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6-N-3-3

Page history last edited by Meagan Habluetzel 5 years, 9 months ago

6.N.3.3 Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.


In a Nutshell

Students must understand the concept of ratios as part to part, part to whole, or whole to part in order to continue their exploration of ratios (See 6.N.3.1). Students will build upon their knowledge of ratios and equivalent fractions and percents and apply that to solve problems involving mixtures and concentrations. Understanding that a ratio written in fraction form does not always represent a part to whole relationship is key when applying this concept to mixture. Mixtures are ratios that compare part to part relationships and concentrations are ratios that compare part to whole.  For example, powder is mixed with water to create Kool-Aid.  This could be a ratio of 1 part powder to 4 parts water, or 1:4.  When looking at the concentration of the powder in the Kool-Aid, the ratio now changes to a part to whole relationship, where 1 part powder is compared with 5 parts of total Kool-Aid, or 1:5. This concentration could also be written as a percentage, or 20%.  If more or less of the mixture is needed, equivalent fractions can be used to find the correct ratio, while keeping the concentration of powder to water the same.

Student Actions

Teacher Actions

  • Develop mathematical reasoning when comparing ratios to determine whether a ratio represents a part to part or a part to whole relationship.

  • Develop a deep understanding of ratios as part to whole by solving problems using percents.

  • Communicate mathematically to explain the difference between a mixture and a concentration.

  • Develop problem-solving strategies for percents by setting up equations involving fractions or decimals.  (Ex:  15 is 30% of what number?  Students could set up an equation, 15=.30x) (See 6.A.3.1 and 6.A.3.2)

  • Use and connect mathematical representations by engaging students in representations as students discuss mixtures and concentrations.

  • Pose purposeful questions to gather evidence of student reasoning and understanding of a ratio as it relates to mixture (part to part) and concentration (part to whole).

  • Facilitate meaningful mathematical discourse by encouraging students to use appropriate math vocabulary when discussing ratios written in fraction form. If the relationship is part to part use “to” if the relationship is part to whole use “out of”.

Key Understandings

Misconceptions

  • A ratio is a multiplicative comparison of two quantities.

  • Ratios written as fractions may represent part to part or part to whole.

  • Mixtures always compare part to part.

  • Concentrations always compare part to whole.

  • Concentrations may be written as percents, but mixtures may not (because of the part to part relationship.)

  • Percent problems can be modeled using equations.

  • Not understand that ratios can be written as a part to part, part to whole, or whole to part relationship.

  • Believe that multiplying or dividing both the numerator and the denominator by the same number increases or decreases the value of the fraction.

  • Misapply additive ideas when creating “equivalent” fractions.

  • Believe mixture ratios may be written as percents.

OKMath Framework Introduction

6th Grade Introduction

 

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