• 5
Top Mathematicians
• Shape and Space
• 5.SS.1
Identify 90º angles.
Provide examples of 90º angles in the environment.
Sketch 90º angles without the use of a protractor.
Label a 90º angle, using a symbol.
• 5.SS.2
Design and construct different rectangles, given either perimeter or area, or both (whole numbers), and make generalizations.
Construct or draw two or more rectangles for a given perimeter in a problem-solving context.
Construct or draw two or more rectangles for a given area in a problem-solving context.
Determine the shape that will result in the greatest area for any given perimeter.
Determine the shape that will result in the least area for any given perimeter.
Provide a real-life context for when it is important to consider the relationship between area and perimeter.
• 5.SS.3
Demonstrate an understanding of measuring length (mm) by:
selecting and justifying referents for the unit mm.
modelling and describing the relationship between mm and cm units, and between mm and m units.
Provide a referent for one millimetre, and explain the choice.
Provide a referent for one centimetre, and explain the choice.
Provide a referent for one metre, and explain the choice.
Show that 10 millimetres is equivalent to 1 centimetre, using concrete materials; e.g., a ruler.
Show that 1000 millimetres is equivalent to 1 metre, using concrete materials; e.g., a metre stick.
Provide examples of when millimetres are used as the unit of measure.
• 5.SS.4
Demonstrate an understanding of volume by:
selecting and justifying referents for cm³ or m³ units.
estimating volume, using referents for cm³ or m³.
measuring and recording volume (cm³ or m³).
constructing right rectangular prisms for a given volume.
Identify the cube as the most efficient unit for measuring volume, and explain why.
Provide a referent for a cubic centimetre, and explain the choice.
Provide a referent for a cubic metre, and explain the choice.
Determine which standard cubic unit is represented by a given referent.
Estimate the volume of a given 3-D object, using personal referents.
Determine the volume of a given 3-D object, using manipulatives, and explain the strategy.
Construct a right rectangular prism for a given volume.
Construct more than one right rectangular prism for the same given volume.
• 5.SS.5
Demonstrate an understanding of capacity by:
describing the relationship between mL and L.
selecting and justifying referents for mL or L units.
estimating capacity, using referents for mL or L.
measuring and recording capacity (mL or L).
Demonstrate that 1000 millilitres is equivalent to 1 litre by filling a 1 litre container using a combination of smaller containers.
Provide a referent for a litre, and explain the choice.
Provide a referent for a millilitre, and explain the choice.
Determine the capacity unit of a given referent.
Estimate the capacity of a given container, using personal referents.
Determine the capacity of a given container, using materials that take the shape of the inside of the container (e.g., a liquid, rice, sand, beads), and explain the strategy.
• 5.SS.6
Describe and provide examples of edges and faces of 3-D objects, and sides of 2-D shapes that are:
parallel.
intersecting.
perpendicular.
vertical.
horizontal.
Identify parallel, intersecting, perpendicular, vertical and horizontal edges and faces on 3-D objects.
Identify parallel, intersecting, perpendicular, vertical and horizontal sides on 2-D shapes.
Provide examples from the environment that show parallel, intersecting, perpendicular, vertical and horizontal line segments.
Find examples of edges, faces and sides that are parallel, intersecting, perpendicular, vertical and horizontal in print and electronic media, such as newspapers, magazines and the Internet.
Draw 2-D shapes that have sides that are parallel, intersecting, perpendicular, vertical or horizontal.
Draw 3-D objects that have edges and faces that are parallel, intersecting, perpendicular, vertical or horizontal.
Describe the faces and edges of a given 3-D object, using terms such as parallel, intersecting, perpendicular, vertical or horizontal.
Describe the sides of a given 2-D shape, using terms such as parallel, intersecting, perpendicular, vertical or horizontal.
• 5.SS.7
Identify and sort quadrilaterals, including:
rectangles according to their attributes.
squares according to their attributes.
trapezoids according to their attributes.
parallelograms according to their attributes.
rhombuses according to their attributes.
Identify and describe the characteristics of a pre-sorted set of quadrilaterals.
Sort a given set of quadrilaterals, and explain the sorting rule.
Sort a given set of quadrilaterals according to the lengths of the sides.
Sort a given set of quadrilaterals according to whether or not opposite sides are parallel.
• 5.SS.8
Identify and describe a single transformation, including a translation, rotation and reflection of 2-D shapes.
Provide an example of a translation, rotation and reflection.
Identify a given single transformation as a translation, rotation or reflection.
Describe a given rotation about a vertex by the direction of the turn (clockwise or counterclockwise).
Describe a given reflection by identifying the line of reflection and the distance of the image from the line of reflection.
Describe a given translation by identifying the direction and magnitude of the movement.
• 5.SS.9
Perform, concretely, a single transformation (translation, rotation or reflection) of a 2-D shape, and draw the image.
Translate a given 2-D shape horizontally, vertically or diagonally, and draw the resultant image.
Rotate a given 2-D shape about a vertex, and describe the direction of rotation (clockwise or counterclockwise) and the fraction of the turn (limited to ¼, ½, ¾ or full turn).
Reflect a given 2-D shape across a line of reflection, and draw the resultant image.
Draw a 2-D shape, translate the shape, and record the translation by describing the direction and magnitude of the movement.
Draw a 2-D shape, rotate the shape about a vertex, and describe the direction of the turn (clockwise or counterclockwise) and the fraction of the turn (limited to ¼, ½, ¾ or full turn).
Draw a 2-D shape, reflect the shape, and identify the line of reflection and the distance of the image from the line of reflection.
Predict the result of a single transformation of a 2-D shape, and verify the prediction.
• Patterns and Relations
• Number
• Statistics & Probability
• 5.SP.1
Differentiate between first-hand and second-hand data.
Explain the difference between first-hand and second-hand data.
Formulate a question that can best be answered using first-hand data, and explain why.
Formulate a question that can best be answered using second-hand data, and explain why.
Find examples of second-hand data in print and electronic media, such as newspapers, magazines and the Internet.
• 5.SP.2
Construct and interpret double bar graphs to draw conclusions.
Determine the attributes (title, axes, intervals and legend) of double bar graphs by comparing a given set of double bar graphs.
Represent a given set of data by creating a double bar graph, label the title and axes, and create a legend without the use of technology.
Draw conclusions from a given double bar graph to answer questions.
Provide examples of double bar graphs used in a variety of print and electronic media, such as newspapers, magazines and the Internet.
Solve a given problem by constructing and interpreting a double bar graph.
• 5.SP.3
Describe the likelihood of a single outcome occurring, using words such as:
impossible.
possible.
certain.
Provide examples of events from personal contexts that are impossible, possible or certain.
Classify the likelihood of a single outcome occurring in a probability experiment as impossible, possible or certain.
Design and conduct a probability experiment in which the likelihood of a single outcome occurring is impossible, possible or certain.
Conduct a given probability experiment a number of times, record the outcomes, and explain the results.
• 5.SP.4
Compare the likelihood of two possible outcomes occurring, using words such as:
less likely.
equally likely.
more likely.
Identify outcomes from a given probability experiment that are less likely, equally likely or more likely to occur than other outcomes.
Design and conduct a probability experiment in which one outcome is less likely to occur than the other outcome.
Design and conduct a probability experiment in which one outcome is equally likely to occur as the other outcome.
Design and conduct a probability experiment in which one outcome is more likely to occur than the other outcome.