• 8
    Grade 8 Standards
Top Mathematicians
  • Shape and Space
    • 8.SS.1
      Develop and apply the Pythagorean theorem to solve problems.
      Achievement Indicators
      - Model and explain the Pythagorean theorem concretely, pictorially or using technology.
      - Explain, using examples, that the Pythagorean theorem applies only to right triangles.
      - Determine whether or not a given triangle is a right triangle by applying the Pythagorean theorem.
      - Determine the measure of the third side of a right triangle, given the measures of the other two sides, to solve a given problem.
      - Solve a given problem that involves Pythagorean triples, e.g., 3, 4, 5 or 5, 12, 13.
    • 8.SS.2
      Draw and construct nets for 3-D objects.
      Achievement Indicators
      - Match a given net to the 3-D object it represents.
      - Construct a 3-D object from a given net.
      - Draw nets for a given right circular cylinder, right rectangular prism and right triangular prism, and verify by constructing the 3-D objects from the nets.
      - Predict 3-D objects that can be created from a given net and verify the prediction.
    • 8.SS.3
      Determine the surface area of:
      right rectangular prisms
      right triangular prisms
      right cylinders
      to solve problems.

      Achievement Indicators
      - Explain, using examples, the relationship between the area of 2-D shapes and the surface area of a given 3-D object.
      - Identify all the faces of a given prism, including right rectangular and right triangular prisms.
      - Describe and apply strategies for determining the surface area of a given right rectangular or right triangular prism.
      - Describe and apply strategies for determining the surface area of a given right cylinder.
      - Solve a given problem involving surface area.
    • 8.SS.4
      Develop and apply formulas for determining the volume of right prisms and right cylinders.
      Achievement Indicators
      - Determine the volume of a given right prism, given the area of the base.
      - Generalize and apply a rule for determining the volume of right cylinders.
      - 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.
      - Demonstrate that the orientation of a given 3-D object does not affect its volume.
      - Apply a formula to solve a given problem involving the volume of a right cylinder or a right prism.
    • 8.SS.5
      Draw and interpret top, front and side views of 3-D objects composed of right rectangular prisms.
      Achievement Indicators
      - Draw and label the top, front and side views for a given 3-D object on isometric dot paper.
      - Compare different views of a given 3-D object to the object.
      - Predict the top, front and side views that will result from a described rotation (limited to multiples of 90 degrees) and verify predictions.
      - Draw and label the top, front and side views that result from a given rotation (limited to multiples of 90 degrees).
      - Build a 3-D block object, given the top, front and side views, with or without the use of technology.
      - Sketch and label the top, front and side views of a 3-D object in the environment with or without the use of technology.
    • 8.SS.6
      Demonstrate an understanding of tessellation by:
      explaining the properties of shapes that make tessellating possible
      creating tessellations
      identifying tessellations in the environment.

      Achievement Indicators
      - Identify, in a given set of regular polygons, those shapes and combinations of shapes that will tessellate, and use angle measurements to justify choices, e.g., squares, regular n-gons.
      - Identify, in a given set of irregular polygons, those shapes and combinations of shapes that will tessellate, and use angle measurements to justify choices.
      - Identify a translation, reflection or rotation in a given tessellation.
      - Identify a combination of transformations in a given tessellation.
      - Create a tessellation using one or more 2-D shapes, and describe the tessellation in terms of transformations and conservation of area.
      - Create a new tessellating shape (polygon or non-polygon) by transforming a portion of a given tessellating polygon, e.g., one by M. C. Escher, and describe the resulting tessellation in terms of transformations and conservation of area.
      - Identify and describe tessellations in the environment.
  • Statistics & Probability
    • 8.SP.1
      Critique ways in which data is presented.
      Achievement Indicators
      - Compare the information that is provided for the same data set by a given set of graphs, including circle graphs, line graphs, bar graphs, double bar graphs and pictographs, to determine the strengths and limitations of each graph.
      - Identify the advantages and disadvantages of different graphs, including circle graphs, line graphs, bar graphs, double bar graphs and pictographs, in representing a specific given set of data.
      - Justify the choice of a graphical representation for a given situation and its corresponding data set.
      - Explain how the format of a given graph, such as the size of the intervals, the width of bars and the visual representation, may lead to misinterpretation of the data.
      - Explain how a given formatting choice could misrepresent the data.
      - Identify conclusions that are inconsistent with a given data set or graph and explain the misinterpretation.
    • 8.SP.2
      Solve problems involving the probability of independent events.
      Achievement Indicators
      - Determine the probability of two given independent events and verify the probability using a different strategy.
      - Generalize and apply a rule for determining the probability of independent events.
      - Solve a given problem that involves determining the probability of independent events.
