1. Poster Place a dot on each continuum.
Rate your familiarity with the content portion of the New Illinois Learning Standards for Mathematics
Rate your familiarity with the practice standards portion of the New Illinois Learning Standards for Mathematics
Rate your familiarity with the PARCC assessment and supporting materials.
Create on poster paper before participants arrive.

2. Math Foundational Services
Heather Brown & Dana Cartier
ISBE Math Content Area Specialist
Introductions – all

3. Who is in the Room? Teachers Curriculum or Content Specialists
School or District Administrators
County or State representatives

4. Norms

5. (Educators Evaluating Quality Instructional Products)
EQuIP Rubric
(Educators Evaluating Quality Instructional Products) I
Handout – Participants should have a copy of the powerpoint.
Handout - Participants should have a copy of the rubric.
The title slide provides participants with the acronym for EQuIP. (Educators Evaluating Quality
Instructional Products) Participants can be provided with a copy of the PowerPoint as well as copies of the rubric when showing this slide.
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6. The History Behind the Tool
The Tri-State Collaborative
EQuIP
(Educators Evaluating Quality Instructional Products)
(Handout – About Equip)
Provide participants with the “About EQuIP” handout.
The EQuIP Rubric began as the Tri-State Rubric. The Tri-State Collaborative was comprised of educational leaders from Massachusetts, New York, and Rhode Island and facilitated by Achieve. This collaborative developed a criterion-based rubric and review process to evaluate the quality of multi-day lessons and units intended to address the Common Core State Standards (CCSS) for English Language Arts/Literacy and Mathematics. The outcome of that effort was the development of the “Tri-State Rubrics” and a quality review process designed to determine the quality and alignment of instructional lessons and units to the CCSS. The EQuIP (Educators Evaluating the Quality of Instructional Products) Rubrics build on the original collaborative effort. Since the spring of 2012, over twenty states, including Illinois, have participated in EQuIP conferences. The result of this collaboration is the Mathematics EQuIP Rubric.
The objectives of EQuIP are two-fold:
o Increase the supply of high quality lessons and units aligned to the CSSS that are available to elementary, middle, and high school teachers as soon as possible; and
o Build the capacity of educators to evaluate and improve the quality of instructional materials for use in their classrooms and schools.
Presently representatives from the PARCC states are meeting regularly with ACHIEVE in Washington D.C. to continue to provide feedback using the rubric.
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7. Purpose Instructional Materials Guidance Lesson/Unit Alignment
Develop a deeper understanding of the CCSS
The primary purpose of the rubric is to provide specific guidance for identifying high quality
instructional materials aligned to the Common Core State Standards. It is to be used for multi-day lessons or units.
This rubric can offer assistance to teachers to align their multi-day lessons/units to the CCSS as they transition to full implementation.
States and other educational organizations may use the rubric as an evaluation tool to determine the quality of multi-day lessons/units they want to provide for teachers.
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8. The EQuIP Rubric Design
Multi-Day Lessons
Units
The EQuIP rubric can be used to align multi-day lessons or larger units to the CCSS.
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9. Single task or activity.
Remind participants that the rubric is NOT designed for a daily lesson plan. For teachers who
make daily lesson plans, the rubric can be viewed to see if the components of the rubric are evident throughout multiple daily lessons.
A daily lesson plan may not necessarily reflect every element found within the rubric.
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10. How States May Use The Rubric
Guide development
Evaluate
Gain deeper understanding of the CCSS
Inform vendors
This slide provides participants with ways states can use the rubric. Beyond using the rubric at
cross-state conferences, many states and districts have embraced the rubric and review process to support their implementation of the CCSS in a variety of ways.
1. As a tool to guide the development of lessons and units;
2. As a tool to evaluate existing lessons and units to identify improvements needed to align with the CCSS;
3. As a tool to build the capacity of teachers to gain a deeper understanding of the CCSS; and
4. As a tool to inform vendors of criteria that will be applied in the evaluation of proposals and final products. (Also see Publishers’ Criteria in CCSS)
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11. EQuIP Rubric Guide for lesson plan/unit alignment
Rating scale - NOT recommended for classroom use or teacher evaluation
This slide provides direction in how teachers can use the rubric to align their lessons and units
to the Illinois Learning Standards Incorporating the Common Core. The slide cautions teachers to disregard the rating scale found at the bottom of the front page of the rubric and to disregard the back of the rubric. Teachers should focus on the criteria listed within each dimension of the rubric.
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12. EQuIP Rubric
Educational organizations may use the backside of the rubric to determine the quality and alignment of lessons and units to:
Identify exemplars/models for teachers’ use within and across states;
Provide constructive criteria-based feedback to developers,
Review existing instructional materials to determine what revisions are needed.
This slide is a reminder to participants that the rubric tool is not for classroom use or to be used
for teacher evaluation. The original intent of the rating scale was for state departments and other educational organizations to determine which multi-day units/lessons become a part of their online resources. EQuIP offers modules and other resources for those organizations that can be found at
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13. The Rubric Organizes Criteria That Describe Quality Lessons/Units
Criteria that define the rubric are organized to describe quality in four dimensions.
Dimension #1
Alignment to the Depth of CCSS
Dimension #2
Key Shifts of Focus in the CCSS
Dimension #3
Instructional Supports
Dimension #4
Assessment
Dimension 1: Alignment to depth of CCSS
Dimension 2: Key Shifts in the CCSS
Dimension 3: Instructional Supports
Dimension 4: Assessments: pre-assessment, self-assessment, formative, summative
The descriptive criteria listed in each Dimension/column represent a high standard of quality which describes the characteristics one would find in an exemplary CCSS lesson or unit.
Slide taken from Tri-State Quality Review Rubric & Process (Achieve)

