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    • ▾6th grade
      • ▾Ratios, rates, and percentages
        • •Percentages
        • •Intro to ratios
        • •Unit rates
        • ▸Equivalent ratios
          • •Simplifying ratios
          • •Equivalent ratios (mathematical problems)
          • •Equivalent ratios (word problems)
          • •Find equivalent ratios using Cuisenaire rods
      • ▸Arithmetic operations
        • •Long division
        • •Decimal arithmetic
        • •Divide fractions
        • •Dividing whole numbers by fractions
        • •Raising numbers to whole number powers
        • •Mentally raising small numbers to small powers
        • •Powers of 10
        • •Multiplying and dividing by powers of 10
        • •Tower of Hanoi
        • •Counting in bases 5 and 2
        • •More on binary
        • •Remainders of large powers
      • ▸Negative numbers
        • •Intro to negative numbers
        • •Absolute value of rational numbers
        • •Plotting points in all four quadrants
      • ▸Factors and multiples
        • •Prime factorization
        • •Common factors
        • •GCD and LCM by making lists
        • •GCD and LCM by prime factorization
        • •GCD and LCM word problems
        • •Properties of the GCD and LCM
        • •Water pouring puzzles
        • •Factor with the distributive property (no variables)
        • •Relatively prime
      • ▸Variables and expressions
        • •Intro to variables
        • •Measurement with an unknown unit of length
        • •Convert phrases to algebraic expressions
        • •Identify parts of expressions
        • •Distributive property with variables
        • •Determining equivalence of algebraic expressions
      • ▸Equations and inequalities introduction
        • •Testing solutions to equations and inequalities
        • •Solving one-step equations, addition and subtraction
        • •Solving one-step equations, multiplication and division
        • •Model with one-step equations
        • •Modeling one-variable inequalities
        • •Dependent and independent variables
      • ▸Geometry
        • •Volume of right rectangular prisms with fractional lengths
        • •Area
        • •Number of diagonals in a convex polygon
        • •Counting vertices, edges, and faces
        • •Nets and surface area
        • •Surface area of rectangular prisms
        • •Coordinate plane
        • •Menseki Meiro puzzles
      • ▸Data and statistics
        • •Identifying statistical questions
        • •Plotting data
        • •Basic statistics
        • •Combining means
        • •Analyzing distributions
     › 6th grade › Ratios, rates, and percentages

    Equivalent ratios

    1. Equivalent ratios (mathematical problems)
    2. Equivalent ratios (word problems)
    3. Find equivalent ratios using Cuisenaire rods
    4. Simplifying ratios

    Solve equivalent ratio problems, both word problems and mathematical problems. Some of these problems can be multiple-choice. For example, which ratio is equivalent to 6 : 10? Next, give your students this challenge, then this one.

    Watch these Khan Academy videos:

    • Finding a percent
    • Percent of a whole number
    • Percent word problem: recycling cans
    • Part:whole ratio word problem
    • Scale drawing: centimeters to kilometers
    • The meaning of percent
    • Meaning of 109%
    • Percent word problem: penguins
    • Percent word problem: 100 is what percent of 80?
    • Percent word problem: 78 is 15% of what number?
    • Percent word problem: guavas
    • Solving ratio problems with tables
    • Solving ratio problems with graph
    • Converting percents to decimals: 59.2%
    • Converting percents to decimals: 113.9%
    • Converting percents to decimals & fractions example
    • Converting decimals to percents: 0.601
    • Converting decimals to percents: 1.501

    Do these Khan Academy exercises:

    • Convert fractions to percents
    • Finding percents
    • Ratios on coordinate plane
    • Equivalent ratio word problems
    • Relate fractions, decimals, and percents
    • Percents from fraction models
    • Percent word problems
    • Ratio tables
    • Convert percents to decimals
    • Part-part-whole ratios
    • Equivalent ratio word problems (basic)
    • Ratios and units of measurement
    • Convert decimals to percents
    • Equivalent representations of percent problems
    • Equivalent ratios in the real world
    • Intro to percents
    • Understand equivalent ratios in the real world
    • Convert percents to fractions

    Conclude by leading this investigation:

    Half Area Quadrilateral
    by MathPickle

    6.RP.A.3: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.