P1

P2

P3

P4

P5

P6

P7

P8

Diagnostic Error Codes

[E-1] Placeholder Zero Omission

Omits 0 in ones place when multiplying by tens factor. Emphasize place-value decomposition.

[E-2] Regrouping Sequence Error

Adds carried value before multiplying or fails to add carry to product. Use structured carry boxes.

[E-3] Column Misalignment

Partial products drift across place-value columns, inducing addition errors. Enforce grid columns.

Multiplication Progress Monitor • Guide & Scoring Protocols Page 1 of 5

Answer Key Standard Algorithm Solutions

Step-by-Step Solutions: Probes 1 & 2

Full Partial Products • Both Rows Detailed

Probe 1 Detailed Solution Key Max Score: 6 problems / 24 digits

#1: 34 × 21 714

34

× 21

34 (34×1)

680 (34×20)

714

#2: 48 × 25 1,200

448 • 148

× 25

240 (48×5)

960 (48×20)

1,200

#3: 62 × 34 2,108

62

× 34

248 (62×4)

1860 (62×30)

2,108

#4: 57 × 43 2,451

257 • 257

× 43

171 (57×3)

2280 (57×40)

2,451

#5: 76 × 52 3,952

176 • 376

× 52

152 (76×2)

3800 (76×50)

3,952

#6: 89 × 67 5,963

689 • 589

× 67

623 (89×7)

5340 (89×60)

5,963

Probe 2 Detailed Solution Key Max Score: 6 problems / 24 digits

#1: 43 × 21 903

43

× 21

43 (43×1)

860 (43×20)

903

#2: 36 × 25 900

336 • 136

× 25

180 (36×5)

720 (36×20)

900

#3: 53 × 34 1,802

153 • 053

× 34

212 (53×4)

1590 (53×30)

1,802

#4: 67 × 43 2,881

267 • 267

× 43

201 (67×3)

2680 (67×40)

2,881

#5: 84 × 52 4,368

084 • 284

× 52

168 (84×2)

4200 (84×50)

4,368

#6: 78 × 69 5,382

778 • 478

× 69

702 (78×9)

4680 (78×60)

5,382

Multiplication Progress Monitor • Solution Key (Probes 1 & 2) Page 2 of 5

Answer Key Standard Algorithm Solutions

Step-by-Step Solutions: Probes 3 & 4

Full Partial Products • Both Rows Detailed

Probe 3 Detailed Solution Key Max Score: 6 problems / 24 digits

#1: 32 × 31 992

32

× 31

32 (32×1)

960 (32×30)

992

#2: 44 × 25 1,100

244 • 044

× 25

220 (44×5)

880 (44×20)

1,100

#3: 71 × 35 2,485

71

× 35

355 (71×5)

2130 (71×30)

2,485

#4: 58 × 42 2,436

158 • 358

× 42

116 (58×2)

2320 (58×40)

2,436

#5: 93 × 47 4,371

293 • 193

× 47

651 (93×7)

3720 (93×40)

4,371

#6: 87 × 68 5,916

587 • 487

× 68

696 (87×8)

5220 (87×60)

5,916

Probe 4 Detailed Solution Key Max Score: 6 problems / 24 digits

#1: 42 × 31 1,302

42

× 31

42 (42×1)

1260 (42×30)

1,302

#2: 52 × 25 1,300

152 • 052

× 25

260 (52×5)

1040 (52×20)

1,300

#3: 63 × 35 2,205

163 • 063

× 35

315 (63×5)

1890 (63×30)

2,205

#4: 74 × 42 3,108

074 • 174

× 42

148 (74×2)

2960 (74×40)

3,108

#5: 86 × 53 4,558

186 • 386

× 53

258 (86×3)

4300 (86×50)

4,558

#6: 96 × 67 6,432

496 • 396

× 67

672 (96×7)

5760 (96×60)

6,432

Multiplication Progress Monitor • Solution Key (Probes 3 & 4) Page 3 of 5

Answer Key Standard Algorithm Solutions

Step-by-Step Solutions: Probes 5 & 6

Full Partial Products • Both Rows Detailed

Probe 5 Detailed Solution Key Max Score: 6 problems / 24 digits

#1: 32 × 21 672

32

× 21

32 (32×1)

640 (32×20)

672

#2: 46 × 25 1,150

346 • 146

× 25

230 (46×5)

920 (46×20)

1,150

#3: 52 × 34 1,768

52

× 34

208 (52×4)

1560 (52×30)

1,768

#4: 68 × 43 2,924

268 • 368

× 43

204 (68×3)

2720 (68×40)

2,924

#5: 74 × 52 3,848

074 • 274

× 52

148 (74×2)

3700 (74×50)

3,848

#6: 88 × 67 5,896

588 • 488

× 67

616 (88×7)

5280 (88×60)

5,896

Probe 6 Detailed Solution Key Max Score: 6 problems / 24 digits

#1: 41 × 32 1,312

41

× 32

82 (41×2)

1230 (41×30)

1,312

#2: 38 × 25 950

438 • 138

× 25

190 (38×5)

760 (38×20)

950

#3: 72 × 35 2,520

172 • 072

× 35

360 (72×5)

2160 (72×30)

2,520

#4: 59 × 42 2,478

159 • 359

× 42

118 (59×2)

2360 (59×40)

2,478

#5: 87 × 53 4,611

287 • 387

× 53

261 (87×3)

4350 (87×50)

4,611

#6: 79 × 68 5,372

779 • 579

× 68

632 (79×8)

4740 (79×60)

5,372

Multiplication Progress Monitor • Solution Key (Probes 5 & 6) Page 4 of 5

Answer Key Standard Algorithm Solutions

Step-by-Step Solutions: Probes 7 & 8

Full Partial Products • Both Rows Detailed

Probe 7 Detailed Solution Key Max Score: 6 problems / 24 digits

#1: 31 × 23 713

31

× 23

93 (31×3)

620 (31×20)

713

#2: 42 × 25 1,050

142 • 042

× 25

210 (42×5)

840 (42×20)

1,050

#3: 64 × 34 2,176

164 • 164

× 34

256 (64×4)

1920 (64×30)

2,176

#4: 69 × 43 2,967

269 • 369

× 43

207 (69×3)

2760 (69×40)

2,967

#5: 85 × 52 4,420

185 • 285

× 52

170 (85×2)

4250 (85×50)

4,420

#6: 94 × 68 6,392

394 • 294

× 68

752 (94×8)

5640 (94×60)

6,392

Probe 8 Detailed Solution Key Max Score: 6 problems / 24 digits

#1: 43 × 31 1,333

43

× 31

43 (43×1)

1290 (43×30)

1,333

#2: 56 × 25 1,400

356 • 156

× 25

280 (56×5)

1120 (56×20)

1,400

#3: 65 × 35 2,275

265 • 165

× 35

325 (65×5)

1950 (65×30)

2,275

#4: 73 × 42 3,066

073 • 173

× 42

146 (73×2)

2920 (73×40)

3,066

#5: 83 × 54 4,482

183 • 183

× 54

332 (83×4)

4150 (83×50)

4,482

#6: 97 × 69 6,693

697 • 497

× 69

873 (97×9)

5820 (97×60)

6,693

Tier 2 Targeted Instructional Next Steps

If Score ≤ 2/6: Re-anchor with partial product expansion or area models (\( (30+4) \times (20+1) \)) before returning to standard algorithm compression.

If Score 3–4/6: Practice "Zero First" routine when multiplying by tens digit; isolate regrouping step with differentiated colored highlighters.

Multiplication Progress Monitor • Solution Key (Probes 7 & 8) Page 5 of 5