Grade 8 Math Rubrics

Subject: Grade 8 Math, Number Strand

Outcome N8.1 – I can demonstrate understanding of the square and principle square root of whole numbers.

Beginning – 1 Approaching – 2 Proficiency – 3 Mastery – 4 I need help. I have a basic understanding. My work consistently meets I have a deeper understanding. expectations. With assistance I can determine I can determine basic perfect I can independently determine if I can explain why a perfect square is basic perfect squares. squares. specific numbers are perfect a perfect square. With assistance I can determine the I can determine the value of a basic squares. I can explain my strategy for value of a basic number squared. number squared. I can determine the value of a determining the square of a number. With assistance I can determine the I can determine the value of basic number squared. I can explain my strategy for value of basic principle square roots. principle square roots. I can determine the value of a determining the value of a principle principle square root. square root. Indicators – please select and assess as appropriate to your unit, bold text indicates possible key indicators.  Recognize, show, and explain the relationship between whole numbers and their factors using concrete or pictorial representations.  Infer and verify relationships between the factors of a perfect square and the principle square root of a perfect square.  Determine if specific numbers are perfect squares through the use of different types of representations and reasoning, and explain the reasoning.  Describe and apply the relationship between the principle square roots of numbers and benchmarks using a number line.  Explain why the square root of a number shown on a calculator may be an approximation.  Apply estimation strategies to determine approximate values for principle square roots.  Determine the value or an approximate value of a principle square root with or without the use of technology.  Identify a number with a principle square root between two given numbers and explain the reasoning.  Share the story, in writing, orally, drama, dance, art, music, or other media, of the role and significance of square roots in personally selected historical or modern application situation.

Refer to the Saskatchewan Curriculum Guide Grade 8 Mathematics.

Subject: Grade 8 Math, Number Strand Outcome N8.2 – I can expand and demonstrate understanding of percent greater than or equal to 0%.

Beginning – 1 Approaching – 2 Proficiency – 3 Mastery – 4 I need help. I have a basic understanding. My work consistently meets I have a deeper understanding. expectations. With assistance I can record the I can recognize situations in which I can independently represent I can apply my understanding of percent, fraction, and decimal forms fractional percents are meaningful. situations concretely, in pictures percent to solve problems involving of a quantity shown by a simple I can record the percent, fraction, and with symbols in which combined percent or percent of representation on grid paper. and decimal forms of a quantity fractional percents are meaningful. percent and explain the reasoning. shown by a simple representation I can independently solve problems I can pose and solve problems on grid paper. involving percent stated as percent, involving percent stated as percent, fraction or decimal quantity. fraction or decimal quantity. Indicators – please select and assess as appropriate to your unit, bold text indicates possible key indicators.  Recognize, represent, and explain situations, including for self, family, and communities, in which percents greater than 100 or fractional percents are meaningful.  Represent a fractional percent and/or a percent greater than 100 using grid paper.  Describe relationships between different types of representation for the same percent.  Record the percent, fraction, and decimal forms of a quantity shown by a representation on grid paper.  Apply understanding of percents to solve problems, including situations involving combined percents or percents of percents and explain the reasoning.  Explain, using concrete, pictorial, or symbolic representations, why the order of consecutive percents does not impact the final value.  Demonstrate, using concrete, pictorial, or symbolic representations, that two consecutive percents applied to a specific situation cannot be added or subtracted to give an overall percent change.  Analyze choices and make decisions based upon percents and personal and community concerns and issues.  Explain the role and significance of percents in different situations.  Pose and solve problems involving percents stated as a percent, fraction, or decimal quantity.

Outcome N8.3 – I can demonstrate understanding of rates, ratios, and proportional reasoning.

Beginning – 1 Approaching – 2 Proficiency – 3 Mastery – 4 I need help. I have a basic understanding. My work consistently meets I have a deeper understanding. expectations. With assistance I can represent I can identify ratios and rates in I can demonstrate the difference I can explain ratios and rates in simple rates or ratios. familiar situations. between ratios and rates. familiar situations. I can identify situations in which a I can write the symbolic form of a I can verify or contradict proposed given quantity represents a fraction, ratio or rate. relationships between the different rate, quotient,percent, probability or I can solve problems involving rates, roles for quantities. ratio. ratios and/or probabilities. I can create problems involving I can represent simple rates or rates, ratios and/or probabilities. ratios. Indicators – please select and assess as appropriate to your unit, bold text indicates possible key indicators.  Identify and explain ratios and rates in familiar situations.  Identify situations in which a given quantity of a/b represents a fraction, rate, quotient, percent, probability or ratio.  Demonstrate the difference between ratios and rates.  Verify or contradict proposed relationships between the different roles for quantities that can be expressed in the form a/b.  Write the symbolic form for a concrete, physical, or pictorial representation of a ratio or rate.  Explain how to recognize whether a comparison requires the use of proportional reasoning or subtraction.  Create and solve problems involving rates, ratios, and/or probabilities.

