• 8
Top Mathematicians
• Patterns and Relations
• 8.RP.1.1
Students will be expected to graph and analyze two-variable linear relations.
Performance Indicators
- PR01.01 Determine the missing value in an ordered pair for a given equation.
- PR01.02 Create a table of values by substituting values for a variable in the equation of a given linear relation.
- PR01.03 Construct a graph from the equation of a given linear relation (limited to discrete data).
- PR01.04 Describe the relationship between the variables of a given graph.
• 8.RP.1.2
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 a ≠ 0
a(x + b) = c

Performance Indicators
- PR02.01 Model a given problem with a linear equation, and solve the equation using concrete models.
- PR02.02 Verify the solution to a given linear equation, using a variety of methods, including concrete materials, diagrams, and substitution.
- PR02.03 Draw a visual representation of the steps used to solve a given linear equation, and record each step symbolically.
- PR02.04 Solve a given linear equation symbolically.
- PR02.05 Identify and correct an error in a given incorrect solution of a linear equation.
- PR02.06 Apply the distributive property to solve a given linear equation.
- PR02.07 Solve a given problem, using a linear equation, and record the process.
• The Number System
• 8.NS.1.1
Students will be expected to demonstrate an understanding of perfect squares and square roots, concretely, pictorially, and symbolically (limited to whole numbers).
Performance Indicators
- N01.01 Represent a given perfect square as a square region, using materials such as grid paper or square shapes.
- 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.
- 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.
- N01.04 Determine the square root of a given perfect square, and record it symbolically.
- N01.05 Determine the square of a given number.
• 8.NS.1.2
Students will be expected to determine the approximate square root of numbers that are not perfect squares (limited to whole numbers).
Performance Indicators
- 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.
- 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).
- N02.03 Explain why the square root of a number shown on a calculator may be an approximation.
- N02.04 Identify a number with a square root that is between two given numbers.
• 8.NS.1.3
Students will be expected to demonstrate an understanding of and solve problems involving percents greater than or equal to 0%.
Performance Indicators
- N03.01 Provide contexts where a percent may be between 0% and 1%, between 1% and 100%, and more than 100%.
- N03.02 Represent a given fractional percent using concrete materials and pictorial representations.
- N03.03 Represent a given percent greater than 100% using concrete materials and pictorial representations.
- N03.04 Determine the percent represented by a given shaded region on a grid, and record it in decimal, fraction, and percent form.
- N03.05 Express a given percent in decimal or fraction form.
- N03.06 Express a given decimal in percent or fraction form.
- N03.07 Express a given fraction in decimal or percent form.
- N03.08 Solve a given problem involving percents mentally, with pencil and paper, or with technology, as appropriate.
- N03.09 Solve a given problem that involves finding the percent of a percent.
• 8.NS.1.4
Students will be expected to demonstrate an understanding of ratio and rate.
Performance Indicators
- N04.01 Explain the multiplicative relationship found within a ratio.
- 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.
- N04.03 Express a three-term ratio from a given context in the forms 4:7:3 or 4 to 7 to 3.
- N04.04 Express a part-to-part ratio as a part-to-whole fraction.
- N04.05 Identify and describe ratios and rates (including unit rates) from real-life examples and record them symbolically.
- N04.06 Express a given rate using words or symbols.
- N04.07 Express a given ratio as a percent, and explain why a rate cannot be represented as a percent.
• 8.NS.1.5
Students will be expected to solve problems that involve rates, ratios, and proportional reasoning.
Performance Indicators
- N05.01 Explain the meaning of a/b within a given context.
- N05.02 Provide a context in which a/b represents a fraction, a rate, a ratio, a quotient, and a probability.
- N05.03 Use pictures, models, or manipulatives to make sense of a proportional situation.
- N05.04 Differentiate between proportional and non-proportional contexts.
- N05.05 Use multiplicative relationships to compare quantities and to predict the value of one quantity based on the values of another.
- N05.06 Use multiple methods to solve proportional tasks and understand that these methods are related to each other.
- N05.07 Use estimation to determine the reasonableness of an answer.
- N05.08 Solve a proportion using mental mathematics, pencil and paper, or technology, as appropriate.
- N05.09 Solve a given problem involving rate, ratio, or percent using mental mathematics, pencil and paper, or technology, as appropriate.
- N05.10 Create problems that are examples of proportional reasoning.
• 8.NS.1.6
Students will be expected to demonstrate an understanding of multiplying and dividing positive fractions and mixed numbers, concretely, pictorially, and symbolically.
Performance Indicators
- N06.01 Identify the operation required to solve a given problem involving positive fractions.
- N06.02 Provide a context that requires the multiplying of two given positive fractions.
- N06.03 Provide a context that requires the dividing of two given positive fractions.
- 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.
- N06.05 Estimate the quotient of two given positive fractions, and compare the estimate to whole number benchmarks.
- N06.06 Express a given positive mixed number as an improper fraction and a given positive improper fraction as a mixed number.
- N06.07 Model multiplication of a positive fraction by a whole number concretely and/or pictorially and record the process.
