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As a coach I would use this tool in PLC's  to help with planning cooperative groups.  Each of the four categories can help teachers as they start to plan their lessons.  From organization of the groups to the assessment of individual students.  Each category has questions to support the planning.
A modification a coach could do is to have one to model for the PLC's, that way teachers can have a visual when they are planning their own lessons. Another modification could be to break each one of the categories up and to make posters out of each one for a specific lesson or task.

Citations
McGatha, M., Bay-Williams, J. M., Kobett, B. M. C., & Wray, J. A. (2018). Everything you need for mathematics coaching: Tools, plans, and a process that works for any instructional leader: Grades K-12. Corwin, a SAGE Publishing Company.

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This tool is to be use as a follow-up to reflect on the teacher's lesson with cooperative groups.  This can be used in the post observation interview. Teachers will need to bring the planning for cooperative groups tool when to the debriefing.   Teachers will reflect on their lesson that they had planned for cooperative groups. After the teacher has filled out the sheet the coach will share the data that was collected while observing the teacher.  The only modification that I would make for this is that it might be helpful if the coach were to write up the data that he/she has collected so that the teacher has a record of it.

Citation: McGatha, M., Bay-Williams, J. M., Kobett, B. M. C., & Wray, J. A. (2018). Everything you need for mathematics coaching: Tools, plans, and a process that works for any instructional leader: Grades K-12. Corwin, a SAGE Publishing Company.

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Sometimes math can be a bit challenging and therefore students tend to retreat and not be engaged in their work. desmos.com can help students be more productive in their work. This site perfectly aligns with many math programs such as Illustrative Math. Desmos is great for when students need to use manipulatives for an activity but need that visual piece as well.  This can also be used for students who need extra practice on a target.

One thing I would suggest is for teachers is to preview the activity.  This is because sometimes what I have found is that just because an activity comes up in your search doesn't mean that that activity will go with the target you are teaching or even be easy for students to do.

Citations:  Let's learn together. Desmos. (n.d.). Retrieved April 10, 2023, from https://www.desmos.com/

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Desmos offers best-in-class calculators, digital math activities, and curriculum to help every student love math and love learning math.

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Planning for Five "Key Strategies" for Formative Assessment

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Planning for Five "Key Strategies" for Formative Assessment

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This planning sheet has all of the key strategies for Formative Assessment.  Learning Targets, Providing Feedback to students, Evidence, Responsive Actions, and Students ownership and involvement.  What I like about this planning form is that it breaks it into two parts.  The lesson a teacher is teaching and the unit that it is in.  As a coach I would use this with a teacher during a coaching cycle or in a PLC with a group of teachers.

The modification I would make is I would have a teacher use this for either a lesson or a unit but not at the same time.  The reason for this is that it can be overwhelming to do both.  If teachers break it down lesson by lesson in the unit then he or she can work with special education and or ELL  teachers. The teacher could then differentiate what evidence they are expecting from students depending on their students' ability.

Citation:
McGatha, M., Bay-Williams, J. M., Kobett, B. M. C., & Wray, J. A. (2018). Everything you need for mathematics coaching: Tools, plans, and a process that works for any instructional leader: Grades K-12. Corwin, a SAGE Publishing Company.

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This is a great tool for coaches to use with teachers to build learning targets and then to create rubrics for students to self-assess their learning.
Teachers will pull the learning targets from the lesson and then using the rubric at the top write task-specific language of what student work would look like at each level.

Modifications: I like how has two ways to use this tool.  I wouldn't start right off with students creating performance levels to self-assess.  I would have the teacher do this a couple of times and then as a class create performance levels.  I think having the students do it without guidance might be a bit too much for students to handle.

Citation:
McGatha, M., Bay-Williams, J. M., Kobett, B. M. C., & Wray, J. A. (2018). Everything you need for mathematics coaching: Tools, plans, and a process that works for any instructional leader: Grades K-12. Corwin, a SAGE Publishing Company.

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 Chapter 4 Get The FACTs!  ( Formative Assessment Classroom Techniques)

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 Chapter 4 Get The FACTs!  ( Formative Assessment Classroom Techniques)

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Teachers can us these at the end of a lesson to see what students have learned.  I have used these to inform me of how my students are learning.  Each of the 75 FACTs will give a description of how each FACT promotes learning, how it informs instruction, how to use the FACT, it gives modifications, and caveats.  Included with each FACT is General Implementation Attributes: How hard is it to use? How much time does it take? As well as the Cognitive Demand.

Modifications: Shuffle the FACTs around that you use. This is so students have a variety of formative assessments and they won't get bored.