14. CCSS Alignment is Four Dimensional
Assessment
Alignment
Focus
Supports
CCSS Alignment is Four Dimensional
While we may look at each dimension separately, it is important that the four dimensions are
thought of as an interlocking pyramid. While they can be considered and analyzed separately, each piece really depends upon the other to form a firm foundation and point toward high expectations.
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15. 1st Step: Make a foldable Show only Dimensions I And IV
When using the rubric, it is beneficial to focus on Dimensions I & IV first. If participants have
the rubric in their hands or if the presenter has the rubric, demonstrate how to fold the rubric so that only Dimensions I & IV show. Discuss the importance of choosing targets (Dimension I) and the assessment (Dimension IV) to measure mastery of the targets first. Then educators may focus on Dimensions II and III to help plan the instruction.
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16. Backward Planning Goals Assessment Methods
So as we look at Dimensions I and IV, we are really following the backward planning model adapted from The Understanding by Design Handbook by Grant Wiggins
Wiggins, G. (2005). Adapted from Understanding by Design
Handbook. Wiggins, et al. Alexandria, Virginia: ASCD.
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17. Backwards Design/EQuIP Rubric
1. Identify the results desired
2. Determine acceptable levels of
evidence that support the
desired results
Design activities that will make
the desired results happen
The backwards design model compares well with the EQuIP rubric with each step matching a
dimension(s) of the rubric.
Backwards Design Model
1. Identify the desired results or outcomes. (Dimension I)
2. Determine acceptable levels of evidence that support the desired results. (Dimension IV)
3. Design activities that will make the desired results happen. (Dimensions II & III)
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18. Dimension I: Alignment to the CCSS
Targets Standard(s)
Content standards
Practice Standards
Balance
Procedural Skill
Conceptual Understanding
Remind participants that the first dimension of the EQuIP Rubric is focused on alignment to
the Common Core State Standards. In Mathematics there are some specific attributes that need to be present. Dimension I: Alignment
Dimension I is non-negotiable. In order for the review to continue, a rating of 2 or 3 is required. If the review is discontinued, consider general feedback that might be given to developers regarding next steps.
To apply the criteria in Dimension I it is helpful to ask the following clarifying questions regarding criteria 1, 2, and 3:
For criterion 1 – Does the lesson/unit articulate alignment to a reasonable standard or set of standards? Do the assignments, tasks, and activities suggest that a standard or set of standards has been targeted for instruction? Does the lesson/unit make a distinction between targeted and supporting standards? Do the assignments and activities make sense given the standards listed? Does the lesson/unit address the targeted standards at the full depth defined in the standards?
For criterion 2 – Which Standards for Mathematical Practice are identified? Which mathematical practices do the assignments and activities provide opportunity for students to demonstrate? Is a focused set of mathematical practices identified that are central to the lesson/unit? Are the mathematical practices tied closely to the content of the lesson or unit?
For criterion 3 – Do the assignments and activities provide opportunities for students to practice mathematical procedures and deepen the emphasized concepts with a balance appropriate for the content and for the grade level?

