GEEM - Skills and Knowledge

E2.1 Identify measurable attributes of two-dimensional shapes and three-dimensional objects, including length, area, mass, capacity, and angle.

Skill: Identifying the Measurable Attributes of Objects, Two-Dimensional Shapes, and Three-Dimensional Objects

To describe an object accurately, it is necessary to examine and manipulate it to bring out some of its particular characteristics called attributes. For example, the gift shown below can be described by highlighting any of the attributes in the following table:

A gift, in the shape of a rectangular prism, is presented in two different positions. In the first position, the gift rests on its base. In the second position, the gift rests on one side.

Inside a box are the following words: "its length," "its area," "its height," "its color," "the number of its faces," "its texture," "its mass," "its capacity," "its use."

Some of these attributes are descriptive in nature, while others are quantitative in nature in and can be represented by a count or number. To determine this number, one can use counting (for example, counting the faces) or measurement (for example, measuring with a ruler or a pan balance).

To develop a sense of measurement, students must first know and understand measurable attributes.

The table below provides a summary of some measurable attributes of two-dimensional shapes and three-dimensional objects that students in the primary grades need to understand and measure effectively.

Attributes	Description	Example
Length	Length is a measure in a one-dimensional space (for example, height, depth, width, thickness, radius, diameter The perimeter is the length around a two-dimensional shape or three-dimensional object.	I determined the height of the box by comparing it to the height of the tower of cubes. I determined its perimeter by measuring the length around the box with a string. Note: A variety of objects can be used to measure the length attribute (for example, tongue depressor, coffee stick, toothpick, string, pencil).
Area	Area is a measure of the space within a two-dimensional shape. Surface area is the total area of all of the sides of a three-dimensional object.	I determined the area of the top face of the box by covering it with sticky notes.
Capacity	Capacity is a measure of the maximum amount that a container can hold.	I determined the capacity of this box by pouring glasses filled with sand into the box. I count the number of glasses of sand I needed.
Mass	Mass is a measure of the amount of matter in an object.	I determined the mass of the gift using a pan balance.
Angle	Angle is the measure of turn between two rays or line segments with a common endpoint.	I determined if there are angles in a geometric shape by targeting two sides of a two-dimensional shape that meet (in a corner) or by overlaying a pattern block.

In order to develop students' understanding of the nature of each attribute and to identify the differences among attributes, teachers should use instruction that goes beyond repetitive measurement exercises presented without context. Instead, they should use an approach that focuses on understanding attributes, the relationships among them, and the ways to measure them. This can be accomplished through a variety of authentic situations that engage students in using benchmarks and concrete materials, making estimates, and taking measurements.

Source: translated from Guide d’enseignement efficace des mathématiques, de la maternelle à la 3^e année, Mesure, p. 45-47.

Knowledge: Measurable Attributes of Two-Dimensional Shapes

Length, height, width
Angles
Perimeter
Area

Knowledge: Measurable Attributes of Three-Dimensional Objects

Length, height, width or depth
Angles
Area of faces
Capacity
Mass

Knowledge: Length

Length is the general term for any quantity in a one-dimensional space.

A length can refer to:

the size of a line segment, in other words the distance between two points;
the distance between two parallel lines or two parallel planes;
a perimeter;
a height, a depth, a thickness, a width, a height (of a person).

Note: For some students, these different terms associated with length may be confusing.

Examples

Perimeter refers to the length of the outline of a two-dimensional shape or any three-dimensional object.

A "stop" sign. A dotted line outlines the sign. A rectangular shape with the word butter marked on one side. A dotted line outlines one side of the prism.

The length of a book becomes its height when stored upright on a shelf, just as its thickness becomes its width.

Two books. The first book is placed on its cover. An arrow shows the length of the book and another arrow shows its thickness. The second book is standing on a shelf, one arrow shows its height and a second arrow shows its thickness.

Source: translated from Fiche de la maternelle à la 3^e année Attribut longueur, p. 2.

Knowledge: Area

Area is a measure of the space within a two-dimensional shape.

Examples of area in everyday life include the size of:

a vegetable garden;
a backyard.

Examples

The neighbor's vegetable garden is larger than the flower bed in front of their house.

A vegetable garden between two trees. A house and it’s flowerbed.

The schoolyard area is divided into three different playgrounds.

Three playgrounds in a schoolyard. The first is a hopscotch and stick figures. The second picture is a slide and two park games (spring horses). The third picture is a soccer field

Source: translated from Fiche de la maternelle à la 3^e année Attribut aire, p. 2.

Knowledge: Mass

Mass is the amount of matter in an object.

Only the kind of matter that makes up an object influences its mass, so the mass of an object does not vary depending on where on Earth (or in space) it is located.

The mass of an object can be determined using a balance or scale, such as a pan balance.

Note: Mass and weight should not be confused. The weight of an object is the force exerted on it by a celestial body. It can be determined with a dynamometer and is expressed in newtons (N). The weight of an object varies according to its mass and according to the place on Earth (or in space) where it is located.

Examples

A beach ball and a baseball. A scale with two trays. In the pans, there is an object on one side and an apple on the other. Below the scale is written, "two pan scale."

Source: translated from Fiche de la maternelle à la 3^e année Attribut masse, p. 2.

Knowledge: Capacity

The capacity of a container is the maximum amount that it can hold.

Note: It is important to distinguish between capacity and volume. Capacity indicates the amount that a container can hold while volume is the space that an object occupies in space.

Examples

This cylinder has a capacity of four tennis balls.