Proportional reasoning is an essential skill. Adults call upon this type of reasoning in everyday situations as well as in many areas of mathematics study. Traditionally, mathematics classes rush to cross-multiplication as the tool of choice for solving proportion problems. However, Keeping Things in Proportion begins by building on students' intuitive knowledge and the multiplicative relationships that are at the heart of proportionality.
The hands-on lessons in this unit connect the central ideas of proportion across the spectrum of mathematics. Students work with rates and ratios in shopping, graphic design, and sampling situations that draw upon data and geometry knowledge while laying the groundwork for algebra study.
As students progress from concrete experiences with ratios to more challenging situations, they develop a bank of tools and strategies to solve proportional problems and to examine the relationships within and between ratios.
- Tools include the rule of equal fractions, tables, graphics, unit rates, and cross-multiplication.
- Students always are asked to use two-solution methods to arrive at an answer.
- Non-proportional situations are considered as well.
To facilitate conceptual development, numbers start out 'friendly' and turn 'messier' as the unit progresses. The numbers, however, prove less daunting to students as they apply their secure knowledge about proportion. Formal proportional reasoning evolves over time, and the lessons in this unit ensure that students are able to make proportional predictions and adjustments using a variety of tools effectively.
The Teacher Book is an essential component of the EMPower program. It is designed to be used in conjunction with the Student Book. The Teacher Book includes:
- Suggestions for facilitating class discussions
- Open-ended questions designed to keep the math on track
- Math Background sections to help teachers deepen their understanding of a concept
- Lesson in Action sections with examples of student work and comments that illuminate the underlying mathematics
- Examples from the authors' and pilot teachers' classroom experiences