As students translate number words into the language of mathematics they explore number composition, equivalent expressions, and patterns in numbers and words. (MKR)

Presents an integrated mathematics and science activity in which students explore the concept of sampling on a soccer field. (ASK)

Features a question that focuses on the use of cryptology to teach modes. (ASK)

Shares the thinking of one seventh-grade student about his discovery concerning Pythagorean triples during the study of the Pythagorean theorem. (MKR)

Describes a game in which students strengthen their number sense by using mental mathematics to find and check factors and multiples of numbers up to 100. (ASK)

Explores the study of ordered pairs to allow students to demonstrate their own creativity, apply previously learned computer skills, evaluate their own work, and draw connections to other mathematical strands. Using a spreadsheet, students construct a drawing composed of connected ordered pairs, the inverse, and the negative of the drawing. (ASK)

Presents mathematics questions to analyze what advertisements are saying mathematically. (ASK)

Presents two different research tests for teachers to conduct in their classrooms to gain insight into their students' number sense. Provides test results from Taiwan for comparison. (ASK)

Presents an activity that integrates music, dance, and mathematics. (ASK)

Describes an activity in which students investigate the symmetry of factor sets of composite numbers using the TI-83 graphing calculator. This activity allows students to observe patterns, make predictions, and verify their accuracy. (ASK)

Presents an activity in which students must arrange five fractions represented by dominoes in ascending order and justify their reasons for the ordering. Representing common fractions with dominoes helps identify students' misconceptions about fractions. (ASK)

Presents two problems with multiple approaches concerning the one hundredth of something. Describes student attempts at solving these nonroutine problems using a variety of strategies. (ASK)

Defines number sense and gives suggestions and activities for teachers to use in helping students develop number sense, including using process questions, using writing assignments, encouraging invented methods, using appropriate calculation tools, helping students establish benchmarks, and promoting internal questioning. (MKR)

Describes a mathematics activity using square pads of notepaper and sticky notes to do simple paper folding in order to increase students' understanding of fractions. (ASK)

Discusses problems related to teaching decimals and fractions and converting between these two representations. Provides problems and activities that teachers can use in their classrooms to overcome student difficulties related to these subjects. (ASK)