Outcome N8.4 – I can demonstrate understanding of multiplying and dividing positive fractions and mixed numbers.

Beginning – 1 Approaching – 2 Proficiency – 3 Mastery – 4 I need help. I have a basic understanding. My work consistently meets I have a deeper understanding. expectations. With assistance I can model the I can identify situations in which the I can apply strategies for multiplying I can critique statements involving multiplication of two basic positive multiplication and division of positive fractions and for the multiplication and division of fractions. fractions are involved. determining the quotients of fractions. With assistance I can model the I can model the multiplication of two positive fractions. I can create problems that involve division of two basic positive basic positive fractions. I can solve problems that involve one or more operations on positive fractions. I can model the division of two basic one or more operations on positive fractions. positive fractions. fractions. Indicators – please select and assess as appropriate to your unit, bold text indicates possible key indicators.  Identify and describe situations relevant to self, family, or community in which multiplication and division of fractions are involved.  Model the multiplication of two positive fractions and record the process symbolically.  Compare the multiplication of positive fractions to the multiplication of whole numbers, decimals, and integers.  Generalize and apply strategies for determining estimate of products of positive fractions.  Generalize and apply strategies for multiplying positive fractions.  Critique the statement “Multiplication always results in a larger quantity” and reword the statement to capture the points of correction or clarification raised.  Explain, using concrete or pictorial models as well as symbolic reasoning, how the distributive property can be used to multiply mixed numbers.  Model the division of two positive fractions and record the process symbolically.  Compare the division of positive fractions to the division of whole numbers, decimals, and integers.  Generalize and apply strategies for determining estimates of quotients of positive fractions.  Estimate the quotient of two given positive fractions and explain the strategy used.  Generalize and apply strategies for determining the quotients of positive fractions.  Critique the statement “Division always results in a smaller quantity” and reword the statement to capture the points of correction or clarification raised.  Identify, without calculating, the operation required to solve a problem involving fractions and justify the reasoning.  Create, represent and solve problems that involve one or more operations on positive fractions. Refer to the Saskatchewan Curriculum Guide Grade 8 Mathematics.

Outcome N8.5 – I can demonstrate understanding of multiplication and division of integers.

Beginning – 1 Approaching – 2 Proficiency – 3 Mastery – 4 I need help. I have a basic understanding. My work consistently meets I have a deeper understanding. expectations. With assistance I can model the I can model the multiplication or I can independently record the I can create problems involving the multiplication or division of two division of two simple integers. process of multiplying two integers multiplication and division of simple integers. I can apply a strategy for multiplying and dividing two integers integers. With assistance I can apply a and dividing integers. symbolically. I can create problems requiring the strategy for multiplying and dividing I can apply appropriate strategies use of the order of operations on integers. for multiplying and dividing integers. integers. Indicators – please select and assess as appropriate to your unit, bold text indicates possible key indicators.  Identify and describe situations that are relevant to self, family, or community in which multiplication or division of integers would be involved.  Model the multiplication of two integers using concrete materials or pictorial representations, and record the process used symbolically.  Model the division of two integers using concrete materials or pictorial representations, and record the process used symbolically.  Identify and generalize patterns for determining the sign of integer products and quotients.  Generalize and apply strategies for multiplying and dividing integers.  Create and solve problems involving the multiplication or division of integers.  Explain how the order of operations can be extended to include integers and provide examples to demonstrate the use of the order of operations.  Create and solve problems requiring the use of the order of operations on integers.

Subject: Grade 8 Math, Patterns and Relations Strand

Outcome: P8.1 – I can demonstrate understanding of linear relations.

