1

Core Academy 2013

Who: ParticipantsMiddle School Teachers of 7th and 8th Grade Mathematics High School Teachers of Secondary I or IIHigh School Teachers of Secondary IIISpecial Education TeachersMath Coaches and LEA leadersLearners at different levels of understanding of the Core and of the CMI ModelFacilitatorsUtah teachers of mathematicsUtah mathematics leadersUtah professors of mathematics and mathematics education

WhyCurrent Reality: The Utah State Board of Education adopted the new Utah Core Standards, based on the Common Core State Standards, in 2011. These standards require a considerable shift in instructional focus and a fair amount of content which may be unfamiliar to teachers.

What (Content)Utah’s Effective Teaching StandardsTeaching CycleLearning CycleUtah’s Core Mathematical Content Standards Utah’s Core Standards for Mathematical PracticeMathematics Tasks which complete a learning cycle grounded in the mathematical content (geometry) of the specific course and illustrate synergy with the effective teaching standardsInstructional design opportunity

What for (Achievement based objectives)At the end of the four days all (participants and facilitators) will:1. Develop a deeper content knowledge around the geometry standards in each course by engaging in learning cycles

built around the Utah Core content standards.2. Learn mathematics and improve teaching by engaging in developmentally appropriate and challenging learning

activities based on learning progressions that move students along a continuum of understanding.3. Explore the Utah Effective Teaching Standards, make connections to the Utah Core, and develop reflective practices

based on those standards.4. Understand and integrate assessment, planning, and instructional strategies in coordinated and engaging ways to

assure learner proficiency.5. Improve practice by developing strategies for differentiation through the implementation of the Standards for

Mathematical Practice.6. Develop understanding and appreciation of the integrated model by making connections among the strands of the

Utah Core.7. Possess increased capacity to collaborate, plan, and teach the Utah Core.

2Day 1: Math Content Focus: Writing and applying formal definitions of the rigid-motion transformations: translations, reflections and rotations.

Pedagogy Focus: UETS St. 3: Modeling learning environments that “support individual and collaborative learning, social

interactions, active engagement in learning, and self-motivation.” Establishing mathematical, socio-mathematical, and classroom norms.

Creating a learning environment that supports the development of the 8 Mathematical Practices. UETS St. 1: The teacher understands cognitive, linguistic, social, emotional and physical areas of student

development. UETS St. 2: The teacher understands individual learner differences and cultural and linguistic diversity.

Time Task Materials

Set out materials for all participants:● Math Notebook● 3-Ring Binder w/ cover (8 Mathematical Practices)● Lanyards

Set out group materials:rulers, scissors, tape, patty paper, transparencies and pens, reflective paper, etc.

Place poster of 8 Mathematical Practices in front of room

9:00 - 9:45

(45 min)

Develop math task- Leaping Lizards! From MVP Secondary One Mathematics – Module 5Math Focus: Developing the definitions of the rigid-motion transformations: translations, reflections and rotations.Pedagogy Focus: UETS St. 3: Modeling learning environments that “support individual and collaborative learning, social interactions, active engagement in learning, and self-motivation.” Establishing mathematical, socio-mathematical, and classroom norms.What’s the experience for the learner? Learners access prior knowledge of rigid transformations by comparing their methods of transformation with their teammates. Validate their method and begin to establish characteristics of rigid transformations.

Leaping Lizards resource page

9:45 - 10:15

(30 min)

Do-Be-Have Protocol: (3 min.) Prompt participants to write in their journal a description of their ideal classroom.(12 min.) Discuss what they wrote with their team. Walk around and listen to what people are saying. Look for specific examples of:

“Have ideas” – tables, self-starter students, comfy chair, etc.“Do ideas” – engaging tasks, students work in teams, etc.

(15 min.) Whole group brainstorm, write the ideas on chart paper (keep for the last day). List all ideas without distinction on the chart paper. Identify the “have ideas” vs. the “do ideas.” Explain that “if I have…., then I can do….” thinking in limiting. If

Chart Paper

3

we reframe the paradigm to: I be….. – facilitatorthen I do… - tasks, collaborating, etcthen I have….. – engaged students, self-starters, problem solvers

Write BE > DO > HAVE on the paper a leave on the wall all 4 days

10:15 - 10:20

BREAK

Facilitators pass out UETS book and teaching notes for Leaping Lizards task.