19. Dimension II: Key Shifts in CCSS
Focus
Coherence
Rigor
Remind participants that the second dimension of the EQuIP Rubric is focused on the Key Shifts
of the CCSS. There are some specific attributes that need to be present aligned to dimension II.
Dimension II: Key Shifts
To apply the criteria in Dimension II it is helpful to ask the following questions regarding criteria 1, 2, and 3:
For criterion 1 –Does the content of the lesson/unit belong to the Common Core State Standards’ emphases (major work) for the grade? Are any aspects of the lesson that relate to supporting work of the grade closely tied to this grade-level focus?
For criterion 2 – Does the lesson/unit provide teachers with connections to related expectations in earlier and later grades? Does it address the “big picture” as specified in the relevant cluster heading? Does it help students make connections among standards within a cluster, clusters within a domain, or domains within a grade?
For criterion 3 – The three aspects of rigor are concepts, procedures/fluency and application. Does the lesson or unit emphasize some aspect(s) more than others? (For example, the lesson or unit might emphasize conceptual understanding but not application or procedure.) Given the goals of the lesson or unit, is the emphasis appropriate and logical? (Facilitators should inform raters that a lesson involving only a single aspect of rigor can receive a score of 3 for Dimension II, provided the single aspect of rigor that is present is handled well in the lesson.) For a unit or longer lesson: How do the instructional materials present a balance of application, conceptual understanding, and procedural skill and fluency?
Participants may want to turn to page 8 of the user guide to see additional suggestions for Dimension II.
Presenters may want to engage the participants with one of the following activities with Dimension II.
1. Participants can highlight in yellow what teachers will feel comfortable and in blue what teachers will feel is challenging.
2. Participants can highlight the vocabulary within the rubric that teachers may need to discuss and come to consensus on what those words/phrases mean.

20. Dimension III: Instructional Supports
Guidance
Accuracy
Engagement
Instructional Expectations
Differentiation
Remind participants that the third dimension is focused on the Instructional Supports teacher
must consider when designing lessons/units.
Dimension III: Instruction
To apply the criteria in Dimension III refer them to the language used in each criterion. It may also be helpful to ask the following questions regarding the criteria:
For criterion 1 – Does the lesson/unit provide clear directions and guidance so that even an inexperienced teacher can successfully guide students to an understanding of the targeted standards? If appropriate, are technology and/or media applied in the lesson/unit?
For criterion 2 – Does this set of instructional materials clearly identify and work to develop key academic language and accurate and precise mathematics?
For criterion 3 – Do you see evidence that all students are given opportunities to engage in a productive struggle through thought-provoking questions with little scaffolding?
For criterion 4 – Does the lesson include expectations for how the instruction should take place and whether the overall organization/format is easy to understand and use?
For criterion 5 – Is there evidence in the lesson/unit that support is provided for a range of learners, including students working both below and above grade level and those who are English language learners?
For criteria 6 through 8 – Is there a mix of instructional approaches, a gradual removal of supports, and an effective sequence for the activities of the lesson/unit? Is there opportunity for student understanding to deepen over the course of the lesson/unit?
For criterion 9 – Does the lesson/unit emphasize and support an appropriate balance of procedural and conceptual understanding?
NOTE: There is an important distinction to be made between criterion 3, which is primarily about opportunity and criterion 5 through 8, which are primarily about access.
Note that criterion 3 asks reviewers to look for evidence that all students are given opportunities to engage with problems and tasks that require them to struggle productively in their solution. Criterion 3 does not require evidence of scaffolds specific to special learning or language needs. Rather, criterion 3 asks for evidence that all students are expected to and given opportunity to do challenging mathematical work.
Note that criterion 5 does require evidence that the lesson/unit includes supports that address a range of learning and language needs.
Possible activities with this dimension:
1. Participants can highlight in yellow what teachers will feel comfortable and in blue what teachers will feel is challenging.
2. Participants can highlight the vocabulary within the rubric that teachers may need to discuss and come to consensus on what those words/phrases mean.
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21. Dimension IV: Assessment
Observable Evidence of Learning
Assesses Proficiency
Aligned Rubrics/Scoring Guides
Remind participants that the fourth dimension of the rubric is focused on assessments. There
are specific attributes that need to be present in this dimension:
Dimension IV: Assessment
To apply the criteria for Dimension IV it is helpful to ask the following questions regarding criteria 1, 2, and 3:
For criterion 1 – Does the lesson/unit provide opportunities for students to independently demonstrate their understanding?
For criterion 2 – Do students have multiple ways to show what they have learned?
For criterion 3 – Is there evidence that the assessments produce a description of how close students have come to meeting expectations (e.g., annotated student work, descriptive rubrics/checklists)?
Possible activities with this dimension:
1. Participants can highlight in yellow what teachers will feel comfortable and in blue what teachers will feel is challenging.
2. Participants can highlight the vocabulary within the rubric that teachers may need to discuss and come to consensus on what those words/phrases mean.

