Northwest Territories

N Number

• N.1 Develop number sense.

  • N.1.1 Determine and explain why a number is divisible by 2, 3, 4, 5, 6, 8, 9 or 10, and why a number cannot be divided by 0.

    • N.1.1.1 Determine if a given number is divisible by 2, 3, 4, 5, 6, 8, 9 or 10, and explain why.

      • Divisibility rules (7-A.4)

    • N.1.1.2 Sort a given set of numbers based upon their divisibility, using organizers such as Venn and Carroll diagrams.

    • N.1.1.3 Determine the factors of a given number, using the divisibility rules.

      • Greatest common factor (7-A.5)

    • N.1.1.4 Explain, using an example, why numbers cannot be divided by 0.

  • N.1.2 Demonstrate an understanding of the addition, subtraction, multiplication and division of decimals to solve problems (for more than 1-digit divisors or 2-digit multipliers, the use of technology is expected).

    • N.1.2.1 Solve a given problem involving the addition of two or more decimal numbers.

      • Add and subtract decimals (7-E.1)
      • Add and subtract decimals: word problems (7-E.2)
      • Maps with decimal distances (7-E.12)

    • N.1.2.2 Solve a given problem involving the subtraction of decimal numbers.

      • Add and subtract decimals (7-E.1)
      • Add and subtract decimals: word problems (7-E.2)
      • Maps with decimal distances (7-E.12)

    • N.1.2.3 Solve a given problem involving the multiplication of decimal numbers.

      • Multiply decimals and whole numbers: word problems (7-E.4)
      • Multiply decimals (7-E.5)

    • N.1.2.4 Solve a given problem involving the multiplication or division of decimal numbers with 2-digit multipliers or 1-digit divisors (whole numbers or decimals) without the use of technology.

      • Multiply decimals and whole numbers: word problems (7-E.4)
      • Divide decimals by whole numbers: word problems (7-E.7)

    • N.1.2.5 Solve a given problem involving the multiplication or division of decimal numbers with more than 2-digit multipliers or 1-digit divisors (whole numbers or decimals) with the use of technology.

      • Multiply decimals (7-E.5)
      • Divide decimals (7-E.8)

    • N.1.2.6 Place the decimal in a sum or difference, using front-end estimation; e.g., for 4.5 + 0.73 + 256.458, think 4 + 256, so the sum is greater than 260.

      • Estimate sums, differences and products of decimals (7-E.9)

    • N.1.2.7 Place the decimal in a product, using front-end estimation; e.g., for $12.33 × 2.4, think $12 × 2, so the product is greater than $24.

      • Estimate sums, differences and products of decimals (7-E.9)

    • N.1.2.8 Place the decimal in a quotient, using front-end estimation; e.g., for 51.50 m ÷ 2.1, think 50 m ÷ 2, so the quotient is approximately 25 m.

      • Multi-step inequalities with decimals (7-E.11)

    • N.1.2.9 Check the reasonableness of solutions, using estimation.

    • N.1.2.10 Solve a given problem that involves operations on decimals (limited to thousandths), taking into consideration the order of operations.

      • Add, subtract, multiply and divide decimals: word problems (7-E.10)
      • Evaluate numerical expressions involving decimals (7-E.13)

  • N.1.3 Solve problems involving percents from 1% to 100%.

    • N.1.3.1 Express a given percent as a decimal or fraction.

      • Convert between percents, fractions and decimals (7-N.2)

    • N.1.3.2 Solve a given problem that involves finding a percent.

      • Estimate percents of numbers (7-N.4)
      • Percents of numbers: word problems (7-N.6)
      • Solve percent equations (7-N.7)
      • Solve percent equations: word problems (7-N.8)

    • N.1.3.3 Determine the answer to a given percent problem where the answer requires rounding, and explain why an approximate answer is needed; e.g., total cost including taxes.

