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Takeaways:
1. It is important for students to understand one-to-one correspondence.
2. Manipulatives are very important, as well as hands on actvities.
3. Introducing five frames before ten frames is beneficial for student learning and understanding.

Lingering Questions:
1. Is the backwards 100s chart useful- should it be incorporated in our math time?
2. If so, when should this be introduced in K?

1 Way To Use:
1. Give students more easy access to manipulatives

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1. Takeaways
Number sense doesn't just happen. Warm ups and practice is needed daily to understand value of numbers to create number sense.

Manipulatives are constantly needed in math instruciton. Hands on makes it easier to grasp.

2. Lingering Questions
How should number sense strategies look in our classrooms? Where do you start when children are not able to grasp numbers on a chart? How do we teach the pattern of numbers? When should we do that?

3. way to use the info
Be slow and steady to maintain knowledge and numbers.

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Takeaways:
1. Use hands on activities to build fluency.
2. Students can use different strategies to solve a problem- give different ways to build/explore.
3. Create a number routine.

Lingering ?-
1. What are visual tools teachers can use to help students build mathematical thinking. Known Charts? Math Journals?
2. Number line or Number path?

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Takeaways:
1) Students need a strong mathematical foundation. We need to slow down and ensure students have the time and opportunities needed to learn and develop early mathematical skills/concepts.
2) Manipulatives are key in student success. Students must have daily opportunities to use hands-on manipulatives as learning is very concrete for K-1 students.
3) Number sense should be apart of your daily math routine. This should be explicitly modeled with multiple opportunities for students to visualize and conceptualize independently.
Lingering Questions:
1) Appropriate usage of 100 chart...
2) Hierarchial inclusion... I would love to know more specific strategies to teach students to move towards this approach to conceptual thinking.
Ways to use the information:
Provide multiple opportunities for student engagement for each mathematical skill/concept. Be intentional with your math block allowing ample time for visual modeling, hands-on practice, exploring, and applying the new skill/concept.

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3 takeaways:
- I want to be sure to always use models consistently throughout my math instruction.
- Students need time to develop their number sense and to be able to apply different strategies.
- Using number work in my room daily is very important. Giving students manipulatives helps them visualize the number we are building.

2 Lingering Questions:
- Should we move towards the 100s chart that is shown in the video?
- If so, what is the best method to go about that? Start fresh next year?

1 Way to use the information:
- Provide plenty of opportunity for students to count and use number sense in my room.

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1. Students need time.
2. They need to have hands on.
3. They need to explore and build.
Lingering -
100 chart yes or no? I think the more the better.

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Takeaways: 1) Don't get the cart before the horse. . . slow down the process to increase the product (specifically through the visual modeling of addition / subtraction /place vaule). 2) Always begin and end with 0. 3) There are a lot of skills being addressed at once as a child begins his/her journey as a mathematician. It was helpful to see the differentiation between concepts and how each could be taught.

Lingering Questions: 1) Would a 100-1 chart be helpful or confusing? I see his reasoning, but does this contradict our practice of reading left to right - as done during the literacy block? 2) Hierarchial inclusion: I'd love to see some "sample lessons" on teaching this skill. How do I "break the habit" of students going back to 1 and counting again to see how many are left? Sometimes I think it is habit, while other times I think there is a gap in the process.

Ways to use the information: Ssssllllllooooooowwww down!! Allow students more time to practice visual modeling, as well as drawing a model.

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3 Takeaways
1 - Students know how to count without have a number sense
2 - Counting objects should begin with 0
3 - Teaching students the idea of fair trade within place values can help with addition and subtraction

2 Questions
1 - Is the backwards 100 chart better than a traditional 100 chart?
2 - Are our current assessments in line with this way of thinking?

1 Way to Use This
1 - Students need more time counting, comparing, and explaining.

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3 Takeaways:
>Number sense takes time to develop.
> Hands-on practice using manipulatives is a must in early development.
> Use five frames before moving on the ten frames.

2 Lingering Questions:
> Should Kindergarten begin practicing with a reversed hundred chart?
> What are the best strategies to help kids who always have to start over when counting --even when they tell you the amount and you add one more to the group they will start completely over.

