Directions: Using the digits -9 to 9, at most two times each, place a digit in each box so that the function is nondifferentiable at the given x value. Extension: Can you make the function continuous but nondifferentiable? Source: Owen Kaplinsky

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make the function continuous/discontinuous at 3. Source: Owen Kaplinsky

Learn how interactive Open Middle problems let students drag, try, and revise ideas directly on screen.

Directions: Using the digits 0 to 9, at most one time each, place a digit in each box to create equivalent ratios. Source: Lorna McClory

Directions: Using the integers -9 to 9, at most one time each, place an integer in each box to create three quadratic equations: one with two imaginary solutions, one with one real solution, and one with two real (rational or irrational) solutions. Source: Ryan D. Fox

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to find the largest possible Greatest Common Factor for the polynomial. Then factor out the GCF. Extension: Repeat the activity with a two-digit GCF. Source: David Groat

Directions: Using the digits 0 to 9, at most one time each, place a digit in each box to make the equation true. Source: Kate Nerdypoo

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to create two separate quadratic equations. Source: Avanti Yamamoto

Directions: Using the digits 0 to 9, at most one time each, place a digit in each box to make the statement true. The composite figure is made of a rectangular prism and a rectangular pyramid; the base for each is congruent. All dimensions must be greater than zero. Source: Jedidiah Butler

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make a true in equality and a true equation. An extension is to do so while leaving the greatest or smallest number unused. Source: John Joseph Vasko jr