This mathematics unit was focused on ratios and rate concepts to solve problems for Mathematics Framework standards for sixth grade. Students were taught four lessons where each lesson focused on a different aspect of ratios and rates. Each lesson used the Gradual Release of Responsibility Model with emphasis on I do it, we do it, you do it together, and you do it alone. The lessons were designed to model and teach new material and skills to students, while giving them opportunities to work with partners, small groups, and independently. The lessons used technology tools and resources to aid students. The third lesson had a multicultural focus embedded in the lesson so students can learn about different cultures in mathematics. Students also focused on making a connection to the material taught in the lesson, to apply those skills and knowledge to solve real world problems.

• Compare: estimate, measure, or note the similarity or dissimilarity between.

• Ratio: the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

  1. We can represent a ratio using a colon, fraction bar, and number to number.

• Part to part: a ratio that compares a selected number of parts. to a number of other parts in a whole.

• Part to whole: a ratio that compares a selected number of parts. to the total number of parts in a whole.

• Whole to part: a ratio that compares the total of parts in a whole. to a selected number of those parts.

• Equivalent: equal in value, amount, function, meaning, etc.

• Bar model: a pictorial representation of a problem or concept where bars or boxes are used to represent the known and unknown quantities.

• Ratio table: a visual representation that represents pairs of corresponding values with an equivalent ratio between each pair.

• Rate: a comparison of two quantities that have different units of measurement.

• • • 6.RPA Understand ration and rate concepts and use ration and rate reasoning to solve problems.

Standards that were also taught that falls underneath this larger standard:

• • • • 6.RPA.1. Understand the concept of a ratio including the distinctions between part:part and part:whole and the value of a ratio; part/part and part/whole. Use ratio language to describe a ratio relationship between two quantities.

      • 6.RPA.2. Understand the concept of a unit rate a/b associated with a ratio a:b with b 0, and use rate language in the context of a ratio relationship, including the use of units.

      • 6.RPA.3. 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. SWBAT describe a relationship between two quantities using mathematical language and models.

2. SWBAT solve real-word problems by using ratios and rates.

3. SWBAT determine if two quantities are equivalent.