Nova Scotia

8.N Number

• Students will be expected to demonstrate number sense.

  • 8.N01 Students will be expected to demonstrate an understanding of perfect squares and square roots, concretely, pictorially, and symbolically (limited to whole numbers).

    • 8.N01.01 Represent a given perfect square as a square region, using materials such as grid paper or square shapes.

    • 8.N01.02 Determine the factors of a given perfect square, and explain why one of the factors is the square root and the others are not.

    • 8.N01.03 Determine whether or not a given number is a perfect square, using materials and strategies such as square shapes, grid paper or prime factorization, and explain the reasoning.

    • 8.N01.04 Determine the square root of a given perfect square, and record it symbolically.

      • Square roots of perfect squares (8-G.11)
      • Relationship between squares and square roots (8-G.13)
      • Solve equations involving squares and square roots (8-G.14)

    • 8.N01.05 Determine the square of a given number.

  • 8.N02 Students will be expected to determine the approximate square root of numbers that are not perfect squares (limited to whole numbers).

    • 8.N02.01 Estimate the square root of a given number that is not a perfect square, using materials such as square shapes and graph paper and strategies such as using the roots of perfect squares as benchmarks.

      • Estimate square roots (8-G.12)

    • 8.N02.02 Approximate the square root of a given number that is not a perfect square using technology (e.g., a calculator or a computer).

      • Estimate square roots (8-G.12)

    • 8.N02.03 Explain why the square root of a number shown on a calculator may be an approximation.

    • 8.N02.04 Identify a number with a square root that is between two given numbers.

  • 8.N03 Students will be expected to demonstrate an understanding of and solve problems involving percents greater than or equal to 0%.

    • 8.N03.01 Provide contexts where a percent may be between 0% and 1%, between 1% and 100%, and more than 100%.

    • 8.N03.02 Represent a given fractional percent using concrete materials and pictorial representations.

    • 8.N03.03 Represent a given percent greater than 100% using concrete materials and pictorial representations.

    • 8.N03.04 Determine the percent represented by a given shaded region on a grid, and record it in decimal, fraction, and percent form.

      • What percentage is illustrated? (7-N.1)

    • 8.N03.05 Express a given percent in decimal or fraction form.

      • Convert between percents, fractions and decimals (8-K.1)
      • Compare percents to fractions and decimals (8-K.2)

    • 8.N03.06 Express a given decimal in percent or fraction form.

      • Convert between percents, fractions and decimals (8-K.1)
      • Compare percents to fractions and decimals (8-K.2)

    • 8.N03.07 Express a given fraction in decimal or percent form.

      • Convert between percents, fractions and decimals (8-K.1)
      • Compare percents to fractions and decimals (8-K.2)

    • 8.N03.08 Solve a given problem involving percents mentally, with pencil and paper, or with technology, as appropriate.

      • Find what percent one number is of another (8-K.3)
      • Find what percent one number is of another: word problems (8-K.4)
      • Percents of numbers and money amounts (8-K.6)
      • Percents of numbers: word problems (8-K.7)
      • Solve percent equations (8-K.9)
      • Percent of change (8-K.10)
      • Percent of change: word problems (8-K.11)
      • Percent of a number: tax, discount and more (8-L.4)
      • Find the percent: tax, discount and more (8-L.5)
      • Sale prices: find the original price (8-L.6)
      • Multi-step problems with percents (8-L.7)
      • Estimate tips (8-L.8)

    • 8.N03.09 Solve a given problem that involves finding the percent of a percent.

  • 8.N04 Students will be expected to demonstrate an understanding of ratio and rate.

    • 8.N04.01 Explain the multiplicative relationship found within a ratio.

    • 8.N04.02 Represent a two-term ratio from a given context concretely and pictorially and record using the forms 3:5 or 3 to 5.

      • Understanding ratios (8-I.1)

    • 8.N04.03 Express a three-term ratio from a given context in the forms 4:7:3 or 4 to 7 to 3.

