In this unit, students explore five models of subtraction (counting, sets, number line, balanced equations, and inverse of addition) using connecting cubes. The lessons focus on the comparative mode of subtraction. In them, children explore the relationship between addition and subtraction, write story problems in which comparison is required, and practice the subtraction facts.
The unit consists of lessons that build on and extend early understandings about counting, addition, and subtraction in the comparative mode. Familiarity with the many models of subtraction in each mode is important to children’s success in problem solving. Together the five models provide a structure for developing a rich conceptual schema for subtraction.
Individual Lessons
Lesson 1 - Counting Back and Counting On
In this lesson, students model subtraction with connecting cubes while the teacher reads to them from counting books. Then children make a train of connecting cubes and write in vertical and horizontal format the differences suggested by adding to and subtracting from the train one cube at a time. Finally, they record, in written form, a train showing one cube being taken away and record the difference in vertical and horizontal format.
Lesson 2 - Comparing Sets
A children’s book sets the stage for this lesson which encourages students to
review counting back. In this lesson, children write subtraction problems and
model them with cubes. They compare sets and record differences in the form of a
table. The additive identity is reviewed in the context of comparing equal sets.
Lesson 3 - Using the Number Line to Compare
In this lesson, students determine differences using the number line to compare lengths. Because this model is based on linear measurement, it is a distinctly different representation from the models presented in the previous two lessons. At the end of this lesson, children are encouraged to predict differences and answer puzzles involving subtraction.
Lesson 4 - Balancing
This lesson encourages students to explore another model of subtraction, the balance. This model leads naturally to recording with equations. Students use actual and virtual pan balances in their explorations and record the modeled subtraction facts and the related addition facts in equation form.
Lesson 5 - Fact Families
In this lesson, the relationship of addition to subtraction is explored with books and with connecting cubes. Students search for related addition and subtraction facts for a given number using a virtual or actual calculator to find differences. They also investigate fact families when one addend is 0 as well as when the addends are the same.
Lesson 6 - Looking Back and Moving Forward
This final lesson of the unit reviews the work of the previous lessons and suggests a framework for summative assessment. During this lesson, students use the mathematical knowledge and skills developed in the previous lessons to demonstrate understanding and the ability to apply that knowledge to playing subtraction games.