- N06.08 Model multiplication of a positive fraction by a positive fraction concretely and/or pictorially, using an area model, and record the process.
- N06.09 Model division of a positive proper fraction by a whole number concretely and/or pictorially and record the process.
- 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.
- N06.11 Model division of a positive proper fraction by a positive proper fraction pictorially and record the process.
- N06.12 Generalize and apply rules for multiplying and dividing positive fractions, including mixed numbers.
- 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).
• 8.NS.1.7
Students will be expected to demonstrate an understanding of multiplication and division of integers, concretely, pictorially, and symbolically.
Performance Indicators
- N07.01 Identify the operation required to solve a given problem involving integers.
- N07.02 Provide a context that requires multiplying two integers.
- N07.03 Provide a context that requires dividing two integers.
- N07.04 Model the process of multiplying two integers, using concrete materials or pictorial representations, and record the process.
- N07.05 Model the process of dividing an integer by an integer, using concrete materials and/or pictorial representations, and record the process.
- N07.06 Generalize and apply a rule for determining the sign of the product and quotient of integers.
- N07.07 Solve a given problem involving the division of integers (two-digit by one-digit) without the use of technology.
- 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.
- N07.09 Symbolically solve a given problem involving integers, taking into consideration order of operations when necessary.
• Measurement and Data
• 8.MD.1.1
Students will be expected to develop and apply the Pythagorean theorem to solve problems.
Performance Indicators
- M01.01 Model and explain the Pythagorean theorem concretely, pictorially, or using technology.
- M01.02 Explain, using examples, that the Pythagorean theorem applies only to right triangles.
- M01.03 Determine whether or not a given triangle is a right triangle by applying the Pythagorean theorem.
- 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.
- M01.05 Solve a given problem that involves Pythagorean triples.
• 8.MD.1.2
Students will be expected to draw and construct nets for 3-D objects.
Performance Indicators
- M02.01 Match a given net to the 3-D object it represents.
- M02.02 Construct a 3-D object from a given net.
- 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.
- M02.04 Predict 3-D objects that can be created from a given net, and verify the prediction
• 8.MD.1.3
Students will be expected to determine the surface area of right rectangular prisms, right triangular prisms, and right cylinders to solve problems.
Performance Indicators
- M03.01 Explain, using examples, the relationship between the area of 2-D shapes and the surface area of a given 3-D object.
- M03.02 Identify all the faces of a given prism, including right rectangular and right triangular prisms.
- M03.03 Identify all the faces of a given right cylinder.
- M03.04 Describe and apply strategies for determining the surface area of a given right rectangular or right triangular prism.
- M03.05 Describe and apply strategies for determining the surface area of a given right cylinder.
- M03.06 Solve a given problem involving surface area.
• 8.MD.1.4
Students will be expected to develop and apply formulas for determining the volume of right rectangular prisms, right triangular prisms, and right cylinders.
Performance Indicators
- M04.01 Determine the volume of a given right prism, given the area of the base.
- M04.02 Generalize and apply a rule for determining the volume of right cylinders.
- 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.
- M04.04 Demonstrate that the orientation of a given 3-D object does not affect its volume.
- M04.05 Apply a formula to solve a given problem involving the volume of a right cylinder or a right prism.
• Geometry
• 8.G.1.1
Students will be expected to draw and interpret top, front, and side views of 3-D objects composed of right rectangular prisms.
Performance Indicators
- G01.01 Draw and label the top, front, and side views for a given 3-D object on isometric dot paper.
- G01.02 Compare different views of a given 3-D object to the object.
- G01.03 Predict the top, front, and side views that will result from a described rotation (limited to multiples of 90°), and verify predictions.
- G01.04 Draw and label the top, front, and side views that result from a given rotation (limited to multiples of 90°).
- G01.05 Build a 3-D block object given the top, front, and side views, with or without the use of technology.
- 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.
• 8.G.1.2
Students will be expected to demonstrate an understanding of the congruence of polygons under a transformation.
Performance Indicators
- G02.01 Determine the coordinates of the vertices of an image following a given combination of transformations of the original figure.
- G02.02 Draw the original figure and determine the coordinates of its vertices, given the coordinates of the imageâ€™s vertices and a description of the transformation (translation, rotation, reflection).
• Statistics & Probability
• 8.SP.1.1
Students will be expected to critique ways in which data is presented.
Performance Indicators
- 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.
- 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.
- SP01.03 Justify the choice of a graphical representation for a given situation and its corresponding data set.
- 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.
- SP01.05 Explain how a given formatting choice could misrepresent the data.
- SP01.06 Identify conclusions that are inconsistent with a given data set or graph, and explain the misinterpretation.
• 8.SP.1.2
Students will be expected to solve problems involving the probability of independent events.
Performance Indicators
- SP02.01 Determine the probability of two given independent events, and verify the probability using a different strategy.
- SP02.02 Generalize and apply a rule for determining the probability of independent events.
- SP02.03 Solve a given problem that involves determining the probability of independent events.