Northwest Territories

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Skills available for Northwest Territories grade 5 math curriculum

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N Number

  • N.1 Develop number sense.

    • N.1.1 Represent and describe whole numbers to 1 000 000.

      • N.1.1.1 Write a given numeral, using proper spacing without commas; e.g., 934 567.

      • N.1.1.2 Describe the pattern of adjacent place positions moving from right to left.

      • N.1.1.3 Describe the meaning of each digit in a given numeral.

      • N.1.1.4 Provide examples of large numbers used in print or electronic media.

      • N.1.1.5 Express a given numeral in expanded notation; e.g., 45 321 = (4 × 10 000) + (5 × 1000) + (3 × 100) + (2 × 10) + (1 × 1) or 40 000 + 5000 + 300 + 20 + 1.

      • N.1.1.6 Write the numeral represented by a given expanded notation.

    • N.1.2 Use estimation strategies in problem-solving contexts.

    • N.1.3 Apply mental mathematics strategies and number properties in order to understand and recall basic multiplication facts (multiplication tables) to 81 and related division facts.

      • N.1.3.1 Describe the mental mathematics strategy used to determine a given basic fact, such as:

        • N.1.3.1.a skip count up by one or two groups from a known fact; e.g., if 5 × 7 = 35, then 6 × 7 is equal to 35 + 7 and 7 × 7 is equal to 35 + 7 + 7.

        • N.1.3.1.b skip count down by one or two groups from a known fact; e.g., if 8 × 8 = 64, then 7 × 8 is equal to 64 – 8 and 6 × 8 is equal to 64 – 8 – 8.

        • N.1.3.1.c doubling; e.g., for 8 × 3 think 4 × 3 = 12, and 8 × 3 = 12 + 12.

        • N.1.3.1.d patterns when multiplying by 9; e.g., for 9 × 6, think 10 × 6 = 60, and 60 – 6 = 54; for 7 × 9, think 7 × 10 = 70, and 70 – 7 = 63.

        • N.1.3.1.e repeated doubling; e.g., if 2 × 6 is equal to 12, then 4 × 6 is equal to 24 and 8 × 6 is equal to 48.

        • N.1.3.1.f repeated halving; e.g., for 60 ÷ 4, think 60 ÷ 2 = 30 and 30 ÷ 2 = 15.

      • N.1.3.2 Explain why multiplying by zero produces a product of zero (zero property of multiplication).

      • N.1.3.3 Explain why division by zero is not possible or is undefined; e.g., 8 ÷ 0.

      • N.1.3.4 Determine, with confidence, answers to multiplication facts to 81 and related division facts.

      • N.1.3.5 Demonstrate understanding, recall/memorization and application of multiplication and related division facts to 9 × 9.

    • N.1.4 Apply mental mathematics strategies for multiplication.

    • N.1.5 Demonstrate, with and without concrete materials, an understanding of multiplication (2-digit by 2-digit) to solve problems.

      • N.1.5.1 Illustrate partial products in expanded notation for both factors; e.g., for 36 × 42, determine the partial products for (30 + 6) × (40 + 2).

      • N.1.5.2 Represent both 2-digit factors in expanded notation to illustrate the distributive property; e.g., to determine the partial products of 36 × 42, (30 + 6) × (40 + 2) = 30 × 40 + 30 × 2 + 6 × 40 + 6 × 2 = 1200 + 60 + 240 + 12 = 1512.

      • N.1.5.3 Model the steps for multiplying 2-digit factors, using an array and base ten blocks, and record the process symbolically.

      • N.1.5.4 Describe a solution procedure for determining the product of two given 2-digit factors, using a pictorial representation such as an area model.

      • N.1.5.5 Solve a given multiplication problem in context, using personal strategies, and record the process.

      • N.1.5.6 Refine personal strategies to increase their efficiency.

      • N.1.5.7 Create and solve a multiplication problem, and record the process.

