# Lesson 1

Tiling the Plane

### Problem 1

Which square—large, medium, or small—covers more of the plane? Explain your reasoning.

### Problem 2

Draw three different quadrilaterals, each with an area of 12 square units.

### Problem 3

Use copies of the rectangle to show how a rectangle could:

a. tile the plane.

b. not tile the plane.

### Problem 4

The area of this shape is 24 square units. Which of these statements is true about the area? Select all that apply.

A:

The area can be found by counting the number of squares that touch the edge of the shape.

B:

It takes 24 grid squares to cover the shape without gaps and overlaps.

C:

The area can be found by multiplying the sides lengths that are 6 units and 4 units.

D:

The area can be found by counting the grid squares inside the shape.

E:

The area can be found by adding $$4 \times 3$$ and $$6 \times 2$$.

### Problem 5

Here are two copies of the same figure. Show two different ways for finding the area of the shaded region. All angles are right angles.

### Solution

Which shape has a larger area: a rectangle that is 7 inches by $$\frac 34$$ inch, or a square with side length of $$2 \frac12$$ inches? Show your reasoning.