EE.6.RP.1. Demonstrate a simple ratio relationship.
Concept: Ratios compare values.
Skills: Recognize and represent many (part to part, part to whole) to 1 ratio.
Big Idea: A ratio tells how much of one thing there is compared to how much of another thing. A ratio compares two quantities- part to part or part to whole.
Essential Questions: What is a ratio? How can I write a ratio? What am I comparing? What does this ratio tell me? How many parts are there in the whole? What does the ratio represent?
Initial Precursor •Recognize wholeness •Recognize a unit •Recognize parts of a given whole or a unit
Initial Precursor: Being able to understand ratios requires a student to recognize a unit and recognize when basic objects are in whole and part forms. Work on this understanding by giving students an opportunity to observe, feel, or otherwise interact with objects and shapes in their whole and part forms. The general goal is to explore the differences between whole units or objects and parts of units or objects. As students explore shapes, label them and describe them as whole or part. NOTE: Educators can work on the Initial Precursor skills using everyday objects and/or using the shapes that students working at the Target level are representing as a ratio.
Distal Precursor •Model equal part Proximal Precursor •Partition any shape into equal parts •Explain unit fraction •Recognize fraction
Distal Precursor: As students begin to recognize whole objects or shapes and parts of objects or shapes, they can move toward building and taking apart shapes.NOTE: Educators can work on the Distal Precursor skills using everyday objects and/or using the shapes that students working at the Target level are representing as a ratio.
Target •Recognize many to 1 ratio •Represent many to 1 ratio Successor •Recognize many to many ratio
EE.7.RP.1–3. Use a ratio to model or describe a relationship.
Concept: Ratios show a comparison and can be used for mathematical reasoning.
Skills: Use ratio language "to" and "out of" to identify how much of one thing there is compared to another thing; write/indicate a ratio comparing part to part or part to whole.
Big Idea: A ratio is used to describe a relationship to part-part or part-whole.
Essential Questions: What does this ratio tell me? How can I model this relationship? How do you write a ratio that describes part to part or part to whole.
Initial Precursor •Recognize subset •Recognize set •Recognize separateness
Initial Precursor: In order to understand ratios, students need to gain experience with creating sets. Educators can provide students with opportunities to take a set of objects (e.g., tiles, linking cubes, buttons) and separate them based on a given characteristic (e.g., shape, color, size) into two distinct sets. Then, separate the objects again based on another characteristic.
Distal Precursor •Recognize fraction •Explain unit fraction •Partition any shape into equal parts
Distal Precursor: As students become more adept at tracking discrete objects, they begin working on one-to-one distribution of objects to person,objects to objects, and objects to available space (e.g., giving each person in the group a pencil; given four counters, they would line up four more counters in front of or on top of the first set; given three chairs at a table, the students would place a cup on the table for each available chair). As students' understanding of one-to-one distribution develops, provide students many opportunities to recognize equivalence in sets with same items and then sets with differing items. As students work on all these skills and concepts, continue to draw their attention to parts and wholes.
Proximal Precursor •Explain ratio•Recognize many to 1 ratio
Target •Recognize many to many ratio •Represent many to many ratio