GEEM - Skills and Knowledge

E1.1 Sort and identify two-dimensional shapes by comparing number of sides, side lengths, angles, and number of lines of symmetry.

Skill: Sorting Two-Dimensional Shapes

Sorting requires one group objects, two-dimensional shapes, or three-dimensional objects according to attributes or characteristics .

When students identify similarities and differences, they can sort objects, two-dimensional shapes, or three-dimensional objects by attribute(s) (colour, texture, etcetera) using organizers such as hoops, boxes, or a double entry table.

By Grade 2, students will be able to sort geometric shapes according to one or more properties (for example, number of sides, length of sides, angles, and number of lines of symmetry).

Once students have classified several two-dimensional shapes according to one property, teachers can ask them to classify two-dimensional shapes by choosing their own classification criteria.

Example

Sorting rules

Two-dimensional shapes formed by a broken closed line
Two-dimensional shapes formed by a closed curved line
Two-dimensional shapes that have three sides
Two-dimensional shapes that have four sides
Two-dimensional shapes without sides

During consolidation, teachers should support students to identify the properties that are common to all shapes in the same class. This will help them distinguish those properties that are important in identifying a two-dimensional shape. Teachers can also emphasize words related to likelihood (for example, certain, impossible, possible) to make connections to the Data strand. For example:

It is certain that triangles have three sides.
It is possible that triangles have a right angle.
It is possible that triangles have three congruent sides.
It is impossible for triangles to have four sides.

Over time, the students realize that families of geometric shapes have common properties (for example, all triangles have three sides) and that subsets have distinct properties (for example, some triangles have two equal sides).

Source: translated from Guide d’enseignement efficace des mathématiques de la 1^re à la 3^e année, Géométrie et sens de l'espace, p. 34-35.

Beginning in Grade 2, the Venn diagram is an excellent tool for sorting geometric shapes according to different properties. Students can use them to classify two-dimensional shapes according to one or two attributes. This allows them to further develop their knowledge of:

properties common to the large families of two-dimensional shapes (polygons or circles);
distinct properties of subsets of two-dimensional shapes (for example, quadrilaterals, pentagons).

Closely related to expectation E2 Measurement is the sorting of two-dimensional shapes according to their geometric properties. Students must be able to use non-standard and standard units of measurement appropriately to compare lengths and angles. For example, they may use the width of their finger (non-standard unit) or a ruler graduated in centimeters (standard unit) to measure the sides of two two-dimensional shapes and then compare the measurements to make a sort.

In the Data strand, one can sort or compare geometric shapes using graphs and describe properties of geometric shapes using probability expressions.

Source: translated from Guide d’enseignement efficace des mathématiques de la 1^re à la 3^e année, Géométrie et sens de l'espace, p. 17.

Relationships Between the Classes of Two-Dimensional Shapes

The relationships between different classes of two-dimensional shapes are important to establish. In elementary school, students learn the properties of a rectangle, square, quadrilateral, and other geometric shapes. As students develop their understanding of these properties, they learn that some classes are actually subsets of other classes. In particular, students learn that:

rectangles are also quadrilaterals, because both have four sides;
squares are also rectangles, because both have four sides and four right angles.

It is unrealistic to expect elementary students to fully understand and explain the relationships between classes of two-dimensional shapes; however, teachers must be careful not to sort two-dimensional shapes so rigidly that they convey misinformation that students will have to “unlearn” later (Clements, 1999; Copley, 2000). For example, the teacher should not say, “No, this is not a rectangle, it is a square.”

Source: translated from Guide d'enseignement efficace des mathématiques, de la 1^re à la 3^e année, Géométrie et sens de l'espace, p. 16.

Skill: Identifying Two-Dimensional Shapes

In Kindergarten, children begin to describe, sort, classify, build and compare two-dimensional shapes and three-dimensional figures by exploring, and comparing their attributes and properties. For example, they might point to a triangle and say that it has three sides. In Grade 1, students begin to name geometric shapes and their features, such as the vertices and sides of a two-dimensional shape and the vertices, edges, faces, and surfaces of a three-dimensional object. In this way, students demonstrate that they are able to associate the appropriate vocabulary with the elements of a geometric form. In Grade 2, students begin to identify the characteristics of two-dimensional shapes, and can begin to compare shapes by considering number of sides, side lengths, angles, and number of lines of symmetry.

Example

Progression of vocabulary related to the concept of a triangle:

Source: translated from Guide d’enseignement efficace des mathématiques de la 1^re à la 3^e année, Géométrie et sens de l'espace, p. 32-33.

Skill: Comparing Two-Dimensional Shapes

By observing and manipulating a variety of familiar objects and representations of two-dimensional shapes (for example, pattern blocks), students first notice visual and tactile differences and similarities.

Source: translated from Guide d’enseignement efficace des mathématiques de la 1^re à la 3^e année, Géométrie et sens de l'espace, p. 33.

Knowledge: Two-Dimensional Shapes

Two-dimensional shapes have geometric properties that allow them to be identified, compared, sorted, and classified.

The following are types of two-dimensional shapes that can be included in Grade 2 student activities.

Source: The Ontario Curriculum. Mathematics, Grades 1-8 Ontario Ministry of Education, 2020.

Knowledge: Number of Sides

Grade 2 students can identify two-dimensional shapes, from triangles (three sides) to octagons (eight sides), including regular and irregular polygons.

Knowledge: Length of the Sides

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 of any three-dimensional object.

A length can refer to:

the size of a line segment, namely. 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

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: Angles

A shape formed by two rays or two line segments with a common endpoint.

An angle can be formed or determined by:

two lines of the same origin;
two intersecting half-planes;
a rotation of a line segment around a fixed point.

Examples

Angle is the measure of turn between two rays or line segments with a common endpoint.

Angles. The first angle is labeled; " B ", " A ", " C ", it is acute. The second angle is labeled: "N", "O", "P" is obtuse.

Angle formed by two intersecting half-planes.

Two half-plans that cross each other. An arrow passes from one plane to another.

Source: translated from Fiche de la 4^e à la 6^e année Attribut angle, p. 2.

Knowledge: Number of Lines of Symmetry

A two-dimensional shape has line symmetry if the shape can be divided into two congruent parts that can be matched by folding along a line, known as the line of symmetry.

Shapes can have:

A line of symmetry
Two or more lines of symmetry
No line of symmetry

Grade 2 students may:

identify examples of symmetry in their environment, including shapes with non-vertical lines of symmetry;
draw or create symmetric shapes using concrete materials;
determine the line of symmetry of two-dimensional shapes. Students easily recognize vertical lines of symmetry, but may have difficulty locating non-vertical lines of symmetry.

Source: translated from Guide d’enseignement efficace des mathématiques de la 1^re à la 3^e année, Géométrie et sens de l'espace, p. 7