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 Operations

Algebra

Review of 7th Grade Skills

Operations with Whole Numbers and Decimals

  • Add, Subtract, Multiply, Divide Whole Numbers and Decimals
  • Compare and Order whole numbers and Decimals on a number line
  • Properties 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 numbers
  • Rational Numbers as Decimals
  • Understand Irrational Numbers
  • Compare and Order Rational Numbers Numbers

Real Numbers

  • Compare and Order Real Numbers
  • Evaluate Square Roots and Cube Roots
  • Solve equations using square roots and cube roots

Operations with Integers

  • Add, Subtract, Multiply, Divide Integers
  • Add, Subtract, Multiply, Divide Rational Numbers

Integers and Exponents

  • Properties of Integer Exponents
  • Negative Exponents
  • Use powers of 10 to estimate quotients in exponents
  • Understand Scientific Notation
  • Operations with Numbers in Scientific Notation

Analyze and Solve Linear Equations

  • Combine Like Terms to Solve Equations
  • Solve equations with variables on both sides
  • Solve multistep equations
  • Equations with No Solutions or Infinitely Many Solutions

Proportional Relationships in Linear Equations

  • Compare Proportional Relationships
  • Connect Proportional Relationships and slope
  • Analyze Linear Equations y = mx
  • Understand the y-intercept of a line
  • Analyze Linear Equations y = mx + b

Number and Operations

Algebra

Functions

  • Understand relations and functions
  • Determine whether a relationship is a function or not
  • Connect representations of functions
  • Compare linear vs. nonlinear functions
  • Define a function using tables and graphs

Functions and Modeling Relationships

  • Find slope of a line
  • Construct functions to model linear relationships
  • Intervals of increase and decrease
  • Sketch graphs and functions from verbal descriptions

Solve Systems of Linear Equations

  • Estimate solutions
  • Solve systems by graphing
  • Solve systems by substitution
  • Solve systems by elimination

Geometry

Measurement

Translations, Reflections, Rotations, Transformations

  • Understand coordinate plane
  • Analyze translations
  • Analyze reflections
  • Analyze rotations
  • Compose transformations

Symmetry and Congruent Figures

  • Understand Congruent figures
  • Angle Measures of Polygons
  • Describe dilations
  • Understand Similar figures
  • Describe lines and transversals

Triangle

  • Interior and Exterior of a triangle
  • Angle-Angle Triangle Similarity

Pythagorean Theorem

  • Understand the Pythagorean theorem
  • Understand the converse of the Pythagorean theorem
  • Apply Pythagorean theorem to solve problems
  • Find distance in the coordinate plane
  • Solve equations using pi

Surface Area

  • Identify solids and skew lines
  • Surface Area of 3-D Figures

Volume

  • Find volume of Cylinders, Cones, and Spheres
  • Use Pythagorean theorem to find slant height of cone and pyramid to determine a figures height
  • Solve in real world situations

Data Analysis

Graphs

  • Scatter Plots
  • Clusters
  • Outliers
  • Positive vs. Negative Correlation
  • Linear vs. Nonlinear Correlation

Linear Models and Graphs

  • Construct and interpret scatter plots
  • Analyze linear associations
  • Use linear models to make predictions

Bivariate Data

  • Interpret graphs to determine bivariate data
  • Estimate and Make predictions

Frequency Tables

  • Interpret two-way frequency tables
  • Interpret two-way relative frequency tables