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Day 2

+Welcome Back Activity

Success, challenge, barrier, breakthrough

Reflect on your experience using one of the assigned tasks in your classroom.

Use separate post-it notes to capture your successes, challenges, barriers, and/or breakthroughs

Post on appropriate poster

Read post-it notes on all posters and select one that resonates with you.

Quick share of selected post-its.

Done early: Update your Classroom Culture reflections

+Reflection

What is your current reality around classroom culture?

What can you do to enhance your current reality?

+Outcomes Day 2: Overall Outcomes on Agenda……Remember the Whole Child! Analyze student work with the Standards for

Mathematical Practice and content standards.

Deepen understanding of the progression of learning and coherence around the CCSS-M Conceptual Category Functions

Understand the SBAC Assessment Claim 4 for Mathematics.

Analyze and adapt tasks with the integrity of the Common Core State Standards.

+

Homework Review

+Collaboration Protocol-Looking at Student Work (55 minutes)

Select one group member to be today’s facilitator to help move the group through the steps of the protocol.

Teachers bring student work samples with student names removed.

1. Individual review of student work samples (10 min)

• All participants observe or read student work samples in silence, making brief notes on the form “Looking at Student Work”

2. Sharing observations (15 min)

The facilitator asks the group

• What do students appear to understand based on evidence?

• Which mathematical practices are evident in their work?

• Each person takes a turn sharing their observations about student work without making interpretations, evaluations of the quality of the work, or statements of personal reference.

3. Discuss inferences -student understanding (15 min)

• Participants, drawing on their observation of the student work, make suggestions about the problems or issues of student’s content misunderstandings or use of the mathematical practices.

Adapted from: Steps in the Collaborative Assessment Conference developed by

Steve Seidel and Project Zero Colleagues

4. Discussing implications-teaching & learning (10 min)

• The facilitator invites all participants to share any thoughts they have about their own teaching, students learning, or ways to support the students in the future.

• How might this task be adapted to further elicit student’s use of Standards for Mathematical Practice or mathematical content.

5. Debrief collaborative process (5 min)

• The group reflects together on their experiences using this protocol.

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+Homework Strategy Sharing

How did your students respond to Think-Pair-Share?

What other strategies did you try out to improve your instructional practice so that student’s had the opportunity to critiquing the reasoning of others?

Say It, Know It Structures handout – choose 1 to try next time.

How did using the Proficiency matrix work? Are there changes you’d like to make?

+Standards of Student Practice in Mathematics Proficiency Matrix

+Digging Deeper: Constructing Viable Arguments & Critiquing Reasoning of Others and Modeling with MathematicsIn table groups

Each person reads one side of the Mathematical Practices (#3 & #4) compilation handouts.

Highlight three new ideas found in your assigned reading

Share in your group. Use these the ideas and what you learned

using the matrix with students to “enhance” the Proficiency matrix on the blank matrix

+Applying your learning

From previous homework: you found/created or adapted to make a rich task.

Have you turned in your item for the Intel CCSS-M Item bank – digital is preferred, hard copy is better than not at all!!!!!

+BREAK TIME!!!

15 minutes….Go

+Functions Progression Cont.

Move back into your brainstorm groups from last session

+FunctionsAssign one Domain to each table group1. Interpret Functions 2. Build Functions or 3. Linear, Quadratic,& Exp

Models

Think: Individually read the Conceptual Category

- Functions overview from CCSS

In Pairs: Brainstorm: What do students need to

know for each of the clusters in your assigned Functions Domain?

Share: In table groups, share your lists with each other & create a “group list”

+Functions: Grade 8

What do students learn about functions in grade 8?

Read Functions Progression, Grade 8 Section

Compare with your group list Notate any items on your group list that are

addressed in grade 8

+Grade 8 Functions Clusters

Major: Define, evaluate and compare functions

Supporting: Use functions to model relationships between quantities

+Functions: Connections

What connections are there between the Functions domains/clusters and the other high school conceptual categories?

Read the CCSS document for assigned function domain Find & enhance details for aligned items on your

group list

+Functions: Connections

What connections are there between the Functions domains/clusters and the other high school conceptual categories?

Look for connections to other high school conceptual categories in the CCSS document—where are the other items from your list? Suggestion: Divide and conquer….. Notate on your list the cluster(s)/standard(s) where

these related items are located in the CCSS

+Functions Domain Poster & Presentation

Meet with other tables working on the same domain.

Poster: Create a poster to represent the information you gathered for your Functions Domain, making sure to include: Key cluster and standard language in the domain Progression of learning from 8th grade Connections to other high school conceptual

categories

Presentation: Select one person to talk about each of the above bullets for @ 2 minutes each

+

Rich Tasks

What makes a rich task? 1. Is the task interesting to students?

2. Does the task involve meaningful mathematics?

3. Does the task provide an opportunity for students to apply and extend mathematics?

4. Is the task challenging to all students?

5. Does the task support the use of multiple strategies and entry points?

6. Will students’ conversation and collaboration about the task reveal information about students’ mathematics understanding?

Adapted from: Common Core Mathematics in a PLC at Work 3-5 Larson,, et al

+Environment for Rich Tasks

Learners are not passive recipients of mathematical knowledge.

Learners are active participants in creating understanding and challenge and reflect on their own and others understandings.

Instructors provide support and assistance through questioning and supports as needed.

+Is this a rich task?