    • 8.N04.04 Express a part-to-part ratio as a part-to-whole fraction.

    • 8.N04.05 Identify and describe ratios and rates (including unit rates) from real-life examples and record them symbolically.

      • Unit rates (8-I.6)

    • 8.N04.06 Express a given rate using words or symbols.

      • Equivalent rates (8-I.7)

    • 8.N04.07 Express a given ratio as a percent, and explain why a rate cannot be represented as a percent.

  • 8.N05 Students will be expected to solve problems that involve rates, ratios, and proportional reasoning.

    • 8.N05.01 Explain the meaning of a/b within a given context.

    • 8.N05.02 Provide a context in which a/b represents a fraction, a rate, a ratio, a quotient, and a probability.

    • 8.N05.03 Use pictures, models, or manipulatives to make sense of a proportional situation.

      • Use tape diagrams to solve ratio word problems (8-I.9)

    • 8.N05.04 Differentiate between proportional and non-proportional contexts.

      • Do the ratios form a proportion? (8-I.13)
      • Do the ratios form a proportion: word problems (8-I.14)

    • 8.N05.05 Use multiplicative relationships to compare quantities and to predict the value of one quantity based on the values of another.

      • Estimate population size using proportions (8-I.16)

    • 8.N05.06 Use multiple methods to solve proportional tasks and understand that these methods are related to each other.

      • Compare ratios: word problems (8-I.10)
      • Compare rates: word problems (8-I.11)
      • Ratios and rates: word problems (8-I.12)
      • Scale drawings: word problems (8-I.17)

    • 8.N05.07 Use estimation to determine the reasonableness of an answer.

    • 8.N05.08 Solve a proportion using mental mathematics, pencil and paper, or technology, as appropriate.

      • Solve proportions (8-I.15)

    • 8.N05.09 Solve a given problem involving rate, ratio, or percent using mental mathematics, pencil and paper, or technology, as appropriate.

      • Compare ratios: word problems (8-I.10)
      • Compare rates: word problems (8-I.11)
      • Ratios and rates: word problems (8-I.12)
      • Scale drawings: word problems (8-I.17)

    • 8.N05.10 Create problems that are examples of proportional reasoning.

  • 8.N06 Students will be expected to demonstrate an understanding of multiplying and dividing positive fractions and mixed numbers, concretely, pictorially, and symbolically.

    • 8.N06.01 Identify the operation required to solve a given problem involving positive fractions.

      • Add, subtract, multiply and divide fractions and mixed numbers: word problems (7-J.9)

    • 8.N06.02 Provide a context that requires the multiplying of two given positive fractions.

    • 8.N06.03 Provide a context that requires the dividing of two given positive fractions.

    • 8.N06.04 Estimate the product of two given positive proper fractions to determine if the product will be closer to 0, 1/2 , or 1.

      • Estimate products and quotients of fractions and mixed numbers (7-J.8)

    • 8.N06.05 Estimate the quotient of two given positive fractions, and compare the estimate to whole number benchmarks.

      • Estimate quotients when dividing mixed numbers (7-I.7)
      • Estimate products and quotients of fractions and mixed numbers (7-J.8)

    • 8.N06.06 Express a given positive mixed number as an improper fraction and a given positive improper fraction as a mixed number.

      • Convert between mixed numbers and improper fractions (7-F.9)

    • 8.N06.07 Model multiplication of a positive fraction by a whole number concretely and/or pictorially and record the process.

      • Multiply unit fractions by whole numbers using number lines (7-H.1)
      • Multiply unit fractions by whole numbers using models (7-H.2)
      • Multiply fractions by whole numbers using number lines (7-H.3)
      • Multiplying fractions by whole numbers: choose the model (7-H.4)

    • 8.N06.08 Model multiplication of a positive fraction by a positive fraction concretely and/or pictorially, using an area model, and record the process.

