grade 8 pre-algebra: algebraic concepts 8 … · grade 8 pre-algebra: algebraic concepts 07/03/2012...

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





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





Algebraic Concepts

Rate of Change

Quarters 4

E – Solve problems involving a constant rate of change. Word problems

Graphs

Data Tables

Formative and


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



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.


CC: 8.EE.8.a,b,c


Grade 8 Pre-Algebra: Data Analysis and Probability 3/7/2012

Grade 8 Pre-Algebra: Data Analysis and Probability



Data Analysis and Probability

Interpret Data Quarter 3

E – Choose and explain the correct representation (graph) for a set of data.

Formative and


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


Grade 8 Pre-Algebra: Data Analysis and Probability 3/7/2012



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.


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


Grade 8 Pre-Algebra: Geometry 3/7/2012

Grade 8 Pre-Algebra: Geometry



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


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.


Grade 8 Pre-Algebra: Geometry 3/7/2012



Geometry

Rights Angles

and the

Pythagorean

Theorem

Quarter 3

E - Explain a proof of the Pythagorean Theorem and its converse.


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


Grade 8 Pre-Algebra: Measurement 3/7/2012

Grade 8 Pre-Algebra: Measurement



Measurement

Convert Measurements

Quarter 2

E – Convert among metric measurements.

Formative and


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


Grade 8 Pre-Algebra: Numbers and Operations 3/7/2012

Grade 8 Pre-Algebra: Numbers and Operation



Numbers and Operations

Equivalent Forms

Quarter 1

E – Convert between fractions to decimals.

Formative and


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






Equivalent Forms

Quarter 2

F – Find the square or cube of a whole number.

Formative and


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






Order of Operations

Quarter 1 E – Simplify numeric expressions involving integers, using the order of operations.

Formative and


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






Compute Problems with and without a calculator

Quarter 2

E – Solve problems involving operations (+, -, x, ÷) of whole numbers.


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, ÷).

grade 8 pre-algebra: algebraic concepts 8 … · grade 8 pre-algebra: algebraic concepts 07/03/2012...

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