      • N.1.5.8 Solve a given problem using the standard/traditional multiplication algorithm.

    • N.1.6 Demonstrate, with and without concrete materials, an understanding of division (3-digit by 1-digit), and interpret remainders to solve problems.

      • N.1.6.1 Model the division process as equal sharing, using base ten blocks, and record it symbolically.

      • N.1.6.2 Explain that the interpretation of a remainder depends on the context:

        • N.1.6.2.a ignore the remainder; e.g., making teams of 4 from 22 people.

        • N.1.6.2.b round up the quotient; e.g., the number of five passenger cars required to transport 13 people.

        • N.1.6.2.c express remainders as fractions; e.g., five apples shared by two people.

        • N.1.6.2.d express remainders as decimals; e.g., measurement and money.

      • N.1.6.3 Solve a given division problem in context, using personal strategies, and record the process.

      • N.1.6.4 Refine personal strategies to increase their efficiency.

      • N.1.6.5 Create and solve a division problem, and record the process.

      • N.1.6.6 Solve a given problem using the standard/traditional division algorithm.

    • N.1.7 Demonstrate an understanding of fractions by using concrete, pictorial and symbolic representations to:

    • N.1.8 Describe and represent decimals (tenths, hundredths, thousandths), concretely, pictorially and symbolically.

    • N.1.9 Relate decimals to fractions and fractions to decimals (to thousandths).

      • N.1.9.1 Write a given decimal in fraction form.

      • N.1.9.2 Write a given fraction with a denominator of 10, 100 or 1000 as a decimal.

      • N.1.9.3 Express a given pictorial or concrete representation as a fraction or decimal; e.g., 250 shaded squares on a thousandth grid can be expressed as 0.250 or 250/1000.

    • N.1.10 Compare and order decimals (to thousandths) by using:

      • N.1.10.a benchmarks.

      • N.1.10.b place value.

      • N.1.10.c equivalent decimals.

      • N.1.10.1 Order a given set of decimals by placing them on a number line that contains the benchmarks 0.0, 0.5 and 1.0.

      • N.1.10.2 Order a given set of decimals including only tenths, using place value.

      • N.1.10.3 Order a given set of decimals including only hundredths, using place value.

      • N.1.10.4 Order a given set of decimals including only thousandths, using place value.

      • N.1.10.5 Explain what is the same and what is different about 0.2, 0.20 and 0.200.

      • N.1.10.6 Order a given set of decimals including tenths, hundredths and thousandths, using equivalent decimals; e.g., 0.92, 0.7, 0.9, 0.876, 0.925 in order is: 0.700, 0.876, 0.900, 0.920, 0.925.

    • N.1.11 Demonstrate an understanding of addition and subtraction of decimals (limited to thousandths).

PR Patterns and Relations

SS Shape and Space

  • SS.1 Use direct and indirect measurement to solve problems.

    • SS.1.1 Identify 90º angles.

      • SS.1.1.1 Provide examples of 90º angles in the environment.

      • SS.1.1.2 Sketch 90º angles without the use of a protractor.

      • SS.1.1.3 Label a 90º angle, using a symbol.

    • SS.1.2 Design and construct different rectangles, given either perimeter or area, or both (whole numbers), and make generalizations.

      • SS.1.2.1 Construct or draw two or more rectangles for a given perimeter in a problem-solving context.

      • SS.1.2.2 Construct or draw two or more rectangles for a given area in a problem-solving context.

      • SS.1.2.3 Determine the shape that will result in the greatest area for any given perimeter.

      • SS.1.2.4 Determine the shape that will result in the least area for any given perimeter.

      • SS.1.2.5 Provide a real-life context for when it is important to consider the relationship between area and perimeter.

    • SS.1.3 Demonstrate an understanding of measuring length (mm) by:

      • SS.1.3.a selecting and justifying referents for the unit mm.

