I have been leading a math group for my daughter's first grade class. We name the club "Mathsters". Here is a list of activities that worked out great for us.
We are bound by our own conception of self. We are all much more capable than we give ourselves credit for. There are no limits. There are no comparisons between smart and dumb. Give kids the space to fail and succeed. All kids can do math. The problem is that math is taught all wrong. Math is a process and way of thinking through problems.
For inspiration here are some great math youtube channels:
Have students practice adding up triangle numbers.
Pascal's triangle on butcher paper
Give each student or pairs of students a large piece of butcher paper. With a yard stick draw a line down the middle from top to bottom and then mark off 2-3 inch rows. Fill in pascal's triangle starting at the top. As they progress point out various patterns that emerge. On the diagonals point out the ordinal and triangle numbers (see Triangle Numbers).
This is a great exercise in deduction. Help the students to reason through the puzzle instead of guessing. Students are often very confused about how to do the puzzles. Walk them through it until it clicks. Once they see how to think through it they really enjoy these.
Using facecards sort out the numbers. Pair up the students and have them play war by both laying cards down at the same time. The first one to call out the sum gets the cards. The person with the most cards wins.
You could also add a dice in for an extra challenge. Lay down the two cards and roll a dice. They have to add up all three numbers.
Another variation is they could multiply the numbers instead.
Stuck in the mud
Give each student 5 dice. Roll the dice. Take away all 5s and 1s. Add up the remaining dice. Keep a rolling sum between turns each time eliminating 5s and 1s. When all dice are eliminated you will have your final score. Try to see what the highest number each student can get.
Given a list of cartesian coordinates draw the shape on the plane. You could also do the reverse and have them create shapes and then share the coordinates with classmates and see if they can reproduce the shape from the coordinates.