Please READ the article “The Five Keys”and fill out the Graphic Organizer while you wait to begin.

Math Content Math Content Network Network MeetingMeetingOctober 25, 2011

Facilitators

Our Norms Be present and engaged in our

work. We are equal partners. Seek first to understand and then to

be understood. Stay positive. Respect ideas of others. One voice rule – no private

conversations. Be productive. Be flexible and willing to change.

Where Am I Going?

Where Am I Now?

How do I Get There?

What do you feel comfortable with? What questions do you have?

October Math Teacher Leader Network Targets

I can describe the design and purpose of a Formative Assessment Lesson

I can provide justified connections among the FAL 5 strategies, 7 strategies of formative assessment, and CHETL.

I can provide effective oral and written feedback to students, in order to move their learning forward.

October Math Teacher Leader Network Targets

I can anticipate student responses to a selected task and plan questions around those anticipated responses.

I can set personal goals for myself and my school/ district related to our vision of next generation learning and identify actions needed to accomplish them.

I will deepen my understanding of number, operations, algebraic thinking and mathematics pedagogy.

I can describe the design and purpose of a Formative Assessment Lesson.

1. How does a Formative Assessment Lesson flow?

2. How was this task turned into a Formative Assessment Lesson?

3. How does a Formative Assessment Lesson fit into an instructional plan?

Think about the Big Picture –

Fair Price FAL

Complete the pre-assessment “A Fair Price”

Guiding QuestionsWhat does “diagram not to scale”

mean?What does r in the formula represent? If you are given diameter, how can

you determine radius?How can you determine the scale of

increase in area using your answers?

Enlarging RectanglesTrue or False

12

If you double the length and

width of a rectangle

then

you double its perimeter.

If you double the length and

width of a rectangle

then

you double its perimeter.

If you double the length and

width of a rectangle

then

you double its area.

If you double the length and

width of a rectangle

then

you double its area.

I CAN

Find the relationship between perimeter, area and volume of shapes after scaling.

3D Shapes

14

True or False?

15

• If you think a statement is false, change the second part of the statement to make it true.

• Try to figure out what it is about the formula for the shape's area or volume that makes the statement true or false.

• Show calculations, draw diagrams, and use algebra to convince yourself that you have made a correct decision.

• When everyone in your group agrees with the decision for one object, place the statements on the poster and write your explanations around it.

• Begin by working with the statements on rectangular

prisms.

Is it correct?16

1.If you triple the length and width of a rectangle

then the perimeter increases by a factor of 3.

1.If you triple the length and width of a rectangle

then the perimeter increases by a factor of 3.

2.If you triple the length and width of a rectangle

then the area increases by a factor of 6.

2.If you triple the length and width of a rectangle

then the area increases by a factor of 6.

3.If you triple the length, width and height of a rectangular prism

then the volume increases by a factor of 9.

3.If you triple the length, width and height of a rectangular prism

then the volume increases by a factor of 9.

Fair Price FAL Post-assessment

Revise your work on the pre-assessment “A Fair Price”

based on your learning from today’s activity.

Analyzing Student WorkWhat questions would you ask these students to move their learning forward?• Make a list

How would you group the students the next day?

Big Picture Discussion1. How does a

formative Assessment Lesson flow?

2. How was this task turned into a Formative Assessment Lesson?

3. How does a Formative Assessment Lesson fit into an instructional plan?

I can provide justified connections among the FAL 5 strategies, 7 strategies of formative assessment, and CHETL.

Last year CASL served as our touchstone for Assessment Literacy.

This year the Formative Assessment Lessons

will serve as the touchstone for CHETL.

Think of how the 100s Chart can be used visualize patterns in mathematics.

If we mark the multiples of 4 in yellow and the multiples of 6 in blue, we can see their common multiples.

Card Sort Activity At your table please gather your 3 sets of

cards. First group the CHETL cards (blue) on your

table. Match the 5 FAL strategy cards (yellow)

below those, then arrange the 7 strategies from CASL (white) to match below the FAL strategies.

Choose someone to share out one connected strand.

Why is it important for us to make these connections?

