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    • ▾7th grade
      • ▸Integers
        • •Adding integers
        • •Subtracting integers
        • •Negative Fibonacci numbers
        • •Distance between two numbers
        • •Multiplying integers
        • •Dividing integers
        • •Equivalent expressions with negative numbers
      • ▾Fractions, decimals, and percentages
        • •Multi-step problems
        • •Percents
        • •Negative signs in fractions
        • •Simplifying complex fractions without variables
        • •Dividing by zero
        • •Converting fractions to decimals
      • ▸Rates and proportional relationships
        • •Rates with fractions
        • •Interpreting graphs of proportional relationships
        • •Constants of proportionality
        • •Writing proportional equations
        • •Solving proportions using equivalent fractions
        • •Solving proportions using inverse operations and by cross multiplying
      • ▸Expressions, equations, and inequalities
        • •Interpreting linear expressions
        • •Solving two-step equations
        • •Mentally solving certain two-step equations
        • •Solving and graphing two-step inequalities
        • •Distributing, factoring, and combining like terms
      • ▸Geometry (grade 7)
        • •Angles around a point
        • •Complementary and supplementary angles
        • •Vertical angles theorem
        • •Finding the midpoint on the number line
        • •Intro to circles and \(\pi\)
        • •Area of an obtuse triangle
        • •Area of a regular polygon
        • •Area, volume, and surface area
        • •Circumference and area of a circle
        • •Volume of extruded figures
        • •Cross sections
        • •Platonic solids
        • •Precursor to the triangle inequality
        • •Scale drawings
      • ▸Statistics and probability (grade 7)
        • •Intro to probability
        • •Simple events
        • •Compound probability of independent events
        • •Comparing distributions
        • •Probability models
        • •Theoretical and experimental probability
        • •Representative samples
     › 7th grade › Fractions, decimals, and percentages

    Dividing by zero

    Students will learn two reasons why division by zero is undefined. First, if division is repeated subtraction, then we cannot reach zero by repeatedly subtracting zero from some number. Second, consider the fractions where the numerator is fixed, and the denominator shrinks. For example, 1/1, 1/0.1, 1/0.01, etc. This value is getting larger and larger, and we can see it approaches positive infinity. But if we define 1/0 to be positive infinity, then we reach the absurdity that 1 = 2. Here's a video on all this.

    Next, give your students these challenges:

    • Cows and Sheep by NRICH
    • 2018 Math Kangaroo Levels 5-6 Problem #23 by STEM4all

    Conclude by leading this investigation:

    EKG Sequences – factorization
    by MathPickle

    Lessons and practice problems