Virginia Mathematics Teacher Fall 2016

STAGE 1: Desired Results ~ What will students be learning?

Task 1 (see Figure 1) asks students to apply ratio concepts they learned to a real world situation. Task 2 (see Figure 2) requires students to compare and order fractions. After the summer institute, teachers used the tasks with their students. During four follow-up sessions, mathematics specialists facilitated discussion around participants’ experiences using the tasks with their students as well as other topics related to current mathematics instruction. In addition to providing professional development for teachers, another aspect of this program focused on the needs of building administrators. During the 2015-2016 school year, workshops for principals were held to address the administrative supports that are necessary for meaningful mathematics instruction. These sessions were offered to all principals, assistant principals, and lead mathematics teachers within the division whose teachers participated in the Rational Numbers course in year 1. Kanold, Briars, & Fennell (2012) believe that in order to build high quality instruction “principals must consider what content issues to address in the mathematics curriculum” (p. 9). Participants engaged in mathematical tasks to understand how these skills were related to the

6.1 The student will describe and compare data, using ratios, and will use appropriate notations, such as , a to b , and a : b . 7.4 The student will solve single-step and multistep practical prob­ lems, using proportional reasoning.

SOL/Learning Objective

Essential Ques- tions & Under- standings/Big Ideas

What is a ratio? How can ratios be used for comparison?

STAGE 2: Assessment Evidence ~ What is evidence of mastery?

Students will find relationships among parts of ratios and make com­ parisons based on the ratios by drawing models of those compari­ sons. Students will explain their mathematical understanding of equivalent ratios.

Assessment Strategies

Students rearranging the order of the ratios. For example: Flipping 7/5 to 5/7 to change it from an improper fraction to a regular fraction not understanding the relationship between two sets. Comparing incorrect parts of ratios. For example: Assuming because 7 is a larger number that it would be the greatest ratio. 7/5 and 5/4 Understanding equivalent ratios. For example: Students may not understand that a ratio of 5:4 is equivalent to a ratio of 10:8. Relationship of part-part-whole within ratios. For example: A win-loss ratio of 2 to 3 represents 5 total games STAGE 3: Learning Plan ~ What are the strategies and activities you plan to use?

Possible mis- conceptions or learning gaps

The teacher will set up the problem by discussing how sports teams use ratios to determine conference standings. The teacher will then break the class into groups of 2-3 and pose the following scenario:

At the middle of the season, the Wildcats and the Vikings have each played 36 games. The Wildcats have a win to loss ratio of 7:5 and the Vikings have a win to loss ratio of 5:4.

Teaching and Learning Activ- ities (Task)

Which team will make the playoffs? Explain how you determined your solution. Draw a picture/diagram that compares the ratios.

Students will discuss in groups of 2-3 how they came up with their answer. Groups must come to a consensus before they explain it to the rest of the class.

Checking for Understanding

Teacher will monitor groups by walking around and asking students to explain their models.

STAGE 4: Closure ~ What did the students master & what are they missing? Task Closure & Student Sum- marizing of their Learning Students will share with the class the different ways in which they solved the problem.

Figure 1 . Mathematical Task Example

Virginia Mathematics Teacher vol. 43, no. 1

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