Students explore the take away model of subtraction in several different contexts (counting, sets, number line, balanced equations, and inverse of addition) using pasta shapes. They also decompose numbers and explore both the zero property and the relationship between addition and subtraction.
Familiarity with the many contexts of subtraction is important to the students’ success in problem solving; therefore, different contexts of subtraction
are included in this unit. Within this unit, the students act out subtraction situations with objects and represent subtraction in pictures, then compose and solve problems involving subtraction.
Prerequisite Knowledge
Pasta shapes are used as manipulatives in most lessons. Any type of pasta can be used, but the appeal of the activities may be enhanced if special shapes such
as teddy bears, sea creatures, or sports equipment are chosen. These are available in the pasta section of many grocery stores. For students with less-developed motor skills, you may want to select large shapes, such as
rigatoni or bow ties.
Individual Lessons
Lesson 1 - Recording Two Ways
The students make sets of pasta shapes and count some away, then record the subtraction in vertical and horizontal formats. They draw a set and cross out some shapes, then write in both formats the subtraction that the drawing represents.
Lesson 2 - How Many Left?
This lesson encourages the students to explore the familiar set model of subtraction. The students write story problems and find differences using sets, including subtracting all and subtracting zero. They record the differences in a chart.
Lesson 3 - Where Will I Land?
In this lesson, the students find differences using the number line, a continuous model for subtraction. [Number can be considered in two ways: discrete and continuous. The counting and set models use the discrete form of number.] Students are encouraged to predict differences and to compose puzzles involving subtraction.
Lesson 4 - What Balances?
This lesson encourages students to explore another meaning of subtraction, the balance. They use subtraction facts to generate related addition facts and explore at the concrete level the idea of subtraction as the inverse of addition.
Lesson 5 - Who's in the Fact Family?
In this lesson, the exploration of the relation of addition to subtraction is continued as the students use problem-solving skills to find fact families, including those in which one addend is zero or in which the addends are alike.
Lesson 6 - What's the Difference?
During this lesson, students use reasoning to find differences from numbers up to 10, using real and virtual calculators and an addition chart as tools. They also play a concentration game.
