PROCESS STRANDS |
- Problem solving
- Reasoning and Proof
- Communication
- Connections
- Representation
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| Problem solving |
| 8.PS.1 Explore, examine, and make observations about a social problem or mathematical situation |
| 8.PS.2 Understand that some ways of representing a problem are more helpful than others |
| 8.PS.3 Interpret information correctly, identify the problem, and generate possible solutions |
| 8.PS.4 Act out or model with manipulatives activities involving mathematical content from literature |
| 8.PS.5 Formulate problems and solutions from everyday situations |
| 8.PS.6 Translate from a picture/diagram to a numeric expression |
| 8.PS.7 Represent problem solving situations in oral, written, concrete, pictorial, and graphical forms |
| 8.PS.8 Select an appropriate representation of a problem |
| 8.PS.9 Use trial and error to solve problems |
| 8.PS.10 Use process of elimination to solve problems |
| 8.PS.11 Make pictures/diagrams of problems |
| 8.PS.12 Use physical objects to model problems |
| 8.PS.13 Work in collaboration with others to solve problems |
| 8.PS.14 Make organized lists to solve numerical problems |
| 8.PS.15 Make charts to solve numerical problems |
| 8.PS.16 Analyze problems by identifying relationships |
| 8.PS.17 Analyze problems by identifying relevant versus irrelevant information |
| 8.PS.18 Analyze problems by observing patterns |
| 8.PS.19 State a problem in their own words |
| 8.PS.20 Determine what information is needed to solve a problem |
| 8.PS.21 Discuss with peers to understand a problem situation |
| 8.PS.22 Discuss the efficiency of different representations of a problem |
| 8.PS.23 Verify results of a problem |
| 8.PS.24 Recognize invalid approaches |
| 8.PS.25 Determine whether a solution is reasonable in the context of the original problem |
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| Reasoning and Proof |
| 8.RP.1 Use representations to support mathematical ideas |
| 8.RP.2 Determine whether a mathematical statement is true or false and explain why |
| 8.RP.3 Investigate the use of knowledgeable guessing by generalizing mathematical ideas |
| 8.RP.4 Make conjectures from a variety of representations |
| 8.RP.5 Justify general claims or conjectures, using manipulatives, models, and expressions |
| 8.RP.6 Develop and explain an argument using oral, written, concrete, pictorial, and/or graphical forms |
| 8.RP.7 Discuss, listen, and make comments that support or reject claims made by other students |
| 8.RP.8 Support an argument by trying many cases |
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| Communication |
| 8.CM.1 Understand and explain how to organize their thought process |
| 8.CM.2 Verbally explain their rationale for strategy selection |
| 8.CM.3 Provide reasoning both in written and verbal form |
| 8.CM.4 Organize and accurately label work |
| 8.CM.5 Share organized mathematical ideas through the manipulation of objects, drawings, pictures, charts, graphs, tables, diagrams, models, symbols, and
expressions in written and verbal form |
| 8.CM.6 Answer clarifying questions from others |
| 8.CM.7 Listen for understanding of mathematical solutions shared by other students |
| 8.CM.8 Consider strategies used and solutions found in relation to their own work |
| 8.CM.9 Increase their use of mathematical vocabulary and language when communicating with others |
| 8.CM.10 Describe objects, relationships, solutions and rationale using appropriate vocabulary |
| 8.CM.11 Decode and comprehend mathematical visuals and symbols to construct meaning |
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| Connections |
| 8.CN.1 Recognize, understand, and make connections in their everyday experiences to mathematical ideas |
| 8.CN.2 Compare and contrast mathematical ideas |
| 8.CN.3 Connect and apply mathematical information to solve problems |
| 8.CN.4 Understand multiple representations and how they are related |
| 8.CN.5 Model situations with objects and representations and be able to make observations |
| 8.CN.6 Recognize the presence of mathematics in their daily lives |
| 8.CN.7 Apply mathematics to solve problems that develop outside of mathematics |
| 8.CN.8 Recognize and apply mathematics to other disciplines |
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| Representation |
| 8.R.1 Use verbal and written language, physical models, drawing charts, graphs, tables, symbols, and equations as representations |
| 8.R.2 Share mental images of mathematical ideas and understandings |
| 8.R.3 Recognize and use external mathematical representations |
| 8.R.4 Use standard and nonstandard representations with accuracy and detail |
| 8.R.5 Understand similarities and differences in representations |
| 8.R.6 Connect mathematical representations with problem solving |
| 8.R.7 Construct effective representations to solve problems |
| 8.R.8 Use mathematics to show and understand physical phenomena (e.g., estimate and represent the number of apples in a tree) |
| 8.R.9 Use mathematics to show and understand social phenomena (e.g., determine the number of buses required for a field trip) |
| 8.R.10 Use mathematics to show and understand mathematical phenomena (e.g., use a multiplication grid to solve odd and even number problems)
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| The Process Strands highlight ways of acquiring and using content knowledge. Though the Process Strands are not individually covered, students are
required to problem solve, reason, and apply their knowledge throughout. |
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CONTENT STRANDS |
Number Sense and Operations Strand |
| Students will understand meanings of operations and procedures, and how they relate to one another.