22. Rubric Activity Multi Day Lesson/ Unit Plan
Presenters will come prepared with a choice of lesson plans for participants to use. During this
part of the presentation, a copy will be given to each participant as the presenter begins explaining the process of reviewing a multi-day lesson/unit.
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23. Giving Feedback
Writing effective feedback is vital to the EQuIP Quality Review Process. Below are the four qualities of effective feedback.
Criteria-based: Written comments are based on the criteria used for review in each dimension. No extraneous or personal comments are included.
Evidence Cited: Written comments suggest that the reviewer looked for evidence in the lesson or unit that address each criterion of a given dimension. Examples are provided that cite where and how the criteria are met or not met.
Improvement Suggested: When improvements are identified to meet criteria or strengthen the lesson or unit, specific information is provided about how and where such improvement should be added to the material.
Clarity Provided: Written comment are constructed in a manner keeping with basic grammar, spelling, sentence structure and conventions.
Facilitator discusses the qualities of effective feedback and lets audience know we will look at a few examples before we beginning with a lesson.

24. Example 1: Mathematics
This unit clearly targets three CCSS, which are noted in the overview. The overview also indicates which Standards for Mathematical Practice are central to the lesson. The activities throughout the unit present a balance of mathematical procedures and deeper conceptual understanding of the standards. The activities reinforce the standards and are well-connected to the content. I think the activities might be challenging with a large class with classroom management issues. Is this feedback criteria-based? Was evidence cited? Was there an improvement suggested? Is clarity provided?
Quick example. Have participants discuss quality of feedback against the quality measures of criteria-based, evidence cited, improvement suggested, and clarity provided. Share out. Answer on next slide.

25. Example 1: Feedback Criteria-based: Yes Evidence Cited: Partial
Improvement suggested: No
Clarity Provided: Yes
This feedback could be more effective. The reviewer mentions three standards and cites evidence: “which are noted in the overview.”
The reviewer states, “ The overview also indicates which Standards for Mathematical Practice are central to the lesson.” The reviewer does not provided any evidence to support the assertion.
The reviewer comments, “the activities through the unit present a balance of mathematical procedures and deeper conceptual understanding of the standards,” but does not cite specific details about why or how they are grade appropriate and well connected to the content being addressed.
No improvements are suggested. The reviewer does insert a personal opinion when saying, “ I think the activities might be challenging with a large class with classroom management issues. Personal opinions and comments unrelated to the criteria should be avoided when providing feedback; criteria-based feedback is more effective.
The written comments are constructed in a manner in keeping with basic
grammar, spelling, sentence structure and conventions.

26. Example 2: Mathematics
The lesson targets two CCSS, which are highlighted in the lesson cover page. Although the lesson does integrate Standards for Mathematical Practice, including appropriate tools strategically, given the CCSS that are targets, modeling may be a better fit. The lesson does present a balance of mathematical procedures and deep content knowledge. Is this feedback criteria-based? Was evidence cited? Was there an improvement suggested? Is clarity provided?
Last example. Have participants discuss quality of feedback against the quality measures of criteria-based, evidence cited, improvement suggested, and clarity provided. Share out. Answer on next slide.

27. Example 2: Feedback Criteria-based: Yes Evidence Cited: Partial
Improvement suggested: Partial
Clarity Provided: No
This feedback could be more effective.
Some specific evidence is cited to support the claims that criteria are present in the lesson.
There is an improvement suggested with, “modeling may be a better fit,” however, it would be beneficial to explain why.
The written comments are not constructed in a manner in keeping with basic grammar, sentence structure and conventions.

