Math Games

Critique ways in which data is presented.
• Achievement Indicators:
- 8SP1.1 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.
- 8SP1.2 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.
- 8SP1.3 Justify the choice of a graphical representation for a given situation and its corresponding data set.
- 8SP1.4 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.
- 8SP1.5 Explain how a given formatting choice could misrepresent the data.
- 8SP1.6 Identify conclusions that are inconsistent with a given data set or graph and explain the misinterpretation.

Solve problems involving probability of independent events.
• Achievement Indicators:
- 8SP2.1 Determine the probability of two given independent events and verify the probability using a different strategy.
- 8SP2.2 Generalize and apply a rule for determining the probability of independent events.
- 8SP2.3 Solve a given problem that involves determining the probability of independent events.

Demonstrate an understanding of perfect squares and square roots, concretely, pictorially and symbolically (limited to whole numbers).
• Achievement Indicators:
- 8N1.1 Represent a perfect square as a square region using materials, such as grid paper or square shapes.
- 8N1.2 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.
- 8N1.3 Determine the factors of a given perfect square, and explain why one of the factors is a square root and the others are not.
- 8N1.4 Determine the square root of a given perfect square and record it symbolically.
- 8N1.5 Determine the square of a given number.

Determine the approximate square root of numbers that are not perfect squares (limited to whole numbers).
• Achievement Indicators:
- 8N2.1 Estimate, or approximate, a square root of a given number that is not a perfect square using the roots of perfect squares as benchmarks.
- 8N2.2 Identify a whole number whose square root lies between two given numbers.
- 8N2.3 Approximate a square root of a given number that is not a perfect square using technology, e.g., calculator, computer.
- 8N2.4 Explain why a square root of a number shown on a calculator may be an approximation.

Demonstrate an understanding of percents greater than or equal to 0%
• Achievement Indicators:
- 8N3.1 Provide a context where a percent may be more than 100% or between 0% and 1%.
- 8N3.2 Represent a given fractional percent using grid paper.
- 8N3.3 Represent a given percent greater than 100 using grid paper.
- 8N3.4 Determine the percent represented by a given shaded region on a grid and record it in decimal, fractional and percent form.
- 8N3.5 Express a given percent in decimal or fractional form.
- 8N3.6 Express a given decimal in percent or fractional form.
- 8N3.7 Express a given fraction in decimal or percent form.
- 8N3.8 Solve a given problem involving percents.
- 8N3.9 Solve a given problem involving combined percents.
- 8N3.10 Solve a given problem that involves finding the percent of a percent.

Demonstrate an understanding of ratio and rate.
• Achievement Indicators:
- 8N4.1 Express a two-term ratio from a given context in the forms 3:5 or 3 to 5.
- 8N4.2 Express a three-term ratio from a given context in the forms 4:7:3 or 4 to 7 to 3.
- 8N4.3 Express a part-to-part ratio as a part-to whole fraction.
- 8N4.4 Express a given ratio as a percent.
- 8N4.5 Identify and describe ratios from real-life examples, and record them symbolically.
- 8N4.6 Express a given rate using words or symbols, e.g., 20 L per 100 km or 20 L/100 km.
- 8N4.7 Identify and describe rates from real-life examples, and record them symbolically.
- 8N4.8 Explain why a rate cannot be represented as a percent.

Solve problems that involve rates, ratios and proportional reasoning.
• Achievement Indicators:
- 8N5.1 Explain the meaning of within a given context.
- 8N5.2 Provide a context in which represents a:
• fraction
• rate
• ratio
• quotient
• probability.
- 8N5.3 Solve a given problem involving ratio.
- 8N5.4 Solve a given problem involving rates.

Demonstrate an understanding of multiplying and dividing positive fractions and mixed numbers, concretely, pictorially and symbolically.
• Achievement Indicators:
- 8N6.1 Model multiplication of a positive fraction by a whole number concretely or pictorially and record the process.
- 8N6.2 Model multiplication of a positive fraction by a positive fraction concretely or pictorially using an area model and record the process.
- 8N6.3 Provide a context that requires the multiplication of two given positive fractions.
- 8N6.4 Estimate the product of two given positive proper fractions to determine if the product will be closer to 0, 1/2, or 1.
- 8N6.5 Generalize and aply rules for multiplying positive proper fractions, including mixed numbers.
- 8N6.6 Model division of a whole number and a positive proper fraction, concretely or pictorially and record the process.
- 8N6.7 Model division of a positive proper fraction by a positive proper fraction pictorially and record the process.
- 8N6.8 Estimate the quotient of two given positive fractions and compare the estimate to whole number benchmarks.
- 8N6.9 Generalize and apply rules for dividing positive proper fractions.
- 8N6.10 Model, generalize and apply rules for dividing fractions with mixed numbers.
- 8N6.11 Provide a context that requires the dividing of two given positive fractions.
- 8N6.12 Identify the operation required to solve a given problem involving positive fractions.
- 8N6.13 Solve a given problem involving positive fractions taking into consideration order of operations (limited to problems with positive solutions).