1 Way to Use the Info:
Give students more time for discovery after thoroughly modeling or allowing students to model strategies.

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1-    MANIPULITVIES , MANIPULAITVES are a must. 2-“It’s all about letting student conceptualize the math”3- Math needs to be real life to help students make sense of the process.

2-    Better way to enforce counting during interventions.  And “how do we use this info to design our math interventions.

3-    Use this to format our math intervention groups starting with cardinality and then progressing. Develop a format similar to reading intervention.

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Takeaways:
1) 1-to-1 correspondence is much more than students tagging number to an object. Students need to be a counter and a producer.
2) This math progression is so crucial to know. You can't expect a student to add and subtract if they don't understand the earlier parts of the progression. I feel like this will be so useful for math small groups and intervention next year.
3) He spoke on the importance of five frames. Next year, I want to incorporate these before introducing tens frames. If we can master filling a five frame, I'm sure our fact fluency will improve more quickly.

Lingering Questions:
1) Would the backwards 100 chart be helpful or hurtful? I get the idea but it's opposite from everything else we teach in K.
2) How do we reach those students that can add and subtract but they are constantly using models to connect amounts with numbers late in the year?

1 way to use:
1) As I said above, the progression will be very helpful when forming math small groups and intervention time next year.

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Takeaways
Just because they know the number name, that doesn't mean they understand why it's that number. I like how he related the number sequence to the alphabet in the way it is possibly memorized without real understanding.  Manipulatives are so helpful, and I have seen this to also be the case in older students.
Lingering questions
I incorporate reading during guidance, of course, but have also included math and will continue to think of ways that are appropriate...
1 Way to Use the Information
Be creative and incorporate it in small ways within my lessons.

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Krista Johnson
3 Takeaways:
1.  Modeling with tens frames in kindergarten sets the base foundation for place value.
2. Strong importance, of including zero on number lines, 100 charts and, when counting.
3. Knowledge of number sense and "hierarchial inclusion" when counting objects.

2 Lingering Questions:
1. I am wondering about using the 100 chart starting at the bottom. Should we be showing it both ways?? So often they see it printed 1-100, but maybe should introduce climbing up first? Show how it can be shown either way?
2. I know for ELA we are staring to focus on essential skills and the readiness into promotion/being prepared for the next year, will/are their essential skills we will be looking at for math as well?

1: Ways to Use this Information:
Model thinking and strategies for counting, addition, subtraction seems to be critical as well as using manipulatives and 10 frames.

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3 Takeaways:
1- When students are learning to subitize they are also learning comparison without having to directly teach that idea (more/less).
2- We should always include 0 in our counting forward AND backward.
3-Students need representation K-2, but they move more conceptually some in 1st, but especially in 2nd.

2 lingering questions:
1. Is there a informal assessment I could use, like the PAST but for these math ideas, to help drive my small groups?
2. When do base 10 blocks become appropriate?

1 way to use this information:
1- We could use this progression in our math small groups the same way we use the PAST and reading assessment LETRS gave us. (Ex. Once they master applying cardinality, you would start working on hierarchial inclusion ideas.)

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Takeaways
*We want our students to move from perceptual subitizing to conceptual subitizing.
*Being able to count backwards from 100 is just as important as being able to count forward from 0.
*Solid base ten rods were actually introduced in 2nd grade. Below 2nd grade it was the connecting cubes attached to make a ten rod.
Lingering Questions
*Do my students have a concept of cardinality?
*Do my students have a sense of hierarchical inclusion?
A Way to Use this Information
I see new skills that my students need to be assessed in and the need for more conversations with my students about their mathematical thinking.

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1. Manipulatives are a must; hands-on
2. Daily number work
3. Five frames could be used before introducing tens frame

1. Are 100-1 charts as effective?
2. Should we use those next year?

1. Give more time and opportunities to explore and count numbers.

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3 Takeaways
-I use rote learning in music frequently, they don't necessarily understand that their voice is moving up and down, but they can mimic it back. It can be difficult to move on from that stage.
-I really like the idea of the ten frames or the five frames
-These methods help take the theoretical into the tangible. It adds more of a kinesthetic element as well.
2 Lingering Questions
-How can I help reinforce counting in my music classroom?
-How do I introduce hierarchical inclusion in note value without just confusing them more?
1 Way to Use the Information
-I think I could make a Four Frame that could represent a four beat measure and use different blocks to represent different note values/quarter note, quarter rest, eighth note ect.