28. Quality Review Steps Step 1. Review Materials
Scan to see what the lesson/unit contains and how it is organized
Read key materials related to instruction, assessment and teacher guidance
Study and work the tasks that serve as the centerpiece for the lesson/unit, analyzing the content and mathematical practices the tasks require
Step 2. Apply Criteria in Dimension I: Alignment to the Depth of the CCSS
Identify the grade-level CCSS that the lesson/unit targets
Closely examine the materials through the “lens” of each criterion
Indicate each criterion for which clear and substantial evidence is found
Record input on specific improvements needed to meet criteria or strengthen alignment
Compare observations and suggestions for improvement
Continued on next page. Discuss the process. Independent read and review. Then group review to develop a consensus. Let participants know that today we are going to alternate between independent review, “team”/group consensus building, and whole group share out and calibration. In the future they would likely just follow the process of independent review of entire lesson/unit then group discussion and consensus.

29. Quality Review Steps Step 3. Apply Criteria in Dimensions II–IV
Examine the lesson/unit through the “lens” of each criterion
Indicate each criterion met and record observations and feedback
When working in a group, individuals may choose to compare observations and suggestions for improvement after each dimension or wait until each person has recorded all input for Dimensions II–IV.
Step 4. Provide Summary Comments (if group determines summary valuable)
Individually review comments for Dimensions I–IV, adding/clarifying comments as needed
Individually write summary comments
When working in a group, individuals should record summary comments prior to conversation.
Discuss the process. Independent read and review. Then group review to develop a consensus. Let participants know that today we are going to alternate between independent review, “team”/group consensus building, and whole group share out and calibration. In the future they would likely just follow the process of independent review of entire lesson/unit then group discussion and consensus.

30. EXAMPLE: Common Lesson for Review — Mathematics
Grade 7 — Draft Unit Plan 7.NS.1-3: Operations with Rational Numbers
This lesson is part of a unit plan titled “Operations with Rational Numbers.” The state that developed this unit plan uses the CCSS and the EQuIP rubrics to guide development of instructional materials and has charged its developers with creating overall conceptual unit plans, based on the CCSS domains, with one standard-based lesson and lesson seeds, based on the cluster. Teachers are able to use these as a model in their planning or to further develop the unit plan.
Pass out 7th grade lesson
This background may be beneficial for some. It isn’t necessary for the review, but any information can be valuable.

31. EXAMPLE: Step 1. Review Materials
Read key materials related to instruction, assessment and teacher guidance
Unit overview narratives (pp. 1–3)
Unit alignment (pp. 4–10)
Common misconceptions (p. 11)
Vocabulary (pp. 13–15)
Lesson plan and materials – 7.NS.1 (pp. 16–34)
Lesson seeds – 7.NS.1b, 7.NS.1d (pp. 35– 40)
Activities:
Four Corners
Traveling Around Maryland Gallery Walk
Rational Flow Chart
The Zero Circle and Block Party (Lesson Seeds)
Instruct audience to read or scan over the lesson pointing out the key materials listed above.

32. Criteria for Dimension I: Alignment to the Depth of the CCSS
The lesson/unit aligns with the letter and spirit of the CCSS:
Targets a set of grade-level CCSS mathematics standard(s) to the full depth of the standards for teaching and learning.
Standards for Mathematical Practice that are central to the lesson are identified, handled in a grade-appropriate way and well connected to the content being addressed.
Presents a balance of mathematical procedures and deeper conceptual understanding inherent in the CCSS.
Participants are given time to complete their individual review of Dimension 1. Then time with team to discuss and come to a consensus. Then share out and use following slide for calibration.

33. EXAMPLE: Step 2. Apply Criteria in Dimension I: Alignment
The lesson/unit aligns with the letter and spirit of the CCSS:
1. Targets a set of grade-level CCSS mathematics standard(s) to the full depth of the standards for teaching and learning.
2. Standards for Mathematical Practice that are central to the lesson are identified, handled in a grade-appropriate way and well connected to the content being addressed.
3. Presents a balance of mathematical procedures and deeper conceptual understanding inherent in the CCSS.

