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Ample opportunity for students to share different strategies. Affirmed as valid ways to solve the problem. Builds confidence when they see there are multiple ways of solving a problem. 

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Ample opportunity for students to share different strategies. Affirmed as valid ways to solve the problem. Builds confidence when they see there are multiple ways of solving a problem. 

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All students are invited to a soft introduction to Math and are able to be successful up front which is great! Whether it's a "which one doesn't belong" or a "notice and wonder", the warm ups are great for all students to be capable of accessing grade level curriculum.

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The context at the beginning of each lesson is accessible for everyone and creates interest.

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Notice and Wonder + Multiple Representations

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Notice and Wonder + Multiple Representations

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Every notice was accepted and celebrated. Multiple representations helps all to connect.

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When planning, making sure we implement positive language to make sure all students feel like a capable learner

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It was community building because each individual explained their own process for how they arrived at their solution. - Micah C

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It was community building because each individual explained their own process for how they arrived at their solution. - Micah C

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In intro, everyone could form an opinion, share thoughts, then use the same strategy in first "hanger" then to multiple "hangers." 

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In intro, everyone could form an opinion, share thoughts, then use the same strategy in first "hanger" then to multiple "hangers." 

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The launches and the problems were very opening to all learners. The different methods for solving problems were valid, and the synthesis at the end by the teacher brought everything together.

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We can build the students confidence with the process of small wins.

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Every student has a jumping on point, no matter their level.

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Helps them develop a cyclical problem solving approach. It isn't linear, students have multiple entry points and are constantly practicing "doing math" with each lesson.

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started with weights, went to forming equations, then solving equations

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started with weights, went to forming equations, then solving equations

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Don't tell students how to do it, let them figure it out and explore it on their own/as a group

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Actively engaged with pictures and diagrams. We were able to connect the deeper concepts back to what we were being asked to do.

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The instructor did a great job of creating safety in learning. Students may not come up with the correct answer or get it right at the first try. Highlighting that it's a collaborative process and that even if kids don't get it the first time, they can get there. Knowing that it's okay to not know the answer right away.

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Students can feel encouraged by watching their peers attempt the problems and skills.

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Students were given the opportunity to attempt math problems independently before the teacher facilitated group work.

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There were multiple instances of collaboration and communication between peers and the class as a whole where each thought was welcomed. None of the conversations were turned down which allowed for each learner to share their piece.

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The launch with the hangers gave all students an opportunity to engage in mathematical thinking and it will serve as a tool as they continue to build more of a mental model. The activity also had a low floor for students of any ability to engage.

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Lots of invitations to do the work, the teacher facilitates the learning. The stuedents were eased into the mathematical ideas/language.

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We started with concrete things: hangers. Then we moved to the diagrams with the shapes. Then finished off with algebraic expressions.

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Can't get better if I don't practice. Makes the math personal.

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Small group interactions share thoughts, sense making, build on to strategies and jot down strategies from others. 

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Small group interactions share thoughts, sense making, build on to strategies and jot down strategies from others. 

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Michael Muniz 6A - Coherent Progression is so critical to success in the classroom. Going back to the lesson from yesterday, as we discuss the notice and wonder, the understanding comes with the many differences of opinions which opens up doors to new possibilities and leads to moments of “Aha!”

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The lessons progress with each activity. It is accessible for all students and progresses in a way that builds their skills and challenges them gradually.

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Started with a very concrete representation of socks on hangers and transitioned to equations (an abstract representation)

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In the warm-up, we got to see real examples of things in the real world, like socks, immediately reminding us how math is everywhere! We also continually did problems that progressed into the abstract.

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Students can move from concrete experiences to more abstract thinking based on their own engagement with the content and materials. This can go both ways.

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The activity after "Notice and Wonder" required the students to use trial and error in order to match equations with diagrams.

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6A- Creating a safe space to be risk takers in problem solving strategies is essential for the success of problem based learning.  Starting off with the picture of socks on a hanger creates a safe situation for all students to share creating safe community environment.

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6A- Creating a safe space to be risk takers in problem solving strategies is essential for the success of problem based learning.  Starting off with the picture of socks on a hanger creates a safe situation for all students to share creating safe community environment.

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Build lessons - start with small and build from there using core knowledge.

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Students' confidence will be boosted by actually seeing that there are different ways to do things. They had the equations while also seeing the visual representation of the equations.

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The activities include individual think time followed by some form of partner or group work. This helps them build confidence within their classroom community.

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Big base getting more fine tuned as you go up in grade level.

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Students can share their thoughts and ideas without any teacher interference. They have a safe environment to talk with one another about what they see or hear or think. They are going through the process without any guidance from the teacher. Student-to-student engagement.

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It gets people out of their comfort zones and promotes collaboration. We all got to share the learning, it wasn't just one person. We got to sharing our findings or help others see what things we didn't see before.

We were able to come to our breakout rooms and take ownership of our learning. Even if someone didn't want to talk they still participated.

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Everyone is able to see each other's thinking. Students have the opportunity to support all methods of problem solving and thinking. This gives the students a chance to tolerate feeling vulnerable.

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Visual supports throughout the launch and intro help to better support students understanding once they dive into equations. 

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Visual supports throughout the launch and intro help to better support students understanding once they dive into equations. 

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Teacher introduces, then students work together to explore, take risks. The warm-up allows for multiple entry points for students for everyone to be successful.

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The warm-up with the hangers allowed all students to start thinking about their learning. This allowed all students to answer questions and feel confident when they answered them.

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Invitation, discovery, and then the synthesis of the learning

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The lesson shifted from starting with more physical, manipulated items then slowly worked towards the abstract idea of balancing an equation.

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All students are capable learners with this activity because of the first question posed "what do you notice and wonder?". This question allows for students to think and answer, and there is no right or wrong answer--

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By having multiple people work together and share their process to their group and then with the class students can see and hear how each other work and that way the struggle is shared and normalized.

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Because of the coherent progression, students experience mathematics in a deep-thinking progression leading them to a greater "depth of knowledge". As teachers we would be able to refer back to these experiences throughout the course - experiences that students share collectively because of the community building that takes place simultaneously.

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For the warm-ups, being able to hear the different inputs from other students build community by building confidence on math thinking. This allows students to hear other students opinions and helps them think that there is no one way of thinking so in math, there is no one way of finding a solution.

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Students explained their own thinking and listened to how others approached the problem. In small groups, they shared ideas, made sense of the math together, added on to each other’s strategies, and even took notes on what their peers shared.

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Groups collaborated with each other after given instruction. As they collaborated, they worked through struggles together in order to learn the concept of balancing equations.

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Allows for all students to be involved and encouraged to be mathematical thinkers. Builds relationships and rapport by having students share thinking. 

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Allows for all students to be involved and encouraged to be mathematical thinkers. Builds relationships and rapport by having students share thinking. 

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Starting with a warm-up helps students access the material especially that the warm-up isn't always obviously math. The warm-up is something that all students could access. As they engage with the warm-up they build up the confidence to then approach real life math problems and eventually can demonstrate their understanding with the cool-down.

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Don't always rely on the teacher for answers. Ask your table mates.

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In 7.2, where students matched equations with pictures, the activity was very open-ended and allowed students to "do" math in any way that made sense to them.

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IM allows students to access math in an organic manner. They are able to find an access point in the content regardless of their background knowledge or prior experience. Students are able to see themselves as scholars and mathematicians even if they are not completing the arithmetic perfectly.

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Students are learning by doing the mathematics because of the open-ended task that allows students to learn for themselves and not copy what the teacher does.