      • Multiply two fractions using models (8-D.14)

    • 8.N06.09 Model division of a positive proper fraction by a whole number concretely and/or pictorially and record the process.

    • 8.N06.10 Model division of a whole number by a positive proper fraction concretely and/or pictorially, using an area model, and record the process.

      • Divide whole numbers by unit fractions using models (8-D.19)

    • 8.N06.11 Model division of a positive proper fraction by a positive proper fraction pictorially and record the process.

    • 8.N06.12 Generalize and apply rules for multiplying and dividing positive fractions, including mixed numbers.

      • Multiply fractions and whole numbers (8-D.13)
      • Multiply fractions (8-D.15)
      • Multiply fractions: word problems (8-D.16)
      • Multiply mixed numbers (8-D.17)
      • Multiply mixed numbers: word problems (8-D.18)
      • Divide whole numbers and unit fractions (8-D.20)
      • Divide fractions (8-D.21)
      • Divide fractions: word problems (8-D.22)
      • Divide mixed numbers (8-D.23)
      • Divide mixed numbers: word problems (8-D.24)

    • 8.N06.13 Symbolically solve a given problem involving positive fractions, taking into consideration order of operations (limited to problems with positive solutions and that exclude exponents).

      • Evaluate numerical expressions involving fractions (7-J.10)

  • 8.N07 Students will be expected to demonstrate an understanding of multiplication and division of integers, concretely, pictorially, and symbolically.

    • 8.N07.01 Identify the operation required to solve a given problem involving integers.

      • Add and subtract integers: word problems (8-C.6)
      • Multiply and divide integers (8-C.8)

    • 8.N07.02 Provide a context that requires multiplying two integers.

    • 8.N07.03 Provide a context that requires dividing two integers.

    • 8.N07.04 Model the process of multiplying two integers, using concrete materials or pictorial representations, and record the process.

      • Understand multiplying by a negative integer using a number line (7-C.15)

    • 8.N07.05 Model the process of dividing an integer by an integer, using concrete materials and/or pictorial representations, and record the process.

    • 8.N07.06 Generalize and apply a rule for determining the sign of the product and quotient of integers.

      • Integer multiplication and division rules (8-C.7)

    • 8.N07.07 Solve a given problem involving the division of integers (two-digit by one-digit) without the use of technology.

      • Divide integers (7-C.20)

    • 8.N07.08 Solve a given problem involving the division of integers (two-digit by two-digit) mentally or with the use of technology, where appropriate.

      • Divide integers (7-C.20)

    • 8.N07.09 Symbolically solve a given problem involving integers, taking into consideration order of operations when necessary.

      • Evaluate numerical expressions involving integers (7-C.25)
      • Multiply and divide integers (8-C.8)
      • Complete multiplication and division sentences with integers (8-C.9)
      • Add, subtract, multiply and divide integers (8-C.10)

8.PR Patterns and Relations

• Patterns - Students will be expected to use patterns to describe the world and solve problems.

  • 8.PR01 Students will be expected to graph and analyze two-variable linear relations.

    • 8.PR01.01 Determine the missing value in an ordered pair for a given equation.

      • Does (x, y) satisfy the linear function? (8-Z.1)

    • 8.PR01.02 Create a table of values by substituting values for a variable in the equation of a given linear relation.

      • Complete a table for a linear function (8-Z.5)

    • 8.PR01.03 Construct a graph from the equation of a given linear relation (limited to discrete data).

      • Ratios and rates: complete a table and make a graph (8-I.8)

    • 8.PR01.04 Describe the relationship between the variables of a given graph.

      • Find the constant of proportionality from a graph (8-J.4)
      • Interpret graphs of proportional relationships (8-J.9)
      • Constant rate of change (8-Z.4)
      • Interpret the graph of a linear function: word problems (8-Z.8)

• Variables and Equations - Students will be expected to represent algebraic expressions in multiple ways.

