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The teacher tells students they can use any manipulatives they want. She also states that the activity is open-ended enough that students can find answers in multiple different ways, but they will still understand what they are supposed to do (they have enough guidance to complete the activity). There are multiple approaches to solving the problem.

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The students had different choices to reach their answer. The idea of having the students explain their thoughts also helps the students because they have to explain what they are doing and why.

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The teacher did not provide step-by-step directions. This causes students to have to figure out how to solve the problem on their own. If the teacher taught this as a lower cognitive demand lesson she would have shown the students exactly how to solve the problem which would have required little to no original and creative thinking.

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The reasoning to have multiple entry and exit tickets is to is so that the learners can have a choice of what to do. Every student thinks and learns differently so the variations helps the students to do so.

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The problems are broad enough that not all the students immediately have the correct answer. They are given different ways to find their answers using things such as tiles but are not given direction on how to do so. There is more than one answer to the questions so the students are challenged.

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The students were given the task to find the area and dimensions given a set of different perimeters. It was an open-ended task because students had a variety of ways they could solve it, as well as the ability to go at their own pace. Since they were using different hands-on strategies to get to their solution, it would be considered a high cognitive demand lesson, given the multiple layers and problems this task has.

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I like that the lesson is meant to meet the needs of all learners. I think this is important since not everyone does learn the same way, it gives those a way to solve on their own and explain how they got the correct answer. Various methods of teaching and learning are shown which leads to student success.

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Students were given the task but were not told any specific procedure to solve it. They had the freedom to determine the areas any way they see fit as well as different ways to come up with their solution.

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This problem had a high cognitive demand because there were multiple ways to solve it, as well as multiple answers. The lesson is "broad enough" for all students to be able to participate, but also still challenging enough to keep all students engaged.

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This lesson was relevant because students were asked to use what they had previously learned about area and perimeter to solve real-life problems. Rather than just asking students to find the perimeter or determine the area, the teacher reverses the students thinking and applies what they have learned to allow them to discover and explore on their own.

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Students were provided perimeters and were required to find all areas and perimeters. In this approach, there were multiple answers, allowing for many entry points of construction and expression of thinking. Throughout the problem, students used manipulatives, graphing sheets, paper strips (constructing a 3-d form), and colored pencils to best present their way of thinking of perimeter and finding the accurate answer(s).

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I like that this lesson let the students create their own perimeter and shape. It allowed the students to take learning into their own hands. It lets them think outside of the box and they are able to come up with new ideas. This will allow the students take responsibility for their learning and make learning fun.

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This lesson had high cognitive demand because students were given a general topic to explore and it was up to the students to narrow the topic down and figure out the parameter and shape they wanted to do. There were more steps to solving their answer instead of a problem that was given to them. Students had to create their own problem and then solve.

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This lesson had high cognitive demand because, there was no definite answer. I was intrigued by the teacher's quote, "during the lesson, no one came up to me and asked me, 'am I finished?'". This indicates that students were engaged in their individual thinking, allowing them to continue to expand on their understanding of perimeter. In this video, the teacher successfully proved her lesson to have no end for learning. The teacher provided an assignment with multiple answers that kept the students invested, allowing them to persistently develop mathematical skills.

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This lesson had high cognitive demand because students were able to access the mathematics at their level and use varied representations to show their thinking. Ultimately, this helps students develop a deeper meaning for mathematical concepts and problem solving.

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I enjoyed how the teacher explained the directions to the students at the very beginning of the video. She said that they have a job to do and they're able to use various tools in order to do their jobs. She showed students all of the tools and told them they can use whatever tools they see fit. She was very direct and straightforward and she gave students a sense of responsibility by telling them that they had jobs to do.

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The lesson had high cognitive demand because the problem was broad enough that students were challenged.  Students needed to think about the problem; they weren't able to solve it right away.  The problem also had high cognitive demand because there was not one right answer.  Students could solve the problem how they liked.  This gave students an opportunity to use manipulatives or find another way to solve the problem allowing students to further understand the concept of perimeter.

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I liked how the teacher wanted to show the students how area and perimeter are interdependent.  This shows students that many math concepts relate to each other.  I also liked that this lesson met the needs of all learners.  Not everyone learns the same way so giving students the opportunity to solve problems in different ways, gives them more of a chance to understand the concepts being taught.  It's important to do this because it shows your students that you care about them and you want them to succeed.

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This lesson had high cognitive demand because right from the beginning the teacher told the students they were able to use any tools they wanted. This showed multiple ways to approach the problem. She also mentioned that she usually does open ended problems which I believe is higher cognitive demand if the wording of the problems vary each time. She had said that every student is challenged by the problem and given the opportunity to discover the answer on their own in their own way. There is no right way to approach the problem which shows procedural fluency.

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Students were able to approach the problem in their own way since they were open ended. Some students use blocks and count each one whereas other students take another approach and might find a shortcut. This shows conceptual understanding since there was a variety of problems and also procedural fluency because students are able to approach the problem in different ways, they just need to be able to explain their thinking and the process. Some children in the video needed physical manipulatives like a paper that represents a shape or blocks. She gave the students many different tools to choose from.

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This lesson provides high cognitive demand as students previously leaned about area and perimeter so they already had the skills to find each, now it was time for them to apply those skills on an open-ended problem. The problem gave them the solution so they had to work backwards. By doing so, they applied the knowledge they have on the topic and show how they were able to figure it out with different tools. This shows that the student have grasped the topic of area and perimeter without having the need to give them multiple questions with one set solution. Instead it was one solution with different ways in finding it.

