Ratio and Use Ratio Language

¶ … ratio and use ratio language to describe a ratio relationship between two quantities.

Level -- 6th Grade

Standard -- MCC6.RP.2 -- Understand the concept of a unit rate a/b associated with a ratio a: b with b not equal to zero (0); use rate language in the context of a ratio relationship.

In general, formative assessment is a self-reflective process that helps students attain a better understanding of whether they have mastered material. Feedback from learning is actual, not theoretical, and has meaning as opposed to simply a percentage or "grade." The instructor- or supervisor, may formatively assess by listening, responding to questions, ask questions, and interact (Crooks, 2001). Assessment research shows that it must become part of students' approach to their own learning. Students appear to learn better when they take an active part of their own assessment and the direction of numerous educational forums provides that the ability to self-assess and to assess peers is essential. Indeed, it is important that formative assessment techniques be used not only by students, but in a way that they are understood by parents, administrators, and the public (Fisher, 2007).

Types of Formative Assessment

1. Continual use of question and response throughout each phase of the lesson; particularly focusing on modeling behaviors and techniques to understand each phase of the lesson (Questioning). This allows the teacher to constantly and continually question and receive feedback and response. Should be done on a regular basis.

2. During significant phases of the lesson, break class into appropirate group levels (2-3). Have each group prepare a "teching summation" of concept using a different ratio example; present to small groups, then class. Size of group and presentation based on complexity of lesson material and time.

3. Instructor walks through classroom while students work on individualized problems; helps or suggests as needed, asks questions to engage critical thinking about the subject (Observation). This is more subjective and regular, although it does provide instructor with hands on and immediate feedback if concepts are not understood. This also allows instructor to re-teach or tailor the lesson if there are problems in cognition.

4. Have students construct a graphic organizer that explains the concept of ratios; as in comparing two things; x is to y, etc. Venn diagrams can be used, compare contast diagrams, histograms, or others. This also allows spatial thinkers to have an opportunity to succeed.

5. Have students construct a visual diagram of the manner in which ratios can be written (fraction, using "to," colon). Have students explain their model to their group, particularly how each method means the same but might be more appropriate in certain situations. This can be done in small, medium and large groups, and also allows students to improve communication skills.

6. On a given worksheet, allow students to peer assess their performance, then meet and discuss the results and ways to improve. By reviewing other student's performance, sometimes the individual weaknesses one student may have are mitigated. This changes the way students often approach a problem, as well as engendering empathy skills.

7. Think-Pair- Share -- at the think stage, instructor asks a question and asks students to think about it for a few minutes, writing notes, etc. If needed. Then students pair up to discuss their approach to the problem; finally, students share with the class in a communications interaction activity. The sharing and pairing often provide differing points-of-view for the lesson.

8. Use blocks or other manipulatives; ask students to visually represent a group of ratios using the manipulatives (Kinesthetic learning). Alternatively, students could visually represent the process. Using manipulatives also offers an alternative explanation of how ratios or other mathematical processes work.

9. Make four broad statements about ratios (formation, use, etc.). Post these one at a time; have students line up in four categories (Four Corners) -- Strongly agree, Agree, Disagree, Strongly Disagree. If time, have students explain their reasons to each other, another group, or the class. Switch questions to find out ways students are processing the information.