  • Number
    • 8.N.1
      Demonstrate an understanding of perfect square and square root, concretely, pictorially and symbolically (limited to whole numbers).
      Achievement Indicators
      - Represent a given perfect square as a square region using materials, such as grid paper or square shapes.
      - Determine the factors of a given perfect square, and explain why one of the factors is the square root and the others are not.
      - 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.
      - Determine the square root of a given perfect square and record it symbolically.
      - Determine the square of a given number.
    • 8.N.2
      Determine the approximate square root of numbers that are not perfect squares (limited to whole numbers).
      Achievement Indicators
      - Estimate the square root of a given number that is not a perfect square using the roots of perfect squares as benchmarks.
      - Approximate the square root of a given number that is not a perfect square using technology, e.g., calculator, computer.
      - Explain why the square root of a number shown on a calculator may be an approximation.
      - Identify a number with a square root that is between two given numbers.
    • 8.N.3
      Demonstrate an understanding of percents greater than or equal to 0%.
      Achievement Indicators
      - Provide a context where a percent may be more than 100% or between 0% and 1%.
      - Represent a given fractional percent using grid paper.
      - Represent a given percent greater than 100 using grid paper.
      - Determine the percent represented by a given shaded region on a grid, and record it in decimal, fractional and percent form.
      - Express a given percent in decimal or fractional form.
      - Express a given decimal in percent or fractional form.
      - Express a given fraction in decimal or percent form.
      - Solve a given problem involving percents.
      - Solve a given problem involving combined percents, e.g., addition of percents, such as GST + PST.
      - Solve a given problem that involves finding the percent of a percent, e.g., A population increased by 10% one year and then increased by 15% the next year. Explain why there was not a 25% increase in population over the two years.
    • 8.N.4
      Demonstrate an understanding of ratio and rate.
      Achievement Indicators
      - Express a two-term ratio from a given context in the forms 3:5 or 3 to 5.
      - Express a three-term ratio from a given context in the forms 4:7:3 or 4 to 7 to 3.
      - Express a part to part ratio as a part to whole fraction, e.g., frozen juice to water; 1 can concentrate to 4 cans of water can be represented as 1/5 , which is the ratio of concentrate to solution, or 4/5 , which is the ratio of water to solution.
      - Identify and describe ratios and rates from real-life examples, and record them symbolically.
      - Express a given rate using words or symbols, e.g., 20 L per 100 km or 20 L/100 km.
      - Express a given ratio as a percent and explain why a rate cannot be represented as a percent.
    • 8.N.5
      Solve problems that involve rates, ratios and proportional reasoning.
      Achievement Indicators
      - Explain the meaning of a/b within a given context.
      - Provide a context in which a/b represents a:
      fraction
      rate
      ratio
      quotient
      probability.
      - Solve a given problem involving rate, ratio or percent.
    • 8.N.6
      Demonstrate an understanding of multiplying and dividing positive fractions and mixed numbers, concretely, pictorially and symbolically.
      Achievement Indicators
      - Identify the operation required to solve a given problem involving positive fractions.
      - Provide a context that requires the multiplying of two given positive fractions.
      - Provide a context that requires the dividing of two given positive fractions.
      - Estimate the product of two given positive proper fractions to determine if the product will be closer to 0, 1/2 or 1.
      - Estimate the quotient of two given positive fractions and compare the estimate to whole number benchmarks.
      - Express a given positive mixed number as an improper fraction and a given positive improper fraction as a mixed number.
      - Model multiplication of a positive fraction by a whole number concretely or pictorially and record the process.
      - Model multiplication of a positive fraction by a positive fraction concretely or pictorially using an area model and record the process.
      - Model division of a positive proper fraction by a whole number concretely or pictorially and record the process.
      - Model division of a positive proper fraction by a positive proper fraction pictorially and record the process.
      - Generalize and apply rules for multiplying and dividing positive fractions, including mixed numbers.
      - Solve a given problem involving positive fractions taking into consideration order of operations (limited to problems with positive solutions).
    • 8.N.7
      Demonstrate an understanding of multiplication and division of integers, concretely, pictorially and symbolically.
      Achievement Indicators
      - Identify the operation required to solve a given problem involving integers.
      - Provide a context that requires multiplying two integers.
      - Provide a context that requires dividing two integers.
      - Model the process of multiplying two integers using concrete materials or pictorial representations and record the process.
      - Model the process of dividing an integer by an integer using concrete materials or pictorial representations and record the process.
      - Solve a given problem involving the division of integers (2-digit by 1-digit) without the use of technology.
      - Solve a given problem involving the division of integers (2-digit by 2-digit) with the use of technology.
      - Generalize and apply a rule for determining the sign of the product and quotient of integers.
      - Solve a given problem involving integers taking into consideration order of operations.
  • Patterns and Relations