UETS Book

Leaping Lizards Teaching Notes

10:20 – 10:45

(25 min)

Read "Ask a Kindergarten Class"

(10 min.) Think of a learning experience that opened your mind to the possibility of being a mathematician. Think of a learning experience closed your mind to possibilities.

Think - write down 3 things that worked and 3 things that didn't Pair - share with your partner Share - discuss with full group

(10 min) Full class discussion writing on chart paper the things that worked which become our norms.

(15 min.) Ask them to turn to page 10-12 look at St 3 rubric. Give them time to read and then ask “How do the norms that we just created reflect the practices of Standard 3?” Discuss

(10 min.) This is what a highly effective set of teacher notes looks like. Refer to Standard 3a and 3b. You can obtain these teacher notes on the wiki, but we won’t be passing them out for the rest of the tasks.

Ask a Kindergarten Class – you may want to make copies for participants

Chart paper

10:45 – 10:55

(10 min)

Solidify math task (1): Is It Right? From MVP Secondary One Mathematics – Module 5Math Content Focus: Examining the slope of perpendicular lines.Pedagogy Focus: Creating a learning environment that supports the development of the 8 Mathematical Practices.What’s the experience for the learner? Learners rotate lines 90 degrees and look at slopes. Uses transformation strategies from previous activity to move to the recognition of slopes of perpendicular lines.

(10 minutes) Prompt participants to read quickly just to get the gist of the task. Bring attention to the idea that a learning cycle does not necessarily have only one of Develop, Solidify, and Practice tasks. Here we have two solidify tasks which lead students to a deeper understanding of rigid motion transformations.

Is It Right? resource page

10:55 – 11:30

(35 min)

Solidify math task (2): Leapfrog From MVP Secondary One Mathematics – Module 5Math Content Focus: Determining which rigid-motion transformations carry one image onto another congruent image.

Leapfrog Resource Page

4

Pedagogy Focus: UETS St. 3 b: Supports students to create and manage learning teams to meet learning goals.What’s the experience for the learner? Student uses the more formal definition that was developed during Leaping Lizards to determine what type of transformation has occurred.

11:30 – 12:15

LUNCH

12:15 – 12:35

(20 min)

Debrief Leapfrog

Video of Leapfrog: Prompt participants to pay attention to how the teacher is/is not reinforcing the 8 Mathematical Practices. Refer to the poster.Debrief after the video: What do teachers do to create the learning environment and how does that support the development of the Mathematical Practices?

Video of Leapfrog

12:35 - 1:05

(30 min)

Practice math task: Leap Year From MVP Secondary One Mathematics – Module 5Math Content Focus: Writing and applying formal definitions of the rigid-motion transformations: translations, reflections and rotations.Pedagogy Focus: Using knowledge of learner development and differences to support learning content focus.UETS St. 1: The teacher understands cognitive, linguistic, social, emotional and physical areas of student development.UETS St. 2: The teacher understands individual learner differences and cultural and linguistic diversity.What’s the experience for the learner? Students will write the definitions of the three rigid transformations and apply them to a new problem.

Discussion of formal definition and characteristics of rigid transformations: Pass out the Navigating through Geometry. Ask participants to open the books to pages 9-10. We may be able to move some of our times around because we need to rethink the Norms and intro to UETS in the morning

Leap Year Resource Page

1:05 – 1:25

(20 min)

Discussion of formal definition and characteristics of rigid transformations: Pass out the Navigating through Geometry. Ask participants to open the books to pages 5-6 (Applying Transformations and Symmetry), 9-10 (Introduction to Transforming our World). Ask participants to read and highlight important information. Quick discussion on how our learning cycle has applied this understanding.

1:25 -2:00

(35 min)

The purpose of this task is to have participants recognize that we are not asking them to do more than they already do. If teachers are teaching the Utah Common Core, emphasizing the 8 Mathematical Practices, then they are meeting the UETS standards. We want our participants to have an understanding of what the UETS standards look like in a math class so they can educate their principals and other stakeholders.

