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- From: Implementing Algebra
- Contributed By: Kevin Hall
This research summary on organizing instruction introduces the design principles underlying the Implementing Algebra project. Citation: Pashler, H., Bain, P., Bottge, B., Graesser, A., Koedinger, K., McDaniel, M., and Metcalfe, J. (2007). Organizing Instruction and Study to Improve Student Learning (NCER 2007-2004). Washington, DC: National Center for Education Research, Institute of Education Sciences, U.S. Department of Education. Retrieved from http://ncer.ed.gov.
Packets for Lessons 2.1-2.6, in a single MS Word file.
Introduces proportions and percents through a pictorial model, building up to the Equivalent Fractions method of solving proportions. Comes with a companion PowerPoint presentation to help implement the lesson. Fully editable. A mix of direct instruction and small-group inquiry.
Companion Powerpoint to accompany Lesson 2.1. The Powerpoint is designed to help the teacher quickly and easily draw diagrams that aid student understanding. It also frees the teacher to wander among the students while they work and discuss...let the computer stay in the front of the room and do the writing for you when you need direct instruction.
In teaching proportions, this lesson shifts students from 2.1's pictorial approach to 2.2's computational approach of equivalent fractions. With deeper comprehension, students move from the concrete (pictures) to the abstract (an algorithm). After some differentiated drill practice, the lesson introduces the concept of Unit Rates. A mix of direct instruction and small-group inquiry.
Companion Powerpoint to accompany Lesson 2.2. Differentiated drill practice displays several questions at once, in increasing order of difficulty, allowing students to work at their own pace through the problems that are right for them. With a remote mouse clicker, the teacher can wander the room as students work, praising and prompting students, while gradually displaying the correct solutions with simple clicks of the mouse. This Powerpoint also includes notes on unit rate and division.
In 2.2, we introduced what Unit Rates mean and how to calculate them. In 2.3, we apply Unit Rates to solve problems and then investigate how the same problems could be solved with proportions. The lesson begins with a pictorial model of applying unit rates (concrete) and moves to a computational method (abstract). A mix of whole-class practice and small-group collaboration.
A companion Powerpoint to Lesson 2.3. The presentation allows the teacher to quickly and easily display diagrams step-by-step to model problem-solving with pictures. The presentation also allows for efficient interleaving of worked examples and practice problems. Worked examples can be displayed with a few clicks of the mouse, leaving more time for class discussion and reflection on the examples.
Begins with an intro to Cross-Multiplying (including a clear presentation of why it works). Then builds fluency with rates. Teaches how to set up rate problems quickly so the proper units cancel. Applies this concept to percent questions, laying the groundwork for Lesson 2.5. A mix of whole-class discussion and small-group practice.
Integrates 3 ways of understanding percents: proportions, rates, and percent equations. In a percent equation, "45% of x" is translated into (0.45)(x). Lessons 2.1-2.4 are prerequisite. This lesson requires students to make connections between all the different was of representing percent questions. Making connections leads to deeper understanding and better retention. A mix of whole-class and small-group instruction.
Teach slope-intercept form now, while rates of change are fresh in their minds. This early focus on slope-intercept form gives students months to master the main ideas. Later, in your unit on linear functions, they'll have a solid foundation for your teaching of standard and point-slope form. This lesson builds smoothly on 2.3-2.5 and uses real-world problems to help students make meaning from the symbols. A companion PowerPoint is being created.
