## How Many More Fish?

Pre-K-2

This unit focuses on comparative subtraction. The students use fish-shaped crackers to explore five meanings for the operations of subtraction (counting, sets, number line, balance, and inverse of addition). Comparative subtraction extends the students early understandings about counting, addition, and subtraction in the take-away mode. Students investigate properties of subtraction, represent subtraction in objects and pictures, and record subtraction in both vertical notation and equations. They create and solve problems involving comparative subtraction. They answer questions such as, "How many more?" and, "How many less?" Missing addend activities provide students with an experience in algebraic thinking.

### Counting Back

Pre-K-2
Students count back to compare plates of fish-shaped crackers, and then they record the comparison in vertical and horizontal format. They apply their skills of reasoning and problem solving during this lesson in several ways. [Because students have associated the word "more" with addition, the comparative approach to subtraction is typically more challenging for the students to understand.]

### How Many More?

Pre-K-2
Students write subtraction problems, model them with sets of fish-shaped crackers, and communicate their findings in words and pictures. They record differences in words and in symbols. The additive identity is reviewed in the context of comparing equal sets.

### Hopping Backward to Solve Problems

Pre-K-2
In this lesson, students determine differences using the number line to compare lengths. Because this meaning is based on linear measurement, it is a distinctly different representation from the meanings presented in Lessons One and Two. At the end of the lesson, the students use reasoning and problem solving to predict differences and to answer puzzles involving subtraction.

### Balancing Equations

Pre-K-2
This lesson encourages the students to explore another meaning for operations of subtraction, the balance. This meaning leads naturally into recording with equations. The students will imitate the action of a pan balance and record the modeled subtraction facts in equation form.

### Fact Family Fun

Pre-K-2
In this lesson, the relation of addition to subtraction is explored with fish-shaped crackers. The students search for related addition and subtraction facts for a given number and also investigate fact families when one addend or the difference is 0.

### Wrapping Up the Unit

Pre-K-2
During this final lesson in the unit, the students use the mathematical knowledge and skills developed in the previous lessons as they visit five stations to review comparative subtraction.