Using technology to solve triangle construction problems, students apply their knowledge of points of concurrency, coordinate geometry, and transformational geometry.

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## Mathematical Explorations: Find the Distance: No Formula Necessary

### classroom-ready activities

### Ryota Matsuura and Yu Yan Xu

This activity involves finding the distance between two points in a coordinate plane and emphasizes reasoning from repeated calculations, which is one of the mathematical practices specified by the Common Core State Standards for Mathematics.

### Kevin C. Moore and Kevin R. LaForest

A connected introduction of angle measure and the sine function entails quantitative reasoning.

### Agida G. Manizade and Marguerite M. Mason

When calculating the area of a trapezoid, students use a range of problem-solving strategies and measurement concepts.

### Hyewon Chang and Barbara J. Reys

Using Clairaut's historic-dynamic approach and dynamic geometry tools in middle school can develop students' conceptual understanding before they encounter formal proof in geometry.

### Harold B. Reiter, John Thornton, and G. Patrick Vennebush

Through KenKen puzzles, students can explore parity, counting, subsets, and various problem-solving strategies.

### Jeffrey J. Wanko and Jennifer V. Nickell

Shapedoku puzzles combine logic and spatial reasoning with an understanding of basic geometric concepts.

### Sherri Ann Cianca

Communicating reasoning and constructing models fold nicely into a geometry activity involving the building of nesting boxes.

### Bobson Wong and Larisa Bukalov

Parallel geometry tasks with four levels of complexity involve students in writing and understanding proof.

### Tutita M. Casa

This instructional tool helps students engage in discussions that foster student reasoning, then settle on correct mathematics.