Part 1: Connecting UETS Standards 1 and 2 to the learning cycle.UETS St. 1: The teacher understands cognitive, linguistic, social, emotional and

UETS St. 1a, 2a-e indicators template on 6 different colored paper

Tape

5

physical areas of student development.UETS St. 2: The teacher understands individual learner differences and cultural and linguistic diversity.

Group all of the develop task charts that were created during the task together on a wall. Group all of the solidify charts on a different wall or away from the first group and group all of the practice charts on a different wall. We need these to be specific groupings so we can talk about the learning cycle. Make sure that the names of the tasks are written clearly on the charts. Assign each group one of the 6 indicators from UETS St. 1 and 2 by giving the group a set of colored cards. (You may want to reassign your participants into 6 groups regardless of the size of the groups).

Draw and talk about the learning cycle on a chart paper or whiteboard writing both Develop Understanding and the name of the task.

Prompt participants to:1 read the indicator they have been assigned2 discuss what it looked like in the develop/soldify/practice tasks that were

done that day3 write a short but specific example of when this indicator was seen during a

specific task4 tape the card to the appropriate chart.

As you excuse participants to go on their break ask them to examine the learning cycle which now includes the colored cards.

2:00 -2:15

BREAK

2:15 - 2:45

(30min)

Part 2: (15 minutes) Prompt participants to look at the learning cycle, ask:● Are there any tasks that do not have all 6 colors?● Why do you think this is?● What could have been done to include this indicator?● How do we educate our principals and other stakeholders that we are

meeting the UETS standards by teaching the Utah Common Core through low threshold, high ceiling tasks, having students work in groups, create lessons based on the learning cycle?

What Utah Core Curriculum standards were met during the learning cycle. (15 minutes) Prompt participants to look at the geometry standards in their Utah Common Core, noting and discussing with their group which standards were addressed in the learning cycle.

Place a sheet of chart paper next to each task and have the whole group call out short phrases that describe the standard being met in that task.

1 sheet of chart paper placed near each of the 3 tasks from that morning

2:45 - 3:10

Reflect on “Learning” through the lens of the Utah Effective Teaching Standards. Introduce the document and have teachers reflect on the learning that has

6

(35 min)happened. Key Themes and Essential Knowledge: (5 minutes) Read through the Key Themes (pages 29 – 32) underlining or highlighting those indicators that seem most critical to effective teaching in a mathematics classroom.(12 - 18 minutes, 3 minutes/participant) Round Table: Each person in the group chooses one bullet and shares how teachers demonstrate this knowledge and understanding in their mathematics classroom. Specifically answering: What would you see in a math class that would be evidence that a teacher has this knowledge and understanding?

(10 minutes) Whole group Brainstorm, write the key ideas on chart paper:Which of these key themes is more important now than might have been true before because of the adoption of the new core? What is your evidence that the theme you chose is more important now using the new Utah Core Standards than it was in the previous core?

UETS book

Highlighters

Chart paper

Marker

3:10 -3:30

(20 min)

Feedback loop for readjustment: Whole group Brainstorm, writing key ideas on chart paper, the following questions:

● What worked for you as a learner?● What didn’t work for you as a learner?● What questions do you have from today’s learning?● Any additional comments, insights, or ideas?

Chart paper

3:35 + Facilitator reflection and planning time to use feedback to inform the next day’s practices. Reflect on scheduling and on learning objectives and analysis of learner experiences.● How did we meet today’s objectives?● What schedule adjustments need to be made?● How did we work together as facilitators?Think both in terms of your own context and in terms of issues that may be common to all groups. Email all the other facilitator groups for your grade level to share insights and suggestions for improving the academy in subsequent weeks.

Day 2

7Math Focus: Develop and use the non-transformed equation for a circle.

Pedagogy Focus: Differentiation is the focus of the day. Some of the strategies include: Use of technology, student errors and misconceptions, a student notebook, and other practical strategies to use where the rubber hits the road while moving learners through the learning cycle. UETS St. 6c: Differentiates instruction for both individuals and groups by choosing appropriate strategies,

accommodations, resources, sequencing, and demonstrations of learning. UETS St. 7: Uses various instructional strategies to ensure that all learners develop a deep understanding

of content areas and their connections and build skills to apply and extend knowledge in meaningful ways. Use technology as a strategy to differentiate instruction.

