Chapter 4 — worked answers and marking guidance
All chapter review and practice examination items
Chapter review solutions
Calculate 24 × 8 using a split or friendly number.
Split 24 into 20 + 4. Then multiply each part by 8 and add the partial products.
Calculate 45 × 3.
45 × 3 = (40 × 3) + (5 × 3) = 135. Each partial product uses its correct place value.
Calculate 72 × 7.
72 × 7 = (70 × 7) + (2 × 7) = 504. Each partial product uses its correct place value.
Calculate 82 × 80.
80 represents 8 tens. Multiply by 8, then scale by 10 to obtain 6,560.
Find 38 × 30 using an area model or partial products.
Expand (30+8)(30+0) = 900+0+240+0 = 1140.
Find 361 × 55 using an area model or partial products.
Expand (360+1)(50+5) = 18000+1800+50+5 = 19855.
Calculate 26 × 6 using a split or friendly number.
Split 26 into 20 + 6. Then multiply each part by 6 and add the partial products.
Calculate 51 × 3.
51 × 3 = (50 × 3) + (1 × 3) = 153. Each partial product uses its correct place value.
Calculate 18 × 5.
18 × 5 = (10 × 5) + (8 × 5) = 90. Each partial product uses its correct place value.
Calculate 182 × 30.
30 represents 3 tens. Multiply by 3, then scale by 10 to obtain 5,460.
Find 66 × 18 using an area model or partial products.
Expand (60+6)(10+8) = 600+480+60+48 = 1188.
Find 177 × 20 using an area model or partial products.
Expand (170+7)(20+0) = 3400+0+140+0 = 3540.
Calculate 25 × 9 using a split or friendly number.
Split 25 into 20 + 5. Then multiply each part by 9 and add the partial products.
Calculate 88 × 7.
88 × 7 = (80 × 7) + (8 × 7) = 616. Each partial product uses its correct place value.
Calculate 158 × 7.
158 × 7 = (150 × 7) + (8 × 7) = 1106. Each partial product uses its correct place value.
Calculate 189 × 30.
30 represents 3 tens. Multiply by 3, then scale by 10 to obtain 5,670.
Find 66 × 50 using an area model or partial products.
Expand (60+6)(50+0) = 3000+0+300+0 = 3300.
Find 357 × 15 using an area model or partial products.
Expand (350+7)(10+5) = 3500+1750+70+35 = 5355.
Calculate 23 × 4 using a split or friendly number.
Split 23 into 20 + 3. Then multiply each part by 4 and add the partial products.
Calculate 59 × 4.
59 × 4 = (50 × 4) + (9 × 4) = 236. Each partial product uses its correct place value.
Calculate 111 × 9.
111 × 9 = (110 × 9) + (1 × 9) = 999. Each partial product uses its correct place value.
Calculate 415 × 90.
90 represents 9 tens. Multiply by 9, then scale by 10 to obtain 37,350.
Find 65 × 52 using an area model or partial products.
Expand (60+5)(50+2) = 3000+120+250+10 = 3380.
Find 412 × 26 using an area model or partial products.
Expand (410+2)(20+6) = 8200+2460+40+12 = 10712.
Calculate 26 × 8 using a split or friendly number.
Split 26 into 20 + 6. Then multiply each part by 8 and add the partial products.
Calculate 77 × 4.
77 × 4 = (70 × 4) + (7 × 4) = 308. Each partial product uses its correct place value.
Calculate 166 × 3.
166 × 3 = (160 × 3) + (6 × 3) = 498. Each partial product uses its correct place value.
A student calculates 43 × 5 using only its tens: 40 × 5. What partial product is missing and what is the correct total?
The ones part 3 × 5 = 15 must also be included. The complete product is 215.
A student calculates 84 × 8 using only its tens: 80 × 8. What partial product is missing and what is the correct total?
The ones part 4 × 8 = 32 must also be included. The complete product is 672.
A student calculates 30 × 6 using only its tens: 30 × 6. What partial product is missing and what is the correct total?
The ones part 0 × 6 = 0 must also be included. The complete product is 180.
A student calculates 43 × 90 as 387. Explain why this is ten times too small and correct it.
90 is 9 tens. Multiply 43 by 9 and then by 10, giving 3870.
A student calculates 37 × 40 by multiplying 37 by the tens digit 4 and the ones digit 0, then adding both results without shifting the tens. Explain the error and give the correct product.
The tens digit is worth 40, not 4. Correct: 37 × 40 + 37 × 0 = 1480.
A student calculates 27 × 35 by multiplying 27 by the tens digit 3 and the ones digit 5, then adding both results without shifting the tens. Explain the error and give the correct product.
The tens digit is worth 30, not 3. Correct: 27 × 30 + 27 × 5 = 945.
Practice examination solutions and scoring
Calculate 159 × 4 using a split or friendly number.
Split 159 into 150 + 9. Then multiply each part by 4 and add the partial products.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 42 × 5.
42 × 5 = (40 × 5) + (2 × 5) = 210. Each partial product uses its correct place value.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 116 × 6.
