• 5
    Grade 5 Standards
Top Mathematicians
  • Shape and Space
    • 5.SS.1
      Design and construct different rectangles given either perimeter or area, or both (whole numbers), and draw conclusions.
      Construct (concretely or pictorially) and record the dimensions of two or more rectangles with a specified perimeter and select, with justification, the dimensions that would be most appropriate in a particular situation (e.g., a rectangle is to have a perimeter of 18 units, what are the dimensions of the possible rectangles, which rectangle would be most appropriate if the rectangle is to be the base of a shoe box or a dog pen).
      Critique the statement "A rectangle with dimensions of 1 cm by 8 cm is different from a rectangle with dimensions of 8 cm by 1 cm". (Note: Any dimensions could be used to demonstrate the idea of orientation and point of view.)
      Construct (concretely or pictorially) and record the dimensions of as many rectangles as possible with a specified area and select, with justification, the rectangle that would be most appropriate in a particular situation (e.g., a rectangle is to have an area of 24 units², what are the dimensions of the possible rectangles, which rectangle would be most appropriate if the rectangle is to fence off the largest garden possible or be the base of a box on a shelf that is 10 units by 8 units).
      Critique the statement: "A rectangle with dimensions of 3 cm by 4 cm is different from a rectangle with dimensions of 2 cm by 5 cm". (Note: Any dimensions with the same perimeter could be used to demonstrate the idea of same perimeter not necessarily resulting in the same area or shape of the rectangle).
      Generalize patterns discovered through the exploration of the areas of rectangles with the same perimeter and through the exploration of the perimeters of rectangles with the same area (e.g., greater areas do not imply greater perimeters and vice versa, the rectangle for a situation closest to a square will have the greatest area, or the rectangle with the smallest width for a given perimeter will have the smallest area).
      Identify situations relevant to self, family, or community where the solution to problems would require the consideration of both area and perimeter, and solve the problems.
    • 5.SS.2
      Demonstrate understanding of measuring length (mm) by:
      selecting and justifying referents for the unit mm
      modelling and describing the relationship between mm, cm, and m units.
      Choose and use referents for 1 mm to determine approximate linear measurements in situations relevant to self, family, or community and explain the choice.
      Generalize measurement relationships between mm, cm, and m from explorations using concrete materials (e.g., 10 mm = 1 cm, 0.01m = 1 cm).
      Provide examples of situations relevant to one's life, family, or community in which linear measurements would be made and identify the standard unit (mm, cm, or m) that would be used for that measurement and justify the choice.
      Draw, construct, or physically act out a representation of a given linear measurement (e.g., the students might be asked to show 4 m; this could be done by drawing a straight line on the board that is 4 m in length, constructing a box (or different boxes) that has a base with a perimeter of 4 m, or carrying out a physical movement that results in moving 4 m).
      Pose and solve problems that involve hands-on linear measurements using either referents or standard units
    • 5.SS.3
      Demonstrate an understanding of volume by:
      selecting and justifying referents for cm³ or m³ units
      estimating volume by using referents for cm³ or m³
      measuring and recording volume (cm³ or m³)
      constructing rectangular prisms for a given volume.
      Provide referents for cm³ and m³ and explain the choice.
      Describe strategies developed for selecting and using referents to determine approximate volume measurements in situations relevant to self, family, or community.
      Estimate the volume of 3-D objects using personal referents.
      Decide what standard cubic unit is represented by a specific referent, and verify.
      Determine the volume of a 3-D object using manipulatives, describe the strategy used, and explain whether the volume is exact or an estimate.
      Construct possible rectangular prisms for a given volume, identify the dimensions of each prism, and explain which prism would be most appropriate for a particular situation.
    • 5.SS.4
      Demonstrate understanding of capacity by:
      describing the relationship between mL and L
      selecting and justifying referents for mL or L units
      estimating capacity by using referents for mL or L
      measuring and recording capacity (mL or L).
      Show, using concrete materials, that 1000 mL has the same capacity as 1 L.
      Provide referents for 1 millilitre and 1 litre and explain the choice.
      Describe strategies for selecting and using referents to determine approximate capacity measurements in situations relevant to self, family, or community.
      Decide what standard capacity unit is represented by a specific referent, and verify.
      Estimate the capacity of a container using personal referents.
      Determine the capacity of a container using concrete materials that closely take on the shape of the container, describe the strategy used, and explain whether the volume is exact or an estimate (e.g., if beads are used, discuss the impact on accuracy because of the space between the beads compared to the accuracy if water is used).
      Sort a set of containers from least to greatest capacity, explain the strategies used, and verify by determining or estimating the capacity.