  • 8.PR02 Students will be expected to model and solve problems, concretely, pictorially, and symbolically, where a, b, and c are integers, using linear equations of the form: ax = b; x/a = b, a ≠ 0; ax + b = c; x/a + b = c, a ≠ 0; a(x + b) = c.

    • 8.PR02.01 Model a given problem with a linear equation, and solve the equation using concrete models.

      • Solve equations: word problems (8-X.12)

    • 8.PR02.02 Verify the solution to a given linear equation, using a variety of methods, including concrete materials, diagrams, and substitution.

      • Which x satisfies an equation? (8-X.1)

    • 8.PR02.03 Draw a visual representation of the steps used to solve a given linear equation, and record each step symbolically.

      • Model and solve equations using algebra tiles (8-X.3)
      • Write and solve equations that represent diagrams (8-X.4)

    • 8.PR02.04 Solve a given linear equation symbolically.

      • Solve one-step equations (8-X.6)
      • Solve two-step equations (8-X.7)
      • Solve equations involving like terms (8-X.9)

    • 8.PR02.05 Identify and correct an error in a given incorrect solution of a linear equation.

    • 8.PR02.06 Apply the distributive property to solve a given linear equation.

      • Solve multi-step equations (8-X.8)

    • 8.PR02.07 Solve a given problem, using a linear equation, and record the process.

      • Solve equations: complete the solution (8-X.11)
      • Solve equations: word problems (8-X.12)

8.M Measurement

• Students will be expected to use direct and indirect measure to solve problems.

  • 8.M01 Students will be expected to develop and apply the Pythagorean theorem to solve problems.

    • 8.M01.01 Model and explain the Pythagorean theorem concretely, pictorially, or using technology.

    • 8.M01.02 Explain, using examples, that the Pythagorean theorem applies only to right triangles.

    • 8.M01.03 Determine whether or not a given triangle is a right triangle by applying the Pythagorean theorem.

      • Converse of the Pythagorean theorem: is it a right triangle? (8-S.6)

    • 8.M01.04 Determine the measure of the third side of a right triangle, given the measures of the other two sides, to solve a given problem.

      • Pythagorean theorem: find the length of the hypotenuse (8-S.1)
      • Pythagorean theorem: find the missing leg length (8-S.2)
      • Pythagorean theorem: find the missing leg or hypotenuse length (8-S.3)
      • Pythagorean theorem: find the perimeter (8-S.4)
      • Pythagorean theorem: word problems (8-S.5)

    • 8.M01.05 Solve a given problem that involves Pythagorean triples.

  • 8.M02 Students will be expected to draw and construct nets for 3-D objects.

    • 8.M02.01 Match a given net to the 3-D object it represents.

      • Parts of three-dimensional figures (8-T.1)
      • Nets of three-dimensional figures (8-T.2)

    • 8.M02.02 Construct a 3-D object from a given net.

      • Nets of three-dimensional figures (8-T.2)

    • 8.M02.03 Draw nets for a given right cylinder, right rectangular prism, and right triangular prism, and verify by constructing the 3-D objects from the nets.

    • 8.M02.04 Predict 3-D objects that can be created from a given net, and verify the prediction.

      • Nets of three-dimensional figures (8-T.2)

  • 8.M03 Students will be expected to determine the surface area of right rectangular prisms, right triangular prisms, and right cylinders to solve problems.

    • 8.M03.01 Explain, using examples, the relationship between the area of 2-D shapes and the surface area of a given 3-D object.

    • 8.M03.02 Identify all the faces of a given prism, including right rectangular and right triangular prisms.

    • 8.M03.03 Identify all the faces of a given right cylinder.

    • 8.M03.04 Describe and apply strategies for determining the surface area of a given right rectangular or right triangular prism.

      • Surface area of prisms (7-BB.18)

    • 8.M03.05 Describe and apply strategies for determining the surface area of a given right cylinder.

      • Surface area of cylinders (7-BB.20)

    • 8.M03.06 Solve a given problem involving surface area.

