Strand Overview: Spatial Sense
Note: Teachers should exercise their professional judgement to select and adapt the materials found in this resource to meet the needs of their students as they learn the expectations outlined in the Ontario Mathematics curriculum.
E1. Geometric and Spatial Reasoning
Describe and represent shape, location, and movement by applying geometric properties and spatial relationships in order to navigate the world around them.
Learning Situation-
Geometric Reasoning
-
E1.1 Sort three-dimensional objects and two-dimensional shapes according to one attribute at a time, and identify the sorting rule being used.
-
E1.2 Construct three-dimensional objects, and identify two-dimensional shapes contained within structures and objects.
-
E1.3 Construct and describe two-dimensional shapes and three-dimensional objects that have matching halves.
-
-
Location and Movement
-
E1.4 Describe the relative locations of objects or people, using positional language.
-
E1.5 Give and follow directions for moving from one location to another.
-
E2. Measurement
Compare, estimate and determine measurements in various contexts.
Learning Situation-
Attribute
-
E2.1 Identify measurable attributes of two-dimensional shapes and three-dimensional objects, including length, area, mass, capacity, and angle.
-
E2.2 Compare several everyday objects and order them according to length, area, mass, and capacity.
-
-
Time
-
E2.3 Read the date on a calendar, and use a calendar to identify days, weeks, months, holidays, and seasons.
-
E1. Geometric and Spatial Reasoning
Describe and represent shape, location, and movement by applying geometric properties and spatial relationships in order to navigate the world around them.
Learning Situation-
Geometric Reasoning
-
E1.1 Sort and identify two-dimensional shapes by comparing number of sides, side lengths, angles, and number of lines of symmetry.
-
E1.2 Compose and decompose two-dimensional shapes, and show that the area of a shape remains constant regardless of how its parts are rearranged.
-
E1.3 Identify congruent lengths and angles in two-dimensional shapes by mentally and physically matching them, and determine if the shapes are congruent.
-
-
Location and Movement
-
E1.4 Create and interpret simple maps of familiar places.
-
E1.5 Describe the relative positions of several objects and the movements needed to get from one object to another.
-
E2. Measurement
Compare, estimate and determine measurements in various contexts.
-
Length
-
E2.1 Choose and use non-standard units appropriately to measure lengths, and describe the inverse relationship between the size of a unit and the number of units needed.
-
E2.2 Explain the relationship between centimetres and metres as units of length, and use benchmarks for these units to estimate lengths.
-
E2.3 Measure and draw lengths in centimetres and metres, using a measuring tool, and recognize the impact of starting at points other than zero.
-
-
Time
-
E2.4 Use units of time, including seconds, minutes, hours, and non-standard units, to describe the duration of various events.
-
E1. Geometric and Spatial Reasoning
Describe and represent shape, location, and movement by applying geometric properties and spatial relationships in order to navigate the world around them.
Learning Situation-
Geometric Reasoning
-
E1.1 Sort, construct, and identify cubes, prisms, pyramids, cylinders, and cones by comparing their faces, edges, vertices, and angles.
-
E1.2 Compose and decompose various structures, and identify the two-dimensional shapes and three-dimensional objects that these structures contain.
-
E1.3 Identify congruent lengths, angles, and faces of three-dimensional objects by mentally and physically matching them, and determine if the objects are congruent.
-
-
Location and Movement
-
E1.4 Give and follow multistep instructions involving movement from one location to another, including distances and half- and quarter-turns.
-
E2. Measurement
Compare, estimate and determine measurements in various contexts.
Learning Situation-
Length, Mass, and Capacity
-
E2.1 Use appropriate units of length to estimate, measure, and compare the perimeters of polygons and curved shapes, and construct polygons with a given perimeter.
-
E2.2 Explain the relationships between millimetres, centimetres, metres, and kilometres as metric units of length, and use benchmarks for these units to estimate lengths.
-
E2.3 Use non-standard units appropriately to estimate, measure, and compare capacity, and explain the effect that overfilling or underfilling, and gaps between units, have on accuracy.
-
E2.4 Compare, estimate, and measure the mass of various objects, using a pan balance and non-standard units.