Time Task Materials

8:30 -9:00

(30 min)

CMI Framework - deepening the ideas of the learning cycle “Re-view”

What do you know about the CMI framework learning cycle?Why is this chosen framework by USOE?What are you currently doing that is similar to this framework?

Facilitator might bring up the idea that this model was chosen as a good model for enabling students to engage in the Utah Core State Standards and the 8 mathematical practices. It meets the goal of encouraging learners to use higher-level thinking.

CMI Framework, Part 1

9:00 -9:45

(45 min)

Develop math task: Triangles Can Do That?Math Focus: For a point on a circle, the x-value, the y-value, and the radius of the circle are related by the Pythagorean Theorem. Pedagogy Focus: UETS St. 6c: Differentiates instruction for both individuals and groups by choosing appropriate strategies, accommodations, resources, sequencing, and demonstrations of learning.Experience for the learner: Using a specific triangle to create a set of points that are equidistant from a center point in order define a circle and to begin developing the general equation of a circle.

Triangles can do that? Resource Page

Construction Paper Triangles

9:45 – 10:10

(55 min)

Think-Pair-Share:1. Think- Give participants two minutes to think about and write a personal

response to the following questions. What strategies help to maintain the high ceiling, low threshold aspects of a

task? What type of strategies can we use for differentiation that are specific to the

math content, and that that go beyond simply putting students in groups or giving them different work?

2. Pair - Give participants two more minutes to discuss what they wrote their partner.3. Share - Share thoughts as a whole group.

Prompt participants read UETS St 6C: Differentiates instruction for individuals and groups of students by choosing appropriate strategies and accommodations, resources, materials, sequencing, technical tools, and demonstrations of learning.

8

Whole group discussion:● How does this standard connect to the task just completed?● Imagine walking into another classroom. If the teacher was highly effective in

standard 6c, what would you see?

Optional: Facilitator may want to also ask these two questions by continuing the Think-Pair-Share protocol. What strategies were evident during the task? What are the teacher moves that you experienced during the task that provided

differentiated access to the task? How do high quality tasks allow opportunities for differentiation? How do the representations allow students to engage in the mathematics and

demonstrate their understanding in various ways?

10:10 –10:20

Break

10:20 -11:00

(40 min)

Solidify Math Task: Graphic CirclesMath Focus: Students will be able to explain why x2 + y2 = r2 for any point on any circlePedagogy Focus: Use technology as a strategy to differentiate instruction. Experience for the learner: Students use technology to determine the equation of a circle.

Graphic Circle Resource Page

Computer or Tablet with Geometry Graphics Software

Geogebra Instructions

11:00 -11:30

(30 min)

Video of Graphic Circles: Prompt participants to write down the types of questions and responses that are generated in the video.

Reflecting on the Video: Each participant receives a card with one of the following questions written on it.

● What types of questions can be asked besides simply checking for right and wrong?

● How can we help students when they are stuck without giving away the next step? How can we scaffold?

● How can we help students communicate their ideas to others?● How can we help students feel safe with our questioning?

Prompt participants to read their question and write a response. Prompt participants to trade their question with someone in their group, read their new question, and respond to the question or the response. Continue doing this two more times.

Index cardwith questionswritten on them

11:30 -12:15

Lunch

12:15 - 1:00

(45 min)

Practice math task: Holy circles, Batman!Math Focus: Attain fluency with the non-transformed equation for a circle.Pedagogy Focus: UETS St. 6dExperience for the learner: Students will apply what they have learned about finding important points on a circle to different types of questions.

Holy circles, Barman! Resource Page

9

1:00 - 2:00

(60 min)

Hand out the “Questioning our Patterns of Questioning” article. Have participants read the article and identify a word, phrase, and sentence that s/he thinks/feels is particularly significant. Record in your notebook using a sentence stem “my __________ is significant because…”

Give participants 10 minutes to read the article and find his/her word, phrase, and sentence.

Next have participants in groups of no more than four share using the following the protocol below.