      • Percents of numbers and money amounts (7-N.5)

  • N.1.4 Demonstrate an understanding of the relationship between positive terminating decimals and positive fractions and between positive repeating decimals and positive fractions.

    • N.1.4.1 Predict the decimal representation of a given fraction, using patterns; e.g., 1/11 = 0.09 (repeating), 2/11 = 0.18 (repeating), 3/11 = ? …

    • N.1.4.2 Match a given set of fractions to their decimal representations.

    • N.1.4.3 Sort a given set of fractions as repeating or terminating decimals.

    • N.1.4.4 Express a given fraction as a terminating or repeating decimal.

      • Convert between decimals and fractions or mixed numbers (7-J.2)

    • N.1.4.5 Express a given repeating decimal as a fraction.

      • Convert between decimals and fractions or mixed numbers (7-J.2)

    • N.1.4.6 Express a given terminating decimal as a fraction.

      • Convert between decimals and fractions or mixed numbers (7-J.2)

    • N.1.4.7 Provide an example where the decimal representation of a fraction is an approximation of its exact value.

  • N.1.5 Demonstrate an understanding of adding and subtracting positive fractions and mixed numbers, with like and unlike denominators, concretely, pictorially and symbolically (limited to positive sums and differences).

    • N.1.5.1 Model addition and subtraction of a given positive fraction or given mixed number, using concrete representations, and record symbolically.

      • Add fractions with unlike denominators using models (7-G.3)
      • Subtract fractions with unlike denominators using models (7-G.5)

    • N.1.5.2 Determine the sum of two given positive fractions or mixed numbers with like denominators.

      • Add and subtract fractions with like denominators (7-G.1)

    • N.1.5.3 Determine the difference of two given positive fractions or mixed numbers with like denominators.

      • Add and subtract fractions with like denominators (7-G.1)

    • N.1.5.4 Determine a common denominator for a given set of positive fractions or mixed numbers.

      • Least common denominator (7-F.5)

    • N.1.5.5 Determine the sum of two given positive fractions or mixed numbers with unlike denominators.

      • Add fractions with unlike denominators (7-G.4)
      • Add and subtract mixed numbers (7-G.13)

    • N.1.5.6 Determine the difference of two given positive fractions or mixed numbers with unlike denominators.

      • Subtract fractions with unlike denominators (7-G.6)
      • Add and subtract mixed numbers (7-G.13)

    • N.1.5.7 Simplify a given positive fraction or mixed number by identifying the common factor between the numerator and denominator.

      • Write fractions in lowest terms (7-F.3)

    • N.1.5.8 Simplify the solution to a given problem involving the sum or difference of two positive fractions or mixed numbers.

    • N.1.5.9 Solve a given problem involving the addition or subtraction of positive fractions or mixed numbers, and determine if the solution is reasonable.

      • Add and subtract fractions with like denominators: word problems (7-G.2)
      • Add and subtract fractions with unlike denominators: word problems (7-G.9)
      • Add and subtract mixed numbers: word problems (7-G.14)
      • Inequalities with addition and subtraction of fractions and mixed numbers (7-G.15)

  • N.1.6 Demonstrate an understanding of addition and subtraction of integers, concretely, pictorially and symbolically.

    • N.1.6.1 Explain, using concrete materials such as integer tiles and diagrams, that the sum of opposite integers is zero.

    • N.1.6.2 Illustrate, using a number line, the results of adding or subtracting negative and positive integers; e.g., a move in one direction followed by an equivalent move in the opposite direction results in no net change in position.

    • N.1.6.3 Add two given integers, using concrete materials or pictorial representations, and record the process symbolically.

      • Add and subtract integers using counters (7-C.11)

    • N.1.6.4 Subtract two given integers, using concrete materials or pictorial representations, and record the process symbolically.

      • Add and subtract integers using counters (7-C.11)

    • N.1.6.5 Solve a given problem involving the addition and subtraction of integers.

