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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

    Multi-step problems

    Solve multi-step real-world and mathematical problems, involving decimal numbers, rationals, percents, or any combination of these.

    Watch these Khan Academy videos:

    • Adding & subtracting rational numbers: 79% - 79.1 - 58 1/10
    • Adding & subtracting rational numbers: 0.79 - 4/3 - 1/2 + 150%
    • Adding & subtracting fractions
    • Rational number word problem: school report
    • Rational number word problem: cosmetics
    • Rational number word problem: cab
    • Converting decimals to fractions 2 (ex 1)
    • Converting decimals to fractions 2 (ex 2)

    Do these Khan Academy exercises:

    • Adding & subtracting rational numbers
    • Rational number word problems
    • Rewriting decimals as fractions challenge

    Next, give your students these challenges:

    • Building with Solid Shapes by NRICH
    • Junior Frogs by NRICH
    • The Thousands Game by NRICH

    Conclude by leading this investigation:

    Plastic Fraction Circles
    by MathPickle

    7.EE.B.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

    Lessons and practice problems