First identify who will be the group facilitator and who will be the scribe. The scribe will be recording the words and phrases on chart paper to hang up for participants to read during the break.

Round 1: Each person shares the word from the article and uses the sentence stem above. The scribe records each word.

Round 2: Each person shares the phrase they selected using the sentence stem. The scribe records each phrase.

Round 3: Each person shares the sentence they identified using the sentence stem.

**Refer back to your list to determine what is important that participants will be sharing in their groups.

Discussion questions:

How does using the “focus interaction pattern of questioning” allow for all students to learn at their level?

What do you think of the author’s recommendations to investigating your own teaching practice with regards to questioning?

Read UETS 6d and 7d, e, f, and h. In partners have participants discuss: How will the ”focusing interaction pattern of questioning” allow me to achieve these standards? (As facilitators make sure participants are citing specific standards from the UETS they just discussed.) Have volunteers share what they discussed in pairs. Make sure each of the five indicators have been discussed and if not, invite participants that you have heard discussing the missing indicators in the explore phase share. (This requires you to make note of groups that are taking about each standard during their partner discussions so you have a list to choose from if needed.)

Questioning our Patterns of Questioning Article

UETS Book

2:00 - 2:15

BREAK

2:15 - 3:00

(45 min)

6c Instructional Planning: Differentiation

Think of a math task you’ve seen or used before. Plan how that task could be adjusted for better differentiation. Keep in mind the following questions:

● How do you see differentiation throughout the learning cycle?● How does keeping a notebook provide the teacher with opportunities for

10

differentiation?● How might technology aid in differentiation?

Optionally, allow time for participants to share the ideas they worked on during this time.

3:00 - 3:30

Feedback loop for readjustment:Affinity MapHave Chart paper posted around the room with one of the following questions posted on each. (Each group receives a packet of Post-It Notes which they use to write their answers, and post onto the posters.)

● What worked for you as a learner?● What didn’t work for you as a learner?● What questions do you have from today’s learning?● Any additional comments, insights, or ideas?

Facilitator reflection and planning time to use feedback to inform the next day’s practices. Reflect on scheduling and on learning objectives and analysis of learner experiences.● How did we meet today’s objectives?● What schedule adjustments need to be made?● How did we work together as facilitators?Think both in terms of your own context and in terms of issues that may be common to all groups. Email all the other facilitator groups at your grade level to share insights and suggestions for improving the academy in subsequent weeks.

Day 3Math Focus: Students will develop and justify constructions.

11Pedagogy Focus: We will look at content knowledge, instructional strategies, and assessment through the lense of the Utah Common Core, emphasizing the mathematical practices. St 4: Content Knowledge: The teacher understands the central concepts, tools of inquiry, and structures of

the discipline. St 7c: Instruction Strategies - Analyzes student errors and misconceptions in order to direct, focus, and

deepen learning. St 7f: Instructional Strategies – Provides opportunities for students to understand, question, and analyze

information from multiple and diverse sources and perspectives to answer questions and solve real-world problems.

St 5: Assessment: The teacher uses multiple methods of assessment to engage learners in their own growth, monitor learner progress, guide planning and instruction, and determined whether the outcomes described in content standards have been met.

Time Task Materials

8:30 - 9:00

CMI Framework - deepening the ideas of the teaching cycle “Re-view”

9:00 - 10:00

Develop math Task: Optical IllusionsMath Focus: The students will make conjectures, justify conjectures, develop strategies to determine parallel-ness, construct a parallel line through a given point not on a given linePedagogy Focus: UETS St 4: Understand the central concepts, tools of inquiry, and structures of the discipline. The teacher will utilize questioning techniques to elicit higher order thinking, require use of prior knowledge, anticipate student moves, help students create and see importance for creating a record of learning. The teacher will also demonstrate making decisions that will enhance student strengths and interests through the use of developmentally appropriate activities.Experience for the learner: Students will access prior knowledge, utilize math notebooks as a record of their learning, and develop skill in the construction of parallel lines. The student will justify a conjecture.

