N5.1.b Critique the way numbers have been said or numerals written in examples of whole numbers found in various types of media and personal conversations, and provide reasons for why certain errors in speech or writing might occur.
N5.1.c Describe the patterns related to quantity and place value of adjacent digit positions moving from right to left within a whole number.
N5.1.d Visualize and explain concrete or pictorial models for the place value positions of 100 000 and 1 000 000.
N5.1.e Describe the meaning of quantities to 1 000 000 by relating them to self, family, or community and explain the contribution each successive numeral position makes to the actual quantity.
N5.1.f Pose and solve problems that explore the quantity of whole numbers to 1 000 000 (e.g., a student might wonder: "How does the population of my community compare to those of surrounding communities?").
N5.1.g Provide examples of large numbers used in print or electronic media and explain the meaning of the numbers in the context used.
N5.1.h Visualize a representation of a given numeral and explain how the representation is related to the numeral's expanded form.
N5.1.i Express a given numeral in expanded notation (e.g., 45 321 = (4 x 10 000) + (5 x 1000) + (3 x 100) + (2 x 10) + (1 x 1) or 40 000 + 5000 + 300 + 20 + 1) and explain how the expanded notation shows the total quantity represented by the given numeral.
N5.2 Analyze models of, develop strategies for, and carry out multiplication of whole numbers.
N5.2.a Describe mental mathematics strategies used to determine multiplication facts to 81 (e.g., skip counting from a known fact, doubling, halving, 9s patterns, repeated doubling, or repeated halving).
N5.2.g Model multiplying two 2-digit factors using an array, base ten blocks, or an area model, record the process symbolically, and describe the connections between the models and the symbolic recording.
N5.2.i Illustrate, concretely, pictorially, and symbolically, the distributive property using expanded notation and partial products (e.g., 36 x 42 = (30 +6) x (40+2) = 30 x 40 + 6 x 40 +30 x 2 + 6 x 2).
N5.4.c Critique the statement "an estimate is never good enough".
N5.4.d Identify and describe situations relevant to self, family, or community when it is best to overestimate or when it is best to underestimate and explain the reasoning.
N5.4.e Determine an approximate solution to a problem not requiring an exact answer and explain the strategies and reasoning used (e.g., number of fish, deer, or elk required to feed a family over a winter; amount of money a family spends on groceries).
N5.6.a Tell a story (orally, in writing, or through movement) that explains what a concrete or pictorial representation of a part of a set, part of a region, or part of a unit of measure illustrates and record the quantity as a decimal.
N5.6.b Represent concretely or pictorially a decimal identified in a situation relevant to self, family, or community.
P5.1 Represent, analyse, and apply patterns using mathematical language and notation.
P5.1.a Describe situations from one's life, family, or community in which patterns emerge, identify assumptions made in extending the patterns, and analyze the usefulness of the pattern for making predictions.
P5.1.b Describe, using mathematics language (e.g., one more, seven less) and symbolically (e.g., r + 1, p - 7), a pattern represented concretely or pictorially that is found in a chart.
P5.2 Write, solve, and verify solutions of single-variable, one-step equations with whole number coefficients and whole number solutions.
P5.2.a Identify aspects of experiences from one's life, family, and community that could be represented by a variable (e.g., temperature, cost of a DVD, size of a plant, colour of shirts, or performance of a team goalie).
P5.2.b Describe a situation for which a given equation could apply and identify what the variable represents in the situation.
SS5.1 Design and construct different rectangles given either perimeter or area, or both (whole numbers), and draw conclusions.
SS5.1.a 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).
SS5.1.b 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.)
SS5.1.c 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).
SS5.1.d 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).
SS5.1.e 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).
SS5.1.f 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.
SS5.2.c 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.
SS5.2.d 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).
SS5.2.e Pose and solve problems that involve hands-on linear measurements using either referents or standard units
SS5.3 Demonstrate an understanding of volume by:
SS5.3.1 selecting and justifying referents for cm³ or m³ units
SS5.4.f 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).
SS5.4.g Sort a set of containers from least to greatest capacity, explain the strategies used, and verify by determining or estimating the capacity.
SS5.5 Describe and provide examples of edges and faces of 3-D objects, and sides of 2-D shapes that are:
SS5.5.a 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).
SS5.5.b 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.
SS5.5.c 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.
SS5.6.a Identify and provide examples for the types of quadrilaterals that are found in one's home, school, and community.
SS5.6.b 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).
SS5.6.e 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.
SS5.7 Identify, create, and analyze single transformations of 2-D shapes (with and without the use of technology).
SS5.7.a 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.
SS5.7.h 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.
SP5 Statistics and Probability
SP5.1 Differentiate between first-hand and second-hand data.
SP5.1.a Provide examples of data relevant to self, family, or community and categorize the data, with explanation, as first-hand or second-hand data.
SP5.1.b 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.").
SP5.1.c 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.
SP5.1.d 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).
SP5.2 Construct and interpret double bar graphs to draw conclusions.
SP5.2.a 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.
SP5.2.b 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.
SP5.3 Describe, compare, predict, and test the likelihood of outcomes in probability situations.
SP5.3.a 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).
SP5.3.b 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.
SP5.3.c 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).