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

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### 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.

### 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.

### Bobson Wong and Larisa Bukalov

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

### Gloriana González and Anna F. DeJarnette

An open-ended problem about a circle illustrates how problem-based instruction can enable students to develop reasoning and sense-making skills.

### Michael K. Weiss and Deborah Moore-Russo

The moves that mathematicians use to generate new questions can also be used by teachers and students to tie content together and spur exploration.

### Anna E. Baccaglini-Frank

In this activity, students learn to make conjectures about properties that do not change.

### Zhonghong Jiang and George E. O'Brien

Using technology to explore the Three Altitudes of a Triangle problem, students devise many proofs for their conjectures.