Math Packet Answer Key
TEACHER KEY
4th Grade Math Packet Answer Key
Unit 1: Place Value
Lessons 1.1 – 1.3 (Packet Pages 1–6) • Reteach & Enrich Answer Reference
Lesson 1.1 Reteach (R1) Page 1
Find the value of the underlined digit:
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756 → 700
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1,025 → 20
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4,279 → 4,000
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35,703 → 30,000
Compare the values of the underlined digits:
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7 in 700 is 10 times the value of 7 in 70.
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5 in 5,000 is 10 times the value of 5 in 500.
Lesson 1.2 Reteach (R2) Page 3
Read and write each number in two other forms:
1. 40,000 + 1,000 + 300 + 70 + 8
• Standard: 41,378
• Word: forty-one thousand, three hundred seventy-eight
2. twenty-one thousand, four hundred
• Standard: 21,400
• Expanded: 20,000 + 1,000 + 400
3. 391,032
• Word: three hundred ninety-one thousand, thirty-two
• Expanded: 300,000 + 90,000 + 1,000 + 30 + 2
Lesson 1.3 Reteach (R3) Page 5
Compare (<, >, =):
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21,409 > 20,891
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$53,621 < $53,760
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82,550 > 80,711
Order from greatest to least:
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16,451; 16,250; 17,014 → 17,014; 16,451; 16,250
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561,028; 582,073; 549,006 → 582,073; 561,028; 549,006
Lesson 1.1 Enrich (E1) Page 2
Comparing Values (multipliers):
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4 in 3,492 is 100 × value of 4 in 704.
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8 in 8,596 is 100 × value of 8 in 985.
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2 in 2,481 is 1,000 × value of 2 in 5,072.
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3 in 43,158 is 100 × value of 3 in 71,435.
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9 in 495,123 is 10,000 × value of 9 in 63,129.
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5 in 506,712 is 10,000 × value of 5 in 324,859.
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8 in 837,164 is 100,000 × value of 8 in 4,508.
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6 in 631,485 is 1,000 × value of 6 in 682.
9. Stretch: 73,000 and 730 (7 is 1,000×; 3 is 100×).
Lesson 1.2 Enrich (E2) Page 4
Period Posers Riddles:
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Fred: 306,095 • Ned: 127,486
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Ann: 9,418 • Jan: 10,000 (Jan > Ann)
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Mo: 80,700 • Bo: 100,020 (Bo has 1 in 100-thousands place so Bo > Mo).
4. Stretch: Posers will vary (e.g. 2 periods comparing digits).
Lesson 1.3 Enrich (E3) Page 6
Place-Value Puzzle (Filled Digits):
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135,120 > 125,220 > 125,110
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41,900 < 423,900 = 423,900 < 424,900
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279,010 < 288,010 < 297,010
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36,788 > 35,788 = 35,788 > 35,588
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648,138 > 637,294 < 639,705
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476,047 > 463,941 = 463,941 > 386,542
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101,582 > 101,508 > 101,362 > 101,357
8. Write Math: No. If A > B and B > C, then A must be greater than C (transitive property). Ex: 10 > 5 and 5 > 2 → 10 > 2.
Grade 4 Math Key • Houghton Mifflin Harcourt Reteach/Enrich Support Page 1 of 5
TEACHER KEY
4th Grade Math Packet Answer Key
Unit 1: Operations
Lessons 1.4, 1.6, 1.7, 1.8 (Packet Pages 7–14) • Rounding, Addition, Subtraction
Lesson 1.4 Reteach (R4) Page 7
- 672,591 is closer to 700,000 than 600,000, so rounds to 700,000.
