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Harbor Creek School District
Grade 8 Pre-Algebra: Algebraic Concepts 07/03/2012
Grade 8 Pre-Algebra: Algebraic Concepts
Major Understandings
Concepts Time Frame Skills Assessments Standards
Algebraic Concepts
Patterns
Quarter 2
E – Continue a numeric or algebraic pattern. Pattern should show at least 3 repetitions
May include one operation, squares, and square roots
Formative and Summative Assessment
PA: M8.D.1.1.1
E – Find missing elements in numeric or geometric patterns and functions.
May be a table or rule
Pattern must show at least 3 patterns.
PA: M8.D.1.1.2
E – Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
PA: M8.D.1.1.3 CC: 8.F.1
E - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
CC: 8.F.2
E – Write sequences with consecutive numbers. PA: M8.D.1.1
E – Write sequences with consecutive even and odd numbers.
PA: M8.D.1.1
Harbor Creek School District
Grade 8 Pre-Algebra: Algebraic Concepts 07/03/2012
Major Understandings
Concepts Time Frame Skills Assessments Standards
Algebraic Concepts
Equations and
Expressions and
Inequalities
Quarter 2
E – Solve linear equations in one variable.
Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
Formative and
Summative Assessment
PA: M8.D.2.1.1 CC: 8.EE.7.a
E – Use substitution to check the accuracy of a given value for an equation or inequality.
PA: M8.D.2.1.2
E – Determine the value of an algebraic expression by simplifying and substituting a number for the variable.
PA: M8.D.2.1.3
E – Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.
PA: M8.D.2.1 CC: 8.EE.7.b
E – Solve equations with variables on both sides of the equation.
E – Match the written situation to its numeric and algebraic expression, equation, or inequality.
PA: M8.D.2.2.1
E – Write and solve an equation for a given problem situation.
PA: M8.D.2.2.2
Harbor Creek School District
Grade 8 Pre-Algebra: Algebraic Concepts 07/03/2012
Major Understandings
Concepts Time Frame Skills Assessments Standards
Algebraic Concepts
Rate of Change
Quarters 4
E – Solve problems involving a constant rate of change. Word problems
Graphs
Data Tables
Formative and
Summative Assessment
PA: M7.D.3.1.1
E - Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
PA: M7.D.3.1.2
CC: 8.EE.5
E - Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
CC: 8.F.5
Graphing Equations
Quarter 4
E – Graph a linear function based on an x/y table (integers only). PA: M8.D.4.1.1
E – Match the graph of a linear function to its x/y table. PA: M8.D.4.1.2
E – Match the linear equation (y=mx + b form) to the x/y table. PA: M8.D.4.1.3
E - Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx +b for a line intercepting the vertical axis at b.
CC: 8.EE.6
E - Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.
CC: 8.F.3
E - Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.
CC: 8.SP.3
E - Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
CC: 8.F.4
Harbor Creek School District
Grade 8 Pre-Algebra: Algebraic Concepts 07/03/2012
Major Understanding
Concepts Timeframe Skills Assessment Standards
Algebraic Concepts
Systems of Equations
E - Analyze and solve pairs of simultaneous linear equations.
Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.
Solve real-world and mathematical problems leading to two linear equations in two variables.
Formative and Summative Assessment
CC: 8.EE.8.a,b,c
Harbor Creek School District
Grade 8 Pre-Algebra: Data Analysis and Probability 3/7/2012
Grade 8 Pre-Algebra: Data Analysis and Probability
Major Understandings
Concepts Time Frame Skills Assessments Standards
Data Analysis and Probability
Interpret Data Quarter 3
E – Choose and explain the correct representation (graph) for a set of data.
Formative and
Summative Assessment
PA: M8.E.1.1.1
E - Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
CC: 8.SP.1
E - Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
CC: 8.SP.2
E - Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.
CC: 8.SP.4
E – Analyze data and answer questions pertaining to data shown in multiple line graphs, circle graphs, histograms, and scatter plots.
PA: M8.E.1.1.2
E – Interpret data shown in stem-and-leaf, box-and-whisker plots.