I can provide effective oral and written feedback to students, in order to move their learning forward.

CASL: Offer regular descriptive feedback.Teacher provides regular and timely feedback to students and parents that moves learners forward. The teacher gives feedback that is focused, descriptive, and qualitative.

Teacher allows students to use feedback to improve their work before a grade is assigned.

Student uses teacher feedback to improve his/her work.

Student poses and responds to meaningful questions. The student:1) listens carefully.2) asks questions to clarify mathematical thinking.3) refutes mathematical processes/solutions.4) shows persistence during the process of learning.

FAL: Providing feedback that moves learning forward

Lunch

Middle: 11:30 – 12:00High: 11:45 – 12:15Elem: 12:00 – 12:30

Feedback sort activity during your down time.

I will deepen my understanding of number, operations, algebraic thinking and mathematics pedagogy.

Elementary Session

Look over the pre-assessment.

What are some misconceptions that a Kindergarten student might have when completing this?

What questions do you haveabout this task?

Counting DotsPre-assessment

Student MisconceptionsShare the misconceptions you

believe that a student might have with this task.

Discuss the misconceptions that are brought up.

Be prepared to share out with the whole group.

Counting Dots Teacher PacketReview the Teacher Packet

with your table group.

If you used Counting Dots with students, how would it fit into the context of your instructional plan?

What does Van de Walle say? Take a few minutes to review your

reading from Teaching Student Mathematics.

Grade 3-5 Participants should pair with a Grade K-2 Participant. Share two take aways from your

particular reading. Discuss conceptual understanding

from each reading.

Early Number Sense

Cognitive Complexity

What did you notice about the cognitive complexity of the Formative Assessment Lessons from today?

Choose one FAL to implement Packets for K-8 have been created by Ky.

Math Content Specialists and other facilitators of the math networks.

These are ALPHA versions. You will be implementing them for research. To access the Formative Assessment

Lessons online:http://map.mathshell.org/materials/lessons.php

Middle School Session

Look over the pre-assessment.

What are some misconceptions that a middle school student might have when completing this?

What questions do you haveabout this task?

Beads under the CloudPre-assessment

Student MisconceptionsShare the misconceptions you believe that a student might have with this task.

Discuss these misconceptions at your table.

Be prepared to share out with the whole group.

Beads under the Cloud Teacher Packet

Review the Teacher Packetwith your table group.

If you used Beads under the Cloud with students, how would it fit into the context of your instructional plan?

What does Van de Walle say?Take a few minutes to review your reading from Teaching Student Mathematics.

Chapter 1 "Foundations of Student-Centered Instruction" What can I tell them?  Should I tell

them anything? How will I be able to teach all of the

basic skills? Why is it okay for a student to "tell"

or "explain" but NOT for me? This approach takes more time. 

How will I have time to cover everything?

Chapter 1 "Foundations of Student-Centered Instruction" Do I need to use a problem-based

approach every day? Is there any place for drill and

practice? My textbook is a traditional basal. 

How can I use it? What do I do when a task bombs

or studnets don't "get it"?

Chapter 2 "Strategies for Whole-Number Computation" When is it appropriate to introduce the

traditional algorithm for each operation? Is it necessary to introduce the traditional algorithm at all?

When students share their strategies, how can the teacher manage them and highlight the most efficient ones?  

Chapter 2 "Strategies for Whole-Number Computation" How do teachers and

students judge if an invented strategy is effective?

What should you do if a student consistently utilizes a specific invented strategy and does not wish to adopt a more efficient one? 

Cognitive Complexity

What did you notice about the cognitive complexity of the Formative Assessment Lessons from today?

Choose one FAL to implement Packets for K-8 have been created by Ky.

Math Content Specialists and other facilitators of the math networks.

These are ALPHA versions. You will be implementing them for research. To access the Formative Assessment

Lessons online:http://map.mathshell.org/materials/lessons.php

High School Session

Look over the pre-assessment.

What are some misconceptions that an Algebra I student might have when completing this?

What questions do you haveabout this task?

Baseball Jerseys

Pre-assessment

Student MisconceptionsShare the misconceptions you believe that a student might have with this task.