34. EXAMPLE: Step 2. Apply Criteria in Dimension I: Alignment
Observations/Feedback and Rating
The lesson clearly targets 7.NS.1a, b and d as the content standard for the lesson. The lesson does not list 7.NS.1c, although the lesson includes discussion of additive inverse. Developers should re-evaluate the omission of 7.NS.1c. It is assumed that further development of lessons beyond the two lesson seeds provided will address the requirements of 7.NS.2 and 7.NS.3.
The lesson plan identifies all eight of the Standards for Mathematical Practice as being addressed in the lesson/unit. And although references to the Practices are listed throughout the lesson/unit, it is not clear how central practices connect to specific activities and tasks. Those that are most central should be identified and their connection clearly defined. Those central Practices should serve as a focal point for the lesson and those that are not central should either be eliminated or noted as serving in a supporting role.
The balance between mathematical procedures and conceptual understanding is strong in the unit. As refinements are made, and as the Lesson Seeds are more fully developed, care needs to be taken to ensure that this balance is maintained.

35. EXAMPLE: Step 2. Apply Criteria in Dimension I: Alignment
Compare Criterion-Based Checks, Observations and Feedback
What is the pattern within our team in terms of the criteria we have checked?
Do our observations and feedback reference the criteria and evidence (or lack of evidence) in the instructional materials?
Does our feedback include suggestions for improvement(s)?
Whole group reflection and discussion on process so far. This slide can be copied and pasted into PowerPoint after each Dimension discussion.

36. Criteria for Dimension II: Key Shifts in the CCSS
The lesson/unit addresses key shifts in the CCSS:
Focus: Lessons and units targeting the major work of the grade provide an especially in- depth treatment, with especially high expectations. Lessons and units targeting supporting clusters have visible connection to the major work of the grade and are sufficiently brief. Lessons and units do not hold students responsible for material from later grades.
Coherence: The content develops through reasoning about the new concepts on the basis of previous understandings and provides opportunities for students to transfer knowledge and skills within and across domains and learning progressions.
Continued on next slide. Participants are given time to complete their individual review of Dimension 2. Then time with team to discuss and come to a consensus. Then share out and use following slide for calibration.

37. Criteria for Dimension II: Key Shifts in the CCSS
Rigor: Requires students to engage with and demonstrate challenging mathematics with appropriate balance among the following:
Application: Provides opportunities for students to independently apply mathematical concepts in real-world situations and problem solve with persistence, choosing and applying an appropriate model or strategy to new situations.
Conceptual Understanding: Provides opportunities for students to demonstrate conceptual understanding through challenging problems, questions, and writing and speaking about their understanding.
Procedural Skill and Fluency: Expects, supports and provides guidelines for procedural skill and fluency with core calculations and mathematical procedures (when called for in the standards for the grade) to be performed quickly and accurately.

38. EXAMPLE: Step 3. Apply Criteria in Dimension II: Key Shifts in the CCSS
The lesson/unit addresses reflects evidence of key shifts that are reflected in the CCSS:
1. Focus: Lessons and units targeting the major work of the grade provide an especially in-depth treatment, with especially high expectations. Lessons and units targeting supporting clusters have visible connection to the major work of the grade and are sufficiently brief. Lessons and units do not hold students responsible for material from later grades.
2. Coherence: The content develops through reasoning about the new concepts on the basis of previous understandings and provides opportunities for students to transfer knowledge and skills within and across domains and learning progressions.

39. EXAMPLE: Step 3. Apply Criteria in Dimension II: Key Shifts in the CCSS
3. Rigor: Requires students to engage with and demonstrate challenging mathematics with appropriate balance among the following:
Application: Provides opportunities for students to independently apply mathematical concepts in real-world situations and problem solve with persistence, choosing and applying an appropriate model or strategy to new situations.
Conceptual Understanding: Develops students’ conceptual understanding through tasks, brief problems, questions, multiple representations and opportunities for students to write and speak about their understanding.
Procedural Skill and Fluency: Expects, supports and provides guidelines for procedural skill and fluency with core calculations and mathematical procedures (when called for in the standards for the grade) to be performed quickly and accurately.