Citation:

Keeley, P., Tobey, C. R., & National Council of Teachers of Mathematics. (2011). Mathematics formative assessment: 75 practical strategies for linking assessment, instruction, and learning. Corwin, A SAGE Publications Company.

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Mathematics Formative Assessment, Volume 1: 75 Practical Strategies for Linking Assessment, Instruction, and Learning

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Amazon.com: Mathematics Formative Assessment, Volume 1: 75 Practical Strategies for Linking Assessment, Instruction, and Learning: 9781412968126: Keeley, Page D., Tobey, Cheryl Rose: Books

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Different Ways to Differentiate a Lesson

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Different Ways to Differentiate a Lesson

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This tool can be use in PLC's or individually within a coaching cycle.  Here teachers put write down what the lesson is in the middle and then plan outwards using the three categories. Think about what you as a teacher want students to know ( final outcome of lesson), How are you going to engage your students in the lesson, and how are students going to demonstrate how they have learned in the lesson. In each triangle think about different ways to differentiate the lesson Then pick one to use in class.

Modifications: I would use this with 10.13 and the Can Do Statements to help teachers as they plan. These are  located under Supporting English Language Learners and Supporting Students with Special Needs.  The reason for this is because these students will be in your classes and your lessons will need to be differentiated to have them succeed.  I would also communicate with the enrichment teacher to help with differentiation for students in the Gifted and Talented programs.

Citation:
McGatha, M., Bay-Williams, J. M., Kobett, B. M. C., & Wray, J. A. (2018). Everything you need for mathematics coaching: Tools, plans, and a process that works for any instructional leader: Grades K-12. Corwin, a SAGE Publishing Company.

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This tool is to be used with 8.4 to gather data of the make up of the teacher's class. Once the teacher has this data then he or she can start to plan their lessons.  There are planning questions to help when differentiating the lesson or unit.  I would also use this with the tools from ELL students as well as Supporting Students with Special Needs.

Misconceptions: You don't have to plan this out by yourself.  Get support from Special education, ELL, and Enrichment teachers. These teachers have more resources for you to use and plan with. These teachers also have a better understanding of learning styles to help plan with you.

Citation:
McGatha, M., Bay-Williams, J. M., Kobett, B. M. C., & Wray, J. A. (2018). Everything you need for mathematics coaching: Tools, plans, and a process that works for any instructional leader: Grades K-12. Corwin, a SAGE Publishing Company.

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Chapter 3 Knowing and Understanding Students as Learners.  The Differentiated Math Classroom

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Chapter 3 Knowing and Understanding Students as Learners.  The Differentiated Math Classroom

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The whole book is a great tool but Chapter 3 is what this tool is about.  Here in this chapter readers dive deep into how students learn math.  Every student learns differently we all know that.  However, every student learns how to do math differently as well.  Within this chapter there are a myriad of tools for teachers to use when planning out a lesson or a unit. From a Habits of Work list that teachers can use when observing their students working on activities to different learning styles are in your classroom and what they need to learn.  There is even a Student Motivation Inventory that teachers can have their students fill out so to help with planning.

Misconceptions: You do not need to read the whole book to help with differentiation.  I am recommending to read chapter 3 first to help teachers get started with understanding their students as learners.

Citation: Murray, M., & Jorgensen, J. (2007). Chapter 3 Knowing and Understanding Students as Learners. In The differentiated math classroom: A guide for teachers, K-8 (pp. 49-72). Heinemann

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The Differentiated Math Classroom: A Guide for Teachers, K-8

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Amazon.com: The Differentiated Math Classroom: A Guide for Teachers, K-8: 9780325009964: Murray, Miki, Jorgensen, Jennifer: Books

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Planning Strategies to Support Emergent Multilingual Students

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Planning Strategies to Support Emergent Multilingual Students

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This tool is a great one for helping teachers planning out their lessons.  With the strategies on the left and then teachers fill out the specific ideas to go along with each strategy when planning out lessons.  These strategies are researched based to help English Language Learners.

Modification: I would use this for all English Language Students who have not exited out the ELL program at your school.  Just because students in the ELL program are not emergent language learners doesn't mean that they don't need help with the learning.

Citation:
McGatha, M., Bay-Williams, J. M., Kobett, B. M. C., & Wray, J. A. (2018). Everything you need for mathematics coaching: Tools, plans, and a process that works for any instructional leader: Grades K-12. Corwin, a SAGE Publishing Company.

