track of their own learning over time (e.g., journals, portfolios) and communicate with others about what they understand and what areas need improvement.

Stage 1Learning Targets

Stage 2Align State Framework and

Math Program

Stage 3Common CABS

Stage 4Student Work on CABS

Stage 5Descriptive Feedback on

CABSUnderstand importance of identifying and articulating big ideas in mathematics to bring consistency to a school’s math program.

Develop meaning for the math embedded in the targets and alignment to state standards and descriptors and to the school’s math program.

Provide a measure of consistency of student learning based on standards/descriptors and targets.

Examine student work to monitor achievement and progress toward the targets and descriptors.

Use student work to inform instructional decisions, and to provide students with appropriate descriptive feedback.

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Looking Back and Looking Forward

Assessment

Plan InstructionContent/process/

product

Model

Guided practiceReadiness/interest/

Learning Inventory

PracticeAnd

Application

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How Does This Look?

Problem-centered teaching opens the mathematics classroom to exploring, conjecturing, reasoning, and communicating.

Lappan, Fey, et al., 2006

What is LESA?

Launch To capture the learner’s attention To activate prior knowledge To stimulate, not stymie, thinking

Explore To become actively involved with the problem, skill, or concept To look for patterns and investigate different strategies To record and organize the work and thinking that is done

What is LESA?

Summarize To lock in the learning To articulate mathematical ideas and vocabulary from the lesson To have students compare and contrast ideas and strategies

Apply To practice what students learned To extend the use of skills and concepts learned To make connections to other learning

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Learning Intention

We are learning to deepen our understanding of the Standards and the district’s vision of Instructional Design and Differentiated Instruction and make connections with classroom practice.

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Success Criteria

We will be successful when we can articulate the connections between the Standards, Instructional Design, and Differentiated Instruction and utilize these ideas when planning a math lesson.

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Let’s Play a Number Game!

Find two numbers that add to 15 and when you subtract them you get 3.

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Let’s Play another Number Game!

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Thinking about the Math

f + s = 163f – s = 33

2f = 196

f = 98

98 + s = 163s = 65

Learning Intention

We are developing our understanding of systems of equations.

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Success Criteria

Given a situation, you can create and solve a system of equations using the elimination method.

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Paper Clips and Pennies

Each pair will be given a set of instructions to complete this investigation as partners.

As a group of four, record and organize the work and thinking that your group completed on chart paper.

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Summarize

Let’s look at those posters.

Given a system of equations, what is necessary to find an answer using the elimination method?

How does what we learned today compare to the strategies that we learned in previous lessons?

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Thinking about the Math

f + s = 163f – s = 33

2f = 196

f = 98

98 + s = 163s = 65

Learning Intention

We are developing our understanding of systems of equations.

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Success Criteria

Given a situation, you can create and solve a system of equations using the elimination method.

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Apply

In your groups, discuss what situations you could give the students to apply their knowledge?

Explain why you chose that situation.

LESA

Launch How did we capture the learner’s

attention? How did we activate prior knowledge? How did we stimulate, not stymie,

thinking?

LESA

Explore How did we become actively involved

with the problem, skill, or concept? How did we look for patterns and

investigate different strategies? How did we record and organize the work

and thinking that is done?

LESA

Summarize How did we lock in the learning? How did we articulate mathematical

ideas and vocabulary from the lesson? How did we have students compare and

contrast ideas and strategies?

LESA

Apply How did we practice what students

learned? How did we extend the use of skills and

concepts learned? How did we make connections to other

learning?

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Learning Intention

We are learning to deepen our understanding of the Standards and the district’s vision of Instructional Design and Differentiated Instruction and make connections with classroom practice.

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Success Criteria

We will be successful when we can articulate the connections between the Standards, Instructional Design, and Differentiated Instruction and utilize these ideas when planning a math lesson.

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Introduction to Differentiation

Read and highlight the important ideas.

Discuss with a partner why differentiation is important in our math classrooms.

Why did the author choose the title, ”The Challenge in Math Classrooms”?