40. EXAMPLE: Step 3. Apply Criteria in Dimension II: Key Shifts in the CCSS
Observations/Feedback and Rating
There is strong focus on 7.NS.1 in the unit plan, including the model lesson plan and lesson seeds—particularly on 7.NS.1a, 7.NS.1b, and 7.NS.1d. The concepts and level of rigor prioritized in the standards are evident in the lessons/lesson seeds. 7.NS.1c is not clearly evident, and may be addressed in future lesson seeds.
There are clear connections made to prior learning in the section on Vertical Alignment. There are other references among the UDL Components, the Overview and Teacher Notes. In the Enduring Understandings there is a hint at how the concepts of this unit will be carried forward. However, more information might be provided for the teacher in how the real number system will evolve from the learning in this unit.
There is evidence of opportunity for application of some skills with the activities involving real-world context (card sort, gallery walk). However, many activities provide the opportunity for students to work in small groups or with partners, so there are few clear opportunities for independent application of concepts and skills to real-world contexts.

41. EXAMPLE: Step 3. Apply Criteria in Dimension II: Key Shifts in the CCSS
Observations/Feedback and Rating cont.
The guiding questions and other question prompts provide tools for teachers to probe for understanding. It is not clear, however, if all students will be expected to respond to questions verbally or in writing or if questions will be used solely to guide student discussion. Students are not presented with contextual problems that require deeper thinking and persistence and that can provide an indication of deeper conceptual understanding.
The unit emphasizes procedural skill and there are specific references in the unit to the development of fluency with operations with rational numbers as a goal of grade 7. However, it is not clear how much calculator usage is allowed, causing some concern as to how quickly and accurately students might perform calculations and procedures without this tool.

42. Criteria for Dimension III: Instructional Supports
The lesson/unit is responsive to varied student learning needs:
Includes clear and sufficient guidance to support teaching and learning of the targeted standards, including, when appropriate, the use of technology and media.
Uses and encourages precise and accurate mathematics, academic language, terminology, and concrete or abstract representations (e.g., pictures, symbols, expressions, equations, graphics, models) in the discipline.
Engages students in productive struggle through relevant, thought-provoking questions, problems and tasks that stimulate interest and elicit mathematical thinking.
Addresses instructional expectations and is easy to understand and use.
Provides appropriate level and type of scaffolding, differentiation, intervention and support for a broad range of learners.
Supports diverse cultural and linguistic backgrounds, interests and styles.
Provides extra supports for students working below grade level.
Provides extensions for students with high interest or working above grade level.
Continued on next slide. Participants are given time to complete their individual review of Dimension 3. Then time with team to discuss and come to a consensus. Then share out and use following slide for calibration.

43. Criteria for Dimension III: Instructional Supports
A unit or longer lesson should:
Recommend and facilitate a mix of instructional approaches for a variety of learners such as using multiple representations (e.g., including models, using a range of questions, checking for understanding, flexible grouping, pair-share).
Gradually remove supports, requiring students to demonstrate their mathematical understanding independently.
Demonstrate an effective sequence and a progression of learning where the concepts or skills advance and deepen over time.
Expect, support and provide guidelines for procedural skill and fluency with core calculations and mathematical procedures (when called for in the standards for the grade) to be performed quickly and accurately.

44. EXAMPLE: Step 3. Apply Criteria in Dimension III: Instructional Supports
The lesson/unit is responsive to varied student learning needs:
1. Includes clear and sufficient guidance to support teaching and learning of the targeted standards, including, when appropriate, the use of technology and media.
2. Uses and encourages precise and accurate mathematics, academic language, terminology, and concrete or abstract representations (e.g., pictures, symbols, expressions, equations, graphics, models) in the discipline.
3. Engages students in productive struggle through relevant, thought-provoking questions, problems and tasks that stimulate interest and elicit mathematical thinking.
4. Addresses instructional expectations and is easy to understand and use.
5. Provides appropriate level and type of scaffolding, differentiation, intervention and support for a broad range of learners.
Supports diverse cultural and linguistic backgrounds, interests and styles.
Provides extra supports for students working below grade level.
Provides extensions for students with high interest or working above grade level.

