Number and Operations

Understanding numbers is a basic mathematical skill. These sites were chosen to address the National Council of Teachers of Mathematics (NCTM) standard #1, Number and Operations, and the Wisconsin Model Academic Standard B, Number Operations and Relationships. Add a new twist to your lessons, or recommend sites to parents and students for a little extra practice. (ECB also provides excellent video resources on numbers and operations for Wisconsin teachers.)

Elementary | Middle School | High School | Teachers | Instructional Video Series for Wisconsin Teachers

Elementary

Learning about Number Relationships, from the NCTM, is interactive and can be completed online or downloaded. In this two-part activity, virtual 100 boards and calculators make it possible to highlight and display various patterns and relationships among numbers. (Linked to grades pre-K-2 number and operations standard; teacher materials provided.)

NCTM's Communicating About Mathematics Using Games: Fraction Track is a game designed to help students learn about fractions. It can be played online or downloaded to a classroom computer. (Linked to grades 3-5 number and operations standard; teacher materials provided.)

More Counting is a set of fun and colorful online counting activities from Cynthia Lanius at Rice University in Texas. Activities such as Let's Count Robots and More or Less Fish give pre-K through grade 1 students an opportunity to practice their number skills. A teacher's guide with alignments to the NCTM standards is included.

All about Ratios, also from Cynthia Lanius, gives students practice with identifying ratios.

These Java Applets for Mathematics give students visual practice with numbers and operations, including counting money and making change, using base 10 blocks, integer bars and fraction bars.

Juice Bottle Jingles, from the Lawrence Hall of Science provides a simple online music machine that integrates number sense and music.

Number Maths, from the Britich Broadcasting Corporation's (BBC) ReviseWise Web site, provides animated tutorials on the number system, fractions, percentages, operations, patterns, and more. Each activity is accompanied by a fact sheet, a printable worksheet, and an online quiz.

In Changemaker from FunBrain.com, students decide how many of each coin or bill would be required to make change from a given sale. Students may pick a difficulty level and currency.

Fun Brain's Linejumper asks students to use a number line to answer simple addition questions. Other games such as Fresh Baked Fractions (identify equivalent fractions) and Number Cracker (identify the next number in a series) also are available.

MacCandy Factory is a set of downloadable simple software programs that allow students to estimate and count using images of candies. The candies may be "packed" into rolls and the rolls into boxes to build a sense of place value. The lesson, intended for about the grade 6 level, includes the use of calculators and optional use of spreadsheets.

Count Us In features 15 simple counting games to play online. Each game also is available in PC or Macintosh format for download.

Coolmath 4Kids features math games such as The Number Monster for practicing addition, subtraction, multiplication, and division.

Simple addition and subtraction practice is available from Count Hoot on the BBC's Little Animals Activity Center. Students click on a ladybug to complete a problem, using either dots (level one) or numerals (level two).

Middle School

Figure This! from NCTM presents mathematics challenges for families. Click on the Math Index to find geometry challenges.

Learning about Multiplication from the NCTM helps students learn to visualize the effects of multiplying a fixed positive number by positive numbers greater than 1 and less than 1, helping them to understand multiplication by fractions and decimals. The activity can be completed online or downloaded. (Linked to grades 6-8 number and operations standard; teacher materials provided.)

Annenberg's Math in Daily Life: Cooking by Numbers demonstrates the practical value of ratios and proportions.

Ask Dr. Math: Selected Answers to Common Questions addresses many questions about numbers and operations. Each section includes background information and additional links. Topics include About Zero, Imaginary Numbers in Real Life, Roman Numerals, Long Division, and many more.

Mathletics, from the University of Virginia, provides four examples of sports that use mathematics. Exercises are provided for each example. A sister site, What Good Is Math?, offers a lively, interactive portrayal of how math is used every day, from shopping to art to sports to cooking.

Fleetkids features Ch-Ching, a change-making game that provides practice with larger amounts of money than the Changemaker site mentioned in the elementary section. Fleetkids sponsored by Fleet Financial Corporation.

Livermore National Laboratory's Mega-Math includes Welcome to the Hotel Infinity, activities designed around a story that explores the concept of infinity. The site includes detailed background information and a good discussion of infinity, as well as vocabulary, big ideas and concepts, and teacher lesson plan.

Visual Fractions is a set of interactive activities using number lines and pie charts to help students understand and then manipulate fractions. Students enter their answers to each problem and get immediate feedback.

High School

Students manipulate a velocity vector to control the movement of an object in Learning About Vectors, from the NCTM. The activity uses a dynamic geometrical representation to help students develop an understanding of vectors and their properties. It can be played online or downloaded. (Linked to grades 9-12 number and operations standard; teacher materials provided.)

The School of Mathematics and Statistics at the University of St. Andrews, Scotland, provides information on Mathematics in Various Cultures. Students will be able to learn about the Babylonian, Egyptian, Greek, Indian, Arabic, and Mayan number systems.

The ABC News.com column Who's Counting offers a sophisticated look at how knowledge of numbers allows us to make sense of a variety of things in the world. For high school students who are wondering about the relevance of numbers to their future, mathematics and journalism professor John Paulos shows how numeracy can help us analyze news reports on anything from the war in Iraq to affirmative action to obesity.

The View from the Back of the Envelope is a Web site all about estimating and its usefulness in the real world. It contains details on how to do rough math and how to use it to answer questions. Some examples include using your body as a ruler and counting by powers of ten.

The Abacus introduces students to the use of this counting and operations tool. It includes an interactive abacus.

The Computer Science Teaching Center provides a tool to convert numbers between decimal and other number systems, base 2-16. An explanation function showing how the conversions are actually done could serve as a review activity or way for students to check their own work. A tutorial and a quiz are also available.

The Prime Pages, from the University of Tennessee, provides an explanation and in-depth exploration of prime numbers, including lists of primes and the largest known prime numbers.

The Math Forum provides more Links to Information on Number Systems.

Teachers

Learning Math: Number and Operation, from the Annenberg Foundation, is a video- and Web-based course for elementary and middle school teachers. It examines the three main categories in the Number and Operations strand of "Principles and Standards of School Mathematics" (NCTM).

Spreadsheets in the Math Class, from a professor at Brigham Young University, provides an explanation and many examples of student spreadsheet activities.

PBS's TeacherSource site provides links to Math lesson plans and activities by grade level and topic. The TeacherLine section provides video clips of teachers modeling lessons.

Wisconsin Model Academic Standards for Mathematics

National Council of Teachers of Mathematics (NCTM) Standards

Instructional Video Series for Wisconsin Teachers
Wisconsin teachers may tape these programs for classroom use. Click on each link to find information about the program, teacher guide and broadcast schedule from the ECB Instructional Database.

How Much? How Many? from Mathematics is Elementary (grades 3-4)

What's a Thousand? from Mathematics is Elementary (grades 3-4)

Is there Action in Fractions? from Mathematics is Elementary (grades 3-4)

What is it Worth? from Mathematics is Elementary (grades 3-4)

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