We introduce the Into Math Graph tool, which students use to graph how “into" mathematics they are over time. Using this tool can help teachers foster conversations with students and design experiences that focus on engagement from the student’s perspective.

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### Amanda K. Riske, Catherine E. Cullicott, Amanda Mohammad Mirzaei, Amanda Jansen, and James Middleton

### LouAnn H. Lovin

Moving beyond memorization of probability rules, the area model can be useful in making some significant ideas in probability more apparent to students. In particular, area models can help students understand when and why they multiply probabilities and when and why they add probabilities.

### Tracy E. Dobie and Miriam Gamoran Sherin

Language is key to how we understand and describe mathematics teaching and learning. Learning new terms can help us reflect on our practice and grow as teachers, yet may require us to be intentional about where and how we look for opportunities to expand our lexicons.

### Kelly Hagan and Cheng-Yao Lin

April 2020's GPS department provides tasks for each grade band that invite students to reason with age-appropriate number theoretic concepts.

### Zachary A. Stepp

“It's a YouTube World” (Schaffhauser, 2017), and educators are using digital tools to enhance student learning now more than ever before. The research question scholars need to explore is “what makes an effective instructional video?”.

### Anne Quinn

The paper discusses technology that can help students master four triangle centers -- circumcenter, incenter, orthocenter, and centroid. The technologies are a collection of web-based apps and dynamic geometry software. Through use of these technologies, multiple examples can be considered, which can lead students to generalizations about triangle centers.

### Patrick Sullivan

Is the “Last Banana” game fair? Engaging in this exploration provides students with the mathematical power to answer the question and the mathematical opportunity to explore important statistical ideas. Students engage in simulations to calculate experimental probabilities and confirm those results by examining theoretical probabilities

### Stephen Phelps

### Edited by Anna F. DeJarnette

A monthly set of problems targets a variety of ability levels.

### Imani M. Goffney

### Edited by Naima F. Goffney

My name is Naima Goffney, and I am an eleven-year-old seventh grader at Julius West Middle School. I am taking algebra 1 this year. I wanted to write the Math for Real because in math class I do not always think that what we are learning is related to the real world. At home, my mom shows me all the different ways I am mathematically smart, which makes me want to try harder in school during the “rougher” days. We can use math to know more about how to improve our skills and find the math we learn in school more interesting and more related to our real world as middle schoolers.

### P. Reneé Hill-Cunningham

Hundreds of species of animals around the world are losing their habitats and food supplies, are facing extinction, or have been hunted or otherwise negatively influenced by humans. Students learn about some of these animals and explore multiple solution strategies as they solve this month's problems. Math by the Month features collections of short activities focused on a monthly theme. These articles aim for an inquiry or problem-solving orientation that includes four activities each for grade bands K–2, 3–4, and 5–6.