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Takeaways
The foundation for adding and subtracting is counting forward and backward.
Five frames may be underused in the primary grades and support future ten frame work.
Students benefit from drawing models as well as using manipulatives.
Questions
Are place value models appropriate for first grade? What are the benefits of the alternate 100 chart?
Using the Information
Provide students with more opportunities to count throughout the day--Give them real world examples to connect to their learning--Spend more time having students explain their thinking.

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3 Takeaways
-Students understand spatial patterns and number recognition before kindergarten, but they do not understand subitizing.
-In progression of early numbers and counting, students can visually notice the difference between more and less, but they can not necessarily understand how many more.
-Hierarchal inclusion means that students understand that numbers are nested inside of other numbers.
2 Lingering Question
-I do create meaningful stations in library, and I do try to incorporate reading and math skills into these whenever possible. How could I incorporate these skills into a library station?
1 Way to Use This
-I could create a station during library time that relates to our story but also includes a number sense activity within in.

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Anna Anderson- 3 "Takeaways" 2 Lingering Questions 1 Way to use this information

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Anna Anderson- 3 "Takeaways" 2 Lingering Questions 1 Way to use this information

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3 "Takeaways"
1) Use of models should be consistent with math instruction.
2) Place value is so important! It allows students to manipulate the numbers and have concrete examples for conceptual understanding when teaching addition and subtraction.
3) When students are visually comparing to similar numbers of objects, (ex: looking at one group of 10 Skittles and another group of 13 Skittles), it gives them a reason to count. Otherwise they can visually see which is more. Give students a reason to count!

2 Lingering Questions
1) How and when should I incorporate a 100-1 chart in a 1st grade classroom?
2) What is the best way to use place value manipulatives in addition/subtraction instruction/assessing?

1 Way to Use This Information
1) I loved how Fletcher used the place value blocks and the large piece of white paper to draw, exchange and manipulate the equation to give a visual representation of the equation being solved.

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3 Takeaways - loved how he broke down the progression of skills needed to help move a perceptual subitizer to a conceptual subitizer, the explanation of being a producer of counter vs. being a counter was helpful, I liked the terminology used when introducing addition as counting sets then joining them

2 lingering questions - how to provide more time for those who are slower at building an understanding of these concepts, how to provide more support for students who have not grasped the concept of unitizing (with the 5 or 10 frame)

1 way to use the information - more 1 to 1 matching activities (like the bear and the green present that he modeled) for students who are struggling with 1:1 correspondence

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3 Takeways
-Always introduce addition and subtraction in context. Students need to explore math concepts in a situation that is real life in order to make sense of the process.
-We want to use models that are consistent throughout math. We don't want them to expire.
-Perceptual substituting helps students build the concept of more or less.

2 Lingering Questions
-How & when do I include place value in daily routines to insure that place value isn't undermined?
-What is the best way to assess my students at the beginning of the year to understand where they are in their number sense?

1 Way to Use this Info
-Implement the use of both number charts 0-120 and 120-0 in daily counting routines.

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3 Takeaways
1. As long as students are using concrete models, they also need to be drawing representations of the math problem they are completing so they can see it in multiple ways.
2. Students need ample amount of time to develop number sense and find how they are the same using different tools and strategies.
3. The counting sequence part was very interesting to me because I see that all the time. The student can count to 100 but struggle with counting on from a given number because they have learned then pattern when counting from 1 to 100 but can't tell you if you give a random number.

2 Lingering Questions
1. Is the backwards 100s chart actually helpful? If all teachers aren't using it year to year, I feel like it would be confusing!
2. What is the best delivery method to teach decomposition? I feel like my kids always get so confused even though it is a form of addition/subtraction.

