Lesson 1: Practice Problems

Problem 1

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

A plane composed of a series of squares. There are 5 large squares, 10 medium squares, and 10 small squares.

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:

tile the plane
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 figure with a top side of 4 units and a bottom side of 6 units. The lower portion of the figure has sides that are 2 units tall, and the upper portion has sides that 3 units tall. All angles are right angles.

The area can be found by counting the number of squares that touch the edge of the shape.
It takes 24 grid squares to cover the shape without gaps and overlaps.
The area can be found by multiplying the side lengths that are 6 units and 4 units.
The area can be found by counting the grid squares inside the shape.
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.

A figure with a bottom of 10 units, a right side of six units, and a left side that rises 3 units, then goes across 5 units, then goes up another 2 units, then across another 3 units, then up another 1 unit, and across another 2 units to connect to the right side. All angles are right angles.

Problem 6

Which shape has a larger area: a rectangle that is 7 inches by $\frac{3}{4}$ inch, or a square with a side length of $2 \frac{1}{2}$ inches? Show your reasoning.