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As a 1^{st} grade math teacher, I never thought I was teaching the same skills as high school math teachers. But as I've gotten to know the Common Core State Standards, the math practice standards have shown me that effective math teaching looks remarkably similar across grade levels. Through the practice standards, K-12 students will develop skills around problem solving, reasoning and proof, connections, representation, and communication. Regardless of the grade level, focusing on these standards helps students feel comfortable explaining their thought processes, learning from others, and building conceptual understanding.

Teaching Channel recently partnered with the American Federation of Teachers to create a series of videos that show how two of the Common Core Math Practice Standards progress throughout the grades. The teachers we filmed for this series are part of Thinking Mathematics, an AFT professional development program that was developed by teachers working with researchers to learn what is known about how children learn mathematics and bring that knowledge into the classroom.

With these fabulous teachers, we created six videos that show students from kindergarten through 11^{th} grade reasoning abstractly and quantitatively (CCSS.Math.Practice.MP2) and constructing viable arguments and critiquing the reasoning of others (CCSS.Math.Practice.MP3).

While the goal is for the math practice standards to be used K-12, we know that nothing looks exactly the same across grade levels. Reasoning in kindergarten, for example, looks very different from reasoning in 11^{th} grade. When watched as a series, these videos show how math practices can be developed over time.

## Elementary

[caption id="attachment_57463" align="alignright" width="160"] Karen Lassiter's Kindergarten Class[/caption]

The first video in the series brings us to Karen Lassiter's kindergarten class, where students begin to reason about the numbers 11-19 and construct arguments using manipulatives to support their thinking. The next video shows first graders in Jeanne Wright's class solving a situational story about leprechaun traps. The students draw pictures and work in teams to reason about addition within 100. We see students sharing their strategies and beginning to provide evidence (saying things like, "I did this because I know…") to support their arguments.

## Upper Elementary

The next two videos in the series take us to upper elementary classrooms. In Amy Spies' 4th grade class and Becky Pittard's 5^{th} grade class, students reason about multiplying and dividing fractions. While the K/1 students were just beginning to provide concrete evidence to support their reasoning, these students are able to clearly explain their thinking and begin to critique the reasoning of others. It's inspiring to see Ms. Pittard deliberately help her students develop their critiquing skills by having them consider both correct and incorrect answers to a problem.

## Middle School

[caption id="attachment_57483" align="alignright" width="160"] Audra McPhillip's 8th Grade Class[/caption]

Next we get a glimpse into Audra McPhillips' 8^{th} grade class, where students take reasoning to a new level. They are presented with sets of functions and are tasked with coming up with conjectures that hold true for all the functions in the sets. By working together to analyze and identify patterns, students are moving beyond solving individual problems and starting to reason about larger mathematical concepts.

## High School

[caption id="attachment_57443" align="alignright" width="160"] Peggy Brookins' and Raymond James' 11th Grade Lesson[/caption]

The grand finale of this series is Peggy Brookins' and Raymond James' 11^{th} grade lesson on trigonometry. This class is *way* different from how I learned trigonometry! These students use the principles of trigonometry to design and test quadcopters. At the beginning of the lesson, we see students applying their knowledge of sine and cosine to reason about the propellers on their quadcopters. Students comfortably explain their thinking, follow along with each other's reasoning and critique the reasoning of others.

Watching these six teachers incorporate the practice standards in their classrooms shows how effective math teaching looks similar across grades. From kindergarten through high school, students are involved in rich math discussions. They are invited to share their strategies, learn from others, and apply their knowledge to real-world contexts. The teacher's role in these classrooms is deceptively complex: They guide their students towards understanding by asking probing questions, encouraging students to share their thinking, and synthesizing student responses.

Beyond seeing the practice standards in action, for me the biggest takeaway from this series is how much fun students and teachers are having in these lively math classrooms. The classrooms are full of students who are eager to participate and teachers who are excited about hearing students share their thinking.

So grab some popcorn, sit back and watch this series from start to finish. How will you use the math practice standards in your classroom?

## 6 Math Videos in this Series

Karen Lassiter's kindergarten class

Jeanne Wright's 1st grade class

Becky Pittard's 5^{th} grade class

Audra McPhillips' 8^{th} grade class

Peggy Brookins' and Raymond James' 11^{th} grade lesson

*Lily Jones taught K/1 for seven years in Northern California. She has experience as a curriculum developer, instructional coach, teacher trainer, and is also a contributing writer for Teaching Channel.*

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