Prelude to Algebra …

... presents a new way of understanding and modeling basic arithmetic opertations. ... reviews arithmetic and introduces algebraic concepts in a dynamic way that makes sense to students ... teaches students to think algebraically while doing arithmetic ... increases students' understanding and reduces students' errors. ... developed from a study of the types of mistakes that students commonly make in algebra.

Unique Features in the Book

Prelude to Algebra introduces a number of new ways of thinking about arithmetic and algebra.  Many of these innovations are introduced in the first half of the book and then used systematically to simplify later topics.  The following chart shows where some of these novel explanations and approaches are first encountered.

Topics	Lessons
§ Using invariant principles to simplify addition, subtraction, multiplication, and division	1.6, 3.6
§ Using operators (increases and decreases) to model addition and subtraction	2.1
§ Using operators to clarify the manipulation of parentheses	2.4, 2.5
§ Defining multiplication in a way that includes the cases of multiplying by 1 and 0	3.1
§ Using operators (expansions and contractions) to model multiplication and division	3.1, 3.2
§ Naming the form of an expression as a guide to the order of operations and a tool in solving equations	3.6, 6.6
§ Using line segments to model the interaction of expansions and contractions	4.1, 4.2
§ Viewing an expression as being built by a sequence of operations	4.3
§ Learning a mathematically correct explanation of canceling	4.4
§ Applying invariant principles to simplify algebraic expressions	4.5
§ Learning a mathematically correct definition of exponents	5.1
§ Using the factoring compound expressions to build skills needed in algebra	5.6
§ Using a simple chart to find the GCF and the LCM	5.7
§ Solving equations before introducing fractions and signed numbers	6.1
§ Solving arithmetic equations without computing as a pattern for algebra	6.1
§ Solving equations by analyzing their structure	6.1 – 6.3
§ Solving equations by removing operators	6.6, 6.7
§ Using the composition of operators to clarify computations with fractions	7.1, 7.2
§ Using linear models to visualize proportions	8.1
§ Using linear models to visualize percent problems	8.3, 8.7
§ Using the composition of operators to model computations with signed numbers	9.1 – 9.4
§ Viewing a negative exponent as a counter of contractions	9.5
§ Explaining the limitations of the “3-number” method of solving equations	10.4