Differentiated Instruction

A strategy that makes it possible to maximize learning for ALL students

A collection of instructionally intelligent strategies based on student-centered best practices

Assists teachers in creating different pathways that respond to the needs of diverse learners

Increases the success of ALL students (including students with disabilities, ELLs and Gifted & Talented)

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Key Components of Successful Inclusive Education

Differentiated Instruction

Co-Teaching/Team Teaching

Common Planning Time

Educating ALL students using their grade level core content standards to the maximum extent possible (Least Restrictive Environment)

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Expected Outcomes of Differentiated Instruction

•High expectations for All students

•Higher academic achievement for All students

•Fewer students in Tier 2 and Tier 3 interventions as well as fewer students referred for special education

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District Definition of DifferentiationDifferentiated Instruction is a concept that makes it possible to maximize learning for ALL students. It is a collection of instructionally intelligent strategies based on student-centered, best practices that make it possible for teachers to meaningfully respond to the needs of diverse learners. It is made possible by modifying the content, process and/or product of instruction of a particular student or small group of students (typically to scaffold and extend learning), rather than the more typical pattern of teaching the class as though all individuals in it were basically the same.  Differentiated instruction is an approach to ensuring all children achieve to the same high standards; instructional approaches are varied, not the expectations or the standards.

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Ways Learners are Different

LEARNING PROFILE INTERESTS READINESS

Social/Emotional Factors:

*Language

*Culture

*Health

*Family Circumstances

*Special Circumstances

Learning Styles

*Auditory

*Visual

*Tactile

*Kinesthetic

Multiple Intelligences

Hobbies

Likes

Dislikes

Skills

*Language Development

*Literacy

*Background Knowledge

*Pre-Assessment

Content

*Formative Assessment

*MAP

Concepts

*Summative Assessment

Ways to Differentiate

Content-What is the standard I am going to teach? What skill am I going to teach?

Process-How am I going to teach that skill in a variety of ways that will hit the developmental levels of each of my students?

Product-What will my student produce as evidence of understanding of the skill?

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Learning Intention

We are learning to deepen our understanding of the Standards and the district’s vision of Instructional Design and Differentiated Instruction and make connections with classroom practice.

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Success Criteria

We will be successful when we can articulate the connections between the Standards, Instructional Design, and Differentiated Instruction and utilize these ideas when planning a math lesson.

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Personal ReflectionsInclude your school name on your index card

An idea that squares with my beliefs. . .

A question or concern going around in my head. . .

A point I would like to make. . .

Lesson Planning with Formative Assessment Principles Date: ______________ Grade: ______________ Lesson: ______________

Part 1: Selecting and Setting Up a Mathematical Task This part contains four critical components that need to be considered when selecting and setting up a mathematical task.

Part 2: Supporting Student Exploration of the Task In this section, construct three questions that will develop the mathematics of the lesson. Be sure to consider the Depth of Knowledge to develop the questions. These questions could be used with students individually or in small groups.

Part 3: Summarizing the Mathematics In this section, construct a question that focuses on orchestrating a whole group discussion of the task that uses different solution strategies produced by the students that highlight the mathematics of the lesson.

1. Important Mathematics to Develop: 2. Learning Target & Descriptors: 3. Lesson Objective in Student Friendly Language: We are learning to… 4. Success Criteria: We know we are successful when…

Q1. Access background knowledge: Q2. Develop understanding of the mathematics by pushing student reasoning: Q3. Summarize the important mathematics in the lesson. This should tie back to the success criteria.

Q. Summarize the important mathematics in the lesson as a whole class discussion. This should tie back to the success criteria.

     

LESSON DESIGN: High School Mathematics

Course: Teacher(s):

Chapter and Lesson # Lesson Name: Date(s):

Lesson Concept(s):

Materials: Teacher Materials, Transparencies

Handouts:

Technology:

Manipulatives/Supplies:

Assessments: Project/Performance Task:

Quizzes and Tests:

Individual or Group Presentation:

Notebook/Portfolio Entries:

Vocabulary Toolkit:

Journal/Closing the Lesson:

Mathematics Standards: Instructional Strategies: Launch:

Questioning Brainstorming Demonstration Inquiry Setting Objectives/Goals Reinforcing Effort Accessing Prior Knowledge Recording Information Graphic Organizers

Explore:

Questioning Cooperative Learning Instructional Technology Presentations/Sharing Problem Solving Compare and Contrast Guided Practice Problem-based Learning Simulations/Modeling Reinforcing Effort Graphic Organizers

Summarize:

Questioning Cooperative Learning Reinforcing Effort Written or Oral Summaries Compare and Contrast Analysis Providing Feedback Discussion Graphic Organizers

Apply:

Questioning Research Problem Solving Presentations and Exhibitions Project Design Connections

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Next Steps…

Ongoing planning at the district and school level

Schools determine their individual school needs

Determine professional development needs at the individual and school level

Move towards more differentiation and inclusive practices at the school and classroom level

54The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership

Academy (MPA), is supported with funding from the National Science Foundation

www.mmp.uwm.edu