E1.5 Describe and perform translations, reflections, and rotations up to 180° on a grid, and predict the results of these transformations.
Activity 1: Geometry in Works of Art
This activity integrates concepts in Spatial Sense as well as the Arts.
Teachers should show students a variety of artists' pieces that include geometric shapes or lines (for example, works by Sonia and Robert Delaunay, Piet Mondrian, Claude Tousignant, Bridget Riley). They should then ask the students to examine the geometric elements in these pieces and to think about how they can describe them using geometric vocabulary for shapes (for example, circles, squares, rhombuses), kinds of lines (for example, curved lines; straight, slanted, horizontal, or vertical lines; perpendicular or parallel lines), and the transformations (for example, rotation, reflection, translation). Teachers should also lead a discussion about the effects of each of the elements (for example, stillness, movement, depth). Finally, they should ask students to read the title of each piece and discuss the connection between the title and the composition.
Teachers should then ask students to choose the artist that most resonates with them and to use that artist as inspiration to create their own piece using geometric shapes, lines and transformations. Students can explore using various materials and techniques, and then produce a few drafts. They should then create their piece and title it. To complete the art-making process, teachers will have students present their piece to the class, identifying the geometric elements chosen and explaining the techniques used. Other students can express their appreciation of the piece by referring to the impact of the geometric elements that were used.
Source: translated from Guide d'enseignement efficace des mathématiques de la 4e à la 6e année, Géométrie et sens de l'espace, Fascicule 1, p. 44.
Activity 2: A Geometric Dance
This activity integrates concepts in Spatial Sense, The Arts and Health and Physical Education.
In a physical education class, teachers can ask students to perform various geometric transformations with their bodies. They can also ask them to perform translations (for example, move forward or to the left), reflections (for example, two students can make movements, as if they were playing a mirror game), and rotations (for example, make a pivot like in basketball or spin around another student).
Teachers then will assign students to prepare a short choreography in pairs or groups of four that incorporates movements from the three types of transformations. To facilitate the execution of their choreography, students should say aloud the sequence of transformations performed (for example, turn clockwise, move two steps back). Teachers can also have the students perform the choreography to music.
Each team will take turns presenting their choreography to the class. Following each presentation, the other students can be asked to identify some of the transformations that were used.
Source: translated from Guide d'enseignement efficace des mathématiques de la 4e à la 6e année, Géométrie et sens de l'espace, Fascicule 2, p. 43-44.