    • 5.SS.5
      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 and describe examples of parallel, intersection, perpendicular, vertical, and horizontal lines, edges, and faces of 2-D shapes and 3-D objects found within one's home, school, and community (including 2-D shapes and 3-D objects in the natural environment, print and multimedia texts).
      Sketch a 2-D shape or 3-D object that is relevant to self, family, or others and identify any lines, edges, or faces that are parallel, intersecting, perpendicular, vertical, or horizontal.
      Describe, orally, in writing, or through physical movement, what it means for a line, edge, or face of a 2-D shape or 3-D object to be parallel, intersecting, perpendicular, vertical, or horizontal.
    • 5.SS.6
      Identify and sort quadrilaterals, including:
      rectangles
      squares
      trapezoids
      parallelograms
      rhombuses
      according to their attributes.
      Identify and provide examples for the types of quadrilaterals that are found in one's home, school, and community.
      Compare different quadrilaterals using concrete materials and pictures, identify common and differing attributes, and sort the quadrilaterals according to one of the attributes (e.g., relationships between side lengths, or number of pairs of parallel sides).
      Analyze a set of sorted quadrilaterals and determine where a new quadrilateral would belong in the sorted set.
      Describe, orally or in writing, the attributes of different quadrilaterals including rectangles, squares, trapezoids, parallelograms, and rhombuses.
      Create a model to illustrate the relationships between different quadrilaterals (e.g., demonstrating that a square is a rectangle and a parallelogram is a trapezoid) including rectangles, squares, trapezoids, parallelograms, and rhombuses.
    • 5.SS.7
      Identify, create, and analyze single transformations of 2-D shapes (with and without the use of technology).
      Carry out different transformations (translations, rotations, and reflections) concretely, pictorially (with or without the use of technology), or physically and generalize statements regarding the position and orientation of the transformed image based upon the type of transformation.
      Determine if a given 2-D shape and its transformed image match a set of transformation instructions and explain the conclusion reached.
      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, and describe the direction of the turn (clockwise or counter clockwise), the fraction of the turn, and the point of rotation.
      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.
      Describe a single transformation that could be used to replicate the given image of a 2-D shape.
      Identify transformations found within one's home, classroom, or community, describe the type and amount of transformations evident (e.g., translation to the left and up, ¼ of a rotation in a clockwise direction, and reflection about the right side of the shape), and create a concrete or pictorial model of the same set of transformations.
  • Number
  • Statistics & Probability
    • 5.SP.1
      Differentiate between first-hand and second-hand data.
      Provide examples of data relevant to self, family, or community and categorize the data, with explanation, as first-hand or second-hand data.
      Formulate a question related to self, family, or community which can best be answered using first-hand data, describe how that data could be collected, and answer the question (e.g., "What game will we play at home tonight?" "I can survey everyone at home to find out what games everyone wants to play.").
      Formulate a question related to self, family, or community, which can best be answered using second-hand data (e.g., "Which has the larger population - my community or my friend's community?"), describe how those data could be collected (I could find the data on the StatsCan website), and answer the question.
      Find examples of second-hand data in print and electronic media, such as newspapers, magazines, and the Internet, and compare different ways in which the data might be interpreted and used (e.g., statistics about health-related issues, sports data, or votes for favourite websites).
    • 5.SP.2
      Construct and interpret double bar graphs to draw conclusions.
      Compare the attributes and purposes of double bar graphs and bar graphs based upon situations and data that are meaningful to self, family, or community.
      Create double bar graphs, without the use of technology, based upon data relevant to one's self, family, or community. Pose questions, and support answers to those questions using the graph and other identified significant factors.
      Pose and solve problems related to the construction and interpretation of double bar graphs.
    • 5.SP.3
      Describe, compare, predict, and test the likelihood of outcomes in probability situations.
      Describe situations relevant to self, family, or community which involve probabilities and categorize different outcomes for the situations as being impossible, possible, or certain (e.g., it is possible that my little sister will be put to bed by 8:00 tonight or it is impossible that I will have time to watch a movie tonight because I have two hockey games).
      Design and conduct probability experiments to determine the likelihood of a specific outcome and explain what the results tell about the outcome including whether the outcome is impossible, possible, or certain.
      Identify all possible outcomes in a probability experiment and classify the outcomes as less likely, equally likely, or more likely to occur and explain the reasoning (e.g., for an upcoming Pow Wow, list the dances that could be done and then classify the likelihood of each of the dances occurring, or of the dances occurring while you are in attendance).
      Predict how the likelihood of two outcomes in a probability experiment, carry out the experiment, compare the results to the prediction, and identify possible reasons for discrepancies.
  • Patterns and Relations