-
E2.5 Use various units of different sizes to measure the same attribute of a given item, and demonstrate that even though using different-sized units produces a different count, the size of the attribute remains the same.
-
-
Time
-
E2.6 Use analog and digital clocks and timers to tell time in hours, minutes, and seconds.
-
-
Area
-
E2.7 Compare the areas of two-dimensional shapes by matching, covering, or decomposing and recomposing the shapes, and demonstrate that different shapes can have the same area.
-
E2.8 Use appropriate non-standard units to measure area, and explain the effect that gaps and overlaps have on accuracy.
-
E2.9 Use square centimetres (cm2) and square metres (m2) to estimate, measure, and compare the areas of various two-dimensional shapes, including those with curved sides.
-
E1. Geometric and Spatial Reasoning
Describe and represent shape, location, and movement by applying geometric properties and spatial relationships in order to navigate the world around them.
Learning Situation-
Geometric Reasoning
-
E1.1 Identify geometric properties of rectangles, including the number of right angles, parallel and perpendicular sides, and lines of symmetry.
-
-
Location and Movement
-
E1.2 Plot and read coordinates in the first quadrant of a Cartesian plane, and describe the translations that move a point from one coordinate to another.
-
E1.3 Describe and perform translations and reflections on a grid, and predict the results of these transformations.
-
E2. Measurement
Compare, estimate and determine measurements in various contexts.
-
The Metric System
-
E2.1 Explain the relationships between grams and kilograms as metric units of mass, and between litres and millilitres as metric units of capacity, and use benchmarks for these units to estimate mass and capacity.
-
E2.2 Use metric prefixes to describe the relative size of different metric units, and choose appropriate units and tools to measure length, mass, and capacity.
-
-
Time
-
E2.3 Solve problems involving elapsed time by applying the relationships between different units of time.
-
-
Angles
-
E2.4 Identify angles and classify them as right, straight, acute, or obtuse.
-
-
Area
-
E2.5Use the row and column structure of an array to measure the areas of rectangles and to show that the area of any rectangle can be found by multiplying its side lengths.
-
E2.6 Apply the formula for the area of a rectangle to find the unknown measurement when given two of the three.
-
E1. Geometric and Spatial Reasoning
Describe and represent shape, location, and movement by applying geometric properties and spatial relationships in order to navigate the world around them.
Learning Situation-
Geometric Reasoning
-
E1.1 Identify geometric properties of triangles, and construct different types of triangles when given side or angle measurements.
-
E1.2 Identify and construct congruent triangles, rectangles, and parallelograms.
-
E1.3 Draw top, front, and side views of objects, and match drawings with objects.
-
-
Location and Movement
-
E1.4 Plot and read coordinates in the first quadrant of a Cartesian plane using various scales, and describe the translations that move a point from one coordinate to another.
-
E1.5 Describe and perform translations, reflections, and rotations up to 180° on a grid, and predict the results of these transformations.
-
E2. Measurement
Compare, estimate and determine measurements in various contexts.
-
The Metric System
-
E2.1 Use appropriate metric units to estimate and measure length, area, mass, and capacity.
-
E2.2 Solve problems that involve converting larger metric units into smaller ones, and describe the base ten relationships among metric units.
-
-
Angles
-
E2.3 Compare angles and determine their relative size by matching them and by measuring them using appropriate non-standard units.
-
E2.4 Explain how protractors work, use them to measure and construct angles up to 180°, and use benchmark angles to estimate the size of other angles.
-
-
Area
-
E2.5 Use the area relationships among rectangles, parallelograms, and triangles to develop the formulas for the area of a parallelogram and the area of a triangle, and solve related problems.
-
E2.6 Show that two-dimensional shapes with the same area can have different perimeters, and solve related problems.
-
E1. Geometric and Spatial Reasoning
Describe and represent shape, location, and movement by applying geometric properties and spatial relationships in order to navigate the world around them.
Learning Situation-
Geometric Reasoning
-
E1.1 Create lists of the geometric properties of various types of quadrilaterals, including the properties of the diagonals, rotational symmetry, and line symmetry.
-
E1.2 Construct three-dimensional objects when given their top, front, and side views.
-
-
Location and Movement
-
E1.3 Plot and read coordinates in all four quadrants of a Cartesian plane, and describe the translations that move a point from one coordinate to another.
