Proportions cause great confusion for many students. This is troubling because proportional relationships run deep into the heart of math, laying the foundation for many other concepts. For example, concepts such as speed (i.e., meters per second), density (grams per cubic centimeter), and concentration (parts per million) all involve proportional relationships. If students do not understand proportions, they will have difficulty understanding algebra. On the other hand, if students can make sense of proportions, it gives them an advantage when learning algebra. This is where Making Sense of...

So far in the Core Advantage system, students have learned how to add, subtract, multiply, and divide positive numbers. However, the world is full of both positive and negative numbers. Consider the following: 1. Temperatures can go both above zero and below zero. 2. A mountain can be thousands of feet above sea level, while a submarine can go thousands of feet below sea level. 3. A house can either increase or decrease in value. 4. Money can be deposited into or deducted from a bank account. This is why integers are so important - they help us understand more of the world around us. Adding,...

Whether you realize or not, mathematics is actually a language. The purpose of a language is to communicate, and mathematics is how we communicate about quantities and logical relationships. We do so by using signs, symbols, and other mathematical terms. One of the most important communication tools in the language of math is an equation. When students can use equations fluently, it helps them communicate in math more precisely, and it helps them more easily make sense of math. Equations help us solve a variety of problems, from figuring out how many laps a swimmer must complete during her...

This is the TEACHER EDITION for 10 Powerful Steps to Multiplication Fluency. The Teacher Edition includes the Practice Pages that are found in the Student Edition as well as Extra "Memory Builders" for use when following a two-day pacing. Handwritten answer keys are also included. The Teacher Edition does not include the perforated Study Cards, which are only available in the coil-bound Student Edition.