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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 › Geometry (grade 7)

    Area of an obtuse triangle

    Students will see a derivation for the area of an obtuse triangle.

    Do you Believe the Area Formula for Triangles? (Tanton Mathematics) by DrJamesTanton

    Next, give your students these challenges:

    • 2019 Math Kangaroo Levels 1-2 Problem #23 by STEM4all
    • 2018 Math Kangaroo Levels 7-8 Problem #29 by STEM4all

    Cycling Squares by NRICH: The trick is to find numbers which can be paired with only one or two of the remaining numbers. Such pairs, or triples, must occur in the loop. Notice, for example, that 2 can only be paired with 14, to make 16, or 34, to make 36. Thus, the sequence 14, 2, 36, or its reverse, must occur in the loop. Next, you would remove 2 from your list of available numbers, because it's surrounded, namely, by 14 and 34. Then you'd continue in this way until no numbers remain. Reading the loop clockwise, starting at 2, the solution is: 2, 34, 30, 19, 17, 8, 28, 21, 15, 10, 6, 3, 13, 12, 4, 5, 11, 14.

    Conclude by leading this investigation:

    Skinny Man Tango (area, algorithm)
    by MathPickle