6.RP.1 - About the Math, Learning Targets, and Increasing Rigor

Grade 5 AGL Ratio and Proportion

6.RP.1

Full Standard

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”

 

Learning Targets (I can)

  • Describe ratios as relating parts to a whole.
  • Describe ratios as relating parts to parts.
  • Identify part-to-part ratios when the parts being compared do not comprise the whole (3 squares, 2 triangles, and 4 circles has a part-to-part ratio of 3:2, 2:4, etc as one shape is discounted in the comparison).
  • Represent ratios using tape diagrams, double number lines, and ratio tables.
  • Solve problems involving ratios.

 

About the Math

Ratios and proportional relationships are foundational for further study in mathematics and science and useful in everyday life. Students use ratios in geometry and in algebra when they study similar figures and slopes of lines, and later when they study sine, cosine, tangent, and other trigonometric ratios in high school. Students use ratios when they work with situations involving constant rates of change, and later in calculus when they work with average and instantaneous rates of change of functions. (Progressions of the Common Core State Standards Links to an external site., Common Core Standards Writing Team, 2011)

 

A ratio is a number that relates two quantities or measure within a given situation in a multiplicative relationship. Ratios can express comparisons of a part to a whole, for example, the number of boys in the class to the entire class. A ratio can also relate one part of a whole to another part of the whole, for example, if we were to compare the number of boys to the number of girls within a class. These ratios compare two measure of the same type of thing. A ratio can also be a rate. When a ratio is a rate, it is a special type in in which two different quantities or things are compared. Common rates include miles per gallon and wages per hour. Often times a unit rate is given that shows the measurement of one unit. For example, tickets to the show are $12 per person. How much will a family of four cost to go to the show? The unit rate is $12 to 1 and the multiplier is 4. It is important that students see many contexts for applying their understanding of ratios.
The following mathematical connections link ratios and fractions:

  • Ratios are often expressed in fraction notation, although ratios and fractions do not have identical meaning.
  • Ratios are often used to make part-part comparisons, but fractions are not.
  • Ratios and fractions can be thought of as overlapping sets.
  • Ratios can often be reinterpreted as fractions.

Essential vocabulary for this standard includes: proportion, ratio, and relationship. Visit the online dictionary Links to an external site. or visual math dictionary Links to an external site. for vocabulary support.

 

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
  • Describe ratios as relating parts to a whole.
  • Describe ratios as relating parts to parts.
  • Solve problems involving ratios. 
  • Describe ratios as relating parts to a whole.
  • Describe ratios as relating parts to parts.
  • Solve problems involving 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
  • Graph two patterns/rules on coordinate plane (5.OA.3)
  • Interpret multiplication as scaling (resizing) (5.NF.5)
  • Compute unit rates associated with ratios of fractions (7.RP.1)

 

 

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