Compass

Ruler

Optical Illusions resource page

graph paper

patty paper

10:00 –10:10

Break

10:10 – 10:55

(45 min)

UETS St 4: Understand the central concepts, tools of inquiry, and structures of the discipline. Debrief with the question: What content knowledge do you need to facilitate the discussion?Website to create your own mind map: https://bubbl.us/Show the example of Construction of Parallel lines Construction of Parallel Lines.jpg Assign groups to Create a Mind Map based on the previous tasks:

1. Leaping Lizards2. Is It Right?3. Leap Frog4. Leap Year5. Triangles Can Do That?6. Graphic Circles7. Holy Circles, Batman

12

What are the tools of inquiry for mathematicians? Student notebook, technology, construction tools, brain, etc.

Turn to page 12-13 of UETS for detailed description - pay attention to the strands and descriptors for the practicing, effective, and highly effective teachers. How do you see teachers moving from one category to the next?

Analyzing Student Work:St. 7 c: Analyzes student errors and misconceptions in order to redirect, focus, and deepen learning.St. 7 f: Provides opportunities for students to understand, question, and analyze information from multiple and diverse sources and perspectives to answer questions and solve real-world problems.

Student Work - Student Work.pdfWhat questions would you ask of the class to help make sense of the work? What questions would you ask to help work through the misconception? What excellent ideas are emerging from the misconceptions? How might you assist them in using these excellent ideas accurately?

Copies ofstudent work

10:55 - 11:30

(35 min)

Solidify Task: The Construction of an Illusion (pt 1)Math Focus: Basic construction skills; construct parallel lines, justify construction steps.Pedagogy Focus: 8 practice standards and levels of cognitive demand.Learner Experience: The student will kindly critique the work of others, utilize a graphic organizer to show the transfer of simple skills to more complex skills, justify the use of basic construction skills.

Construction of an Illusion Resource page

11:30 – 12:15

Lunch

12:15 - 12:55

(40 min)

Solidify Task: The Construction of an Illusion (pt 2)Math Focus: Basic construction skills; construct parallel lines, justify construction steps.Pedagogy Focus: 8 practice standards and levels of cognitive demand.Learner Experience: The student will kindly critique the work of others, utilize a graphic organizer to show the transfer of simple skills to more complex skills, justify the use of basic construction skills.

12:55 – 2:00

(65 min)

Use the Mathematics Practice Standards and Levels of Cognitive Demand. Askparticipants to write a prompt with a rubric that can assess student thinking andrespond to it related to the learning cycle they just participated in. What assessmentquestions can you use to capture a lot of student thinking with a few quickquestions? Emphasize the use of the notebook and collecting written responses.How can you use the rubric to provide feedback to students?

2:00 – 2:15

Break

2:15 - Practice Task: An Inscribed Illusion An Inscribed

13

3:15

(60 min)

Math Focus: Students will construct perpendicular bisectors, an inscribed regular hexagon, an inscribed equilateral triangle, and an inscribed square. They will be asked to transfer this knowledge to the justification that the sides of the Ehrenstein optical illusion are not caving in . Students will also demonstrate their understanding of parallel-ness in their justifications on an inscribed square being a parallelogram containing perpendicular angles.Pedagogy Focus: Formative assessment and questioning techniques. Timing of formative assessments. Precision and transfer of knowledge. Use of notebooks as a learning record that can be shared with other students, teachers, and parents. What type of assessment items could be used to assess the work done during the practice task? How might assessment of a practice task at the end of a learning cycle be different than assessment during or after a solidify task?

Illusion Resource Page

If time is available, have participants write assessments for the work that they did on the previous day.

3:15 - 3:30

(15 min)

Feedback loop for readjustmentWhat worked for you as a learner?What didn’t work for you as a learner?What questions do you have from today’s learning?Any additional comments, insights, or ideas?

Facilitator reflection and planning time to use feedback to inform the next day’s practices. Reflect on scheduling and on learning objectives and analysis of learner experiences.● How did we meet today’s objectives?● What schedule adjustments need to be made?● How did we work together as facilitators?Think both in terms of your own context and in terms of issues that may be common to all groups. Email facilitator groups to share insights and suggestions for improving the academy in subsequent weeks.