      • Add and subtract integers (7-C.12)
      • Complete addition and subtraction sentences with integers (7-C.13)
      • Add and subtract integers: word problems (7-C.14)

  • N.1.7 Compare and order positive fractions, positive decimals (to thousandths) and whole numbers by using:

    • N.1.7.a benchmarks.

    • N.1.7.b place value.

    • N.1.7.c equivalent fractions and/or decimals.

    • N.1.7.1 Order the numbers of a given set that includes positive fractions, positive decimals and/or whole numbers in ascending or descending order; and verify the result, using a variety of strategies.

      • Compare and order decimals (7-D.2)
      • Compare and order fractions (7-F.6)
      • Compare fractions using benchmarks (7-F.7)
      • Compare fractions: word problems (7-F.8)
      • Put a mix of decimals, fractions and mixed numbers in order (7-F.12)

    • N.1.7.2 Identify a number that would be between two given numbers in an ordered sequence or on a number line.

    • N.1.7.3 Identify incorrectly placed numbers in an ordered sequence or on a number line.

    • N.1.7.4 Position fractions with like and unlike denominators from a given set on a number line, and explain strategies used to determine order.

    • N.1.7.5 Order the numbers of a given set by placing them on a number line that contains benchmarks, such as 0 and 1 or 0 and 5.

    • N.1.7.6 Position a given set of positive fractions, including mixed numbers and improper fractions, on a number line; and explain strategies used to determine position.

PR Patterns and Relations

• PR.1 Use patterns to describe the world and to solve problems.

  • PR.1.1 Demonstrate an understanding of oral and written patterns and their equivalent linear relations.

    • PR.1.1.1 Formulate a linear relation to represent the relationship in a given oral or written pattern.

      • Write equations for proportional relationships from tables (7-M.2)
      • Write a two-variable equation (7-W.5)
      • Write an equation from a graph using a table (7-W.9)

    • PR.1.1.2 Provide a context for a given linear relation that represents a pattern.

    • PR.1.1.3 Represent a pattern in the environment, using a linear relation.

  • PR.1.2 Create a table of values from a linear relation, graph the table of values, and analyze the graph to draw conclusions and solve problems.

    • PR.1.2.1 Create a table of values for a given linear relation by substituting values for the variable.

      • Complete a table for a two-variable relationship (7-W.4)

    • PR.1.2.2 Create a table of values, using a linear relation, and graph the table of values (limited to discrete elements).

      • Graph a two-variable equation (7-W.7)

    • PR.1.2.3 Sketch the graph from a table of values created for a given linear relation, and describe the patterns found in the graph to draw conclusions; e.g., graph the relationship between n and 2n + 3.

    • PR.1.2.4 Describe, using everyday language in spoken or written form, the relationship shown on a graph to solve problems.

      • Interpret graphs of proportional relationships (7-M.8)
      • Interpret a graph: word problems (7-W.8)

    • PR.1.2.5 Match a set of linear relations to a set of graphs.

      • Identify the graph of an equation (7-W.6)

• PR.2 Represent algebraic expressions in multiple ways.

  • PR.2.3 Demonstrate an understanding of preservation of equality by:

    • PR.2.3.a modelling preservation of equality, concretely, pictorially and symbolically.

    • PR.2.3.b applying preservation of equality to solve equations.

    • PR.2.3.1 Model the preservation of equality for each of the four operations, using concrete materials or pictorial representations; explain the process orally; and record the process symbolically.

    • PR.2.3.2 Write equivalent forms of a given equation by applying the preservation of equality, and verify, using concrete materials; e.g., 3b = 12 is the same as 3b + 5 = 12 + 5 or 2r = 7 is the same as 3(2r) = 3(7).

    • PR.2.3.3 Solve a given problem by applying preservation of equality.

  • PR.2.4 Explain the difference between an expression and an equation.

    • PR.2.4.1 Identify and provide an example of a constant term, numerical coefficient and variable in an expression and an equation.

