Christ the Redeemer

6th Grade Math Curriculum Scope and Sequence

 Numbers and Operations (Whole Numbers, Decimals, Fractions) Algebra(Proportionality) Compare and order fractions and decimals using <, >, and =, and on a number line.Compute using basic operations with fractions and mixed numbers. Express answers in simplest form. Use estimation strategies to determine the reasonableness of results in a variety of situations with decimals and fractions.Explain the meaning of multiplication and division of fractions and decimals. Prime factorization using exponents.  Find and use prime factorization of composite numbers.  Determine the GCF and LCM of two or more numbers.Add, subtract, multiply and divide fractions and decimals.Graph rational numbers on a coordinate plane, both positive and negative.Plot rational numbers on a horizontal and vertical number line. Plot points on all four quadrants on a coordinate plane. Compare and order non-negative rational numbers.   Use integers to represent real-life situations.  Use order of operations to simplify whole number expressions in problem solving situations. Write ratios and use them to compare quantities.Find and use unit rates to find unit costs and relate them to ratios. Apply ratios and rates to solving real world problems using tables, diagrams and/or equations.Plot ratios on a coordinate plane.Apply unit rate problems to unit pricing and constant speed (gearing toward rate of change.)Solve problems involving the “3 Cases of Percent”, the percent, the part and the whole.Estimate with percents. Solve problems involving percent increase and percent decrease.Solve problems involving tax, tip, and discounts. Algebra(Functional Relationships) Define and understand the independent and dependent variables in a quantitative relationship. Understand the relationship(s) between an equation, table, graph and verbal description of a quantitative relationship. Use a graph to create a table, an equation and a verbal description of the quantitative relationship. Use an equation to create a table, a graph and a verbal description of the quantitative relationship. Use a table to create a graph, an equation and a verbal description of the quantitative relationship. Use a verbal description to create a table, an equation and a graph of the quantitative relationship. Use variables to represent two quantities that relate to each other. Understand and recognize independent and dependent variables in real world situations.Understand and recognize the relationship between two related quantities in a verbal description, table, graph and equation. Graph the relationship between two related quantities on a coordinate plane. Algebra(Expressions and Equations) Geometry Apply integers, opposites, and absolute values to represent real world situations. Add, subtract, multiply and divide integers.Order and compare the absolute values of rational numbers.Find the distance between two points on a coordinate plane with the same first or the same second coordinates. (horizontal and vertical segments)Read and evaluate numerical expressions with exponents.Read and evaluate algebraic expressions.Translate words into algebraic symbols.Simplify expressions using like terms.Simplify expressions using the properties of operations.Apply properties to solve expressions in problem solving situations. Apply the distributive property to factoring a number out of a sum of two whole numbers between 1 and 100.Solve and check 1-step and 2-step equations and inequalities from a given solution set.Solve and check 1-step and 2-step equations and inequalities.Identify the variable when applying equations and inequalities to a real world situation.Apply equation and inequality skills to real world situations. Represent the solution of an inequality on a number line. Justify why two or more complex figures are congruent or similar. Recognize the characteristics that make up a Cartesian Plane (rectangular coordinate plane).Plot points on a number line and on a Cartesian Plane, identify the coordinate pair of each.Use technology to explore graphs of linear and non-linear relationships to make predictions or form conclusions.Find vertical and horizontal distances on coordinate systems. Use angle measurements to classify angles as acute, obtuse, or right.  Describe a series of transformations on two-dimensional shapes.  Identify and describe line and rotational symmetry.Construct common three-dimensional shapes using manipulatives and/or two-dimensional nets.Construct a three-dimensional object from a set of two-dimensional plans.Draw a two-dimensional representation of a three-dimensional object.Understand and apply cubic units of measure when determining the volume of a solid.Apply volume problems in real world situations.Determine the volume of a right rectangular prism.Compare and contrast the formulas V = l × w × h and V = B × h for rectangular prisms using whole numbers.Identify relationships among points, lines, andplanes.

 Measurement Data Analysis Convert within the measurement systems using ratios and proportions. Determine the distance between two points on a coordinate plane with the same x and y coordinates. Estimate measurements.Select and use appropriate units, tools, or formulas to measure and to solve problems involving length, area, time, temperature, volume, and weight.Explain the relationship between area and perimeter of a rectangle.  Find perimeter and area using formulas for triangles, quadrilaterals, and to find the area and circumference of a circle.  Area and perimeter of irregular figures.  Identify rate as a form of measurement. Write a statistical question designed to collect data.Recognize that collected data has a distribution that can be described by the center, spread and shape.Recognize and understand the Measures of Central Tendency and how they relate to a set of data.Plot numerical data on a histograms, box-and-whisker, scatter plots and stem-and-leaf plots.Analyze numerical data sets by frequencies, Measures of Central Tendency, quartiles, and data distributions. Display numerical data on a coordinate plane. Describe and model all possible outcomes of simple events using tree diagrams, organized lists.Use 0, 1, and ratios between 0 and 1 to represent to represent the probability of outcomes for an event.  Solve problems that incorporate understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness.