Elementary school math enrichment activities
2014-2019 while my children were in elementary school, I ran a weekly
lunchtime math enrichment program for students at the school. We had
about 35-40 minutes per session, with students from grades 4-7. The
goal was to introduce some fun and interesting extracurricular math
topics; the sessions were almost entirely activity-based, usually in
the form of some game or competition. Some of the students participated
in the Caribou Contest (6x per year, see resources below) and the grade
6 and 7 students participated in the University of Waterloo Gauss
contest (see resources section below), though preparing for these
contests was not the focus.
worksheets below were used during guided activities with elementary
school students between grades 4 and 7, but they would also be
appropriate for older students. They are most appropriate for an
interactive teacher or parent led session with someone who is familiar
with the topic in advance. In some cases, I don't have
the original worksheet, but noted the topic.
of the sessions didn't have specific worksheets, and were based around
solving a set of problems on some topic in the context of a game or
activity that made the session more exciting. I have summarized a few
of the popular activities that I used below. I've also included a list
of resources that I used to find problems and get ideas.
Building the numbers from 1 to 40 using basic operations
the numbers from 1 to N using geometry (motivate by how many games
would need to be played between N people if everyone plays everyone
else exactly once).
Basic combinatorics (counting):
A set of counting problems
Sequences and patterns:
Guessing the next number in a sequence
Some problems with pattern finding
Questions on area and perimeter
A few more area questions
The mathematics of cutting
Introduction to angles
Pythagorus's theorem (elementary proof by rearrangement of shapes).
Area optimization (the mathematics of chicken farming)
Basic geometric constructions (see e.g. www.euclidea.xyz).
Basics of probability
Probability practice questions
A game with dice - You can make use of this simulation
The Josephus problem
The Sieve of Eratosthenes and some questions about primes
Deciphering codes with prime factorization
An introduction to binary numbers
A different introduction to binary and other number systems
Basics of computation with binary numbers and logic gates (followed first worksheet above)
Math with computers:
Using Scratch to calculate things
The seven bridges of Konigsberg
The travelling salesman
The four colour theorem
Finding the heavy/light coin
worksheet with "function machines"
(original examples were lost, but you can fill in each "machine" with a
rule e.g. N -> N + 4 or A,B -> A + B and some input values. The
goal is to fill in the table)
Some algebra problems
A list of algebra problems
Ideas for activities:
1) The "Math Computer": Divide
the students into small groups. Choose a set of problems, number them
and print them, and cut up the sheets so there is one problem on each
piece of paper.
Give the first problem to each group. When the
students have an answer, they can check it by entering the answer on
the "Math Computer" (running on a laptop at the front). If they get it
right, the math computer will tell them how many points they get.
Sometimes, for each point, the group got a raffle ticket placed in a
bin (e.g. if group A got 3 points, they put three tickets marked with
an A in the bin). At the end of the session, I did a draw for prizes.
If students get a wrong answer, you can help them figure out what went
Example: here is a Scratch program
for students to check answers on the "set of counting problems" above
in the Combinatorics section. The answers in this program can be
modified to fit any other set of problems.
2) Envelopes: Divide
the students into small groups. Choose a set of problems on individual
slips of paper, and order them. Label an envelope with the answer to
the first problem and put enough copies of problem 2 for each group in
this envelope. Label a second envelope with the answer to problem 2 and
put copies of question 3 in that envelope and so forth. Continue until
all the problems are in envelopes. You can label an envelope with the
answer to the last problem and fill it with a congratulatory message.
Finally, put a bunch of decoy answers on empty envelopes and place all
the envelopes around the room. Give a copy of the first problem to each
group, and tell them that when they get the answer to a question, they
should find the next question in the envelope with that answer written
3) Treasure hunt: The
worksheets below required the students to work through a series of
problems in order to find the coordinates to a hidden prize on a
treasure map. They could then go and search for the prize using the map.
For example, the following hunts made use of this Treasure Map
Hunt 1 Hunt 2 Hunt 3
Two more hunts with their own map:
Hunt 4 Hunt 5
There were a variety of resources that I used to get ideas while running the sessions.
Books: These are mostly appropriate for the upper elementary school level (or higher):
Math for Smarty Pants
The I Hate Mathematics Book
Math Circles for Elementary School Students
Mathematical Circles Diaries
Moscow Math Circles
The Caribou Contest
runs fun online math contests for students of all ages. Their website
has many past contests, games, etc... The past contests on this site
were an excellent source of problems for all grade levels, though they
are now charging a fee to access all of the past contests.
Another math contest for elementary school students is the Kangaroo Contest. They have a bunch of freely available past contests for different grade levels.
For older grades (5+), there are lots of excellent problems available at the University of Waterloo math and computer contests website. They even have a problem set generator that allows you to specify a topic and difficulty level and get a set of problems.
A lot of reseources on more advanced topics are available at the Art of Problem Solving website. They have a free online learning system called Alcumus with lots of good problems. This site is more oriented for high school students.