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, and
  • planes.

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.  

Objective

Skills

Quarter 1

Numbers and Operations

(Whole, Decimals, Fractions)

Algebra

Review of 5th grade Skills

  • Place Value
  • Add, Subtract, Multiply, Divide Large Numbers
  • Rounding
  • Write, Order, Compare, and Read Whole Numbers and Decimals

Add, Subtract, Multiply, Divide Decimals

  • Recognize place value patterns when multiplying and dividing decimals
  • Identify Properties of Addition and Multiplication

Exponents and Order of Operations

  • Use order of operations to evaluate expressions with exponents
  • Contrast constants and variables

Prime Factorization

  • Identify multiples, LCM, factors, GCF
  • Prime vs. Composite Numbers
  • Use a factor tree
  • Squaring Numbers

Simplify, Compare, and Order Fractions

Mixed Numbers and Improper Fractions

  • Locate fractions on a number line
  • Determine decimal equivalents of fractions
  • Convert fractions to decimals and decimals to fractions
  • Repeating decimals as fractions

Add, Subtract, Multiply, and Divide Fractions and Mixed Numbers

  • Add. Subtract, multiply, and divide using computational strategies
  • Apply reciprocal numbers to dividing by fractions
  • Express remainders in division as fractions

Scientific Notation

  • Scientific Notation to standard form
  • Standard form to Scientific notation

Compare and Order Integers

  • Apply integers, opposites, and absolute value to represent real world situations
  • Define and recognize integers
  • Use a number line to compare integers

Add and Subtract Integers

  • Add and Subtract Integers

Multiply and Divide Integers

  • Multiply and Divide Integers

Quarter 2

Algebra

(Expressions and Equations)

(Proportionality)

Rational Numbers

  • Understand Types of Numbers: Whole, Integers, Rational, Irrational
  • Add, Subtract, Multiply, Divide Rational Numbers

Evaluating Numerical Expressions

  • Understanding Variables
  • Using variables to write equations
  • Parts of an expression
  • Using expressions to describe patterns
  • Equivalent Expressions
  • Translate words into algebraic  expressions

Equations

  • Evaluate and write algebraic expressions
  • Use number sense to solve equations
  • Add, Subtract, Multiply, Divide Equations by solving

Inequalities

  • Add, Subtract, Multiply, Divide Inequalities
  • Writing inequalities
  • Solving inequalities
  • Graph Inequalities

Exploring Two-Step Equations

  • Write and evaluate expressions with two variables
  • Solve multi-step equations with rational numbers

Ratios

  • Understand ratios
  • Modeling Rations
  • Ratios, Tables, and Graphs
  • Solve Ratio equations

Rates

  • Understand and compare rates
  • Unit rates vs. unit price
  • Constant price
  • Customary vs. metric units

Maps and Scale Drawings

  • Use ratios, rates and proportions to create maps
  • Word problems

Quarter 3

Geometry

Measurement

Algebra (Proportionality)

Percents

  • Understand Percents
  • Fractions, Decimals, and Percents
  • Find percent of a number
  • Percents greater than 100 or less than 1

Applications of Percents

  • Sales Tax
  • Tip
  • Commision
  • Simple Interest
  • Percent of Change

Coordinate Geometry

  • Integers on Coordinate Plane; Graphing equations
  • Rational Numbers on Coordinate Plane
  • Polygons on Coordinate Plane
  • Charts, Graphs, Quadrants

Lines, Planes, and Angles

  • Understand Lines, planes, and angles
  • Use protractor to measure angles

Shapes

  • Triangles, Polygons, Quadrilaterals, Congruent Figures, Circles

Classify Angles

  • Supplementary vs Complementary
  • Adjacent vs. Vertical
  • Congruent Angle

Area

  • Find area of Parallelogram
  • Area of a triangle
  • Area of quadrilaterals
  • Circumference and Area of a circle

Geometric Figures

  • Identify 3-D figures
  • Square roots and irrational numbers
  • Pythagorean Theorem
  • Faces, Vertices, Edges

Quarter 4

Geometry

Measurement

Algebra (Functional Relationships)

Data Analysis

Surface Area and Volume

  • Surface Areas of Prisms and Cylinders
  • Volume of Prisms and Cylinders
  • Cross Sections

Analyzing Data

  • Random Samples and Surveys
  • Statistical Questions
  • Estimating Population Size
  • Inferences

Statistics

  • Data Variability
  • Statistical Questions
  • Looking at Data Sets

Statistical Data

  • Mean, Median, Mode, Range
  • Outliers
  • Recognize misleading data

Graphs and Tables

  • Frequency Tables
  • Histograms
  • Box Plots
  • Measures of Variability
  • Summarizing Data Distributions

Patterns and Equations

  • Dependent vs. Independent Variables
  • Patterns in Tables and Graphs
  • Formulate equations

Probability

  • Conduct experiments and express probability based on possible outcomes
  • Outcomes likely vs. not likely
  • Express probabilities as fractions, ratios, decimals, and percents

Sample Spaces and Compound Events

  • Use counting principle to find a sample space
  • Probability of Dependent events
  • Probability of Independent events
  • Compound Events and Simulations