# Robots and Cell Phones

Task:  If three robots make 17 cell phones in 10 minutes, then 12 robots can make how many cell phones in 45 minutes?

Research Question(s):  How do we develop students’ problem solving skills using rich word problems

Lesson Goal/Objectives:

SOL 8.3 The student will solve practical problems involving rational numbers, percents, ratios, and proportions.

The basis for our group’s lesson is to involve students in a meaningful activity that they can understand in real terms.  The problem involves explicit and implicit relationships among the variables.  Students will be given the time and resources to explore and discover different methods of solving the problem, as they work together in groups.  The focus is to follow the key principle concepts of teaching proportional reasoning, as described in Developing an Essential Understanding of Ratios, Proportions & Proportional Reasoning (2010).  The goal is to set a high standard for instruction, wherein lessons are designed to be challenging, but where students feel supported in their own methods of discovery and not that they are expected to follow only one specific strategy.

Another key principle is the formulation of significant assessment tools.  In our lesson, we include a warm-up to first assess the students’ understanding of explicit relationships.  At the conclusion of our lesson, we administered a short assessment on their understanding of implicit relationships among the variables, requiring a higher level of understanding of proportional reasoning and the relationship among the various terms in the problems.

In developing our primary lesson, the group also followed the steps outlined by Van de Wall in Teaching Student-Centered Mathematics, Volume III (2006).  Van de Wall describes eight steps that should precede all planning in a problem-based lesson; 1) articulate the ideas you want students to learn from this lesson; 2) modify the lesson to your students and what they may or may not already know or understand; 3) identify the specific tasks you want them to accomplish, but keep it simple and at their level; 4) predict what answers you think they will find; 5) let students know they will need to articulate and explain their work; 6) start the lesson providing some direction, as we will with our warm-up; 7) identify what might be a challenge for many students, and be prepared to provide the minimum guidance so they can discover the answers on their own; 8) consider how the students can best share their ideas and work, whether that is presenting to the entire class or sharing with the table next to them, as we will do in our lesson.

Relationship between this Lesson and Mathematics Content Standards for VA SOL: vertical and horizontal connections:

Foundational Objectives:

SOL 7.4 The student will solve single-step and multi-step practical problems, using proportional reasoning.

SOL 6.1 The student will describe and compare data, using ratios, and will use appropriate notations such as , a to b, and a:b.

Essential Questions and Understandings:

How do proportions show a relationship of equality between two ratios?

How can proportional reasoning be used to solve practical problems?

Students will understand that there are different ways to represent the proportional reasoning used to solve a problem.

Students will understand that proportions use ratios to show a relationship of equality.

Problem:  If three robots make 17 cell phones in 10 minutes, then 12 robots can make how many cell phones in 45 minutes?