Essential Questions:
How can we use student thinking to achieve our mathematical goals?
How does dialogue and discourse develop solid understanding of mathematical definitions?

Session 5 (cont.) Solidify Understanding Task - Dilation and Similarity
Practice Standards—how we handle the pedagogy impacts how students interact with the practices. If we don’t make sure they are doing the Practices, the understanding won’t be solidified. Don’t forget the Practices all through the Learning Cycle.
How high level tasks bring out the practices.

Talk about intentionality of problems to highlight student misconceptions around this particular learning cycle.

Session 6 Practice Understanding Task - Similar Figures
1. Remind participants of the three ways to determine if figures are similar on the chart that has been created.
2. Hand out the task and ask participants to work in groups to determine if the figures are similar.
3. Monitor participant thinking and encourge them to use various strategies besides simply counting squares. Identify participants that have considered the figures as dilations and drawn diagonals, used slopes, and other strategies that illustrate the definition in the core.
4. Faciliate a discussion going through the problems and discussing the strategies that participants used to determine if the figures are similar. (Don't need to do all of the problems.)

Looking at the Core
1. Ask participantss to look at he CCSS in 8th grade and see what standards are addressed in this learning cycle and what other standards are connected.
2. Then ask participants to look through the 7th grade and secondary I core to see how the ideas progress.If time, ask them to look at other grades.
3. Be prepared to project the core during the whole group discussion. Ask participants what they found about what experiences student have had before 8th grade and how they will use the work done in 8th grade in Secondary I.

Focus: A vertical look of the Utah core.
Goals:

Break

Sequencing Student Work
1. Look at the 8th Grade Core and find the standards that pertain to the Pythagorean Theorem.
2. Go back to the Circles and Squares task. Identify a potential lesson objective from the core for this task. (Assume that the task is now being used as a teaching task, rather than an assessment task.
3. Hand out the student work and the rubric. Ask participants to go through the student work and discuss the ideas of each student.
4. Decide how to sequence the student work for a class discussion related to the objective you have for the lesson.
5. Facilitate a whole group discussion of their objective and their sequencing of the student work.

Identify and sequence a group of tasks that could be used to achieve the mathematical goals you chose on Day 1. Select one of these tasks and
anticipate student responses to the task.
Daily Reflection

Resources for tasks:
Curriculum Guides
Illustrated Mathematics
Dan Meyer
Illuminations
Navigations
Making it Happen
MARS
Essential Understandings
CMP
Teaching with Focal Points

## Day 3: How are students thinking about mathematics?

To Print:Rectangles.docx

Simply Similar.docx

Circles and Squares Unscored.pdf

Dilation and Similarity.docx

Essential Questions:

How can we use student thinking to achieve our mathematical goals?

How does dialogue and discourse develop solid understanding of mathematical definitions?

Session 5Developing Understanding - Sorting Rectangles

Pedagogy Focus: Addressing the range of learners

Differentiation

Hint cards

Big color rectangles

Sorting Rectangles Facilitator Notes.docx

Large Rectangles (red).docx

Large Rectangles (blue).docx

Large Rectangles (yellow).docx

Solidify Understanding Task - Dilation and Similarity

Practice Standards—how we handle the pedagogy impacts how students interact with the practices. If we don’t make sure they are doing the Practices, the understanding won’t be solidified. Don’t forget the Practices all through the Learning Cycle.

How high level tasks bring out the practices.

Facilitator Note - Dilation.docx

Session 6Practice Understanding Task - Similar Figures1. Remind participants of the three ways to determine if figures are similar on the chart that has been created.

2. Hand out the task and ask participants to work in groups to determine if the figures are similar.

3. Monitor participant thinking and encourge them to use various strategies besides simply counting squares. Identify participants that have considered the figures as dilations and drawn diagonals, used slopes, and other strategies that illustrate the definition in the core.

4. Faciliate a discussion going through the problems and discussing the strategies that participants used to determine if the figures are similar. (Don't need to do all of the problems.)

Goals:

Looking at the Core1. Ask participantss to look at he CCSS in 8th grade and see what standards are addressed in this learning cycle and what other standards are connected.

2. Then ask participants to look through the 7th grade and secondary I core to see how the ideas progress.If time, ask them to look at other grades.

3. Be prepared to project the core during the whole group discussion. Ask participants what they found about what experiences student have had before 8th grade and how they will use the work done in 8th grade in Secondary I.

Goals:

Sequencing Student Work1. Look at the 8th Grade Core and find the standards that pertain to the Pythagorean Theorem.

2. Go back to the Circles and Squares task. Identify a potential lesson objective from the core for this task. (Assume that the task is now being used as a teaching task, rather than an assessment task.

3. Hand out the student work and the rubric. Ask participants to go through the student work and discuss the ideas of each student.

4. Decide how to sequence the student work for a class discussion related to the objective you have for the lesson.

5. Facilitate a whole group discussion of their objective and their sequencing of the student work.

Goal:

Circles and Squares Unscored.pdf

Circles and Squares Scored.pdf

anticipate student responses to the task.

Daily Reflection

Curriculum Guides

Illustrated Mathematics

Dan Meyer

Illuminations

Navigations

Making it Happen

MARS

Essential Understandings

CMP

Teaching with Focal Points

Book: 5 Practices, 6, 7,8