Problem
The dividend is 4 times the quotient plus remainder 1. Since the quotient ends in 7 and the dividend is in the 60s, the quotient is 17.
Multiplying back from quotient and remainder is the inverse of dividing, so it pins down the dividend exactly.
3.OA.B.6Work BackwardsThe dividend equals the divisor times the quotient plus the remainder — here 4 times 17 plus 1 — which is why it comes out to 69.
Dividing the dividend by 4 sorts it into whole groups of 4 with a small leftover, so rebuilding the dividend means taking those whole groups back together and adding the leftover — the leftover is the remainder 1 and the number of groups is the quotient 17.
The dividend holds 17 whole groups of 4, and 17 groups of 4 is the same amount as 4 counted 17 times, which is 4 times 17.
Seventeen equal groups of 4 is just 4 added over and over, seventeen times, so the total is exactly seventeen 4's.
Seventeen 4's and four 17's fill the very same array of dots, so 17 times 4 and 4 times 17 give the same total.
The 17 whole groups and the single leftover together cover the whole dividend with no gap and nothing counted twice, so adding them returns the dividend.
The dividend is 69, so its hidden ones digit is 9. The quotient is 17, so its hidden tens digit is 1.
Once the dividend is 69, reading its ones digit and the quotient's tens digit is direct.
3.OA.C.7Guess And Check4 goes into 6 once. Quotient digit 1 times divisor 4 gives the partial product 4. Subtracting leaves 2.
Each long-division step multiplies the new quotient digit by the divisor, so the partial product must be 4.
3.OA.C.7Work BackwardsBring down the 9 to make 29. Ones digit 7 times 4 is 28, leaving remainder 1.
The bring-down row 29 and the product 28 differ by exactly the remainder 1, confirming all boxes.
3.OA.C.7Guess And CheckThis only needs Grade 3 division facts: multiply the quotient back to get the dividend, then redo the steps to fill every box!