In this Unit Plan, students explore the five models of subtraction (counting, sets, number line, balanced equations, and inverse of addition) using links. They also learn that the order property does not hold for subtraction and explore the relation between addition and subtraction. Students also write story problems in which subtraction is required and begin to memorize the subtraction facts. A brief bibliography of related books for children is provided.
Individual Lessons
Lesson 1 - Counting Back and Counting On
This lesson, which focuses on the counting model for subtraction, begins with reading a counting book. The students model the numbers as the book is read. Then they make a chain of links and write in vertical and horizontal format the differences suggested by adding and subtracting one link at a time from their chains. Finally, they draw a chain showing one link being taken away and write in two formats the difference it represents.
Lesson 2 - Taking Away Sets
This lesson encourages students to explore another model for subtraction, the familiar set model. Reading one of the many books that feature subtraction set the stage for this lesson in which the students write story problems, find differences using sets, and present results in a table. In the discussion of the table, they focus on the effects of subtracting all and subtracting 0.
Lesson 3 - Hopping Backward on the Number Line
In this lesson, students generate differences using a number line model. Because this model highlights the measurement aspect of subtraction, it is a distinctly different representation from the models presented in the previous lessons of this unit. The order property for subtraction is investigated. At the end of the lesson, children are encouraged to predict differences and solve puzzles involving subtraction.
Lesson 4 - Finding the Balance
This lesson encourages students to explore another model of subtraction, the balance. Students will use real and virtual balances. Students also explore recording the modeled subtraction facts in equation form.
Lesson 5 - Finding Fact Families
In this lesson, students explore the relation of addition to subtraction with books and links. Then the children search for related addition and subtraction facts for a given number. They also investigate fact families, including those where one addend is 0 and where the addends are alike.
Lesson 6 - Practice Makes Perfect
During this lesson, students use what they know about fact families to play a concentration game. They will also identify subtraction facts they need to learn.
Lesson 7 - Looking Back and Moving Forward
This final lesson reviews the work of the previous lessons and suggests a framework for summative assessment. Students will self-select a solution strategy for subtraction from the models introduced in this unit. An extension activity is suggested in which students use the mathematical knowledge and skills developed in the previous lessons to demonstrate understanding and ability to apply that knowledge to playing a new game.