In (a)–(e), determine whether the quantity is changing in a linear or exponential fashion. Be prepared to justify your answer.a. A savings account, which earns no interest, receives a deposit of $723 per month.b. The value of a machine depreciates by 17% per year.c. Every week, 9/10 of a radioactive substance remains from the beginning of the week.d. A liter of water evaporates from a swimming pool every day.e. Every 124 minutes, ½ of a drug dosage remains in the body.

Is this a rich task?

+Old Way of Doing Business MSP PE 7.1.E and CCSS 7.EE.4

Katarina bought n apples. She gave half of the apples to Jens. Then she put some of the apples in sack lunches. After that, she had 1 apple remaining. The equation shown represents this situation.

n/2 – 3 = 1

Solve the equation for n to determine the number of apples Katarina bought.

Write your answer on the line.

 

How many apples did Katarina buy? _____________________ apples

+New Ways of Doing Business SBAC 7.EE.4

David wants to buy 2 pineapples and some bananas.

• The price of 1 pineapple is $2.99.

• The price of bananas is $0.67 per pound.

David wants to spend less than $10.00. Write an inequality that represents the number of pounds of bananas, b, David can buy.

On the number line below, draw a graph that represents the number of pounds of bananas David can buy.

+New Ways of Doing Business

SBAC 7.EE.1 & 7.EE.2

For numbers 1a–1e, select Yes or No to indicate whether each of these expressions is equivalent to 2(2x + 1).

1a. 4x + 2 Yes No

1b. 2(1 + 2x) Yes No

1c. 2(2x) + 1 Yes No

1d. 2x + 1 + 2x + 1 Yes No

1e. x + x + x + x + 1 + 1 Yes No

+New Ways of Doing Business

SBAC 7.EE.1

In the following equation, a and b are both integers. a(3x – 8) = b – 18x

What is the value of a?

What is the value of b?

+Applying your learning

From previous homework: you found/created or adapted to make a rich task.

Find/create or adapt a task to make another rich task

Have you turned in your item for the Intel CCSS-M Item bank – digital is preferred, hard copy is better than not at all!!!!!

+…… are your students this excited by rich tasks?

+

+

SBAC Claim 4

+Let’s do some Math

Work on the Salary Task

Be sure to read the entire problem before getting started

Be prepared for us to call time, even if you are not yet finished.

Using your task analysis worksheet, determine the DOK level(s), CCSS content standard, SMP (Standards for Mathematical Practice)

+ SBAC Assessment Claims for Mathematics

Overall Claim (Gr. 3-8)

Overall Claim (High School)Claim 1

Concepts and Procedures

Claim 2

Problem SolvingClaim 3

Communicating Reasoning

Claim 4

Modeling and Data Analysis

+Claim 4 – Modeling and Data Analysis

A. Apply mathematics to solve problems arising in everyday life, society, and the workplace.

B. Construct, autonomously, chains of reasoning to justify mathematical models used, interpretations made, and solutions proposed for a complex problem.

C. State logical assumptions being used.D. Interpret results in the context of a situation.E. Analyze the adequacy of and make improvement to an existing

model or develop a mathematical model of a real phenomenon.

F. Identify important quantities in a practical situation and map their relationships.

G. Identify, analyze, and synthesize relevant external resources to pose or solve problems.

Claim 4: Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.

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You have information in this location on your handout – check to see how well you determined the DOK, SMP, and content standards.

+Share out - Task Analysis

What content cluster is addressed in this task?

What is the depth of knowledge of this task?

What mathematical practices does it promote?

Is this a rich task?

+

Instructional Actions

+Deepen conceptual understanding using tasks found in your Current Materials

Change the tasks

Use richer tasks provided in your instructional materials (usually found at end of lesson or in “extras” with book)

Adjust existing tasks – raise DOK level

Change how you implement the task

Refer to Standards for Mathematical Practices Compilations for strategies

Think, Pair, Share strategies

Ask good questions: teacher to student, student to teacher, student to student

+DOK 1 Task adjusted to DOK 2 Which statement is true

about the relation shown below?

[1] It is a function because there exists one y-coordinate for each x-coordinate.[2] It is a function because there exists one x-coordinate for each y-coordinate.[3] It is not a function because there are multiple x-values for a given y-value.[4] It is not a function because there are multiple y-values for a given x-value.

Which statements are true about the relation shown below?

[1] It is a function because there exists one y-coordinate for each x-coordinate.[2] It is a function because there exists one x-coordinate for each y-coordinate.

[3] It is a function because it passes the vertical line test.[4] It is not a function.

+Change this DOK 1 task to

DOK 2 or 3

What type of function is shown by the graph at the right?

[1]  linear[2]  exponential[3]  quadratic[4]  absolute value 

Write up on the Intel task sheet.

Find someone at another table to share your task with.

+Critiquing the Reasoning of Others in Action

+Video Task

5 minutes to work on independently

Work in table groups to discuss thinking

Analyze task using task analysis worksheet (from Day 1 – add to bottom of sheet)

Discuss whole group

Watch video

+Looking into a high school classroomInside Mathematics Public Lesso

n: Quadratic Functions

• What makes this activity evidence of critiquing the reasoning of others? Modeling?

• What observable conditions supported critiquing the reasoning of others? Modeling?

• What observable conditions constrained critiquing the reasoning of others? Modeling?

+

Publishers Criteria Shifts

+Key Shifts to look for….

Focus:

Coherence:

Rigor:At your table, choose folks to read one of each of these sections. Underline one sentence from your section that helps you “make sense” of this shift. Share at your table.

+Reflection

What is your current reality around classroom culture?

What can you do to enhance your current reality?

+Wrap up Activity

Evaluations

Handouts, ppts, and items written are located on:

www.psesd-math.wikispaces.com

Thank You!