A Closer Look
Thinking Blocks is rich in both educational content and research supported instructional methods. Students not only learn to model and solve word problems; they also learn to understand and write algebraic equations. While guided practice sets encourage students to create models with concrete objects; the independent practice sets help students transition to more abstract representations using paper and pencil. Feedback in the guided practice sets offers more than yes or no responses. Incorrect answers elicit helpful questions, hints, and suggestions that lead students toward thecorrect solution.

Addition and Subtraction Word Problems
Word problems in this program are built around three distinct problem situations known as Change, Combine, and Compare.

Change
A simple one step change situation is one in which some amount is added to or subtracted from a starting amount. Thinking Blocks focuses on two-step change problems because it is the problem type that can be most difficult for students. Problems may require two addition steps, two subtraction steps, or one of each. More challenging variations of this type include problems in which the amount of change is unknown and those in which the final amount is given and students must work backward to find the starting amount.

Combine
Simple combine situations consist of two static sets of objects and their union. In Thinking Blocks, we refer to this problem situation as Part-Whole. When the whole is unknown, we have an addition situation. When one of the parts is unknown, the problem requires a subtraction step. Students working through the practice sets in Thinking Blocks first encounter Part-Whole problems in which there are only two parts. After successfully solving these problems, students may move on to problems with three parts.

Compare
In simple comparison problems, two independent quantities are compared to each other. If the difference between the two quantities is unknown or the lesser of the two quantities is unknown, the problem requires subtraction. If the greater quantity is unknown, the problem requires addition. Thinking Blocks begins with very basic single step problems and leads to two step comparison problems. In these problems, a new element (the total) is introduced. Students may be asked to solve for any one of the four parts contained in the model. The third type of comparison problem contains three quantities. Students may be asked to find the total, one of the two differences, or any one of the three quantities.

Multiplication and Division Word Problems
Thinking Blocks contains a number of situations in which multiplication or division is the required algorithm.

Multiplicative Comparisons
Problems of this type involve two distinct quanitities that are compared to each other and often include the phrase, "times as many." When the lesser quantity is known, the problem requires multiplication. When the greater quantity is known, the problem requires division. The terms, "twice as many" and "half as many" are also emphasized. Thinking Blocks presents situations in which one or two steps are required. Two step problems ask students to solve find the total. More advanced two step problems ask students to find the difference between the two quantities.

Division Situations
Thinking Blocks emphasizes two division models, partitive and measurement. In partitive division, the whole and the number of parts is known. Students must find the size of each part. In measurement division, the number of parts is unknown. While each model requires exactly the same arithmetic step to arrive at a solution, it is important for students to be familiar with both interpretations. A more challenging type of division problem asks students to interpret the remainder. Thinking Blocks includes problems in which the answer is the whole number part of the solution, the next whole number, or the remainder.

Algebraic Models
The most challenging section in this program presents word problems that, at first glance, appear to require knowledge of simultaneous equations. It is here that the model approach really dazzles. Students as young as 8 or 9 can arrange the draggable blocks to create a model that reveals a very simple but clever solution.