-
E1.4 Describe and perform combinations of translations, reflections, and rotations up to 360° on a grid, and predict the results of these transformations.
-
E2. Measurement
Compare, estimate and determine measurements in various contexts.
-
The Metric System
-
E2.1 Measure length, area, mass, and capacity using the appropriate metric units, and solve problems that require converting smaller units to larger ones and vice versa.
-
-
Angles
-
E2.2 Use a protractor to measure and construct angles up to 360°, and state the relationship between angles that are measured clockwise and those that are measured counterclockwise.
-
E2.3 Use the properties of supplementary angles, complementary angles, opposite angles, and interior and exterior angles to solve for unknown angle measures.
-
-
Area and Surface Area
-
E2.4 Determine the areas of trapezoids, rhombuses, kites, and composite polygons by decomposing them into shapes with known areas.
-
E2.5 Create and use nets to demonstrate the relationship between the faces of prisms and pyramids and their surface areas.
-
E2.6 Determine the surface areas of prisms and pyramids by calculating the areas of their two-dimensional faces and adding them together.
-
E1. Geometric and Spatial Reasoning
Describe and represent shape, location, and movement by applying geometric properties and spatial relationships in order to navigate the world around them.
-
Geometric Reasoning
-
E1.1 Describe and classify cylinders, pyramids, and prisms according to their geometric properties, including plane and rotational symmetry.
-
E1.2 Draw top, front, and side views, as well as perspective views, of objects and physical spaces, using appropriate scales.
-
-
Location and Movement
-
E1.3 Perform dilations and describe the similarity between the image and the original shape.
-
E1.4 Describe and perform translations, reflections, and rotations on a Cartesian plane, and predict the results of these transformations.
-
E2. Measurement
Compare, estimate and determine measurements in various contexts.
Learning Situation-
The Metric System
-
E2.1 Describe the differences and similarities between volume and capacity, and apply the relationship between millilitres (mL) and cubic centimetres (cm3) to solve problems.
-
E2.2 Solve problems involving perimeter, area, and volume that require converting from one metric unit of measurement to another.
-
-
Circles
-
E2.3 Use the relationships between the radius, diameter, and circumference of a circle to explain the formula for finding the circumference and to solve related problems.
-
E2.4 Construct circles when given the radius, diameter, or circumference.
-
E2.5 Show the relationships between the radius, diameter, and area of a circle, and use these relationships to explain the formula for measuring the area of a circle and to solve related problems.
-
-
Volume and Surface Area
-
E2.6 Represent cylinders as nets and determine their surface area by adding the areas of their parts.
-
E2.7 Show that the volume of a prism or cylinder can be determined by multiplying the area of its base by its height, and apply this relationship to find the area of the base, volume, and height of prisms and cylinders when given two of the three measurements.
-
E1. Geometric and Spatial Reasoning
Describe and represent shape, location, and movement by applying geometric properties and spatial relationships in order to navigate the world around them.
Learning Situation-
Geometric Reasoning
-
E1.1 Identify the geometric properties of tessellating shapes and identify the transformations that occur in the tessellations.
-
E1.2 Make objects and models using appropriate scales, given their top, front, and side views or their perspective views.
-
E1.3 Use scale drawings to calculate actual lengths and areas, and reproduce scale drawings at different ratios.
-
-
Location and Movement
-
E1.4 Describe and perform translations, reflections, rotations, and dilations on a Cartesian plane, and predict the results of these transformations.
-
E2. Measurement
Compare, estimate and determine measurements in various contexts.
-
The Metric System
-
E2.1 Represent very large (mega, giga, tera) and very small (micro, nano, pico) metric units using models, base ten relationships, and exponential notation.
-
-
Lines and Angles
-
E2.2 Solve problems involving angle properties, including the properties of intersecting and parallel lines and of polygons.
-
-
Length, Area, and Volume
-
E2.3 Solve problems involving the perimeter, circumference, area, volume, and surface area of composite two-dimensional shapes and three-dimensional objects, using appropriate formulas.
-
E2.4 Describe the Pythagorean relationship using various geometric models, and apply the theorem to solve problems involving an unknown side length for a given right triangle.
-