1 Way to Use This Information
1. Teach more flexible ways and strategies for my students to learn these concepts. I feel like I always teach the way I think is the easiest for them instead of letting them pick what works best for them personally.

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Jordan Rivers
3 Takeaways
1. Having a strong number sense is the best foundation for a student. Strong number sense allows students to understand concepts and find connections.
2. Looking at larger numbers by place value, helps students understand the quantity of a number rather than the numeral itself.
3. It is important for students to develop a deeper understanding by using different strategies.

2 Lingering Questions
1. What is the most accurate way of assessing these skills for our students?
2. Thoughts on the 100's chart starting from the bottom up???

1 Way to Use this Information
1. Model to my students how to "think flexibly" about numbers and allow them to more.

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1. Students need time to develop number sense at the most basic foundational level- just as they do with reading. Manipulatives are key. Encourage students to explain their thinking.
2. Ways to incorporate into reading intervention?
3. Connecting counting with phonological awareness, using manipulatives to count and demonstrate sounds within words and sentences. Counting using the alphabet arch.

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3 Takeaways
1. Using a 100-1 chart in addition to the 1-100 chart. This chart will give students a visual anchor as well.
2. Allow struggling students (or all students at the beginning of the year) to use a 5-chart rather than a 10-chart.
3. Use consistent models and strategies (that compliment both addition and subtraction).

2 Lingering Questions
1. What is the best way to assess and monitor these skills for students?
2. What is the best delivery method for this instruction? (Whole group? Small group? Stations for practice?)

1 Way to Use the Information
1. I feel that I need to do a better job of explicitly showing my thinking through the use of visual models.

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1. Daily number work is important.   It will take time to grasp number sense.  The use of manipulatives will help them to see number representation.  Have the students explain their thinking.   Help them organize materials for counting so they are not recounting the same object.
2. How can I apply to EL classes?
3. Practice makes perfect, the more we work with numbers the more we understand.

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3 Takeaways
-The learning of the whole concept of math for our students takes time and daily devotions. What may seem like the easiest task that could be skipped probably is the framework to visit everyday to grow that base knowledge to grasp and grow our little math minds.
-Showing and using items is key to students understanding concepts.
-Letting our students explain what and how can and may reach classmates faster than we as teachers could.
2 Lingering Questions
-Do we need to remove all 100 charts and start over with the one he shows? Makes sense.
-Where does the skill of writing numbers fit into learning the concepts of numbers?
1 Way to Use the Information
-The tortoise wins the race. Slow and steady with the introduction, exploration, and daily interaction will pay off. We tend to rush as educators to move on the next skill.

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3 Takeaways

-Allow students time to find similarities between numbers with different types of tools (10 frames, number charts, counters, number lines, rekenreks, etc.)

-Students should have practice counting forwards and backwards as well as to a certain number and from a certain number.

-Visualization is so important! Also, the turtle won the race…take time to slow down and really dive into these different concepts.

2 Lingering Questions

-Should we try using the number chart that begins at 100 and goes to 1? What are the benefits?

-What are some different activities/ways to incorporate the rekenreks?

1 Way to Use the Information

-Giving students plenty of time to explore numbers independently with visual and concrete representations.

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3 Takeaways
*When introducing comparing numbers, first begin with obvious differences. Next, provide the students with a need to count. I loved the example with the skittles!
*When number sequencing, use a 100's chart that starts with 0 and counts up from the bottom of the page.
*Purposely use concrete models to build a foundation for conceptual understanding in addition and subtraction.

2 Lingering Questions
-In order to provide continued support for our learners, how often should we review these concepts?
-What is the best method/preferred method to review?

1 Way to Use the Information
-Provide more opportunities for students to need to count.

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3 Takeaways
--When students come to K and can visually compare, they now they have a "reason to count"!
--Students need to count forward and backward including 0.
--"It's all about the conceptual understanding and allowing students to visualize the math!" Graham Fletcher

2 Lingering Questions
--Benefits of students using a 100's chart that begins with 1 at the bottom instead of the top??
--How much does maturity (or lack of) play a part in students gaining the concept of seeing numbers "conceptually"?

1 Way to Use the Information
--Giving students additional time for exploring of numbers with concrete models and pictorial representations