Christ the Redeemer

Pre-Algebra Curriculum Scope and Sequence

 Numbers and Operations Algebra Apply rational approximations/estimations of irrational numbers. Order and compare rational and irrational numbers, including integers, percents, positive and negative fractions and decimals from a list and on a number line.Find and estimate square roots and classify numbers as rational or irrational.Find cube roots and solve cube root equations.Represent large and small rational numbers using scientific and exponential notation.Write numbers in standard form and scientific notation.Relate and apply the four basic operations to the properties of real numbers.Divide and compare numbers written in scientific notation.Multiply and divide powers with the same base.Multiply numbers written in scientific notation, choosing appropriate units of measure. Use rational numbers to solve real life problems.Compare and order real numbers using a calculator.  Select appropriate operations to solve problems. Identify and explain mathematical properties for the real number system (Commutative, Associative, Distributive). Determine whether a number is rational or irrational.Relate the four basic operations to the properties of integer exponents.Simplify powers with negative exponents.Multiply numbers written in scientific notation, choosing appropriate units of measure.Combine like terms.Simplify algebraic equations using the distributive properties. Translate a verbal description into an equation.Solve one-step, two-step, multi-step and variables on both sides of the equal sign equations that contain integers, fractions and decimals. Identify whether a linear equation with one variable has one, infinitely many, or no solutions. Apply and understand the different uses of variables.Determine whether a relationship is a function or not.Define a function using tables and graphs.Evaluate functions and complete input-output tables.Compare properties of two functions represented in different ways.Interpret and translate functions between verbal descriptions, tables, equations and graphs.Recognize linear functions and use tables and equations (y = mx + b) to graph them.Identify nonlinear functions.Write function rules from words, tables and graphs.Find the slope of a line from a graph or table.Interpret and sketch graphs that represent real-world situations.Use similar triangles to prove that the slope is the same between any two distinct points on a non-vertical line on the coordinate plane. Determine whether a linear relationship is proportional.Determine the missing measures of a two-dimensional figure using your equation and formula skills. Geometry Prove congruence or similarity of figures using a series of transformations. Graph and describe translations of a line and angle in a coordinate plane. Graph reflections of lines, parallel lines and angles in a coordinate plane and identify lines of symmetry. Describe a sequence of transformations that map one figure onto another, to determine whether two figures are congruent by using a sequence of transformations. Graph rotations and identify rotational symmetry.Graph dilations and determine the scale factor of a dilation.Identify parallel lines and the angles formed by parallel lines and transversals.Determine measures of the angles of triangles and use them to help prove that triangles are similar.Find the angle measures of polygon.Solve problems using the Pythagorean Theorem and its converse.Use pictures and models to demonstrate the Pythagorean Theorem.  Use the Pythagorean Theorem to find the length of the hypotenuse of a right triangle.Use the Pythagorean Theorem to find the missing measurements of triangles.Use the Pythagorean Theorem to solve real world problems.Graph points and apply the Pythagorean Theorem to find distances in the coordinate plane.Solve rational expressions using . Understand relationships among angles, side lengths, perimeters, areas, and volumes of similar objects. Draw 3-D figures from different perspectives. Locate, name, and plot points on a coordinate plane in all four quadrants.

 Measurement Data Analysis Apply perimeter, area, surface area and volume skills/formulas in real world situations. Find lateral and total surface area of prisms, pyramids, and cylinders using concrete models and nets.  Estimate measurements and use formulas to solve application problems involving surface area and volume.Identify solids, parts of solids, and skew line segments.Find the volume of prisms, cylinders, pyramids, cones and spheres. Apply the Pythagorean Theorem and the slant height of a cone and pyramid to determine the figure’s height.Apply solving volume of prisms, cylinders, pyramids, cones and sphere in real world situations. Find missing measurements for 2-D and 3-D figures.  Find the sum of the interior and exterior angles of a regular convex polygon with and without a protractor. Interpret and create scatter plots of bivariate data.Describe patterns in scatter plots, such as clustering, outliers, positive or negative correlation and linear or nonlinear correlation. Assess the fit of a trend line on a scatter plot.Apply trend lines to estimate and make predictions.Create and apply an equation in the form of y = mx + b of the trend line and explain/label the parts of the equation.Create and understand how to use two-way frequency tables and two-way relative frequency tables. Find the probabilities of dependent and independent events.Make predictions and decisions using probabilities and experimental results.Simulate an event using different models. Use IQR (interquartile range) and central tendency to describe a set of data.

 Objective Skills Number and OperationsAlgebra Review of 7th Grade Skills Operations with Whole Numbers and Decimals Add, Subtract, Multiply, Divide Whole Numbers and DecimalsCompare and Order whole numbers and Decimals on a number lineProperties of Addition and Multiplication Fractions and Mixed Numbers Add, Subtract, Multiply, and Divide Mixed Numbers and Fractions with common and not common denominators Solve word problems with fractions and Mixed numbers Rational Numbers Classify numbers in the real number system Understand difference between Rational and Irrational numbersRational Numbers as DecimalsUnderstand Irrational NumbersCompare and Order Rational Numbers Numbers Real Numbers Compare and Order Real Numbers Evaluate Square Roots and Cube RootsSolve equations using square roots and cube roots Operations with Integers Add, Subtract, Multiply, Divide IntegersAdd, Subtract, Multiply, Divide Rational Numbers Integers and Exponents Properties of Integer ExponentsNegative ExponentsUse powers of 10 to estimate quotients in exponentsUnderstand Scientific NotationOperations with Numbers in Scientific Notation Analyze and Solve Linear Equations Combine Like Terms to Solve EquationsSolve equations with variables on both sidesSolve multistep equationsEquations with No Solutions or Infinitely Many Solutions Proportional Relationships in Linear Equations Compare Proportional RelationshipsConnect Proportional Relationships and slopeAnalyze Linear Equations y = mx Understand the y-intercept of a lineAnalyze Linear Equations y = mx + b Number and OperationsAlgebra Functions Understand relations and functionsDetermine whether a relationship is a function or notConnect representations of functionsCompare linear vs. nonlinear functionsDefine a function using tables and graphs Functions and Modeling Relationships Find slope of a lineConstruct functions to model linear relationshipsIntervals of increase and decreaseSketch graphs and functions from verbal descriptions Solve Systems of Linear Equations Estimate solutionsSolve systems by graphingSolve systems by substitutionSolve systems by elimination GeometryMeasurement Translations, Reflections, Rotations, Transformations Understand coordinate planeAnalyze translationsAnalyze reflectionsAnalyze rotationsCompose transformations Symmetry and Congruent Figures Understand Congruent figuresAngle Measures of PolygonsDescribe dilationsUnderstand Similar figuresDescribe lines and transversals Triangle Interior and Exterior of a triangleAngle-Angle Triangle Similarity Pythagorean Theorem Understand the Pythagorean theoremUnderstand the converse of the Pythagorean theoremApply Pythagorean theorem to solve problemsFind distance in the coordinate planeSolve equations using pi Surface Area Identify solids and skew linesSurface Area of 3-D Figures Volume Find volume of Cylinders, Cones, and SpheresUse Pythagorean theorem to find slant height of cone and pyramid to determine a figures heightSolve in real world situations Data Analysis Graphs Scatter PlotsClustersOutliersPositive vs. Negative CorrelationLinear vs. Nonlinear Correlation Linear Models and Graphs Construct and interpret scatter plotsAnalyze linear associationsUse linear models to make predictions Bivariate Data Interpret graphs to determine bivariate dataEstimate and Make predictions Frequency Tables Interpret two-way frequency tablesInterpret two-way relative frequency tables