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When a new student comes to the United States and does not know any English, it take that student 7 years to learn English to be proficient enough to exit out of the ELL program at a school.  Each year ELL students need to take a test that is called the ACCESS test.  The student needs to get a proficiency level of 4 to exit the ELL program. After an ELL student takes the Access test the ELL teachers will fill out a Can Do Descriptor sheet for each student. These Can Do Descriptors tell where the student is in learning English.

I would use these Can Do Descriptors to help me plan lessons to make sure that I had activities that every student could participate in.  This will help when using the tool Planning Strategies to Support Emergent Multilingual Students. You will differentiate your activities depending on where your ELL students fall on the Can Do Descriptors.

Modifications: I would use this for ALL of my ELL students. Not just the Emergent Language Learners.  I would even still use this to help me when a student had exited the program.  Sometimes students do slip back when they have exited due to speaking their native language at home because parents may not be able to speak English.

Citations:
Can Do Descriptors Grades 6-8. (n.d.). https://wida.wisc.edu/sites/default/files/resource/CanDo-KeyUses-Gr-6-8.pdf

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Connecting Shifts to Support Emergent Multilingual Students Self-Assessment

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Connecting Shifts to Support Emergent Multilingual Students Self-Assessment

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This tool can be used in a coaching cycle or even in PLCs.  This is a self-assessment that teachers can do to find where they are on the Shift scales.  The shifts are Shift 1, Shift 2, Shift 3, and shift 4, and Shift 6. These shifts are related to differentiations to help student learn. These shifts go from the teacher showing everything to students to asking probing questions to have students think more.  After teachers take the self-assessment use the questions during a coaching conversation.

Modifications: None.  They are already done for the coach.  Teachers do not have to self-assessment on all eight shifts only the shifts pertaining to differentiation.

Citation:
McGatha, M., Bay-Williams, J. M., Kobett, B. M. C., & Wray, J. A. (2018). Everything you need for mathematics coaching: Tools, plans, and a process that works for any instructional leader: Grades K-12. Corwin, a SAGE Publishing Company.

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Structuring a Lesson to Support Students with Special Needs

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Structuring a Lesson to Support Students with Special Needs

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This tool can be used two different ways: One for planning purposes or for a coach to take notes when observing a teacher teaching a lesson.  There are four key areas: Summarizing the lesson, developing the lesson, introduction to the lesson, and organization and environment. Then in each key area are planning considerations that teachers can have in their lessons for students with special needs.  The planning considerations have notes such as but not limited to:  smooth transitions, building on prior knowledge, providing ways to organize work, and provide support in communicating ideas, such as writing prompts.

Modifications: If using it as a planning tool I would come up with two planning considerations for the key areas.  If using it as a observation tool I would choose one focus from each key idea or a particular are with many considerations to work on.

Citations:

McGatha, M., Bay-Williams, J. M., Kobett, B. M. C., & Wray, J. A. (2018). Everything you need for mathematics coaching: Tools, plans, and a process that works for any instructional leader: Grades K-12. Corwin, a SAGE Publishing Company.

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This tool can be used in a PLC to gather ideas or it can be used when planning a lesson. Here teachers can discuss challenges that might be present in their classrooms.  Once teachers figure the challenges out teachers can plan support structures that can help their students with special needs.  I would also ask for the assistance of a special education teacher who has more knowledge of the students and their specific disability.

Modifications: I would look at a students' IEP to help with the challenges part of this tool. I also believe a model would help here as well.

Citation:
McGatha, M., Bay-Williams, J. M., Kobett, B. M. C., & Wray, J. A. (2018). Everything you need for mathematics coaching: Tools, plans, and a process that works for any instructional leader: Grades K-12. Corwin, a SAGE Publishing Company.

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Building Fact Fluency ( A Tool Kit for Multiplication and Division)

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Building Fact Fluency ( A Tool Kit for Multiplication and Division)

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This tool is amazing! We all know that students don't want to sit there and do timed tests for learning their multiplication and division facts.  This kit helps students build strategies to help them learn their facts.  In this kit you will find image talks, tool talks, and games to help students learn strategies to help them to know their math facts.  (There is also one for Adding and Subtracting too).  All of the Image Talks, Tool Talks, as well as the games are online and you will have access to them when you register your kit.

Modifications: I would read the facilitator's guide.  In this guide it will have a schedule of how to use the kit as well as where to start for facts.  You could use this in small groups if you wanted to target specific students rather than working as a whole class.

Citation:

Building Fact Fluency: A Toolkit for Multiplication & Division © 2021 Grades 3–5 Graham Fletcher and Tracey Johnson Zager. Stenhouse Publishing.
from $589.00 USD

Building Fact Fluency: A Toolkit for Addition &