Discuss these misconceptions at your table.

Be prepared to share out with the whole group.

Baseball Jerseys Teacher Packet

Review the Teacher Packetwith your table group.

If you used Baseball Jerseys with students, how would it fit into the context of your instructional plan?

Cognitive Complexity

What did you notice about the cognitive complexity of the Formative Assessment Lessons from today?

FAL websitehttp://map.mathshell.org/materials/lessons.php

Let’s explore!

How do the FALs connect with KCAS Appendix A?TRADITIONAL PATHWAY

Algebra I

Geometry

Choose one FAL to implement Packets for K-8 have been created by Ky.

Math Content Specialists and other facilitators of the math networks.

These are ALPHA versions. You will be implementing them for research. To access the Formative Assessment

Lessons online:http://map.mathshell.org/materials/lessons.php

Survey Please fill in the chart to let us

know which districts are using Quality Core standards and which are using Common Core standards in their pacing guides.

One of the GRREC Superintendents would like to know.

BREAK

I can anticipate student responses to a selected task and plan questions around those anticipated responses.

Good Questions Books

Take a few minutes to look through your new book. The books are

organized into the Big Ideas of mathematics.

Characteristics of Good Feedback Questions…

In general, not yes/no questions

The need for the question arises out of the math that the student is using to solve the problem and is designed to address a specific issue in the logic that they are applying

An example:

Suppose a student is trying to figure out the slope of a line from an equation.

“What form of the equation could help you find the slope?”

may not help the student move forward from where they are, if where they are is thinking about how to get the slope from the coordinates of two points.

Slope example “What are some ways to find the

slope of a line?” might provide more of an opportunity for

the teacher to learn how the student is connecting equations of lines to slopes.

Teachers can then ask questions that build on what is correct about the student’s logic, once they know what it is.

Characteristics of Good Feedback Questions…Avoid cueing questions where key words are used to jog students’ memories (a suggestion in the form of a question).Example: A student is presented with the task of finding the length of the diagonal of a rectangular prism and has no idea how to start. Cueing question: Can you think of a way to use the Pythagorean Theorem?Better question: Where have you seen a problem like this before? (From Polya’s How to Solve It).

Ask questions about what things mean rather than about what procedures students could use.

• Example: Explain why (3x)2 is not equivalent to 9x2. The student substitutes x = 2: (3·2)2 = 62 = 36

9·22 = 182 = 324

• Question focused on procedures: What does order of operations tell us to do first?

• Questions focused on the meaning of the symbols: In (3x)2, what is being squared?

In 9x2, what is being squared?

Consider the following student response:Locate ½ on the number line.

0 1 2 3

o Talk with an elbow partner about a question that could move this learner forward.o Where is the whole? o If that is ½, then where on the

number line is 1 ½?

What insight can be gained that can inform the teacher about his/her teaching?

Student Response:Choose the correct response.

x + 6 = y + 6Sometimes trueAlways trueNever true

“You can’t solve this because x and y aren’t

‘like terms’.”

What question can you ask to move this learner forward?

What happens when x = 2?

“A Fair Price” Questions

Self-assess your work from this morning.

Would you change any of the questions you wrote?

Questions that Clarify Thinking

We will use the student work from the FAL you just completed in your grade level group.

You have analyzed this work for misconceptions.

Questions that Clarify ThinkingOn your own, create questions

that will move learners with these misconceptions forward.

Share these at your table. After you have discussed the

questions you each created, pick one to share. Write it on a post-it and place it on the chart paper.

I can set personal goals for myself and my school/ district related to our vision of next generation learning and identify actions needed to accomplish them.

Action Plan Reflect on last month’s action plan.

If you haven’t filled out the Review column, do so now.

Network with others about how you are sharing this work.

Set next month’s goals on your own.

KDE Updates

Homework Everyone will read pages 251-263

(middle of page)in the CASL book. K-8 Teachers read chapter 3 in Van

de Walle. High School teachers read chapter

4 in Reasoning and Sense Making. EVERYONE will implement a FAL

before they come back in Nov. Bring student work from the FAL.