 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            Session 10, Part B:
Reasoning About Number and Operations (40 minutes)

In This Part: Exploring Standards | Examining Students' Reasoning

The National Council of Teachers of Mathematics (NCTM, 2000) has identified number and operations as a strand in its Principles and Standards for School Mathematics. In grades pre-K through 12, instructional programs should enable all students to do the following:

 • Understand numbers, ways of representing numbers, relationships among numbers, and number systems • Understand the meaning of operations and how they relate to one another • Compute fluently and make reasonable estimates

In grades 3-5, students are expected to do the following:

 • Describe classes of numbers according to characteristics such as the nature of their factors • Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers • Develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results

"Throughout their study of numbers, students in grades 3-5 should identify classes of numbers and examine their properties. For example, integers that are divisible by 2 are called even numbers, and numbers that are produced by multiplying a number by itself are called square numbers. Students should recognize that different types of numbers have particular characteristics; for example, square numbers have an odd number of factors, and prime numbers have only two factors" (NCTM, 2000, p. 151).  Problem B1 Try creating your own puzzle. Watch another video segment from Ms. Donnell's class, and think about how the students are developing an understanding of number and operations.   Video Segment In this segment, Ms. Donnell prepares the students to create their own puzzles by discussing how to categorize all of the possible numbers. If you are using a VCR, you can find this segment on the session video approximately 21 minutes and 2 seconds after the Annenberg Media logo.    Problem B2 How does this activity deepen the students' sense of number? Problem B3 What misconceptions might students have about this type of problem? How would you address these misconceptions? Join the discussion! Post your answer to Problem B3 on Channel Talk; then read and respond to answers posted by others. Problem B4 How would you help students figure out which pair of clues would identify a particular number -- for example, 6? Problem B5 What are some ways that you see the NCTM Standards being incorporated into Ms. Donnell's lesson?

 Principles and Standards for School Mathematics Copyright © 2000 by the National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved. This material may not be copied or redistributed electronically or in other formats without written permission from NCTM. standards.nctm.org Standards are listed with the permission of the National Council of Teachers of Mathematics (NCTM). NCTM does not endorse the content or validity of these alignments.   Session 10, Grades 3-5: Index | Notes | Solutions | Video