Grade 7

Directions: Decide if 30x – 12 could be a result of using the distributive property. If it is, find the possible combinations of factors whose product would be 30x – 12 (using integer coefficients and constants). Source: adapted from Nathan Charlton

Directions: Find three numbers whose product is -64. You may use integers from -10 to 10. You may not use the same absolute value twice. Find all possible combinations. Source: Nathan Charlton and Daniel Martinez

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make the smallest (or largest) difference. Note: This problem’s difficulty can be adjusted by altering the number of digits (boxes), picking smallest or largest, or by picking either a positive, negative, or both. Source: Robert Kaplinsky

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make the smallest (or largest) quotient. Note: This problem’s difficulty can be adjusted by altering the number of digits (boxes), picking smallest or largest, or by picking either a positive, negative, or both. Source: Robert Kaplinsky

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make the smallest (or largest) sum. Note: This problem’s difficulty can be adjusted by altering the number of digits (boxes), picking smallest or largest, or by picking either a positive, negative, or both. Source: Robert Kaplinsky

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make the smallest (or largest) difference. Note: This problem’s difficulty can be adjusted by altering the number of digits (boxes), picking smallest or largest, or by picking either a positive, negative, or both. Source: Robert Kaplinsky

Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make the smallest (or largest) product. Note: This problem’s difficulty can be adjusted by altering the number of digits (boxes), picking smallest or largest, or by picking either a positive, negative, or both. Source: Robert Kaplinsky

Directions: What is the fewest number of people surveyed if exactly 93.6% of people completed a survey? Source: Robert Kaplinsky

Directions: Using the digits 1 to 9, at most one time each, place a digit in each blank to complete this sentence: Rolling a sum of ___ on two ___-sided dice is the same probability as rolling a sum of ___ on two ___-sided dice. Source: Audrey Mendivil, Daniel Luevanos, and Robert Kaplinsky

Directions: What value(s) have a 1/12 chance of being rolled as the sum of two 6-sided dice? Source: Daniel Luevanos