Round to place value of underlined digit:
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3,452 → 3,500
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180 → 200
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$72,471 → $70,000
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572,000 → 600,000
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950 → 1,000
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6,495 → 6,000
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835,834 → 840,000
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96,625 → 100,000
Lesson 1.6 Reteach (R6) Page 9
Add Whole Numbers (Estimates & Sums):
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238,503 + 341,978 • Est: 580,000 • Sum: 580,481
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52,851 + 65,601 • Est: 120,000 • Sum: 118,452
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54,980 + 24,611 • Est: 80,000 • Sum: 79,591
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604,542 + 87,106 • Est: 690,000 • Sum: 691,648
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147,026 + 106,792 • Est: 260,000 • Sum: 253,818
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278,309 + 422,182 • Est: 700,000 • Sum: 700,491
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540,721 + 375,899 • Est: 920,000 • Sum: 916,620
Lesson 1.7 Reteach (R7) Page 11
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6,253 − 3,718 • Est: 2,000 • Diff: 2,535
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74,529 − 38,453 • Est: 35,000 • Diff: 36,076
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232,318 − 126,705 • Est: 100,000 • Diff: 105,613
Lesson 1.4 Enrich (E4) Page 8
Rounding Ranges Riddles:
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Near 100 → 500: 450 to 549
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Near 10 → 500: 495 to 504
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Near 1,000 → 3,000: 2,500 to 3,499
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Near 100 → 3,000: 2,950 to 3,049
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Near 100,000 → 600,000: 550,000 to 649,999
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Near 10,000 → 600,000: 595,000 to 604,999
7. Write Math: Ranges in 2, 4, 6 are much smaller because rounding to a smaller place value requires values to be closer to the target.
Lesson 1.6 Enrich (E6) Page 10
Correct Path: A (20,165) + Y (14,292) = A (34,457); 34,457 + R (128,615) = D (163,072).
Riddle: Where can you buy a 3-ft ruler?
AT Y A R D SALE
Lesson 1.7 Enrich (E7) Page 12
Unknown Digits Solutions:
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42,350 − 27,134 = 15,216
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90,731 − 43,795 = 46,936
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241,618 − 128,721 = 112,897
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630,442 − 175,634 = 454,808
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60,347 − 28,759 = 31,588
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700,000 − 238,172 = 461,828
7. Write Math: Use addition as inverse of subtraction to work backwards column by column.
Lesson 1.8 Reteach & Enrich Pages 13–14
R8 (p. 13): 1. 5,923 + 4,182 = 10,105 cans & containers • 2. 4,182 − 216 = 3,966 plastic containers.
E8 (p. 14): 1. 20,562 − 251 = 20,311 • 2. 20,562 − 18,500 = 2,062
- Est: 20,000 − 19,000 = 1,000 • 4. 18,624 + 18,500 = 37,124
5. Write Math: Greater; 6,186 more (20,562 + 18,624 = 39,186 > 33,000).
Grade 4 Math Key • Houghton Mifflin Harcourt Reteach/Enrich Support Page 2 of 5
TEACHER KEY
4th Grade Math Packet Answer Key
Unit 2: 1-Digit Multiplication
Lessons 2.3, 2.4, 2.10, 2.11, 2.12 (Packet Pages 15–24) • Reteach & Enrich
Lesson 2.3 Reteach & Enrich Pages 15–16
R11 (p. 15) Patterns & Products:
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180; 1,800; 18,000
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320; 3,200; 32,000
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360; 3,600; 36,000
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280; 2,800; 28,000
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7 × 3 hundreds = 21 hundreds = 2,100
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5 × 8 thousands = 40 thousands = 40,000
E11 (p. 16) Multiplication Inequalities:
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420 > 400
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700 < 720
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2,400 < 2,500
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2,000 = 2,000
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48,000 > 40,000
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27,000 < 39,000
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5,400 < 5,600
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24,000 = 24,000
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36,000 = 36,000
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7,200 < 9,000
Lesson 2.4 Reteach & Enrich Pages 17–18
R12 (p. 17) Estimate Products:
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1,800
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150
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2,800
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1,500 & 1,800 • 5. 1,400 & 2,100 • 6. 2,400 & 3,200
E12 (p. 18) Find Unknown Factors:
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1,800 = 3 × 624
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500 = 5 × 126
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5,000 = 5 × 957
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900 = 9 × 126
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1,800 = 6 × 273
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6,300 = 7 × 899
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3,200 = 8 × 435
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2,100 = 7 × 273
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30,000 = 5 × 6,149
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6,000 = 2 × 3,044
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9,000 = 3 × 3,044
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45,000 = 5 × 8,756
13. Stretch: 2 × 4,892 (or 5 × 2,134) → Est. 10,000.
Lesson 2.10 Reteach & Enrich Pages 19–20
R18 (p. 19) Multiply 2-Digit with Regrouping:
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42 × 6 = 252 (Est: 240)
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$98 × 6 = $588 (Est: $600)
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37 × 8 = 296 (Est: 320)
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$54 × 9 = $486 (Est: $450)
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37 × 5 = 185 (Est: 200)
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93 × 4 = 372 (Est: 360)
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86 × 9 = 774 (Est: 810)
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59 × 7 = 413 (Est: 420)
E18 (p. 20) Regrouping Review Errors:
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72×8 = 576 (Err: 8×2 is 16, not 26).
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65×9 = 585 (Err: 9×5 is 45, not 54).
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36×5 = 180 (Err: added 5+6=11 instead of 5×6=30).
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47×4 = 188 (Err: 4×40 is 160, not 16).
5. Stretch: Product 44 is smaller than factor 47, impossible when multiplying whole numbers > 1.
Lessons 2.11 & 2.12 Pages 21–24
R19 (p. 21):
- 6,368 • 2. $3,312 • 3. 13,185 • 4. $48,300
E19 (p. 22) Riddle Mystery:
IT'S A M A N A T E E !
L1: M(13) • L2: A(1) • L3: N(14) • L4: A(1) • L5: T(20) • L6: E(5) • L7: E(5)
R20 (p. 23) Multistep:
- 215 + 216 + 25 → n = 456 • 2. 203 + 184 − 56 → n = 331
E20 (p. 24) Same Answer Multistep:
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n = 384 • 2. n = 354
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n = 374 • 4. n = 364
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n = 374 • 6. n = 384
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n = 384 • 8. n = 374
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n = 354 • 10. n = 364
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Ex 6, 7 • 12. Ex 9 • 13. Ex 5, 8 • 14. Ex 4 & 10 both = 364.
Grade 4 Math Key • Houghton Mifflin Harcourt Reteach/Enrich Support Page 3 of 5
TEACHER KEY
4th Grade Math Packet Answer Key
Unit 3: 2-Digit Multiplication
Lessons 3.1, 3.3, 3.5, 3.6 (Packet Pages 25–32) • Reteach & Enrich
Lesson 3.1 Reteach & Enrich Pages 25–26
R21 (p. 25) Multiply by Tens:
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1,800
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1,600
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4,200
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1,500
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4,800
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3,600
E21 (p. 26) Word Problems:
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480 ÷ 24 = 20 cases
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630 ÷ 30 = 21 stacks
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2,000 ÷ 40 = 50 rolls
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3,850 ÷ 10 = 385 strips
5. Write Math: Basic fact 20 ÷ 4 = 5, so 200 tens ÷ 4 tens = 50.
Lesson 3.3 Reteach & Enrich Pages 27–28
R23 (p. 27) Area Models & Partials:
1. 21 × 25: 400 + 100 + 20 + 5 = 525
2. 16 × 14: 100 + 40 + 60 + 24 = 224
3. 24 × 15: 200 + 100 + 40 + 20 = 360
E23 (p. 28) Lattice Method:
1. 31 × 22 = 682 (Lattice sums: 0, 6, 8, 2)
2. 32 × 56 = 1,792 (Lattice sums: 1, 7, 9, 2)
3. Write Math: Diagonals group numbers by place value columns (ones, tens, hundreds) identical to adding partial products.
