It is beneficial for students to discover intuitive strategies, as opposed to the teacher presenting strategies to them. Certain proportional reasoning tasks are more likely to elicit intuitive strategies than other tasks. The strategies that students are apt to use when approaching a task, as well as the likelihood of a student's success or…

This article presents a sequence of learning activities that lead to using the area model of multiplication to understand the distributive property (DP). The connection between area and multiplication is an important one, both for algebraic thinking and for geometry, as indicated in two of the critical areas for the third grade in the Common Core…

Presents a technique for multiplying two-digit numbers whose tens digits are equal and whose units digits have a sum of 10. Then various mental calculations with other types of two-digit and larger numbers are discussed. (MNS)

Students who can compute mathematical problems in their heads have learned a skill that is important for estimating and for understanding the number system. Practice activities that can help students master mental computation skills are described. (PP)

Presents five activities focusing on mental computation and estimation for the K-3, 3-5, 4-6, and 6-8 grade levels that require the student, acting as a judge, to review solutions to problems and to pronounce and justify a verdict. Provides suggested materials, questions, possible extensions, answers, and worksheets for each activity. (MDH)

A method of multiplying using fingers is described and an explanation given. The method is then generalized to other number bases. (MP)

Directions are given for preparing a puzzle that may be used to provide practice in computation. (MP)

Using the calculator to do addition and multiplication in base 2 is discussed, with the stress on how to change numbers from one base to another using the calculator. (MNS)

Comments on the history of negative numbers, some methods that can be used to introduce the multiplication of negative numbers to students, and an explanation of why the product of two negative numbers is a positive number are included. (MNS)

This book is designed to introduce and provide motivational practice on basic multiplication facts for students in grades 2-6. The facts are presented in order from 0 through 12, with activities designed to review previously presented facts at three points. A test is provided. Searches, magic squares, mazes, and puzzles are among the activities…

Instructional sequences are presented for teaching two-digit multiplication and division with one- and two-digit divisors using a base-oriented approach. (MN)

This article presents a teaching experiment on the relationship between informal out-of-school and formal in-school mathematics, and the ways each can inform the other in the development of abstract mathematical knowledge. This study concerns the understanding of some aspects of the multiplicative structure of decimal numbers. It involved a series…

Four worksheets and teaching suggestions are presented, with the focus on mental computation for levels 2-3; factors, levels 3-4; and nonroutine problems, levels 5-6 and 7-8. (MNS)

Certain properties of lenses provide a physical model of the mathematical concepts of multiplication of integral numbers and of similarity transformations in geometry. Further, they can provide a realistic concrete representation for rules governing multiplication of signed numbers. Suggestions for problems and classroom demonstrations involving…

A way to use tongue depressors in a model of multiplication is presented. The original intent was to use the sticks to teach about fractions, but "mistakes" in student responses led to new ideas. It is felt that teachers should use the model in teaching multiplication. (MP)