      • SS.1.3.b modelling and describing the relationship between mm and cm units, and between mm and m units.

      • SS.1.3.1 Provide a referent for one millimetre, and explain the choice.

      • SS.1.3.2 Provide a referent for one centimetre, and explain the choice.

      • SS.1.3.3 Provide a referent for one metre, and explain the choice.

      • SS.1.3.4 Show that 10 millimetres is equivalent to 1 centimetre, using concrete materials; e.g., a ruler.

      • SS.1.3.5 Show that 1000 millimetres is equivalent to 1 metre, using concrete materials; e.g., a metre stick.

      • SS.1.3.6 Provide examples of when millimetres are used as the unit of measure.

    • SS.1.4 Demonstrate an understanding of volume by:

      • SS.1.4.a selecting and justifying referents for cm³ or m³ units.

      • SS.1.4.b estimating volume, using referents for cm³ or m³.

      • SS.1.4.c measuring and recording volume (cm³ or m³).

      • SS.1.4.d constructing right rectangular prisms for a given volume.

      • SS.1.4.1 Identify the cube as the most efficient unit for measuring volume, and explain why.

      • SS.1.4.2 Provide a referent for a cubic centimetre, and explain the choice.

      • SS.1.4.3 Provide a referent for a cubic metre, and explain the choice.

      • SS.1.4.4 Determine which standard cubic unit is represented by a given referent.

      • SS.1.4.5 Estimate the volume of a given 3-D object, using personal referents.

      • SS.1.4.6 Determine the volume of a given 3-D object, using manipulatives, and explain the strategy.

      • SS.1.4.7 Construct a right rectangular prism for a given volume.

      • SS.1.4.8 Construct more than one right rectangular prism for the same given volume.

    • SS.1.5 Demonstrate an understanding of capacity by:

      • SS.1.5.a describing the relationship between mL and L.

      • SS.1.5.b selecting and justifying referents for mL or L units.

      • SS.1.5.c estimating capacity, using referents for mL or L.

      • SS.1.5.d measuring and recording capacity (mL or L).

      • SS.1.5.1 Demonstrate that 1000 millilitres is equivalent to 1 litre by filling a 1 litre container using a combination of smaller containers.

      • SS.1.5.2 Provide a referent for a litre, and explain the choice.

      • SS.1.5.3 Provide a referent for a millilitre, and explain the choice.

      • SS.1.5.4 Determine the capacity unit of a given referent.

      • SS.1.5.5 Estimate the capacity of a given container, using personal referents.

      • SS.1.5.6 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.

  • SS.2 Describe the characteristics of 3-D objects and 2-D shapes, and analyze the relationships among them.

    • SS.2.6 Describe and provide examples of edges and faces of 3-D objects, and sides of 2-D shapes that are:

      • SS.2.6.a parallel.

      • SS.2.6.b intersecting.

      • SS.2.6.c perpendicular.

      • SS.2.6.d vertical.

      • SS.2.6.e horizontal.

      • SS.2.6.1 Identify parallel, intersecting, perpendicular, vertical and horizontal edges and faces on 3-D objects.

      • SS.2.6.2 Identify parallel, intersecting, perpendicular, vertical and horizontal sides on 2-D shapes.

      • SS.2.6.3 Provide examples from the environment that show parallel, intersecting, perpendicular, vertical and horizontal line segments.

      • SS.2.6.4 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.

      • SS.2.6.5 Draw 2-D shapes that have sides that are parallel, intersecting, perpendicular, vertical or horizontal.

      • SS.2.6.6 Draw 3-D objects that have edges and faces that are parallel, intersecting, perpendicular, vertical or horizontal.

      • SS.2.6.7 Describe the faces and edges of a given 3-D object, using terms such as parallel, intersecting, perpendicular, vertical or horizontal.

      • SS.2.6.8 Describe the sides of a given 2-D shape, using terms such as parallel, intersecting, perpendicular, vertical or horizontal.

