This answer key shows the full solution for each test question and explains how the 20 points are awarded. Partial credit is given when a student sets up the division correctly but makes one arithmetic slip.
Question 1: Divide with one-digit and two-digit divisors (2 points)
a) 7 into 35 is 5 (\(35\)), remainder 0. Bring down 2: 7 does not go into 2, write 0. Bring down 8 to get 28: \(4 \times 7 = 28\). Quotient 504. Check \(7 \times 504 = 3{,}528\).
b) 18 into 19 is 1, \(19 – 18 = 1\). Bring down 9 to get 19: 1, remainder 1. Bring down 8 to get 18: 1, remainder 0. Quotient 111. Check \(18 \times 111 = 1{,}998\).
Scoring: 1 point for each correct quotient.
Question 2: Quotients with larger divisors (2 points)
a) 38 into 95 is 2 (\(76\)), \(95 – 76 = 19\). Bring down 7 to get 197: \(5 \times 38 = 190\), remainder 7. Bring down 6 to get 76: \(2 \times 38 = 76\), remainder 0. Quotient 252.
b) 52 into 64 is 1 (\(52\)), \(64 – 52 = 12\). Bring down 0 to get 120: \(2 \times 52 = 104\), remainder 16. Bring down 7 to get 167: \(3 \times 52 = 156\), remainder 11. Quotient 123 R 11. Check \(52 \times 123 + 11 = 6{,}396 + 11 = 6{,}407\).
Scoring: 1 point for each correct answer. In part b, the remainder must be included.
Question 3: Estimate and divide (2 points)
a) \(8{,}000 : 40 = 200\). Any estimate from 190 to 210 that uses compatible numbers earns the point.
b) 41 into 81 is 1 (\(41\)), \(81 – 41 = 40\). Bring down 1 to get 401: \(9 \times 41 = 369\), remainder 32. Bring down 2 to get 322: \(7 \times 41 = 287\), remainder 35. Quotient 197 R 35. Check \(41 \times 197 + 35 = 8{,}077 + 35 = 8{,}112\).
Scoring: 1 point for a reasonable estimate; 1 point for the exact quotient and remainder.
Question 4: Find the error (2 points)
Check: \(27 \times 168 = 4{,}536\), which is not 4,806, so Liam is not correct.
Divide: 27 into 48 is 1 (\(27\)), \(48 – 27 = 21\). Bring down 0 to get 210: \(7 \times 27 = 189\), remainder 21. Bring down 6 to get 216: \(8 \times 27 = 216\), remainder 0. Check \(27 \times 178 = 4{,}806\).
Liam is not correct; the quotient is 178.
Scoring: 1 point for showing that \(27 \times 168 \ne 4{,}806\); 1 point for the correct quotient 178.
Question 5: Vans for a trip (2 points)
\(389 : 14 = 27\text{ R }11\), because \(14 \times 27 = 378\) and \(389 – 378 = 11\). Twenty-seven vans seat 378 students, so 11 students still need a seat.
28 vans
Scoring: 1 point for the division (27 R 11); 1 point for rounding up to 28 with a reason.
Question 6: Concert tickets (2 points)
\(250 : 16 = 15\text{ R }10\), because \(16 \times 15 = 240\) and \(250 – 240 = 10\).
He can buy 15 tickets and has \$10 left.
Scoring: 1 point for 15 tickets; 1 point for \$10 left.
Question 7: Pencil packing (3 points)
a) \(5{,}880 : 24\): 24 into 58 is 2 (\(48\)), remainder 10. Bring down 8 to get 108: \(4 \times 24 = 96\), remainder 12. Bring down 0 to get 120: \(5 \times 24 = 120\). Quotient 245 boxes.
b) \(245 : 15 = 16\text{ R }5\), because \(15 \times 16 = 240\) and \(245 – 240 = 5\). 16 full cartons and 5 boxes left over.
Scoring: 1 point for part a; in part b, 1 point for 16 full cartons and 1 point for 5 boxes left over.
Question 8: Work backward from a quotient (3 points)
a) The number is \(23 \times 64 + 9 = 1{,}472 + 9 = \)1,481.
b) \(1{,}481 : 31\): 31 into 148 is 4 (\(124\)), remainder 24. Bring down 1 to get 241: \(7 \times 31 = 217\), remainder 24. Quotient 47 R 24. Check \(31 \times 47 + 24 = 1{,}457 + 24 = 1{,}481\).
Scoring: in part a, 1 point for multiplying quotient by divisor and 1 point for adding the remainder; 1 point for part b.
Question 9: Weekly earnings (2 points)
a) \(1{,}404 : 36 = 39\), because \(36 \times 39 = 1{,}404\). \$39 per week.
b) \(2{,}145 : 39 = 55\), because \(39 \times 55 = 2{,}145\). 55 weeks.
Scoring: 1 point for each part.
20 points
See every chapter on the Grade 6 math page.