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I liked how this lesson required students to think backwards instead of simply working on problems from the textbook or a worksheet. Like the teacher said students did not say "i'm done now what do i do?" They were was actively engaged in the problem using the different tools. One student worked it out in one way but the classmate next to him found it completely different. It was a great problem to show how students can approach this problem.

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In this lesson, students were given the freedom to work through the problem in whatever way they'd like. The teacher provided them with different tools and allowed them to choose which approach they would take.

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I really liked that students had to work backwards in the activity and I think that this style of problem solving was probably very beneficial to them in the future. This also allowed students to work for longer and find as many answers to the problem as possible rather than coming up with one solution and checking if it is right or not.

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This lesson had multiple entry/exit points because it was an open-ended question and students could use any manipulative they wanted and find the many different possibilities. Also, there was not just one answer. Since they were given a set perimeter, there are many areas as the solutions. All students were at different levels of understanding and could work at their own pace.

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This lesson had relevant context because it was in addition to what they previously learned. Previously, students practiced using area and perimeter formulas so they are applying their knowledge to different ways to find a solution. This lesson also teaches students to look for multiple approaches when solving any problem they face educationally or personally.

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This lesson had a high cognitive demand because there were multiple ways for the students to solve the problems appealing to different types of learners, as well as helping the students connect the different ways to solve together and make sense of it all. Since this problem had more than one answer, the teacher established a continuous learning flow throughout the lesson, challenging the students.

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I agree with what both Nick and Brielle said. By building on the students' prior knowledge of area and perimeter, the students were more able to master the content. Also, with connecting the problems to real life situations, is what makes the context relevant. This helps the students make connections within their own life.

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This lesson had high cognitive demand because it allowed students to go about solving the problem in multiple ways. Some students were using the tiles to count the perimeter and others just increased and decreased the length without using tiles. They both came to the same conclusion but were able to use different strategies to find their answers.

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This lesson had multiple entry/exit points because the problem was open-ended and it was broad enough to allow the students to choose how they wanted to solve it. The teacher gave them many different tools and manipulatives to choose from to help them solve the problem.

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This lesson contained high cognitive demand from the students because it instead of close ended problems, students are solving open ended problems with multiple tools that they can use whatever they want given by the teacher. This enables them to strategically think about the tasks they must solve and challenge themselves to broad possibilities of instead of just one way of thinking and solving. It is challenging for them on their level where they can discuss their thoughts with their peers and work through the lesson together in finding the solution without quickly knowing the answer. Students had to explore and realize how perimeter and area are interconnected, which was the goal of the lesson in working backwards of their problem solving.

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The way the teacher instructed this lesson felt a like a mix of inquiry and cooperative learning because the teacher acted as a guide to the students, but the majority of them were independent or worked in partners. This displays high cognitive demand learning as well as understanding the lesson concepts being taught and having prior knowledge to multiple strategies of finding area and perimeter. I particularly liked how each student used a different means of reaching to similar conclusions and were knowledgeable enough to explain their reasoning for their work.

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The questions asked were broad, therefore the students had to use their prior knowledge to explore and find the answers through their own work.  There was no step-by-step guide given to students to solve the problems, they instead had to use a higher level of thinking to generate ideas and solve the problems on their own.

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I liked that the teacher designed the lesson to have multiple right answers, which allowed the students to work through the problem and not simply solve for the right answer.  I also thought that it was important how the teacher mentioned the students did not ask her what to do when they were done, because the task was challenging enough for all students to really work through for the entire time.

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I liked that the teacher also gave problems that required the students to work backwards. She also gave problems that had more than one answer so that they cannot rush through their work. This challenges the students to really think through the problems being solved.

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The students were given different manipulatives to complete the activity. This lesson had high cognitive demand because the students we able to solve problems in ways that best worked for them. They each had their own way to work through the task at different levels of understanding, as opposed to being told that they had to solve the problems a certain way.

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The students all had different ways of approaching the problems. They were hard enough so that the students had to work through the problem to find the answer, and it didn't come to them immediately. They were able to use problem solving strategies that worked for them which may be different than other students.

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This lesson had multiple entry/exit points because they weren't told exactly what to do. The students had a choice in how they wanted to solve the problem. The teacher provided them with different tools and resources to help them solve the problem in different ways.

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By creating a multitude of entry and exit points, the instructor was able to compartmentalize the information being disseminated to the students. By creating these simple pockets of information, students were able to focus more on the details of each section rather than on the whole picture all at once. This allowed the instructor to then take the sum pieces of the whole lesson and bring them together for the students due to the structure of the lesson.

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The lesson's cognitive demand was rather high due to the level of skills that were employed by the students as they broke down the skills the instructor was teaching them through. The students had to address a multitude of problems with creative solutions, putting their brains into high gear to continue to keep up with the pace and level of content being presented.

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The students were given a task, enough information of the task and manipulative to use to get them to their answer. The students had to use problem solving strategies and high level of thinking in order to come up with the answers. Each student may approach it differently.

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I really liked this style of thinking. I think it makes the students really engaged and they are able to apply their prior knowledge to think at a deeper level to solve the problem. I also liked the style the teacher stated in the video of reverse thinking. This allows students to come up with multiple ways to get the answer.