TITLE: CALCULATOR PATTERN PUZZLES
AUTHOR: Allison Holsten, Alaska
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.