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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 › Rates and proportional relationships

    Constants of proportionality

    Students will learn how to identify unit rates in tables (video), graphs (video), equations (video), and word problems (video). Students should be shown two ways of identifying unit rates in tables. The first way is to plot the points, finding the unit rate graphically. The second way is to find the unit rate by arithmetic.

    Next, give your students these challenges:

    • 2019 Math Kangaroo Levels 7-8 Problem #27 by STEM4all
    • Add 3 Dice by NRICH

    How many corners does a 10-dimensional cube have (source)?

    Conclude by leading this investigation:

    Hex (strategy game)
    by MathPickle

    7.RP.A.2.b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

    Lessons and practice problems