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Achievement Chart

 

Geometry and Spatial Sense - Grade 4

Overall Expectations

Achievement Levels
By the end of grade 4, students will:
1
2
3
4
4m61 - solve problems using geometric models;

 

 

 

 

4m62 - investigate the attributes of three-dimensional figures and two-dimensional shapes using concrete materials and drawings;

 

 

 

 

4m63 - draw and build three-dimensional objects and models;

 

 

 

 

4m64 - explore transformations of geometric figures;

 

 

 

 

4m65 - understand key concepts in transformational geometry using concrete materials and drawings;

 

 

 

 

4m66 - describe location and movements on a grid;

 

 

 

 

4m67 - use language effectively to describe geometric concepts, reasoning, and investigations, and coordinate systems.

 

 

 

 

Note: Record the most consistent level observed.

 

Specific Expectations

Two and three-Dimensional Geometry
Achievement Levels
By the end of grade 4, students will:
1
2
3
4
4m68 - identify the two-dimensional shapes of the faces of three-dimensional figures;

 

 

 

 

4m69 - sketch the faces that make up a three-dimensional figure using concrete materials as models;

 

 

 

 

4m70 - design and make skeletons (e.g., with straws or toothpicks and marshmallows) for three-dimensional figures;

 

 

 

 

4m71 - identify and sort quadrilaterals (e.g., square, trapezoid);

 

 

 

 

4m72 - sort and classify two-dimensional figures according to shape;

 

 

 

 

4m73 - identify similar and congruent figures using a variety of media;

 

 

 

 

4m74 - construct congruent figures in a variety of ways (e.g., cutting and matching, using a geoboard);

 

 

 

 

4m75 - discover geometric patterns and solve geometric puzzles with and without the use of computer applications;

 

 

 

 

4m76 - measure angles using a protractor;

 

 

 

 

4m77 - use mathematical language to describe geometric ideas (e.g., line, angle);

 

 

 

 

4m78 - recognize and describe the occurrence and application of geometric properties and principles in the everyday world;

 

 

 

 

4m79 - discuss geometric concepts with peers and explain their understanding of the concepts;

 

 

 

 

4m80 - discuss ideas, make connections, and articulate hypotheses about geometric properties and relationships;

 

 

 

 

 
Transformational Geometry
Achievement Levels
By the end of grade 4, students will:
1
2
3
4
4m81 - demonstrate an understanding of translations, reflections, and rotations (e.g., on a geoboard or dot paper);

 

 

 

 

4m82 - apply translations, reflections, and rotations using concrete materials and drawings to pose and solve problems;

 

 

 

 

4m83 - discover transformation patterns with and without the use of computer applications;

 

 

 

 

4m84 - draw lines of symmetry on two-dimensional shapes;

 

 

 

 

 
Coordinate Geometry
Achievement Levels
By the end of grade 4, students will:
1
2
3
4
4m85 - demonstrate an understanding of coordinate systems and an ability to use them in simple games (e.g., battleship, bingo, chess).

 

 

 

 

 

Six of the Ontario Ministry of Education expectations for Mathematics: Geometry and Spatial Sense are not addressed in this chess unit. They may be taught using a more traditional approach to Geometry.

These exceptions are:

Two and three-dimensional Geometry

4m64 - explore transformations of geometric figures;

4m69 - sketch the faces that make up a three-dimensional figure using concret materials as models;

4m71 - identify and sort quadrilaterals (e.g., square, trapezoid);

4m76 - measure angles using a protractor;

4m78 - recognize and describe the occurrence and application of geometric properties and principles in the everyday world;

4m84 - draw lines of symmetry on two-dimensional shapes.

However, eight additional Ontario Ministry of Education expectations for Mathematics - Grade 4, can be applied to chess instruction.

These additional expectations are:

Patterning and Algebra

4m86 - demonstrate an understanding of mathematical relationships in patterns using concrete materials, drawings, and symbols;

4m87 - identify, extend, and create linear and non-linear geometric patterns, number and measurement patterns, and patterns in their environment;

4m88 - recognize and discuss patterning rules;

4m89 - apply patterning strategies to problem-solving situations;

4m95 – use a calculator and computer applications to explore patterns;

4m96 – pose and solve problems by applying a patterning strategy (e.g., solve an area problem by extending a geometric grid pattern);

4m98 – discuss and defend the choice of a pattern rule;

4m99 – given a rule expressed in informal language, extend a pattern.

Source:  Ontario Ministry of Education resource document(s)
 
 
Achievement Levels
 
 
Expectations in Mathematics: Grade 4