116 × 6 = (110 × 6) + (6 × 6) = 696. Each partial product uses its correct place value.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 267 × 60.
60 represents 6 tens. Multiply by 6, then scale by 10 to obtain 16,020.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Find 18 × 66 using an area model or partial products.
Expand (10+8)(60+6) = 600+60+480+48 = 1188.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Find 297 × 65 using an area model or partial products.
Expand (290+7)(60+5) = 17400+1450+420+35 = 19305.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 73 × 4.
73 × 4 = (70 × 4) + (3 × 4) = 292. Each partial product uses its correct place value.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 185 × 3.
185 × 3 = (180 × 3) + (5 × 3) = 555. Each partial product uses its correct place value.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 293 × 50.
50 represents 5 tens. Multiply by 5, then scale by 10 to obtain 14,650.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Find 39 × 34 using an area model or partial products.
Expand (30+9)(30+4) = 900+120+270+36 = 1326.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Find 153 × 35 using an area model or partial products.
Expand (150+3)(30+5) = 4500+750+90+15 = 5355.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 26 × 4 using a split or friendly number.
Split 26 into 20 + 6. Then multiply each part by 4 and add the partial products.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 162 × 3.
162 × 3 = (160 × 3) + (2 × 3) = 486. Each partial product uses its correct place value.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 248 × 90.
90 represents 9 tens. Multiply by 9, then scale by 10 to obtain 22,320.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Find 61 × 50 using an area model or partial products.
Expand (60+1)(50+0) = 3000+0+50+0 = 3050.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Find 245 × 54 using an area model or partial products.
Expand (240+5)(50+4) = 12000+960+250+20 = 13230.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 94 × 2 using a split or friendly number.
Split 94 into 90 + 4. Then multiply each part by 2 and add the partial products.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 43 × 8.
43 × 8 = (40 × 8) + (3 × 8) = 344. Each partial product uses its correct place value.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 99 × 70.
70 represents 7 tens. Multiply by 7, then scale by 10 to obtain 6,930.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Find 56 × 43 using an area model or partial products.
Expand (50+6)(40+3) = 2000+150+240+18 = 2408.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Find 352 × 54 using an area model or partial products.
Expand (350+2)(50+4) = 17500+1400+100+8 = 19008.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 28 × 6 using a split or friendly number.
Split 28 into 20 + 8. Then multiply each part by 6 and add the partial products.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 89 × 5.
89 × 5 = (80 × 5) + (9 × 5) = 445. Each partial product uses its correct place value.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 49 × 8.
49 × 8 = (40 × 8) + (9 × 8) = 392. Each partial product uses its correct place value.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Find 64 × 12 using an area model or partial products.
Expand (60+4)(10+2) = 600+120+40+8 = 768.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Find 385 × 37 using an area model or partial products.
Expand (380+5)(30+7) = 11400+2660+150+35 = 14245.
Scoring (2 points): Award one point for a sound method and one for the correct result.
Calculate 28 × 9 using a split or friendly number.
Split 28 into 20 + 8. Then multiply each part by 9 and add the partial products.
Scoring (2 points): Award one point for a sound method and one for the correct result.
A student calculates 73 × 7 using only its tens: 70 × 7. What partial product is missing and what is the correct total?
The ones part 3 × 7 = 21 must also be included. The complete product is 511.
Scoring (4 points): Award one point for finding the mistaken step, one for a correct mathematical model, one for the corrected answer, and one for a clear explanation.
A student calculates 78 × 4 using only its tens: 70 × 4. What partial product is missing and what is the correct total?
The ones part 8 × 4 = 32 must also be included. The complete product is 312.
Scoring (4 points): Award one point for finding the mistaken step, one for a correct mathematical model, one for the corrected answer, and one for a clear explanation.
A student calculates 73 × 8 using only its tens: 70 × 8. What partial product is missing and what is the correct total?
The ones part 3 × 8 = 24 must also be included. The complete product is 584.
Scoring (4 points): Award one point for finding the mistaken step, one for a correct mathematical model, one for the corrected answer, and one for a clear explanation.
A student calculates 82 × 70 as 574. Explain why this is ten times too small and correct it.
70 is 7 tens. Multiply 82 by 7 and then by 10, giving 5740.
Scoring (4 points): Award one point for finding the mistaken step, one for a correct mathematical model, one for the corrected answer, and one for a clear explanation.
A student calculates 74 × 45 by multiplying 74 by the tens digit 4 and the ones digit 5, then adding both results without shifting the tens. Explain the error and give the correct product.
The tens digit is worth 40, not 4. Correct: 74 × 40 + 74 × 5 = 3330.
Scoring (4 points): Award one point for finding the mistaken step, one for a correct mathematical model, one for the corrected answer, and one for a clear explanation.
A student calculates 59 × 41 by multiplying 59 by the tens digit 4 and the ones digit 1, then adding both results without shifting the tens. Explain the error and give the correct product.
The tens digit is worth 40, not 4. Correct: 59 × 40 + 59 × 1 = 2419.
Scoring (4 points): Award one point for finding the mistaken step, one for a correct mathematical model, one for the corrected answer, and one for a clear explanation.