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Grade 7

Maximizing Rectangular Prism Volume

Directions: Using the whole number 1 through 9, at most one time each, fill in the boxes to list the dimensions of a rectangular prism with the greatest volume. Source: Robert Kaplinsky

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Undefined Quotient with Fraction Division

Directions: Give at least two different examples where the quotient is undefined by filling in the boxes with whole numbers 0 through 9, using each number at most once for each example. Source: Daniel Luevanos

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Product of Distributive Property

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

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Multiply to Make -64

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

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Subtracting Decimals (Middle School)

Directions: Make the smallest (or largest) difference by filling in the boxes using the whole numbers 1-9 no more than one time each. 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

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Dividing Two-Digit Numbers (Middle School)

Directions: Make the smallest (or largest) quotient by filling in the boxes using the whole numbers 1-9 no more than one time each 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

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Adding Two-Digit Numbers (Middle School)

Directions: Make the smallest (or largest) sum by filling in the boxes using the whole numbers 1-9 no more than one time each 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

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Subtracting Two-Digit Numbers (Middle School)

Directions: Make the smallest (or largest) difference by filling in the boxes using the whole numbers 1-9 no more than one time each 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

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