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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 › Data and statistics

    Combining means

    Students will learn how to solve four different types of problems involving means. In the first type of problem, the mean of the original group is given, and the mean of the group plus one member is given. The objective here is to find the value of the added member. Basically, the mean of group A is x, and the mean of group A plus member m is y, what is the value of m? In the second type of problem, the mean and size for each of two groups is given, and the objective is to determine the mean overall. In the third type of problem, the overall mean is given, the size of each of two groups is given, and the mean of one of the two groups is given. The objective is to find the mean of the other group. In the fourth type of problem, the size of a group and its mean are given. We are told the value of member m, and from this, must determine the mean of the group after m is removed.

    Combining Means by DrFrostMaths

    Next, give your students these challenges:

    • Clever Santa by NRICH
    • Butterfly Flowers by NRICH

    Conclude by leading this investigation:

    Egyptian Fractions
    by MathPickle