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| Operations
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| 8.N.1 - Develop and apply the laws of exponents for multiplication and division
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| 8.N.2 - Evaluate expressions with integral exponents
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| 8.N.3 - Read, write, and identify percents less than 1% and greater than 100%
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8.N.4 - Apply percents to:
Tax
Percent increase/decrease
Simple interest
Sale price
Commission
Interest rates
Gratuities
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| Students will compute accurately and make reasonable estimates.
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| Estimation
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| 8.N.5 - Estimate a percent of quantity, given an application
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| 8.N.6 - Justify the reasonableness of answers using estimation
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Algebra Strand |
| Students will represent and analyze algebraically a wide variety of problem solving situations.
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| Variables and Expressions
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| 8.A.1 - Translate verbal sentences into algebraic inequalities
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| 8.A.2 - Write verbal expressions that match given mathematical expressions
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| 8.A.3 - Describe a situation involving relationships that matches a given graph
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| 8.A.4 - Create a graph given a description or an expression for a situation involving a linear or nonlinear relationship
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| 8.A.5 - Use physical models to perform operations with polynomials
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| Students will perform algebraic procedures accurately.
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| Variables and Expressions
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| 8.A.6 - Multiply and divide monomials
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| 8.A.7 - Add and subtract polynomials (integer coefficients)
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| 8.A.8 - Multiply a binomial by a monomial or a binomial (integer coefficients)
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| 8.A.9 - Divide a polynomial by a monomial (integer coefficients) Note: The degree of the denominator is less than or equal to the degree of the numerator
for all variables.
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| 8.A.10 - Factor algebraic expressions using the GCF
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| 8.A.11 - Factor a trinomial in the form ax2 + bx + c; a=1 and c having no more than three sets of factors
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| Equations and Inequalities
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| 8.A.12 - Apply algebra to determine the measure of angles formed by or contained in parallel lines cut by a transversal and by intersecting lines
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| 8.A.13 - Solve multi-step inequalities and graph the solution set on a number line
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| 8.A.14 - Solve linear inequalities by combining like terms, using the distributive property, or moving variables to one side of the inequality (include
multiplication or division of inequalities by a negative number)
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| Students will recognize, use, and represent algebraically patterns, relations, and functions.
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| Patterns, Relations, And Functions
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| 8.A.15 - Understand that numerical information can be represented in multiple ways: arithmetically, algebraically, and graphically
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| 8.A.16 - Find a set of ordered pairs to satisfy a given linear numerical pattern (expressed algebraically); then plot the ordered pairs and draw the line
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| 8.A.17 - Define and use correct terminology when referring to function (domain and range)
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| 8.A.18 - Determine if a relation is a function
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| 8.A.19 - Interpret multiple representations using equation, table of values, and graph
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Geometry Strand |
| Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.
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| Constuctions
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8.G.0 - Construct the following using a straight edge and compass:
Segment congruent to a segment
Angle congruent to an angle Perpendicular bisector
Angle bisector
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| Students will identify and justify geometric relationships, formally and informally.
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| Geometric Relationships
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| 8.G.1 - Identify pairs of vertical angles as congruent
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| 8.G.2 - Identify pairs of supplementary and complementary angles
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| 8.G.3 - Calculate the missing angle in a supplementary or complementary pair
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| 8.G.4 - Determine angle pair relationships when given two parallel lines cut by a transversal
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| 8.G.5 - Calculate the missing angle measurements when given two parallel lines cut by a transversal
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| 8.G.6 - Calculate the missing angle measurements when given two intersecting lines and an angle
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| Students will apply transformations and symmetry to analyze problem solving situations.
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| Transformational Geometry
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| 8.G.7 - Describe and identify transformations in the plane, using proper function notation (rotations, reflections, translations, and dilations)
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| 8.G.8 - Draw the image of a figure under rotations of 90 and 180 degrees
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| 8.G.9 - Draw the image of a figure under a reflection over a given line
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| 8.G.10 - Draw the image of a figure under a translation
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| 8.G.11 - Draw the image of a figure under a dilation
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| 8.G.12 - Identify the properties preserved and not preserved under a reflection, rotation, translation, and dilation
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| Students will apply coordinate geometry to analyze problem solving situations.
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| Coodinate Geometry
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| 8.G.13 - Determine the slope of a line from a graph and explain the meaning of slope as a constant rate of change
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| 8.G.14 - Determine the y-intercept of a line from a graph and be able to explain the y-intercept
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| 8.G.15 - Graph a line using a table of values
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| 8.G.16 - Determine the equation of a line given the slope and the y-intercept
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| 8.G.17 - Graph a line from an equation in slope-intercept form (y=mx+b)
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| 8.G.18 - Solve systems of equations graphically (only linear, integral solutions, y=mx+b format, no vertical/horizontal lines)
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| 8.G.19 - Graph the solution set of an inequality on a number line
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| 8.G.20 - Distinguish between linear and nonlinear equations ax2 + bx + c; a=1 (only graphically)
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| 8.G.21 - Recognize the characteristics of quadratics in tables, graphs, equations, and situations
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Measurement Strand |
| Students will determine what can be measured and how, using appropriate methods and formulas.
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| Units of Measurement
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| 8.M.1 - Solve equations/proportions to convert to equivalent measurements within metric and customary measurement systems Note: Also allow
Fahrenheit to Celsius and vice versa.
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