Day 4

14Pedagogy Focus: The purpose of the four morning tasks is for participants to reflect over the week, to deepen participant understanding of teaching and learning relative to the progression of the Geometry standards (both the sequence of when we teach certain topics and the inclusion of new content) and to make connections across the Core standards. UETS St. 8d - Actively investigates and considers new ideas that improve teaching and learning and draw

on current education policy and research as sources of reflection.

Time Task Materials

Preparation for Task 2 prior to the arrival of participants:● Reorganize your participants into an even number of groups (2, 4, 8, or 8

groups) even if the number of participants within each group is small or larger than 4.

● Tape the Grade Level Headers (Math 7 thru Secondary Math III) in order along a wall, one set of headers taped to a wall for every two groups. You will have at most eight groups using four walls for this task. You may want to tape the header to some chart paper. Rather than use new paper you can use the back of some of your previous work done on chart paper.

Grade Level Headers

8:30 - 9:00

(30 min)

Task 1: How is teaching the Utah Common Core geometry standards different than how we taught geometry in the past?Write to Learn: “In your notebooks reflect on what we have done over the past week. How is what we have done different than what you have done with geometry in your classroom in the past?”Share: Brainstorm with the full group “How is it different?” Write these on chart paper.Read: Geometry Introductions for grades 7 - 11. Prompt participants to read and highlight things that are different from their past experiences with geometry.Add: Any new differences to the chart.Make sure the following items are discussed:1. congruence through rigid transformations2. similarity through rigid transformations followed by dilations3. functions can be used to describe these transformations.Closing question: Have you had any new “aha’s” during this discussion?

Chart Paper

Markers

CCSS Secondary Geo Standards

9:00 - 10:00

(60 min)

Task 2: What is the progression of geometry through Grade 7 to Math III? The purpose of this task is to highlight the progression of the geometry standards from 7th grade through Secondary III.

Part 1 – Task Sort (20 minutes):● Instruct participants that each group will receive a set of 8 tasks. They are

to work with their group to sort them by grade level and tape them to the wall underneath the grade level header. Two groups will be working the same set of headers.

● Together, the two groups will look at the 16 total tasks on the wall and come to consensus for the placement of the tasks. The tasks have been chosen to instigate discussion. Make sure the groups know they should be able to justify their reasoning for placement of the tasks.

Tasks_Group A

Tasks_Group B Tasks_Key

Painters Tape

Transparent Tape

15

Part 2 – Wall Comparisons (20 minutes) — Participants are to sit with their original groups. Prompt participants to notice compare their work with the other groups’ work, identifying those tasks that are placed in different grade levels. Discuss justifications for placement of the tasks.

Part 3 — Standards across the grades and focus questions (20 minutes) At the end of the comparison, have participants ‘flip’ the grade level signs to show the standards for each grade level.Have each “wall group” determine if any tasks need to be moved based on what they have learned from reading the standards across the grade levels. Discuss the following questions:

● How does this progression of ideas differ from the development of geometry that you have seen in the past?

● How does the progression of geometric ideas build a foundation for the things that you are teaching?

What things that you are teaching are foundational for future work? In what way?

10:00 - 10:15

Break

10:15 – 11:00

(45 min)

Task 3: The purpose of this task is for participants to compare the other domains within their Core to the geometry standards.Jigsaw: Give them a copy of the How does the Other Conceptual Categories Relate to

Geometry template. Participants should be organized in groups of 4. Count off each participant 1

through 4. Assign each number a Conceptual Category:

1 Number and Quantity2 Algebra3 Functions4 Statistics and Probability

(25 min) Instruct participants to go to designated corners of the room so they can become experts at their assigned Conceptual Category with members of the other teams. They need to take the template, their CCSS book, and a pencil/pen with them. You may suggest that each group open some of their CCSS books to the geometry standards and others open their books to their assigned conceptual category. They use the template to write down the connections between the geometry standards and the other standards.

(20 min, 5 min/conceptual category) Participants return to their original group and share their findings.

Task 3 template

11:00 - 11:30

(30 min)

Task 4: Geometry seems to develop very differently, what about the other standards? How do the ideas in each of the other standards develop differently than what you have done in the past? The purpose of this task is for participants to deepen their understanding of the progression of standards in the other domains in their Core area. Prompt participants to fold a piece of paper into 4 quadrants, one box for each

domain.

