4th Grade Adding and Subtracting Multi-Digit Numbers Test Solutions and Scoring (PDF)

Ones: \(8 + 5 = 13\), carry 1. Tens: \(6 + 4 + 1 = 11\), carry 1. Hundreds: \(9 + 7 + 1 = 17\), carry 1. Thousands: \(5 + 2 + 1 = 8\).

\(8,713\)

Scoring: 2 points for 8,713. 1 point if one carry is missed.

Regroup: 73,204 is 6 ten thousands, 12 thousands, 11 hundreds, 9 tens, and 14 ones.

Ones: \(14 – 7 = 7\). Tens: \(9 – 5 = 4\). Hundreds: \(11 – 9 = 2\). Thousands: \(12 – 8 = 4\). Ten thousands: \(6 – 4 = 2\).

\(24,247\)

Scoring: 2 points for 24,247. 1 point for one place error.

Ones: \(10 – 2 = 8\). Tens: \(9 – 6 = 3\). Hundreds: \(9 – 8 = 1\). Thousands: \(9 – 7 = 2\). Ten thousands: \(8 – 3 = 5\).

Check: \(52{,}138 + 37{,}862 = 90{,}000\).

\(52,138\)

Scoring: 2 points for 52,138. 1 point for correct regrouping with one subtraction error.

Ones: \(4 + 9 = 13\), write 3, carry 1. Tens: \(6 + 5 + 1 = 12\), write 2, carry 1. Hundreds: \(7 + 6 + 1 = 14\), write 4, carry 1. Thousands: \(5 + 7 + 1 = 13\), write 3, carry 1. Ten thousands: \(8 + 1 + 1 = 10\), write 0, carry 1. Hundred thousands: \(2 + 4 + 1 = 7\).

\(703,423\)

Scoring: 2 points for 703,423. 1 point if one carry is missed.

Check: \(3{,}861 + 2{,}739 = 6{,}600\), not 6,500. Maya is not correct.

Correct: 6,500 is 5 thousands, 14 hundreds, 9 tens, and 10 ones. Ones: \(10 – 9 = 1\). Tens: \(9 – 3 = 6\). Hundreds: \(14 – 7 = 7\). Thousands: \(5 – 2 = 3\). The difference is \(3,761\). Check: \(3{,}761 + 2{,}739 = 6{,}500\).

Not correct; \(3,761\)

Scoring: 1 point for the check showing 6,600. 1 point for 3,761.

Ones: \(7 + 5 = 12\), write 2, carry 1. Tens: \(6 + 4 + 1 = 11\), write 1, carry 1. Hundreds: \(3 + 8 + 1 = 12\), write 2, carry 1. Thousands: \(8 + 5 + 1 = 14\), write 4, carry 1. Ten thousands: \(4 + 2 + 1 = 7\).

Noah forgot to carry from the tens to the hundreds, so his hundreds digit is 1 instead of 2. Correct sum: \(74,212\).

Scoring: 1 point for naming the missed carry. 1 point for 74,212.

1. \(18{,}450 – 14{,}963 = 3{,}487\). \(3,487\) seats
2. \(14{,}963 + 16{,}209 = 31{,}172\). \(31,172\) fans
3. \(16{,}209 – 14{,}963 = 1{,}246\). \(1,246\) more fans

Scoring: 1 point for each part.

1. \(12{,}480 + 9{,}765 = 22{,}245\). \(\$22,245.00\)
2. \(22{,}245 – 7{,}950 = 14{,}295\). \(\$14,295.00\)
3. \(14{,}295 + 7{,}950 = 22{,}245\), which is the total raised, so the answer is correct.

Scoring: 1 point for each part.

\(62,185\) rounds to \(60,000\) and \(24,790\) rounds to \(20,000\). Estimate: \(60{,}000 – 20{,}000 = 40{,}000\).

Sofia’s answer, \(47,395\), is more than 7,000 away from the estimate, so it is not reasonable.

Correct difference: \(62{,}185 – 24{,}790 = 37{,}395\), which is close to 40,000.

\(37,395\)

Scoring: 1 point for the estimate and the decision. 1 point for 37,395.