Demonstrate an understanding of multiplication and division of integers, concretely, pictorially and symbolically.
• Achievement Indicators:
- 8N7.1 Model the process of multiplying two integers using concrete materials or pictorial representations and record the process.
- 8N7.2 Generalize and apply a rule for determining the sign of the product of integers.
- 8N7.3 Provide a context that requires multiplying two integers.
- 8N7.4 Solve a given problem involving the multiplication of integers.
- 8N7.5 Model the process of dividing an integer by an integer using concrete materials or pictorial representations and record the process.
- 8N7.6 Generalize and apply a rule for determining the sign of the quotient of integers.
- 8N7.7 Provide a context that requires dividing two integers.
- 8N7.8 Solve a given problem involving the division of integers (2-digit by 1-digit) without the use of technology.
- 8N7.9 Solve a given problem involving the division of integers (2-digit by 2-digit) with the use of technology.
- 8N7.10 Identify the operation required to solve a given problem involving integers.
- 8N7.11 Solve a given problem involving integers taking into consideration order of operations.

Develop and apply the Pythagorean theorem to solve problems.
• Achievement Indicators:
- 8SS1.1 Model and explain the Pythagorean theorem concretely, pictorially or using technology.
- 8SS1.2 Determine the measure of the third side of a right triangle, given the measures of the other two sides, to solve a given problem.
- 8SS1.3 Explain, using examples, that the Pythagorean theorem applies only to right triangles.
- 8SS1.4 Determine whether or not a given triangle is a right triangle by applying the Pythagorean theorem.
- 8SS1.5 Solve a given problem that involves Pythagorean triples, e.g. 3, 4, 5 or 5, 12, 13.

Draw and construct nets for 3-D objects.
- 8SS2.1 Match a given net to the 3-D object it represents.
- 8SS2.2 Draw nets for a given right circular cylinder, right rectangular prism, and verify by constructing the 3-D objects from the nets.
- 8SS2.3 Predict 3-D objects that can be created from a given net and verify the prediction.
- 8SS2.4 Construct a 3-D object from a given net.

Determine the surface area of:
• right rectangular prisms
• right triangular prisms
• right cylinders
to solve problems.
- 8SS3.1 Identify all the faces of a given prism, including right rectangular and right triangular prisms.
- 8SS3.2 Explain, using examples, the relationship between the area of a 2-D shape and the surface area of a given 3-D object.
- 8SS3.3 Describe and apply strategies for determining the surface area of a given right rectangular or right triangular prism.
- 8SS3.4 Solve a given problem involving surface area.
- 8SS3.5 Describe and apply strategies for determining the surface area of a given right cylinder.

Develop and apply formulas for determining the volume of right prisms and right cylinders.
- 8SS4.1 Determine the volume of a given right prism, given the area of the base.
- 8SS4.2 Explain the connection between the area of the base of a given right 3-D objects and the formula for the volume of the object.
- 8SS4.3 Generalize and apply a rule for determining the volume of right cylinders.
- 8SS4.4 Demonstrate that the position of a given 3-D object does not affect its volume.
- 8SS4.5 Apply a formula to solve a given problem involving the volume of a right cylinder or a right prism.

Draw and interpret top, front and side views of 3-D objects composed of right rectangular prisms.
• Achievement Indicators:
- 8SS5.1 Draw and label the top, front and side views for a given 3-D object on isometric dot paper.
- 8SS5.2 Compare different views of a given 3-D object to the object.
- 8SS5.3 Predict the top, front and side views that will result from a described rotation (limited to multiples of 90 degrees) and verify predictions.
- 8SS5.4 Draw and label the top, front and side views that result from a described rotation (limited to multiples of 90 degrees).
- 8SS5.5 Build a 3-D block object, given the top, front and side views, with or without the use of technology.
- 8SS5.6 Sketch and label the top, front and side views of a 3-D object in the environment with or without the use of technology

Demonstrate an understanding of tessellation by:
• explaining the properties of shapes that make tessellating possible
• creating tessellations
• identifying tessellations in the environment.

• Achievement Indicators:
- 8SS6.1 Identify, in a given set of regular polygons, those shapes and combinations of shapes that will tessellate, and use angle measurements to justify choices.
- 8SS6.2 Identify, in a given set of irregular polygons, those shapes and combinations of shapes that will tessellate, and use angle measurements to justify choices.
- 8SS6.3 Identify and describe tessellations in the enviornment.
- 8SS6.4 Identify a translation, reflection or rotation in a given tessellation.
- 8SS6.5 Identify a combination of transformations in a given tessellation.
- 8SS6.6 Create a tessellation using one or more 2-D shapes, and describe the tessellation in terms of transformations and conservation of area.
- 8SS6.7 Create a new tessellating shape (polygon or nonpolygon) by transforming a portion of a given tessellating polygon and describe the resulting tessellation in terms of transformations and conservation of area.

Graph and analyze two variable linear relations.
• Achievement Indicators:
- 8PR1.1 Create a table of values by substituting values for a variable in the equation of a given linear relation.
- 8PR1.2 Determine the missing value in an ordered pair for a given equation.
- 8PR1.3 Construct a graph from the equation of a given linear relation (limited to discrete data).
- 8PR1.4 Describe the relationship between the variables in a given graph.

Model and solve problems 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, where a, b, and c are integers.

• Achievement Indicators:
- 8PR2.1 Model a given problem with a linear equation and solve the equation using concrete models.
- 8PR2.2 Draw a visual representation of the steps used to solve a given linear equation and record each step symbolically.
- 8PR2.3 Verify the solution to a given linear equation using a variety of methods, including concrete materials, diagrams and substitution.
- 8PR2.4 Solve a given linear equation symbolically.
- 8PR2.5 Apply the distributive property to solve a given linear equation of the form a(x + b) = c.
- 8PR2.6 Identify and correct an error in a given incorrect solution of a linear equation.
- 8PR2.7 Solve a given problem using a linear equation and record the process.