Paper (1/person)

Utah Common Core book

16

Ask them to write the following sentence stem at the top of the boxes:The differences in the development of [conceptual categories] in Secondary Math I and II are evidenced by....

The four [conceptual categories] are:1 Number and Quantity2 Algebra3 Functions4 Statistics and Probability

Groups work together to complete each sentence stem. Facilitators should be marking time with the groups by saying “Your group should be discussing [conceptual category] right now. If you aren’t please summarize your current comments and move on.”

Whip Around (10 minutes): Participants will quickly name one thing they noticed in their previous

work. This should be a quick 1-4 word phrase. The idea is to “whip around the entire group multiple times until there is nothing left to add.

Call on participants from different groups and then repeat until everyone has participated. Continue, whipping around the room, until the comments are exhausted.

Direct participants to open their UETS book to St. 8d: The teacher actively investigates and considers new ideas that improve teaching and learning and draws on current education policy and research as sources of reflection. Quickly discuss how by participating in these types of discussions, both here and with our colleagues in our math departments at our schools, we are meeting this standard.

11:30 - 12:15 Lunch

12:15 – 1:15

(60 min)

Reflecting on the Effective Teaching StandardsIntroduce the Key Cross-Cutting Concepts: organization of the UETS standards by concepts. Organize participants in 6 groups. Assign groups one of the following six concepts or pair of concepts by giving each group a strip from the UETS Key-Cross Groups sheet. Inform participants that the standards that we specifically looked at during the week are listed but that during their discussion they may look at all the standards within their concept.

Key Cross-Cutting Concepts (page 25-27)1. Basic teacher responsibilities: 4a, 4b, 4e2. Collaboration: 3b3. Communication: 7f, 7h and Creativity/innovation: 6d4. English language learners: 2e and Individual learning differences: 1a,

2a-c, 6c (7a&b)5. Multiple perspectives: 2d, 4d, 7d and Student-directed learning: 4c6. Student engagement/motivation: 4c and Technology: 3e

Swapmeet:1 (5 minutes individual contemplation, 10 minutes group discussion) Ask what

an observer might see in a classroom as evidence of meeting the standards within their assigned concept. They may refer to a task or activity done during the week or describe something they may have done in their classroom. Jot some ideas that can be shared with other teams in their math notebooks.

2 (10 minutes) Two participants from each group rotate to the next group.

UETS Key-Cross Groups sheet cut into strips (1/group)

17

Share the ideas and thinking of both groups. 1->2, 2->3, 3->4, 4->5, 5->6, 6->1

3 (10 minutes) Move back to original groups and discuss what was learned from the other groups.

4 (10 minutes) Two new participants from each group rotate to a different group. Share the ideas and thinking of both groups.

1->3, 2->4, 3->5, 4->6, 5->1, 6->25 (10 minutes) Move back to original groups and discuss what was learned

from the other groups.**This rotation allows each group to have discussed four of the concepts.

1:15 – 2:15

(60 min)

Prompt participants to re-examine their ideal classroom and the chart from the first day. How do we move from “Have – Be – Do” to “BE – DO – HAVE” ? What have we done in the past 4 days that help us make this change? What further support would help us maintain this change? How do we help the rest of our math departments to make this change?

Chart of ideal classroom from day 1

2:15 – 2:30 BREAK

2:30 – 3:00(30 min)

Use video of teacher stories that reflect how the adoption of the new core and new teaching strategies has led to increased student achievement.

3:00 – 3:30 Facilitator reflection and planning time to use feedback to inform the next day’s practices. Reflect on scheduling and on learning objectives and analysis of learner experiences.● How did we meet today’s objectives?● What schedule adjustments need to be made?● How did we work together as facilitators?Think both in terms of your own context and in terms of issues that may be common to all groups. Email all the other facilitator groups at your grade level to share insights and suggestions for improving the academy in subsequent weeks.

Feedback loop for readjustmentWhat worked for you as a learner?What didn’t work for you as a learner?What questions do you have from today’s learning?Any additional comments, insights, or ideas?