45. EXAMPLE: Step 3. Apply Criteria in Dimension III: Instructional Supports
Observations/Feedback and Rating
The guiding questions posed in the unit are thought provoking and are likely to stimulate student interest and some mathematical thinking. However the level of rigor required does not indicate that they are likely to engage students in a productive struggle.
The Possible Student Outcomes defined in the Draft Unit Plan help clearly define the instructional expectations. The varied questions and activities offered in the Model Lesson Plan provide teachers with a range of ways to address instructional expectations. The materials are user-friendly and generally easy to understand.
There is not enough support for students working below grade level in the unit or those with language difficulties. The concepts presented in this unit might prove to be challenging for English-language learners, who would benefit from the use of manipulatives and visual supports to demonstrate their mathematical understanding independently. There are places in the unit where activities are listed for intervention (a video), extension (writing a rap song), and for ELL (using the Frayer method of writing definitions). It is not clear how these activities would support those students needing more support from this lesson.

46. Criteria for Dimension IV: Assessment
The lesson/unit regularly assesses whether students are mastering standards-based content and skills:
Is designed to elicit direct, observable evidence of the degree to which a student can independently demonstrate the targeted CCSS.
Assesses student proficiency using methods that are accessible and unbiased, including the use of grade-level language in student prompts.
Includes aligned rubrics, answer keys and scoring guidelines that provide sufficient guidance for interpreting student performance.
A unit or longer lesson should:
Uses varied modes of curriculum-embedded assessments that may include pre-, formative, summative and self-assessment measures.
Participants are given time to complete their individual review of Dimension 4. Then time with team to discuss and come to a consensus. Then share out and use following slide for calibration.

47. EXAMPLE: Step 3. Apply Criteria in Dimension IV: Assessment
The lesson/unit regularly assesses whether students are mastering standards-based content and skills:
1. Is designed to elicit direct, observable evidence of the degree to which a student can independently demonstrate the targeted CCSS.
2. Assesses student proficiency using methods that are accessible and unbiased, including the use of grade-level language in student prompts.
3. Includes aligned rubrics, answer keys and scoring guidelines that provide sufficient guidance for interpreting student performance.
A unit or longer lesson should:
4. Use varied modes of curriculum-embedded assessments that may include pre-, formative, summative and self-assessment measures.

48. EXAMPLE: Step 3. Apply Criteria in Dimension IV: Assessment
Observations/Feedback and Rating
This lesson includes a readiness assessment but no formative or end-of-lesson assessment to determine the degree to which students can independently demonstrate the targeted CCSS. An observation checklist for the teacher to use when observing students working collaboratively with others would be helpful, as would adding opportunities for independent demonstration of understanding and skill.
Since there are no actual assessment tasks, there is no evidence for this criterion.
Answer keys are provided for some, but not all, of the student activities. This feature will be very helpful for teachers but reviewers suggested that in some cases an answer key could be more fully developed.

49. Where to Access Sample Lesson Plans/Units
Click Mathematics
Click Lessons
Participants bring their own multi-day lesson plan/unit.
Other ideas?
This slide provides online links for lesson plans/units that can be used in the training. Trainers
may have participants bring in their own lesson plans/units.
The 1st link is where the equip rubrics are housed. Also on this link, Achieve has modules for states who are choosing to evaluate units and who will utilize the scoring guide. Illinois will not be emphasizing that piece of the rubric.
The 2nd link houses lesson plans available for professional developers to utilize in sessions such as these. Follow the directions on the slide to access them.
The idea is not to find the perfect lesson but to find units of instruction that can be aligned to the rubric and find areas of need for improvement.
Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License
Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

50. EQuIP Resources Optional Lesson Plan Template Grades K-12
Web-based version
PDF version
and
Both of the websites on this slide house the EQuIP resources. Trainers may want to click on
both links and walk through the resources.
Additional resources not previously discussed include a K-12 lesson plan template.
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Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

51. What are the benefits of doing this activity with schools in your ROE?
Share Out!
What are the benefits of doing this activity with schools in your ROE?
What are the challenges of doing this activity with schools in your ROE?
Participants can be placed in groups to answer the questions on the slide.
1. What are the benefits of doing this activity with schools in your ROE?
2. What are the challenges of doing this activity with your ROE?
3. What ideas do you have?
After participants share their findings, the presenter or participants can record (on chart paper) overall strengths and challenges the group found when aligning lesson plans/units with the rubric.
What ideas do you have?
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Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

52. Next Steps Planning
Participants will then have time to plan as individual ROEs or collaboratively.
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Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

53. Content contained is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License

54. Dana Cartier – dcartier@illinoiscsi.org
Heather Brown –
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