Percentages and Double Number Lines

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

6

Overview

Students explore percentages of quantities other than 100 and 1 in a variety of contexts. All of the tasks use comparison contexts—describing one quantity relative to another quantity—rather than part-whole contexts.

Students can continue to use the double number lines as a reasoning tool. The equal intervals on the double number line are useful for reasoning about percentages. In addition, using the same representation that was used for other ratio and rate reasoning reinforces the idea of a percentage as a rate per 100 (MP7). Students should also be encouraged to use other strategies to solve percentage problems.

Grade 6, Episode 7: Unit 3, Lesson 11 | Illustrative Math

Mathematics (2019) Grade(s): 6

MA19.6.3

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.

UP:MA19.6.3

Vocabulary

  • 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

Knowledge

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.

Skills

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.

Understanding

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.

CR Resource Type

Audio/Video

Resource Provider

PBS

License Type

CUSTOM
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