PA: M8.E.1.1.3
E – Create a box-and-whisker and a scatter plot. PA: M8.E.1.1
Harbor Creek School District
Grade 8 Pre-Algebra: Data Analysis and Probability 3/7/2012
Major Understandings
Concepts Time Frame Skills Assessments Standards
Data Analysis and Probability
Measures of Central
Tendency Quarter 2
E – Identify and calculate the mean, median, mode, and range of a set of data.
Formative and Summative Assessment
PA: M7.E.2.1.1
E – Decide and choose which measure of central tendency (mean, median, mode, or range) would be most appropriate for a given situation.
PA: M7.E.2.1.2
Probability Quarter 3 & 4 E – Find the probability for a mutually exclusive or an independent event.
PA: M8.E.3.1.1.1
Combinations and
Permutations Quarter 3
E – Determine and show the number of permutations and combinations for an event using up to four choices.
PA: M8.E.3.2.1
Draw Conclusions and Make
Predictions
Quarter 3 E – Make predictions based on survey results or graphs.
PA: M8.E.4.1.2
Harbor Creek School District
Grade 8 Pre-Algebra: Geometry 3/7/2012
Grade 8 Pre-Algebra: Geometry
Major Understandings
Concepts Time Frame Skills Assessments Standards
Geometry
Characteristics of two and
three dimensional
shapes
Quarters 3
F – Match the three – dimensional figure with its net (cube, cylinder, cone, prism, and pyramid).
Formative and
Summative Assessment
PA: M8.C.1.1.1
F – Define, identify, and use properties of angles formed by intersecting lines (complementary, supplementary, adjacent, and vertical angles).
PA: M8.C.1.1.2 CC: 8.G.5
F – Define, identify, and use properties of angles formed when two parallel lines are cut by a transversal (alternate interior, alternate exterior, vertical corresponding).
PA: M8.C.1.1.3 CC: 8.G.5
Congruence and Similarity of Polygons
Quarters 3
E – Identify and use polygons that are similar and congruent, given either measurements or tic and angle marks.
PA: M7.C.1.2.1
E - Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
PA: M7.C.1.2.2 CC: 8.G.2 CC: 8.G.4
E – Identify corresponding sides and angles of congruent or similar polygons.
E - Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
Harbor Creek School District
Grade 8 Pre-Algebra: Geometry 3/7/2012
Major Understandings
Concepts Time Frame Skills Assessments Standards
Geometry
Rights Angles
and the
Pythagorean
Theorem
Quarter 3
E - Explain a proof of the Pythagorean Theorem and its converse.
Formative and Summative Assessment
CC: 8.G.6
E – Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
PA: M8.C.1.2.1 CC: 8.G.7
E- Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
CC: 8.G.8
Transformation
and Symmetry Quarter 3
E - Verify experimentally the properties of rotations, reflections, and translations:
Lines are taken to lines, and line segments to line segments of the same length.
Angles are taken to angles of the same measure.
Parallel lines are taken to parallel lines.
CC: 8.G.1.a,b,c
E - Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
PA: M8.C.2 CC: 8.G.3
E– Identify and manipulate translation.
E– Identify and manipulate reflection.
E– Identify and manipulate rotation.
Coordinate Plane
Quarter 1 E – Plot, locate or identify ordered pairs on a coordinate plane.
PA: M8.C.3.1.1
Harbor Creek School District
Grade 8 Pre-Algebra: Measurement 3/7/2012
Grade 8 Pre-Algebra: Measurement
Major Understandings
Concepts Time Frame Skills Assessments Standards
Measurement
Convert Measurements
Quarter 2
E – Convert among metric measurements.
Formative and
Summative Assessment
PA: M8.B.1.1.1
E – Convert customary measurements up to 2 units above or below the given unit.
PA: M8.B.1.1.2
E – Convert time up to 2 units above or below given unit. PA: M8.B.1.1.3
E – Convert from Fahrenheit to Celsius and vice versa. PA: M8.B.1.1.4
Polygons
Quarter 2
E - Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
CC: 8.G.5
E – Determine the total number of degrees in the interior angles of a polygon in 3-8 sided figures.