      • Surface area of prisms and cylinders (8-U.11)

  • 8.M04 Students will be expected to develop and apply formulas for determining the volume of right rectangular prisms, right triangular prisms, and right cylinders.

    • 8.M04.01 Determine the volume of a given right prism, given the area of the base.

    • 8.M04.02 Generalize and apply a rule for determining the volume of right cylinders.

      • Classify quadrilaterals II (8-P.5)

    • 8.M04.03 Explain the connection between the area of the base of a given right 3-D object and the formula for the volume of the object.

    • 8.M04.04 Demonstrate that the orientation of a given 3-D object does not affect its volume.

    • 8.M04.05 Apply a formula to solve a given problem involving the volume of a right cylinder or a right prism.

      • Volume (8-U.10)

8.G Geometry

• 3-D Objects and 2-D Shapes - Students will be describe the characteristics of 3-D objects and 2-D shapes and analyze the relationships among them.

  • 8.G01 Students will be expected to draw and interpret top, front, and side views of 3-D objects composed of right rectangular prisms.

    • 8.G01.01 Draw and label the top, front, and side views for a given 3-D object on isometric dot paper.

    • 8.G01.02 Compare different views of a given 3-D object to the object.

    • 8.G01.03 Predict the top, front, and side views that will result from a described rotation (limited to multiples of 90°), and verify predictions.

    • 8.G01.04 Draw and label the top, front, and side views that result from a given rotation (limited to multiples of 90°).

    • 8.G01.05 Build a 3-D block object given the top, front, and side views, with or without the use of technology.

    • 8.G01.06 Sketch and label the top, front, and side views of a 3-D object in the environment, with or without the use of technology.

      • Front, side and top view (8-T.3)

• Transformations - Students will be expected to describe and analyze position and motion of objects and shapes.

  • 8.G02 Students will be expected to demonstrate an understanding of the congruence of polygons under a transformation.

    • 8.G02.01 Determine the coordinates of the vertices of an image following a given combination of transformations of the original figure.

      • Compositions of congruence transformations: graph the image (8-Q.10)

    • 8.G02.02 Draw the original figure and determine the coordinates of its vertices, given the coordinates of the image's vertices and a description of the transformation (translation, rotation, reflection).

8.SP Statistics and Probability

• Data Analysis - Students will be expected to collect, display, and analyze data to solve problems.

  • 8.SP01 Students will be expected to critique ways in which data is presented.

    • 8.SP01.01 Compare information provided for the same data set by a given set of graphs, including circle graphs, line graphs, bar graphs, and pictographs, to determine the strengths and limitations of each graph.

    • 8.SP01.02 Identify the advantages and disadvantages of different graphs, including circle graphs, line graphs, bar graphs, and pictographs, in representing a given set of data.

    • 8.SP01.03 Justify the choice of a graphical representation for a given situation and its corresponding data set.

      • Choose the best type of graph (8-AA.18)

    • 8.SP01.04 Explain how the format of a given graph, such as the size of the intervals, the width of the bars, and the visual representation, may lead to misinterpretation of the data.

    • 8.SP01.05 Explain how a given formatting choice could misrepresent the data.

    • 8.SP01.06 Identify conclusions that are inconsistent with a given data set or graph, and explain the misinterpretation.

• Chance and Uncertainty - Students will be expected to use experimental or theoretical probabilities to represent and solve problems involving uncertainty.

  • 8.SP02 Students will be expected to solve problems involving the probability of independent events.

    • 8.SP02.01 Determine the probability of two given independent events, and verify the probability using a different strategy.

      • Probability of independent events (8-CC.8)

    • 8.SP02.02 Generalize and apply a rule for determining the probability of independent events.

      • Probability of independent events (8-CC.8)

    • 8.SP02.03 Solve a given problem that involves determining the probability of independent events.

      • Identify independent and dependent events (8-CC.7)
      • Probability of independent events (8-CC.8)