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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

    Basic statistics

    Students will learn how to find the mean, median, mode, and range, given a finite list of numbers. Students can go here to practice finding the mean, and here to practice finding the median. Students should also learn the etymology of the word median. After all that, students will learn how to find the mean, median, etc. from stem and leaf plots, dot plots, and frequency tables. Here's a good video for dot plots.

    Find the mean and median given a list of numbers. Given the mean and a partial list, find the missing number.

    Here's an example problem:

    $$7,\ 10,\ ?$$

    The mean is 8. What's the missing number? Here's the solution.

    Have your students try this challenge, then this one. Next, have your students try this one. Then have them try this one and this one. The order doesn't matter here, because the two aforementioned challenges are equally difficult. Then have them try this one, then this one, then this one, then this one. After that, give your students this challenge, and this one too. The two aforementioned challenges can be given in any order, they are equally difficult. Give your students this as the last challenge.

    Watch these Khan Academy videos:

    • Representing data
    • Impact on median & mean: increasing an outlier
    • Impact on median & mean: removing an outlier

    Do these Khan Academy exercises:

    • Data set warm-up
    • Effects of shifting, adding, & removing a data point

    Next, give your students these challenges:

    • Match the Matches by NRICH
    • Who Can Be the Winner? by NRICH

    Conclude by leading this investigation:

    Rainbow Squares
    by MathPickle

    6.SP.A.3: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

    Lessons and practice problems