      • Identify terms and coefficients (7-T.7)

    • PR.2.4.2 Explain what a variable is and how it is used in a given expression.

    • PR.2.4.3 Provide an example of an expression and an equation, and explain how they are similar and different.

  • PR.2.5 Evaluate an expression, given the value of the variable(s).

    • PR.2.5.1 Substitute a value for an unknown in a given expression, and evaluate the expression.

      • Evaluate linear expressions (7-T.3)
      • Evaluate multi-variable expressions (7-T.4)

  • PR.2.6 Model and solve, concretely, pictorially and symbolically, problems that can be represented by one-step linear equations of the form x + a = b, where a and b are integers.

    • PR.2.6.1 Represent a given problem with a linear equation; and solve the equation, using concrete models, e.g., counters, integer tiles.

    • PR.2.6.2 Draw a visual representation of the steps required to solve a given linear equation.

    • PR.2.6.3 Solve a given problem, using a linear equation.

    • PR.2.6.4 Verify the solution to a given linear equation, using concrete materials and diagrams.

    • PR.2.6.5 Substitute a possible solution for the variable in a given linear equation into the original linear equation to verify the equality.

  • PR.2.7 Model and solve, concretely, pictorially and symbolically, problems that can be represented by linear equations of the form:

    • PR.2.7.a ax + b = c where a, b and c are whole numbers.

    • PR.2.7.b ax = b where a, b and c are whole numbers.

    • PR.2.7.c x/a = b, a ≠ 0 where a, b and c are whole numbers.

    • PR.2.7.1 Model a given problem with a linear equation; and solve the equation, using concrete models, e.g., counters, integer tiles.

      • Model and solve equations using algebra tiles (7-U.3)

    • PR.2.7.2 Draw a visual representation of the steps used to solve a given linear equation.

    • PR.2.7.3 Solve a given problem, using a linear equation, and record the process.

      • Write and solve equations that represent diagrams (7-U.4)
      • Solve one-step equations (7-U.5)
      • Solve one- and two-step equations: word problems (7-U.7)

    • PR.2.7.4 Verify the solution to a given linear equation, using concrete materials and diagrams.

    • PR.2.7.5 Substitute a possible solution for the variable in a given linear equation into the original linear equation to verify the equality.

      • Which x satisfies an equation? (7-U.1)

SS Shape and Space

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

  • SS.1.1 Demonstrate an understanding of circles by:

    • SS.1.1.a describing the relationships among radius, diameter and circumference.

    • SS.1.1.b relating circumference to pi.

    • SS.1.1.c determining the sum of the central angles.

    • SS.1.1.d constructing circles with a given radius or diameter.

    • SS.1.1.e solving problems involving the radii, diameters and circumferences of circles.

    • SS.1.1.1 Illustrate and explain that the diameter is twice the radius in a given circle.

    • SS.1.1.2 Illustrate and explain that the circumference is approximately three times the diameter in a given circle.

    • SS.1.1.3 Explain that, for all circles, pi is the ratio of the circumference to the diameter (C/d) and its value is approximately 3.14.

    • SS.1.1.4 Explain, using an illustration, that the sum of the central angles of a circle is 360°.

    • SS.1.1.5 Draw a circle with a given radius or diameter, with and without a compass.

    • SS.1.1.6 Solve a given contextual problem involving circles.

  • SS.1.2 Develop and apply a formula for determining the area of:

    • SS.1.2.a triangles.

    • SS.1.2.b parallelograms.

    • SS.1.2.c circles.

    • SS.1.2.1 Illustrate and explain how the area of a rectangle can be used to determine the area of a triangle.

    • SS.1.2.2 Generalize a rule to create a formula for determining the area of triangles.

    • SS.1.2.3 Illustrate and explain how the area of a rectangle can be used to determine the area of a parallelogram.

    • SS.1.2.4 Generalize a rule to create a formula for determining the area of parallelograms.