    • SS.2.7 Identify and sort quadrilaterals, including:

  • SS.3 Describe and analyze position and motion of objects and shapes.

    • SS.3.8 Identify and describe a single transformation, including a translation, rotation and reflection of 2-D shapes.

      • SS.3.8.1 Provide an example of a translation, rotation and reflection.

      • SS.3.8.2 Identify a given single transformation as a translation, rotation or reflection.

      • SS.3.8.3 Describe a given rotation about a vertex by the direction of the turn (clockwise or counterclockwise).

      • SS.3.8.4 Describe a given reflection by identifying the line of reflection and the distance of the image from the line of reflection.

      • SS.3.8.5 Describe a given translation by identifying the direction and magnitude of the movement.

    • SS.3.9 Perform, concretely, a single transformation (translation, rotation or reflection) of a 2-D shape, and draw the image.

      • SS.3.9.1 Translate a given 2-D shape horizontally, vertically or diagonally, and draw the resultant image.

      • SS.3.9.2 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).

      • SS.3.9.3 Reflect a given 2-D shape across a line of reflection, and draw the resultant image.

      • SS.3.9.4 Draw a 2-D shape, translate the shape, and record the translation by describing the direction and magnitude of the movement.

      • SS.3.9.5 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).

      • SS.3.9.6 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.

      • SS.3.9.7 Predict the result of a single transformation of a 2-D shape, and verify the prediction.

SP Statistics and Probability

  • SP.1 Collect, display and analyze data to solve problems.

    • SP.1.1 Differentiate between first-hand and second-hand data.

      • SP.1.1.1 Explain the difference between first-hand and second-hand data.

      • SP.1.1.2 Formulate a question that can best be answered using first-hand data, and explain why.

      • SP.1.1.3 Formulate a question that can best be answered using second-hand data, and explain why.

      • SP.1.1.4 Find examples of second-hand data in print and electronic media, such as newspapers, magazines and the Internet.

    • SP.1.2 Construct and interpret double bar graphs to draw conclusions.

      • SP.1.2.1 Determine the attributes (title, axes, intervals and legend) of double bar graphs by comparing a given set of double bar graphs.

      • SP.1.2.2 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.

      • SP.1.2.3 Draw conclusions from a given double bar graph to answer questions.

      • SP.1.2.4 Provide examples of double bar graphs used in a variety of print and electronic media, such as newspapers, magazines and the Internet.

      • SP.1.2.5 Solve a given problem by constructing and interpreting a double bar graph.

  • SP.2 Use experimental or theoretical probabilities to represent and solve problems involving uncertainty.

    • SP.2.3 Describe the likelihood of a single outcome occurring, using words such as:

      • SP.2.3.a impossible.

      • SP.2.3.b possible.

      • SP.2.3.c certain.

      • SP.2.3.1 Provide examples of events from personal contexts that are impossible, possible or certain.

      • SP.2.3.2 Classify the likelihood of a single outcome occurring in a probability experiment as impossible, possible or certain.

      • SP.2.3.3 Design and conduct a probability experiment in which the likelihood of a single outcome occurring is impossible, possible or certain.

      • SP.2.3.4 Conduct a given probability experiment a number of times, record the outcomes, and explain the results.

    • SP.2.4 Compare the likelihood of two possible outcomes occurring, using words such as:

      • SP.2.4.a less likely.

      • SP.2.4.b equally likely.

      • SP.2.4.c more likely.

      • SP.2.4.1 Identify outcomes from a given probability experiment that are less likely, equally likely or more likely to occur than other outcomes.

      • SP.2.4.2 Design and conduct a probability experiment in which one outcome is less likely to occur than the other outcome.

      • SP.2.4.3 Design and conduct a probability experiment in which one outcome is equally likely to occur as the other outcome.

      • SP.2.4.4 Design and conduct a probability experiment in which one outcome is more likely to occur than the other outcome.