Lesson 3.5 Reteach & Enrich Pages 29–30
R25 (p. 29) Multiply with Regrouping:
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36 × 12 • Est: 400 • Product: 432
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43 × 29 • Est: 1,200 • Product: 1,247
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51 × 47 • Est: 2,500 • Product: 2,397
E25 (p. 30) Multiplication Mystery:
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800+280+60+21 → 43 × 27 = 1,161
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600+40+180+12 → 32 × 26 = 832
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2,000+280+300+42 → 57 × 46 = 2,622
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3,600+300+300+25 → 65 × 65 = 4,225
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2,100+560+0+0 → 38 × 70 = 2,660
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7,200+270+320+12 → 83 × 94 = 7,802
7. Write Math: #5 because zeros indicate a factor ending in 0.
Lesson 3.6 Reteach & Enrich Pages 31–32
R26 (p. 31) Choose Method:
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76×31 → 2,356 (Est 2,400)
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24×35 → 840 (Est 800)
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14×28 → 392 (Est 300)
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64×56 → 3,584 (Est 3,600)
E26 (p. 32) Product Pairs:
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34×15 = 510 → 30 × 17
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46×25 = 1,150 → 50 × 23
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54×39 = 2,106 → 81 × 26
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75×27 = 2,025 → 45 × 45
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44×32 = 1,408 → 88 × 16
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90×24 = 2,160 → 80 × 27
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64×49 = 3,136 → 56 × 56
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38×35 = 1,330 → 95 × 14
9. Stretch: 20 × 30 = 600 and 15 × 40 = 600.
Grade 4 Math Key • Houghton Mifflin Harcourt Reteach/Enrich Support Page 4 of 5
TEACHER KEY
4th Grade Math Packet Answer Key
Unit 4: Division & Riddles
Lessons 4.5, 4.10, 4.11 (Packet Pages 33–38) & Master Riddle Summary
Lesson 4.5 Reteach (R32) Page 33
Estimate Quotients Using Compatible Numbers:
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252 ÷ 3 → 80 (240÷3)
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546 ÷ 6 → 90 (540÷6)
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2,545 ÷ 4 → 600 (2,400÷4)
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314 ÷ 5 → 60 (300÷5)
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1,578 ÷ 2 → 800 (1,600÷2)
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289 ÷ 8 → 35 or 40 (320÷8)
Lesson 4.5 Enrich (E32) Page 34
Make the Best Estimate (Circled Choices):
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B (545÷8)
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A (251÷3)
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C (780÷9)
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A (350÷9)
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B (593÷6)
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A (1,584÷4)
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C (1,742÷9)
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C (5,026÷7)
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A (532÷2)
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C (483÷4)
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B (198÷4)
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C (141÷6)
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A (8,250÷9)
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A (909÷6)
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B (189÷3)
16. Write Math: Use multiples of divisor to round dividend mentally.
Lesson 4.11 Reteach (R38) Page 37
Divide and Check:
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868 ÷ 4 = 217 (Check: 217 × 4 = 868)
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657 ÷ 2 = 328 r1 (Check: 328 × 2 + 1 = 657)
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8,473 ÷ 7 = 1,210 r3 (Check: 1,210 × 7 + 3 = 8,473)
Lesson 4.10 Reteach & Enrich Pages 35–36
R37 (p. 35) Place First Digit:
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531 ÷ 2 = 265 r1
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628 ÷ 4 = 157
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349 ÷ 9 = 38 r7
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794 ÷ 7 = 113 r3
E37 (p. 36) How Many Digits?
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173 (3 digits • N)
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12 (2 digits • A)
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163 (3 digits • H)
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42 (2 digits • S)
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15 (2 digits • C)
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27 (2 digits • E)
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60 (2 digits • M)
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111 (3 digits • I)
Riddle: What can run but cannot walk?
M A C H I N E S
Lesson 4.11 Enrich (E38) Page 38
What Is Left Over? (Remainders):
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170 ÷ 6 = 28 r2 → Letter F
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130 ÷ 9 = 14 r4 → Letter L
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229 ÷ 8 = 28 r5 → Letter A
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$204 ÷ 7 = 29 r1 → Letter G
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115 ÷ 9 = 12 r7 → Letter S
Riddle: What flies around all day but never goes anywhere?
F L A G S
Packet Riddle & Puzzle Quick Key
p. 10 (E6): 3-Foot Ruler → YARD SALE
p. 22 (E19): Florida Mystery → IT'S A MANATEE!
p. 36 (E37): Run but cannot walk → MACHINES
p. 38 (E38): Flies all day → FLAGS
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