6.RP.3 - About the Math, Learning Targets, and Increasing Rigor

Grade 5 AGL Ratio and Proportion

6.RP.3

Full Standard

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

  1. Make tables of equivalent ratios relating quantities with whole- number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
  2. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
  3. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
  4. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

 

Learning Targets (I can)

  • Represent ratios using tape diagrams and double number lines.
  • Make, use and complete ratio tables to solve problems.
  • Plot values from a ratio table on a coordinate plane.
  • Solve problems with unit rates.
  • Describe percent as a unit rate.
  • Find a percent of a given quantity as a rate per 100.
  • Find a whole given a part and a percent.
  • Describe conversions between units as a ratio.
  • Convert measurement units using ratios.

 

About the Math

Ratios, unit rates, and percents are critical tools for solving real-world problems. The term percent comes from the Latin expression meaning "per hundred." A percent is also defined as a ratio comparing one number to 100. So 56% is understand as a ration of 56:100 or the fraction 56/100 or the decimal 0.56. Depending on the context, quantities may be represented as a ratio, fraction, decimal, or percent. Baseball statistics are presented in the decimal form, measurements are presented as fractions or decimals, and weather data are referred to as percents (40% chance of rain). Essential vocabulary for this standard includes: convert, coordinate pair, coordinate plane, divide/division, double number line, equation, equivalent ratio, percent, plot, rate, ratio, tape diagram, transform, unit price, unit rate, and value. Visit the online dictionary Links to an external site. or visual math dictionary Links to an external site. for vocabulary support.

 

Common Misconceptions

  • Students may focus on only one quantity instead of the relationship between two quantities.
  • Students may be unfamiliar with multiple strategies, including ratio tables.
  • Students may confuse mathematical terms such as ratio, rate, unit rate and percent.
  • Students may not understand how to set up a table or graph.
  • Students may not understand the difference between an additive relationship and a multiplicative relationship.

 

 

Progression of Standard within Grade 6 (5 AGL)

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

Progression Throughout Year
Quarter 1 Quarter 2 Quarter 3 Quarter 4
  • Make, use and complete ratio tables to solve problems.
  • Plot values from a ratio table on a coordinate plane.
  • Solve problems with unit rates.
  • Describe percent as a unit rate.
  • Find a percent of a given quantity as a rate per 100.
  • Find a whole given a part and a percent.
  • Describe conversions between units as a ratio.
  • Convert measurement units using ratios.
  • Make, use and complete ratio tables to solve problems.
  • Plot values from a ratio table on a coordinate plane.
  • Solve problems with unit rates.
  • Describe percent as a unit rate.
  • Find a percent of a given quantity as a rate per 100.
  • Find a whole given a part and a percent.
  • Describe conversions between units as a ratio.
  • Convert measurement units using ratios.

 

 

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades
Grade 5 Grade 7
  • Recognize and represent proportional relationships between quantities (7.RP.2)
  • Use proportional relationships to solve multistep ratio and percent problems (7.RP.3)

 

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