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Finding This Percent of That

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This video lesson focuses on finding “A% of B” as efficiently as possible. The numbers in this lesson are purposefully chosen to be difficult for students to calculate mentally or to represent on a double number line diagram, in order to motivate them to find the simplest way to do the calculation by hand.

Grade 6, Episode 8: Unit 3, Lesson 15 | Illustrative Math

    Mathematics (2019) Grade(s): 6


    Use ratio and rate reasoning to solve mathematical and real-world problems (including but not limited to percent, measurement conversion, and equivalent ratios) using a variety of models, including tables of equivalent ratios, tape diagrams, double number lines, and equations.

    Unpacked Content



    • Rate
    • Ratio
    • Rate reasoning
    • Ratio reasoning
    • Transform units
    • Quantities
    • Ratio Tables
    • Double Number Line Diagram
    • Percents
    • Coordinate Plane
    • Ordered Pairs
    • Quadrant I
    • Tape Diagrams
    • Unit Rate
    • Constant Speed


    Students know:
    • Strategies for representing contexts involving rates and ratios including. tables of equivalent ratios, changing to unit rate, tape diagrams, double number lines, equations, and plots on coordinate planes.
    • Strategies for finding equivalent ratios,
    • Strategies for using ratio reasoning to convert measurement units.
    • Strategies to recognize that a conversion factor is a fraction equal to 1 since the quantity described in the numerator and denominator is the same.
    • Strategies for converting between fractions, decimals and percents.
    • Strategies for finding the whole when given the part and percent in a mathematical and contextual situation.
    • Strategies for finding the part, given the whole and the percent in mathematical and contextual situation.
    • Strategies for finding the percent, given the whole and the part in mathematical and contextual situation.


    Students are able to:
    • Represent ratio and rate situations using a variety of strategies (e.g., tables of equivalent ratios, changing to unit rate, tape diagrams, double number line diagrams, equations, and plots on coordinate planes).
    • Use ratio, rates, and multiplicative reasoning to explain connections among representations and justify solutions in various contexts, including measurement, prices and geometry.
    • Understand the multiplicative relationship between ratio comparisons in a table by writing an equation.
    • Plot ratios as ordered pairs.
    • Solve and justify solutions for rate problems including unit pricing, constant speed, measurement conversions, and situations involving percents.
    • Solve problems and justify solutions when finding the whole given a part and the percent.
    • Model using an equivalent fraction and decimal to percents.
    • Use ratio reasoning, multiplication, and division to transform and interpret measurements.


    Students understand that:
    • A unit rate is a ratio (a:b) of two measurements in which b is one.
    • A symbolic representation of relevant features of a real-world problem can provide for resolution of the problem and interpretation of the situation.
    • When computing with quantities the transformation and interpretation of the resulting unit is dependent on the particular operation performed.
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