    • SS.1.2.5 Illustrate and explain how to estimate the area of a circle without the use of a formula.

    • SS.1.2.6 Apply a formula for determining the area of a given circle.

      • Circumference of circles (7-BB.7)
      • Circles: word problems (7-BB.9)

    • SS.1.2.7 Solve a given problem involving the area of triangles, parallelograms and/or circles.

      • Area of rectangles and parallelograms (7-BB.2)
      • Area of triangles (7-BB.3)
      • Area of compound figures with triangles, semicircles and quarter circles (7-BB.13)

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

  • SS.2.3 Perform geometric constructions, including:

    • SS.2.3.a perpendicular line segments.

    • SS.2.3.b parallel line segments.

    • SS.2.3.c perpendicular bisectors.

    • SS.2.3.d angle bisectors.

    • SS.2.3.1 Describe examples of parallel line segments, perpendicular line segments, perpendicular bisectors and angle bisectors in the environment.

    • SS.2.3.2 Identify line segments on a given diagram that are parallel or perpendicular.

      • Parallel, perpendicular and intersecting lines (7-X.10)

    • SS.2.3.3 Draw a line segment perpendicular to another line segment, and explain why they are perpendicular.

      • Construct a perpendicular line (7-Z.4)

    • SS.2.3.4 Draw a line segment parallel to another line segment, and explain why they are parallel.

      • Construct parallel lines (7-Z.5)

    • SS.2.3.5 Draw the bisector of a given angle, using more than one method, and verify that the resulting angles are equal.

      • Construct an angle bisector (7-Z.2)

    • SS.2.3.6 Draw the perpendicular bisector of a line segment, using more than one method, and verify the construction.

      • Construct the midpoint or perpendicular bisector of a segment (7-Z.1)

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

  • SS.3.4 Identify and plot points in the four quadrants of a Cartesian plane, using integral ordered pairs.

    • SS.3.4.1 Label the axes of a four quadrant Cartesian plane, and identify the origin.

    • SS.3.4.2 Identify the location of a given point in any quadrant of a Cartesian plane, using an integral ordered pair.

      • Objects on a coordinate plane: positive and negative numbers (6-V.3)

    • SS.3.4.3 Plot the point corresponding to a given integral ordered pair on a Cartesian plane with units of 1, 2, 5 or 10 on its axes.

    • SS.3.4.4 Draw shapes and designs in a Cartesian plane, using given integral ordered pairs.

      • Graph triangles and quadrilaterals (7-X.6)

    • SS.3.4.5 Create shapes and designs, and identify the points used to produce the shapes and designs, in any quadrant of a Cartesian plane.

  • SS.3.5 Perform and describe transformations (translations, rotations or reflections) of a 2-D shape in all four quadrants of a Cartesian plane (limited to integral number vertices).

    • SS.3.5.1 Identify the coordinates of the vertices of a given 2-D shape on a Cartesian plane.

    • SS.3.5.2 Describe the horizontal and vertical movement required to move from a given point to another point on a Cartesian plane.

    • SS.3.5.3 Describe the positional change of the vertices of a given 2-D shape to the corresponding vertices of its image as a result of a transformation, or successive transformations, on a Cartesian plane.

    • SS.3.5.4 Determine the distance between points along horizontal and vertical lines in a Cartesian plane.

      • Distance between two points (7-R.4)

    • SS.3.5.5 Perform a transformation or consecutive transformations on a given 2-D shape, and identify coordinates of the vertices of the image.

      • Translations: graph the image (7-Y.3)
      • Reflections: graph the image (7-Y.5)
      • Rotations: graph the image (7-Y.7)

    • SS.3.5.6 Describe the image resulting from the transformation of a given 2-D shape on a Cartesian plane by identifying the coordinates of the vertices of the image.