Beginning – 1 Approaching – 2 Proficiency – 3 Mastery – 4 With assistance I can model a I can model a simple linear I can independently model a I can explain how a given linear simple linear relation as an relation as an equation, a graph, a linear relation shown as an relation is represented by a given equation, a graph, a table of table of values or a concrete or equation, a graph, a table of table of values. values or a concrete or pictorial pictorial representation. values and a concrete or pictorial I can determine which of a set of representation. I can identify personal situations representation. graphs, equations, table of values, that appear to define linear I can independently determine set of ordered pairs represent a relations. which of a set of graphs, linear relation and explain the equations, tables of values, set of reasoning. ordered pairs and concrete or pictorial representations represent a linear relation. Indicators – please select and assess as appropriate to your unit, bold text indicates possible key indicators.  Analyze and describe the relationship shown on a graph for a given situation.  Explain how a given linear relation is represented by a given table of values.  Model a linear relation shown as an equation, a graph, a table of values, or a concrete or pictorial representation in one or more other forms.  Analyze a set of equations, graphs, ordered pairs, and tables of values, sort the set according to representing the same linear relations, and explain the reasoning.  Determine the missing coordinate or an ordered pair given the equation of a linear relation, a table of values, or a graph and explain the reasoning.  Determine which of a set of graphs, equations, tables of values, sets of ordered pairs, and concrete or pictorial representations represent a linear relationship and justify the reasoning.  Determine if an ordered pair satisfies a linear relation given as a table of values, concrete or pictorial representation, graph, or equation and explain the reasoning.  Identify situations relevant to self, family, or community that appear to define linear relations and determine, with justification, whether the graph for the situation would be shown with a solid line or not. Refer to the Saskatchewan Curriculum Guide Grade 8 Mathematics. Subject: Grade 8 Math, Patterns and Relations Strand

Outcome: P8.2 – I can model and solve problems using linear equations with integers.

Beginning – 1 Approaching – 2 Proficiency – 3 Mastery – 4 With assistance I can identify I can identify situations that can I can independently model and I can model, solve and explain the situations that can be modeled by be modeled by a linear equation. solve problems using linear process orally and symbolically. a linear equation. I can identify problems that can equations. I can explain why some linear With assistance I can identify be represented using linear I can independently apply relations have a given restriction. problems that can be equations. symbolic strategies for solving represented using linear linear equations. equations. Indicators – please select and assess as appropriate to your unit, bold text indicates possible key indicators.  Identify and describe situations, which are relevant to self, family, or community, that can be modeled by a linear equation.  Model and solve linear equations using concrete materials and describe the process orally and symbolically.  Discuss the importance of the preservation of equality when solving equations.  Explain the meaning of and verify the solution of a given linear equation using a variety of methods, including concrete materials, diagrams, and substitution.  Generalize and apply symbolic strategies for solving linear equations.  Identify, explain, and correct errors in a given solution of a linear equation.  Demonstrate the application of the distributive property in the solving of linear equations.  Explain why some linear relations have a given restriction and provide an example of a situation in which such a restriction would be necessary.  Identify and solve problems that can be represented using linear equations and explain the meaning of the solution in the context of the problem.  Explain the algebra behind algebra puzzles. Refer to the Saskatchewan Curriculum Guide Grade 8 Mathematics. Subject: Grade 8 Math, Shape and Space Strand

Outcome: SS8.1 – I can demonstrate understanding of the Pythagorean Theorem.

Beginning – 1 Approaching – 2 Proficiency – 3 Mastery – 4 I need help. I have a basic understanding. My work consistently meets I have a deeper understanding. expectations. With assistance I can explore right I can explore right and non-right I can use the Pythagorean Theorem I can explain how to use the and non-right triangles to generalize triangles to generalize the to determine if a triangle is a right Pythagorean Theorem to determine the relationship between the type of relationship between the type of triangle. if a triangle is a right triangle. triangle and the Pythagorean triangle and the Pythagorean I can use the Pythangorean Theorem I can create and solve problems Theorem. Theorem. to determine the missing using the Pythagorean Theorem, hypotenuse or side of a right Pythagorean triples and the triangle. Converse of the Pythagorean I can solve problems involving the Theorem. Pythagorean Theorem and Pythagorean triples.

Indicators – please select and assess as appropriate to your unit, bold text indicates possible key indicators. Generalize the results of an investigation of the expression a² + b² = c². Explore right and non-right triangles, using technology, and generalize the relationship between the type of triangle and the Pythagorean Theorem. Explore right triangles, using technology, using the Pythagorean Theorem to identify Pythagorean triples, hypothesize about the nature of triangles with side lengths that are multiples of the Pythagorean triples, and verify the hypothesis. Create and solve problems involving the Pythagorean Theorem, Pythagorean triples, or the Converse of the Pythagorean Theorem. Give a presentation that explains a historical or personal use or story of the Pythagorean Theorem.

