Mathematics materials for
high ability learners are appropriate when:
- The materials contain a high level
of sophistication of ideas. Topics such as infinity
are explored.
- Opportunities for extensions that
challenge the most able learners are present. Gifted
learners use up resources faster than other students.
There are countless challenging
problems and ideas for lessons on the web.
- Potential exists for tailoring content
to individual needs of high ability learners. There
is something for many different levels, interests,
and backgrounds. Age is not a gatekeeper for activities,
projects, and problems.
- Use of higher order thinking skills.
There are a number of projects and problems that
promote reasoning and problem solving.
- Materials have less emphasis on
basic skills once mastery level has been demonstrated.
Most web sites go beyond what textbooks include.
They do not duplicate textbook-style activities.
- Opportunities for student
exploration based on interest are included. If
students have access to the web directly, they can
find a wealth of rich topics and problems for exploration.
Mathematics
Materials
Beyond Base Ten and Spatial Reasoning (Grades 2-4) are now available for purchase from Prufrock Press. Effective June 1, 2008, the Center for Gifted Education will no longer be processing orders for these two units.
The following mathematics materials are available from
the Center for Gifted Education. Click here to view our curriculum materials descriptions and order form.
Beyond Base Ten
This unit will investigate the concept of place value
and the representation of numbers by using place value
and non-place value systems. Number bases other than Base
10 will be featured, especially through historical contexts
of early civilizations that developed number systems that
are different from the one we use today. Grades 3-6 Spatial
Reasoning
These units approach spatial reasoning through
one-dimensional, two-dimensional, and three-dimensional
tasks. They also ask students to explore the transition
between dimensions and representations of 3-dimensional
objects in 2 dimensions. Grades 2-4 and Grades 6-8
Resource Guide to Mathematics
Curriculum for High Ability Learners in Grades K-8
Revised and available online! (pdf)
Math Curriculum Extensions: Using the Web
(pdf)
Internet Resources
for Mathematics
Web sites are not formal curriculum. Some of the web
sites listed are of interest to teachers as a source
of ideas for classroom instruction and activities. However,
many are accessible and interesting for students to
explore independently. Once you get into one of these
sites, you will discover many other hot links to other
great resources. A trip to the web will not be the same
experience for any two people nor will it be the same
each time you visit. Everything on the web is subject
to change and some changes occur frequently.
The following are among the most comprehensive and
useful web sites that we have encountered. They include
something for all levels of students. Many will link
you to other sites that we have not listed here.
Eisenhower National Clearing
House for Math and Science – goENC.com
This site is useful to both teachers and students alike.
It includes successful lesson plans and student activities.
Mega Math - www.c3.lanl.gov/mega-math
This site is a good teacher resource for inspiration
at many levels of complexity. Each lesson includes activities,
vocabulary, background, big ideas and concepts, evaluation,
prep and materials, NCTM, and further study. Projects
include coloring a map, knots, graphs, algorithms, and
infinity.
K-12 Resources for Mathematics
Education - archives.math.utk.edu/k12.html
This web site is mostly useful for teachers. This site
includes lesson plans from all different states and
specialty schools.
Bob Wilcox's Mathematics Page
- geocities.com/Athens/3352
This link includes a problem of the week and links to
sites all over the web.
Directory of Mathematics Links
- www.math.fsu.edu/Virtual/index.php?f=4
This is a great resource site to lead you to link with
other sites. This specific site would be best accessed
by a teacher and have him/her link to a more appropriate
student oriented program.
Directory of Mathematics Resources
- galaxy.einet.net/galaxy/Science/Mathematics.html
This is also a resource site that will guide you to
other sites. The resources are once again best accessed
by a teacher who can then allow the student to link
to the appropriate sites.
Math Forum - mathforum.org
This site is loaded with information for both students
and teachers. Under the Student Center there are Interactive
Forum Projects and Links for Students. You can also
find a problem of the week under the Projects title
which could be used by teachers or students. Other titles
include Math Tips and Tricks, Beat Calc, Divisibility
Rules, and Multiplication Tips. Under the Link for Students
check out the elementary and middle school student centers.
