Problem
The visible cards 3 and 1 aren't 0, so one hidden card must be 0.
Zero times any number is always zero, so a product of 0 means one of the two cards must be 0.
Eliminate Possibilities3.OA.B.5Among single digits, only 5×1 makes 5, so the card paired with the 1 must be 5.
Multiplying a number by 1 leaves it unchanged, so the only number that becomes 5 when multiplied by 1 is 5 itself — that fixes the last card.
Eliminate Possibilities3.OA.C.7The remaining hidden card must be 5.
A pair of cards multiplies to 5, and since the 3 and the 0 card cannot build a 5, that pair has to be the hidden card together with the 1 on card 4 — so the hidden card multiplied by 1 must equal 5.
Multiplying a number by 1 leaves it exactly as it is, so the only card that comes out as 5 after multiplying by 1 is 5 itself.
The four cards are 5, 3, 0, 1 — multiplying the two largest gives 5×3=15, the greatest product.
To make the biggest product, multiply the two largest numbers. Among the four cards, 5 and 3 are the largest, so their product 15 is the greatest possible.
Make A Systematic List3.OA.C.7Zero makes any product 0, and one keeps a number unchanged. These two facts alone reveal the hidden cards and the greatest product, 15.