Refer to the Saskatchewan Curriculum Guide Grade 8 Mathematics. Subject: Grade 8 Math, Shape and Space Strand

Outcome: SS8.2 – I can demonstrate understanding of the surface area of 3-D objects limited to right prisms and cylinders.

Beginning – 1 Approaching – 2 Proficiency – 3 Mastery – 4 I need help. I have a basic understanding. My work consistently meets I have a deeper understanding. expectations. With assistance I can determine a I can determine a simple 3-D object I can determine a 3-D object from a I can use sketches of the top, front and simple 3-D object from a sketch or net. from a sketch or net. sketch and a net, regardless of side views to build 3-D objects. With assistance I can sketch the top, I can sketch the top, front or side views orientation. I can use my sketches of the top, front front or side views of 3-D objects. of 3-D objects. I can sketch top, front and side views of and side views of a 3-D object to With assistance I can construct nets of I can construct nets of 3-D objects when 3-D objects. determine the surface area. 3-D objects when the orientation is the orientation is familiar to me. I can construct nets of 3-D objects I can use the surface area to create a net familiar to me. I can choose the appropriate formula to regardless of orientation. of a 3-D object. With assistance I can choose the determine the surface area of 3-D I can use strategies and formulae to I can develop strategies to determine appropriate formula to determine the objects. determine the surface area of 3-D the surface area of 3-D objects. surface area of 3-D objects. I can solve basic problems involving the objects. I can create and solve complex surface area of 3-D objects. I can solve problems involving the problems involving the surface are of 3- surface area of 3-D objects. D objects. Indicators – please select and assess as appropriate to your unit, bold text indicates possible key indicators.  Manipulate concrete 3-D objects to identify, describe, and sketch top, front, and side views of the 3-d object on isometric paper.  Sketch a top, front, or side view of a 3-D object that is within the classroom or that is personally relevant, and ask a peer to identify the 3-D object it represents.  Predict the top, front, and side views for a 3-D object that is to be rotated by a multiple of 90⁰, discuss the reasoning for the prediction, and then verify concretely and pictorially.  Identify and describe nets of 3-D objects that are used in everyday experiences.  Relate the parts of a net to the faces and edges of the 3-D object it represents.  Create a net for a 3-D object, have a peer predict the type of 3-D object that the net represents, explain to the peer the reasoning used in designing the net, and have the peer verify the net by constructing the 3-D object from the net.  Build a 3-D object made of right rectangular prisms based on the top, front, and side views.  Demonstrate how the net of a 3-D object can be used to determine the surface area of the 3-D object and describe strategies used to determine the surface area.  Generalize and apply strategies for determining the surface area of 3-D objects.  Create and solve personally relevant problems involving the surface area or nets of 3-D objects. Refer to the Saskatchewan Curriculum Guide Grade 8 Mathematics. Subject: Grade 8 Math, Shape and Space Strand

Outcome: SS8.3 – I can demonstrate understanding of volume limited to right prisms and cylinders.

Beginning – 1 Approaching – 2 Proficiency – 3 Mastery – 4 I need help. I have a basic understanding. My work consistently meets I have a deeper understanding. expectations. With assistance I can identify when I can identify when to find the I can describe the relationship I can develop and explain strategies to find the volume of a right prism volume of a right prism or right between the area of the base of a to find the volume of right prisms or right cylinder. cylinder. right prism or right cylinder and the and right cylinders. With assistance I can choose the I can choose the appropriate volume of the 3-D object. I can create problems involving right appropriate formula to use in a formula to use in a situation to find I can use the appropriate formula to prisms and right cylinders. situation to find the volume of a the volume of a right prism or right find the volume of a right prism or I can solve complex problems right prism or right cylinder. cylinder. right cylinder, regardless of involving right prisms and right With assistance I can solve basic I can solve basic problems involving orientation. cylinders. problems involving the volume of the volume of right prisms and right I can solve problems involving the right prisms or right cylinders. cylinders. volume of right prisms and right cylinders. Indicators – please select and assess as appropriate to your unit, bold text indicates possible key indicators.  Identify situations from one’s home, school, or community in which the volume of right prism or right cylinder would need to be determined.  Describe the relationship between the area of the base of a right prism or right cylinder and the volume of the 3-D object.  Generalize and apply formulas for determining the area of a right prism and right cylinder.  Explain the effect of changing the orientation of a right prism or right cylinder on the volume of the 3-D object.  Create and solve personally relevant problems involving the volume of right prisms and right cylinders.