PA: M8.B.2.1.1
E – Determine the measurement of one interior angle of a regular polygon.
PA: M8.B.2.1.2
E – Determine the number of sides of a polygon given the total number of degrees in the interior angles.
PA: M8.B.2.1.3
Perimeter, Circumference,
Area, and Volume
Quarter 3
E – Calculate the surface area of cubes, rectangular prisms, cylinders, cones, and pyramids.
PA: M8.B.2.2.1
E – Know the formulas for the volumes of cones, cylinders, and spheres and use them to sole real-world and mathematical problems.
PA: M8.B.2.2.2 CC: 8.G.9
E – Determine the appropriate type of measurement for a given situation.
PA: M8.B.2.2.3
Harbor Creek School District
Grade 8 Pre-Algebra: Numbers and Operations 3/7/2012
Grade 8 Pre-Algebra: Numbers and Operation
Major Understandings
Concepts Time Frame Skills Assessments Standards
Numbers and Operations
Equivalent Forms
Quarter 1
E – Convert between fractions to decimals.
Formative and
Summative Assessment
PA: M7.A.1.1.1 E – Convert between decimals to percent.
E – Convert between fractions to percents.
E – Represent numbers using scientific notation. PA: M8.A.1.1.1
E - Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
CC: 8.EE.4
E – Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.
PA: M8.A.1.1.1 CC: 8.EE.3
Harbor Creek School District
Grade 8 Pre-Algebra: Numbers and Operations 3/7/2012
Major Understandings
Concepts Time Frame Skills Assessments Standards
Numbers and Operations
Equivalent Forms
Quarter 2
F – Find the square or cube of a whole number.
Formative and
Summative Assessment
PA: M8.A.1.1.2 CC: 8.EE.2
E - Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3= p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.
F – Find the square root of a perfect square and estimate the value of a non-perfect square without a calculator and explain the relationship between the two.
E – Simplify exponents with a negative base. PA: M8.A.1.1
E - Simplify expressions with negative exponents. CC: 8.EE.1 E - Know and apply the properties of integer exponents to
generate equivalent numerical expressions.
E – Apply shortcuts for multiplying powers of 10. PA: M8.A.1.1.1
E - Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually and convert a decimal expansion which repeats eventually into a rational number.
CC: 8.NS.1
E - Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions.
CC: 8.NS.2
Harbor Creek School District
Grade 8 Pre-Algebra: Numbers and Operations 3/7/2012
Major Understandings
Concepts Time Frame Skills Assessments Standards
Numbers and Operations
Order of Operations
Quarter 1 E – Simplify numeric expressions involving integers, using the order of operations.
Formative and
Summative Assessment
PA: M8.A.2.1.1
Ratios, Proportions,
Percents, Rates
Quarter 3
E – Solve problems involving percents.
PA: M8.A.2.2.1 E – Calculate the original price given percent and new amount.
E – Solve problems involving percents using both increase and decrease.
E – Represent or solve rate problems.
Unit rates
Simple interest Distance, etc.
PA: M8.A.2.2.2
Estimation Quarter 3
E – Identify, use and explain when it is appropriate to round up or round down.
PA: M8.A.3.1.1
E – Identify, apply, and explain when an exact answer is needed or when estimation is appropriate.
PA: M8.A.3.1.2
E - Estimate answers to problems involving percents. PA: M8.A.3.2.1
Harbor Creek School District
Grade 8 Pre-Algebra: Numbers and Operations 3/7/2012
Major Understandings
Concepts Time Frame Skills Assessments Standards
Numbers and Operations
Compute Problems with and without a calculator
Quarter 2
E – Solve problems involving operations (+, -, x, ÷) of whole numbers.
Formative and Summative Assessment
PA: M8.A.3.3.1
E – Solve problems involving operations (+, -, x, ÷) of decimals.
E – Solve problems involving operations (+, -, x, ÷) of fractions.
E – Solve problems involving operations (+, -, x, ÷) of integers.
E – Solve word problems or straight computation involving all operations (+, -, x, ÷).
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