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Grade 7

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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Multiplying Two-Digit Numbers (Middle School)

Directions: Make the smallest (or largest) product 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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Interpreting Percentages

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

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Rolling with the Same Probability

Directions: Fill in the blanks to complete this sentence using the whole numbers 1 through 9, no more than one time each. 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

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