      • Translations: find the coordinates (7-Y.4)
      • Reflections: find the coordinates (7-Y.6)
      • Rotations: find the coordinates (7-Y.8)

SP Statistics and Probability

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

  • SP.1.1 Demonstrate an understanding of central tendency and range by:

    • SP.1.1.a determining the measures of central tendency (mean, median, mode) and range.

    • SP.1.1.b determining the most appropriate measures of central tendency to report findings.

    • SP.1.1.1 Determine mean, median and mode for a given set of data, and explain why these values may be the same or different.

      • Calculate mean, median, mode and range (7-DD.2)

    • SP.1.1.2 Determine the range for a given set of data.

      • Calculate mean, median, mode and range (7-DD.2)

    • SP.1.1.3 Provide a context in which the mean, median or mode is the most appropriate measure of central tendency to use when reporting findings.

    • SP.1.1.4 Solve a given problem involving the measures of central tendency.

      • Interpret charts to find mean, median, mode and range (7-DD.4)

  • SP.1.2 Determine the effect on the mean, median and mode when an outlier is included in a data set.

    • SP.1.2.1 Analyze a given set of data to identify any outliers.

    • SP.1.2.2 Explain the effect of outliers on the measures of central tendency for a given data set.

    • SP.1.2.3 Identify outliers in a given set of data, and justify whether or not they are to be included in reporting the measures of central tendency.

    • SP.1.2.4 Provide examples of situations in which outliers would and would not be used in reporting the measures of central tendency.

  • SP.1.3 Construct, label and interpret circle graphs to solve problems.

    • SP.1.3.1 Identify common attributes of circle graphs, such as:

      • SP.1.3.1.a title, label or legend.

      • SP.1.3.1.b the sum of the central angles is 360°.

      • SP.1.3.1.c the data is reported as a percent of the total, and the sum of the percents is equal to 100%.

    • SP.1.3.2 Create and label a circle graph, with and without technology, to display a given set of data.

    • SP.1.3.3 Find and compare circle graphs in a variety of print and electronic media, such as newspapers, magazines and the Internet.

    • SP.1.3.4 Translate percentages displayed in a circle graph into quantities to solve a given problem.

    • SP.1.3.5 Interpret a given circle graph to answer questions.

      • Interpret circle graphs (7-CC.11)
      • Circle graphs and central angles (7-CC.12)

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

  • SP.2.4 Express probabilities as ratios, fractions and percents.

    • SP.2.4.1 Determine the probability of a given outcome occurring for a given probability experiment, and express it as a ratio, fraction and percent.

      • Probability of simple events (7-EE.1)
      • Probability of simple events - word problems (7-EE.2)
      • Experimental probability (7-EE.4)

    • SP.2.4.2 Provide an example of an event with a probability of 0 or 0% (impossible) and an example of an event with a probability of 1 or 100% (certain).

  • SP.2.5 Identify the sample space (where the combined sample space has 36 or fewer elements) for a probability experiment involving two independent events.

    • SP.2.5.1 Provide an example of two independent events, such as:

      • SP.2.5.1.a spinning a four section spinner and an eight-sided die and explain why they are independent.

      • SP.2.5.1.b tossing a coin and rolling a twelve-sided die and explain why they are independent.

      • SP.2.5.1.c tossing two coins and explain why they are independent.

      • SP.2.5.1.d rolling two dice and explain why they are independent.

    • SP.2.5.2 Identify the sample space (all possible outcomes) for each of two independent events, using a tree diagram, table or other graphic organizer.

      • Compound events: find the number of outcomes (7-EE.6)

  • SP.2.6 Conduct a probability experiment to compare the theoretical probability (determined using a tree diagram, table or other graphic organizer) and experimental probability of two independent events.

    • SP.2.6.1 Determine the theoretical probability of a given outcome involving two independent events.

    • SP.2.6.2 Conduct a probability experiment for an outcome involving two independent events, with and without technology, to compare the experimental probability with the theoretical probability.

    • SP.2.6.3 Solve a given probability problem involving two independent events.

      • Make predictions (7-EE.5)