GRADE LEVEL/SUBJECT: K-5, (gifted & talented) Primary mathematics, including Kindergarten, grades 1 through 3. Originally planned for gifted students, but tried and adapted for heterogeneous classrooms, where it can also be very successful. Students will recognize and explore the patterns based on their current concept level with numbers. First and Second Graders will instantly make connections to the idea of multiplication. Third Graders will refine and extend that same concept.

OVERVIEW: In mathematics education today, there is a growing awareness that the following is true: children need experience with problem-solving, math instruction can be inquiry-based, and the use of calculators should be introduced and applied at every level. This lesson was designed along these lines, and can be further adapted by individual teachers to suit their own needs and purposes.

PURPOSE: This lesson was designed to allow young children to explore number patterns and relationships while introducing them to the calculator at the same time. Please note that this will be easier for some children than others, but all children are highly motivated by the use of the calculator, and even a child having difficulty with the underlying concepts is usually rewarded by mastering the ability to use the "counting constant" function and the practice in following directions and sequencing that requires. As an inquiry-based lesson, particularly with students talented in mathematics, you may want to rely on their own "discoveries" to generate the questions and explorations. Another approach, more structured, will model for students how to use the counting constant function as a way to set up "pattern puzzles" for other students to solve. In creating their own puzzles, they are essentially required to explain the strategies with which they can solve these puzzles, all the while practicing higher-level thinking skills. In either case, the activity is engrossing and is a sure way to stimulate enthusiasm, excitement, and an appreciation for numbers.

OBJECTIVE(s): Students will learn how to use the "counting constant" function of the calculator, and using this function will explore patterns and relationships with numbers, including the concept of multiples and negative numbers. Students will demonstrate their mastery of the function with the calculator with the creation of "pattern puzzles" that they will share with other students. For evaluation, all students will explain in their own words the strategies they have discovered for solving each other's puzzles.

RESOURCES/MATERIALS: It is recommended that a classroom set of calculators be used. Texas Instruments TI-108 works well even with Kindergarteners. Their overhead projector calculator will work for a class presentation type of lesson, although that prohibits the ability for the children to learn how to use the counting constant function and explore on their own. The only other supplies would be paper and pencil. Encourage children to organize their numbers for themselves, perhaps after seeing a model that the whole class can follow.

ACTIVITIES AND PROCEDURES: Students will need their own calculators, or an alternative would be to use a transparent calculator designed for use on an overhead projector. Introduce the idea of the "counting constant" and demonstrate how to make the calculator count. (Note: this varies from instrument to instrument, but is usually based on the following simple "code"--punch 1+1= then continue to punch the = button continually to have the calculator count sequentially. By changing the "code" students will be able to begin to explore patterns, i.e. 2+2 = ?, 6+6 = ?, 100+100 = ?, etc. The same works for subtraction, starting say at 100-1 = ?, or 100-5 = ?)

Students will discover what the calculator does after 0. This has never failed to generate curiosity and excitement. You can then explain further the concept of negative numbers, or simply allow children to explore on their own, attempting then to explain the nature of these numbers, comparing them to other concepts of "negative" (a wonderful extension into metaphor and language-or history, as one class of third graders did, noting the similarities to our current calendar system, by examining a historical timeline, etc.)

Model for students a pattern puzzle: 4, 8, 12, 16, ____what comes next? Or, 24, 28, 32, ____, 40, ____, 48, ____? Fill in the missing numbers.

These pattern puzzles can be presented on level for whatever-aged group you are working with. Most Kindergarteners are working with numbers in sequence 1-100. They happily explore counting "forwards and backwards". First and Second Graders explore concepts of multiples, and it is a terrific way to introduce multiplication as patterns of numbers. After demonstrating the counting constant function with 1 and 5, challenge students to find more interesting (less predictable) patterns such as the following:

0, 6, ____, 18, 24, ____, 36, 42, ____, 54, 60.

Third Graders are often ready to play with patterns with zero, and multiples of ten. This extends the activity beyond number concept and into place value. To create a cooperative learning model for these activities, have children work with partners or teams in the creation of the pattern puzzles, and trade them with other teams for solving.

TYING IT ALL TOGETHER: At the end of the lesson, give students the opportunity to explain their strategies for solving the pattern puzzles, either using the calculator and the counting constant function, or pencil and paper, or their heads. You should get an excellent idea of where each child stands with number concept and/or place value. To allow further exploration and extensions as well as calculator practice, set up as an independent math lab activity. Post pattern puzzles for viewing and allow other students to attempt to solve.

SUGGESTIONS/MODIFICATIONS

• Teachers may have the children share calculators or simply model their functions on the board.
• Students may use calculators, share calculators, or create a paper model of the functions of a calculator at their seats.
• Students may complete the drills of this lesson with or without a calculator, but could be encouraged to have a classroom project to request calculators from a near by company or donor if necessary.