# Lesson 4 Leap Year Practice Understanding

## Jump Start

Today’s task contains this calendar page for February 28. For each definition, draw and label a diagram to show the meaning of the words.

A circle is the set of all points in a plane that are equidistant from a fixed point called the center of the circle. An angle is the union of two rays that share a common endpoint. An angle of rotation is formed when a ray is rotated about its endpoint. The ray that marks the pre-image of the rotation is referred to as the “initial ray” and the ray that marks the image of rotation is referred to as the “terminal ray.” Angle of rotation can also refer to the number of degrees a figure has been rotated around a fixed point, with a counterclockwise rotation being considered a positive direction of rotation. |

### 1.

A circle...

### 2.

An angle...

### 3.

An angle of rotation...

### 4.

The calendar page for March 1 discusses some interesting facts about degree measurement, but doesn’t define it. What is a degree?

## Learning Focus

Write precise definitions of the rigid transformations.

How do I use my intuition, and the insights gained during the past few tasks, to identify or produce a rigid transformation?

How can I make my intuitive and insightful thinking explicit in words and diagrams?

What can I add to the words **slide**, **flip**, and **turn** to more precisely define the rigid transformations—translation, reflection, and rotation?

## Open Up the Math: Launch, Explore, Discuss

What is wrong with **slide**, **flip**, and **turn** as words for defining the rigid transformations?

**Slide**, **flip,** and **turn** are verbs; they describe an action.

Here are ways these words might be used in a sentence:

Slide: “Slide over here for a minute.”

Flip: “Flip the card over, so we can see which card it is.”

Turn: “Turn the lid counterclockwise to open the jar.”

### 1.

Think about the work you did in class with *Leaping Lizards* and *Leap Frog*. What is missing in each of these sentences that would need to be included to make these actions a **translation**, a **reflection,** or a **rotation**?

The word “flip” can create a misconception—a wrong way of thinking.

### 2.

Draw a picture to illustrate the sentence, “Flip the card over, so we can see which card it is.” (Be as accurate as possible when drawing the two pictures of the card.)

### 3.

Does your picture show a reflection? Why or why not?

Carlos and Clarita are discussing their latest business venture with their friend Juanita. They have created a daily planner that is both educational and entertaining. The planner consists of a pad of

The twins are excited to share the prototype of their planner with Juanita before sending it to printing. Juanita, however, has a major concern. “Next year is leap year,” Juanita explains. “You need

So now Carlos and Clarita have the dilemma of needing to create an extra page to insert between February 28 and March 1.

Here are the planner pages they have already designed.

A circle is the set of all points in a plane that are equidistant from a fixed point called the center of the circle. An angle is the union of two rays that share a common endpoint. An angle of rotation is formed when a ray is rotated about its endpoint. The ray that marks the pre-image of the rotation is referred to as the “initial ray” and the ray that marks the image of rotation is referred to as the “terminal ray.” Angle of rotation can also refer to the number of degrees a figure has been rotated around a fixed point, with a counterclockwise rotation being considered a positive direction of rotation. |
Why are there One theory is that ancient astronomers established that a year was approximately Another theory is that Babylonians first divided a circle into parts by inscribing a hexagon consisting of six equilateral triangles inside a circle. The angles of the equilateral triangles, located at the center of the circle, were further divided into Another reason for |

Since February’s theme is mathematics, Clarita suggests that they write formal definitions of the three rigid-motion transformations they have been using to create the images for the flip-book animation.

How would you complete each of the following definitions?