The Teacher's Place is an excellent resource for K-12
teachers with everything from issues in math education
to Internet math projects. An especially good place
to check out is Steve's Dump, which has dozens of math
resources for the teacher “Ask Dr. Math”
is a great resource for students (or teachers) who have
questions. Dr. Math responds to questions at all levels
by e-mail and responses are accessible in archives on
the site.
Linda Sheffield’s Web
Pages
Linda Sheffield is a mathematics educator who has an
interest in gifted students. She has a large number
of resources listed at her web sites:
Mathematics
Competitions
Mathematics competitions are a good way to encourage
problem solving among mathematically able students who
usually enjoy participating. Sets of old problems are
a good resource for competition practice or classroom
activities. The three contests listed here are among
the most well-known.
American Mathematics Competitions
(AMC) - www.unl.edu/amc
The purpose of the AMC is to increase interest in mathematics
and to develop problem solving ability through a friendly
competition. The questions range in difficulty from
easy to very difficult in order to appeal to a broad
range of students. The exam covers material normally
associated with the 7th and 8th grade mathematics curriculum
including (but not limited to) such topics as the arithmetic
of integers, fractions and decimals, percent and proportion,
number theory, informal geometry, perimeter, area, volume,
probability and statistics, and logical reasoning. Copies
of prior year exams are available for purchase.
MATHCOUNTS - mathcounts.org/
MATHCOUNTS is a national program for competition in
mathematics for 7th and 8th graders. School teams use
materials provided by MATHCOUNTS to practice throughout
the fall. Four students are selected to compete as a
team and as individuals in written and oral competitions
at a local meet held in February. Winners progress to
state and national competitions.
Mathematics Olympiads for Elementary
and Middle Schools - www.moems.org/
These are contest problems that are administered 5 times
during the school year within the school. The top few
scores are sent as the "team score" as part
of the competition. The problems are challenging and
engaging. The elementary section is challenging for
grades 4-6 but precocious third graders have been known
to participate. The middle school level is geared to
grades 7 and 8. The most benefit can be obtained from
this program if the problems are debriefed in a classroom
workshop where strategies are shared. There is a fee
for participating in the competition. Previous problems
are available and are an excellent source of rigorous
problems for upper elementary students who need a challenge.
| Here is a sample Olympiad problem for elementary
grades: |
A H
+ A =
H E E
In the addition problem above, different letters
stand for different digits. A H represents a
two digit number and H E E represents a three
digit number. What number does H E E represent? |
| |
|
| Here is a sample problem from the
Middle School contest problems: |
Of all the mathletes at Smith Middle
School, 80% own computers and 40% are in the band.
However, 10% of all mathletes neither own their
own computers nor are in the band. What percent
of the mathletes both own their own computers
and are in the band?
|
Mathematics Games
Games can provide challenging contexts in which learning
takes place. The following are some suggestions.
Krypto - www.mphgames.com/
This card game for all ages consists of a deck of cards
that contains numbers from 1 to 15. A hand of five cards
is dealt with a sixth or "target" card. The
challenge is to use all five cards and the four basic
operations to get the number on the target card. This
is an excellent game for developing number sense, mental
arithmetic skills, and sharpening computation skills.
It can be played as a whole class, small group, or solitaire
game.
GEMS Math Around the World
- www.lhs.berkeley.edu/gems/
Math Around the World is a unit in the Great Explorations
in Math and Science (GEMS) series, which was developed
by the Lawrence Hall of Science in Berkeley, CA. While
most of the units in this series have science as a primary
focus, with mathematics used as needed, Math Around
the World uses games played in different parts of the
world to integrate math and cultural studies. Eight
games and puzzles from four continents are presented,
including Mancala, NIM, Kalah, and The Tower of Hanoi. |
