## Learning Math: Number and Operations

# Classroom Case Studies, 3-5

## Watch this program in the 10th session for grade 3-5 teachers. Explore how the concepts developed in this course can be applied through case studies of grade 3-5 teachers (former course participants) who have adapted their new knowledge to their classrooms.

**In This Session:**

**Part A:**Observing a Case Study

**Part B:**Reasoning About Number and Operations

**Part C:**Problems That Illustrate Reasoning About Number and Operations

**Homework**

In the previous sessions, you explored number and operations as a mathematics learner, both to analyze your own approach to solving problems and to gain some insight into your personal conception of number and operations. It may have been difficult to separate your thinking as a mathematics learner from your thinking as a mathematics teacher — most teachers think about teaching as they are learning and think about learning as they are teaching. In this session, we shift the focus to your own classroom and to the approaches your students might take to mathematical tasks involving number and operations concepts.

As in other sessions, you will be prompted to view short video segments throughout the session; you may also choose to watch the full-length video for this session. See Note 1 below.

**LEARNING OBJECTIVES**

In this session, you will do the following:

• Explore the development of number and operations concepts at your grade level

• Examine students understanding of number and operations concepts

• Explore how you would teach problems involving different number and operations concepts

### Notes

**Note 1**

This session uses classroom case studies to examine how students in grades 3-5 think about and work with number and operations. If possible, work on this session with another teacher or a group of teachers. Using your own classroom and the classrooms of fellow teachers as case studies will allow you to make additional observations.

### Key Terms

**Previously Introduced**

even numbers

Even numbers are integers divisible by 2. Any number that ends with the digit 0, 2, 4, 6, or 8 is an even number.

**factor**

A factor of a number is a counting number that divides evenly into that number. For example, 3 is a factor of 15, since 3 divides evenly into 15 (five times). Four is not a factor of 15, but it is a factor of 16.

**prime number**

A counting number is a prime number if it has exactly two factors: 1 and the number itself. For example, 17 is prime, 16 is not prime, and 1 itself is not prime, since it has only one factor.

New in This Session

cubic number

A cubic number is obtained as a result of multiplying a number by itself three times. For example, 1 (i.e., 1^{3} or 1 • 1 • 1), 8 (i.e., 2^{3} or 2 • 2 • 2), 27 (i.e., 3^{3} or 3 • 3 • 3), 64 (i.e., 4^{3} or 4 • 4 • 4), and so on, are cubic numbers. Cubic numbers of dots can be arranged to make a cube.

**square number**

A square number is obtained by multiplying a number by itself (e.g., 1, 4, 9, 25, …).

**triangular number
**

A triangular number is a number obtained as the sum of consecutive integers. For example, 1 (i.e., 0 + 1), 3 (i.e., 1 + 2), 6 (i.e., 1 + 2 + 3), 10 (i.e., 1 + 2 + 3 + 4), and so on are triangular numbers.