 ## Grade 5 Math: Quadrilaterals

### Trapezoids and Parallelograms

In a prior lesson, students learned what a quadrilateral is and to recognize examples of quadrilaterals.

In this lesson, students begin to learn to categorize and recognize special types of quadrilateral figures. This lesson introduces trapezoids and parallelograms.

A trapezoid can be defined in either of two ways: 1) as a quadrilateral that has exactly two sides that are parallel, or 2) as a quadrilateral than has at least two sides that are parallel. The first definition is used in this lesson.

A parallelogram is a quadrilateral that has two pairs of opposite sides that are parallel.

Students learn to identify when a quadrilateral figure is a trapezoid or a parallelogram.

### Rhombuses, Rectangle, and Squares

In prior lessons, students have learned the definition of a quadrilateral and two special types of quadrilaterals – trapezoids and parallelograms. In this lesson, students are introduced to three additional types of quadrilaterals – rhombuses, rectangles, and squares.

A rhombus is defined as a special type of parallelogram. It has two pairs of opposite sides that are parallel, but all sides must be the same length.

A rectangle is also defined as a special type of parallelogram. It also has two pairs of opposite sides that are parallel, but all four angles must be right angles. The two pairs of opposite sides need not be the same length.

A square is defined as a special type of rectangle, so it is also a special type of parallelogram. A square is a rectangle that has all four sides the same length. A square is also a special kind of rhombus. It is a rhombus because it has two pairs of opposite sides that are parallel and the length of all the sides is the same. It is a special case of a rhombus because it has one additional requirement that a rhombus does not have – all four of the angles must be right angles. This is not a requirement of all rhombuses.

### Estimate Volume

In this lesson, students start to learn about volume. The concept of a cubic unit is first introduced. A cubic unit is a three-dimensional unit in which the length of all sides is equal to one unit. The concept of volume is introduced as the number of cubic units that will fit inside a three-dimensional figure.

In an earlier lesson, students learned to estimate area by counting the number of square units that will fit inside a two-dimensional figure. In this lesson, they extend the same approach by learning to estimate volume by counting the number of cubic units that will fit inside a three-dimensional figure.

### Volume of Rectangular Prisms

In this lesson, the concept of volume that students learned in the prior lesson is extended to measuring volume using cubic units.

Students learn that the number of cubic units that fit inside a three-dimensional figure can be determined by measuring the length of the sides, then multiplying these lengths.

This results in the definition of volume as the length times the width times the height.

Students learn to recognize that this definition is the same thing as the area of the base times the height.

### Coordinate Grid: First Quadrant

In this lesson, students are introduced to a coordinate grid for plotting pairs of numbers as points on the grid. Only the first, or positive, quadrant is used.

The axis is created by two axises – the x axis that extends horizontally, and the y axis that extends vertically. These axises are perpendicular to each other and extend to infinity in the positive direction. The positive direction for the x axis is to the right. The positive direction for the y axis is up. The point where they intersect is called the origin.

Points are plotted on the grid by specifying a value for the point on the x axis and the y axis. The value on the x axis is called the x coordinate. The value on the y axis is called the y coordinate.

Students learn to determine the coordinates of points plotted on the coordinate grid.

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