Subject: Grade 8 Math, Shape and Space Strand Outcome: SS8.4 – I can demonstrate an understanding of tessellation.

Beginning – 1 Approaching – 2 Proficiency – 3 Mastery – 4 I need help. I have a basic understanding. My work consistently meets I have a deeper understanding. expectations. With assistance I can create a I can predict 2-D shapes that will I can explain the properties of 2-D I can explain the specific terms of tessellation involving at least one 2- tessellate. shapes that will tessellate. tessellation (translations, reflections D shape. I can create a tessellation involving I can design a tessellation involving and rotations). With assistance I can compare one or more 2-D shapes. one or more 2-D shapes and I can make a new tessellating shape tessellations in my environment. I can compare similar tessellations document the mathematics by tranforming a portion of a known in my environment. involved. tessellating shape. I can identify tessellations from my I can identify complex tessellations environment. from my environment.

Indicators – please select and assess as appropriate to your unit, bold text indicates possible key indicators.  Identify, describe, and reproduce a tessellation that is relevant to self, family, or community.  Predict and verify which of a given set of 2-D shapes will tessellate and generalize strategies for determining whether a new 2-D shape will tessellate.  Identify one or more 2-D shapes that will tessellate with a given 2-D shape and explain the choice.  Design and create a tessellation involving one or more 2-D shapes, and document the mathematics involved within the tessellation.  Identify different transformations present within a tessellation.  Make a new tessellating shape by transforming a portion of a known tessellating shape and use the new shape to create an Escher-type design that can be used as a picture or wrapping paper.

Subject: Grade 8 Math, Statistics and Probability Strand

Outcome: SP8.1 – I can analyze the modes of displaying data and the reasonableness of conclusions.

Beginning – 1 Approaching – 2 Proficiency – 3 Mastery – 4 With assistance I can find I can find examples of graphs of I can independently suggest I can suggest alternative ways to examples of graphs of data in the data in the media. alternative ways to represent represent data from a given media. I can identify examples of data from a given situation. situation and explain the choices With assistance I can identify misrepresentations of data found I can independently find made. examples of misrepresentations within different media. examples of graphs of data in I can provide examples of of data found within different media and interpret the misrepresentations of data found media. information in the graphs. within different media and I can independently provide explain what types of examples of misrepresentations misinterpretations might result of data found within different from such displays. media.

Indicators – please select and assess as appropriate to your unit, bold text indicates possible key indicators.  Investigate and report on the advantages and disadvantages of different types of graphs, including circle graphs, lines graphs, bar graphs, double bar graphs, and pictographs.  Engage in a project.  Suggest alternative ways to represent data from a given situation and explain the choices made.  Find examples of graphs of data in media and personal experiences and interpret the information in the graphs for personal value.  Analyze a data graph found in media for features that might bias the interpretation of the graph and suggest alterations to remove or downplay the bias.  Provide examples of misrepresentations of data and data graphs found within different media and explain what types of misinterpretations might result from such displays.

Subject: Grade 8 Math, Statistics and Probability Strand

Outcome: SP8.2 – I can demonstrate understanding of the probability of independent events. Beginning – 1 Approaching – 2 Proficiency – 3 Mastery – 4 With assistance I can explore the I can explore the probability of I can independently explore and I can explore and explain the probability of independent independent events. represent the relationship relationship between the events. I can make predictions about the between the probability of two probability of two independent With assistance I can make results of probability of independent events and the events and the probability of predictions about the results of independent events. probability of each event each event separately. probability of independent I can ask questions in which separately. I can create and solve problems events. probabilities involving two I can independently make and related to independent events, events are known. test predictions about the results probability of independent of experiments and simulations events and decision making. for two independent events.

Indicators – please select and assess as appropriate to your unit, bold text indicates possible key indicators.  Ask questions relevant to self, family, or community in which probabilities involving two events are known or which can be researched.  Explore and explain the relationship between the probability of two independent events and the probability of each event separately.  Make and test predictions about the results of experiments and simulations for two independent events.  Create and solve problems related to independent events, probabilities of independent events, and decision making.