One-straight-cut activities engage middle-school students in learning about symmetry and geometric transformations.

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## Encouraging Students to LOVE MATH with One-Straight-Cut Letters

### Yi-Yin (Winnie) Ko, Connor A. Goodwin, Lauren Ream, and Grace Rebber

## GPS: Composing and Decomposing Shapes Across the Grades

### Kyle Carpenter and Sarah Roller Dyess

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners' growth as problem solvers across their years of school mathematics.

## GPS: Growing Constantly: Building to Systems of Linear Equations

### Michelle T. Chamberlin and Robert A. Powers

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

## Problems to Ponder

### Chris Harrow, Justin Johns, and Hassan Lakiss

Problems to Ponder provides 28 varying, classroom-ready mathematics problems that collectively span PK–12, arranged in the order of the grade level. Answers to the problems are available online. Individuals are encouraged to submit a problem or a collection of problems directly to mtlt@nctm.org. If published, the authors of problems will be acknowledged.

## The Search for Perfect Donuts

### Wayne Nirode and Norm Krumpe

We define and investigate the concept of perfect donuts—rectangular donuts with a uniform width that is a natural number. Our investigation leads us to an interesting connection between the area of perfect donuts and the area of Pythagorean-triple triangles. We also provide ideas for further investigation.

## Simple Mathematical Model for Designing a Corbeled Arch

### Matthew S. Neel

This mathematical method can be used to find the size and shape of the bricks necessary to create a corbeled arch of nearly any shape. This method focuses on finding the minimum lengths of the bricks necessary to create a mathematically stable arch subject to certain constraints.

## Point-Line Ellipses and Hyperbolas

### Wayne Nirode

The author alters the definitions of ellipses and hyperbolas by using a line and a point not on the line as the foci, instead of two points. He develops the resulting prototypical diagrams from both synthetic and analytic perspectives, as well as making use of technology.

## Problems to Ponder

### Chris Harrow, Justin Gregory Johns, Ryne Cooper, and Vivekanand Mandel

Problems to Ponder provides 28 varying, classroom-ready mathematics problems that collectively span PK–12, arranged in the order of the grade level. Answers to the problems are available online. Individuals are encouraged to submit a problem or a collection of problems directly to mtlt@nctm.org. If published, the authors of problems will be acknowledged.

## “Fostering Mathematical Thinking and Problem Solving: The Teacher’s Role”

### Nicole R. Rigelman and Introduction by: Sam Rhodes

From the Archives highlights articles from NCTM’s legacy journals, previously discussed by the *MTLT* Journal Club.

## Delving Deeper: What Else Comes after 1 + 2 = 3?

### Charles F. Marion

The simplest of prekindergarten equations, 1 + 2 = 3, is the basis for an investigation involving much of high school mathematics, including triangular numbers, arithmetic sequences, and algebraic proofs.