Mystery Numbers Worksheet Case Files
Mystery Numbers
Place Value & Comparison
Name: ________________________________ Date: ______________
Score: _______ / 20
Directions: Read all three clues for each mystery number. Eliminate choices that break any clue to identify the matching number.
Case 01
The list shows three clues about a number:
Greater than 64,381
Less than 98,456
Digit > 3 in thousands place
Which of these could be the number?
A 62,895
B 74,109
C 82,940
D 99,120
Case 02
The list shows three clues about a number:
Greater than 35,620
Less than 71,400
Digit < 4 in hundreds place
Which of these could be the number?
A 34,980
B 58,725
C 63,218
D 72,015
Case 03
The list shows three clues about a number:
Greater than 48,150
Less than 83,900
Ten thousands digit is odd
Which of these could be the number?
A 67,420
B 42,890
C 85,210
D 75,340
Case 04
The list shows three clues about a number:
Greater than 21,750
Less than 54,300
Tens digit has a value of 60
Which of these could be the number?
A 38,465
B 19,860
C 47,625
D 56,162
Case 05
The list shows three clues about a number:
Greater than 52,400
Less than 89,150
Digit in thousands place is 7
Which of these could be the number?
A 47,800
B 91,720
C 67,345
D 75,280
Number Detective: Place Value Investigation Page 1 of 4 • Cases 1–5
Case Files Mystery Numbers
Name: ___________________________ Date: ______________
Case 06
The list shows three clues about a number:
Greater than 40,290
Less than 76,850
Ones digit is even & > 5
Which of these could be the number?
A 54,318
B 39,846
C 62,504
D 78,128
Case 07
The list shows three clues about a number:
Greater than 18,600
Less than 63,450
Digit > 6 in hundreds place
Which of these could be the number?
A 16,920
B 45,380
C 64,810
D 39,842
Case 08
The list shows three clues about a number:
Greater than 57,820
Less than 92,300
Thousands digit is 0
Which of these could be the number?
A 70,540
B 54,090
C 83,015
D 95,024
Case 09
The list shows three clues about a number:
Greater than 26,450
Less than 68,190
Ten thousands digit > 4
Which of these could be the number?
A 24,800
B 39,720
C 53,814
D 71,200
Case 10
The list shows three clues about a number:
Greater than 73,100
Less than 96,500
Digit < 3 in tens place
Which of these could be the number?
A 84,615
B 71,920
C 88,472
D 97,310
Number Detective: Place Value Investigation Page 2 of 4 • Cases 6–10
Case Files Mystery Numbers 6-Digit Level
Name: ___________________________ Date: ______________
Case 11
The list shows three clues about a number:
Greater than 145,280
Less than 289,600
Ten thousands digit > 5
Which of these could be the number?
A 138,700
B 192,450
C 241,830
D 295,100
Case 12
The list shows three clues about a number:
Greater than 320,400
Less than 560,900
Thousands digit is odd
Which of these could be the number?
A 315,900
B 448,250
C 572,100
D 417,630
Case 13
The list shows three clues about a number:
Greater than 258,300
Less than 495,100
Hundred thousands digit is 3
Which of these could be the number?
A 249,800
B 374,620
C 426,890
D 512,300
Case 14
The list shows three clues about a number:
Greater than 408,650
Less than 735,200
Hundreds digit has value of 800
Which of these could be the number?
A 396,820
B 582,340
C 614,875
D 748,810
Case 15
The list shows three clues about a number:
Greater than 512,000
Less than 840,500
Thousands digit is 0
Which of these could be the number?
A 630,940
B 498,020
C 725,080
D 850,210
Number Detective: Place Value Investigation Page 3 of 4 • Cases 11–15
Case Files Mystery Numbers Final Cases
Name: ___________________________ Date: ______________
Case 16
The list shows three clues about a number:
Greater than 164,750
Less than 398,200
Digit > 7 in tens place
Which of these could be the number?
A 159,890
B 245,630
C 402,190
D 283,594
Case 17
The list shows three clues about a number:
Greater than 82,400
Less than 95,800
Digit < 5 in hundreds place
Which of these could be the number?
A 89,320
B 79,650
C 91,780
D 96,150
Case 18
The list shows three clues about a number:
Greater than 670,500
Less than 895,300
Ten thousands digit is even
Which of these could be the number?
A 658,400
B 741,920
C 835,600
D 912,400
Case 19
The list shows three clues about a number:
Greater than 43,900
Less than 81,250
Thousands digit > 6
Which of these could be the number?
A 38,950
B 54,820
C 83,100
D 68,415
Case 20
The list shows three clues about a number:
Greater than 525,800
Less than 780,400
Thousands digit has value 4,000
Which of these could be the number?
A 614,290
B 518,400
C 659,420
D 794,150
Number Detective: Place Value Investigation Page 4 of 4 • Cases 16–20
Mystery Numbers Answer Key Teacher Key
Mystery Numbers Answer Key
Grade 4 • Place Value
Quick Grading Reference (Cases 1–20) Score: ____ / 20
01B
02C
03D
04A
05C
06A
07D
08A
09C
10A
11B
12D
13B
14C
15A
16D
17A
18B
19D
20A
Case 01: B
74,109: 64,381 < 74,109 < 98,456; thousands digit is 4 (> 3). Eliminations: A < 64,381; C thousands digit is 2; D > 98,456.
Case 02: C
63,218: 35,620 < 63,218 < 71,400; hundreds digit is 2 (< 4). Eliminations: A < 35,620; B hundreds digit is 7; D > 71,400.
Case 03: D
75,340: 48,150 < 75,340 < 83,900; ten thousands digit is 7 (odd). Eliminations: A ten thousands digit is 6 (even); B < 48,150; C > 83,900.
Case 04: A
38,465: 21,750 < 38,465 < 54,300; tens digit is 6 (value 60). Eliminations: B < 21,750; C tens digit is 2 (value 20); D > 54,300.
Case 05: C
67,345: 52,400 < 67,345 < 89,150; thousands digit is 7. Eliminations: A < 52,400; B > 89,150; D thousands digit is 5.
Case 06: A
54,318: 40,290 < 54,318 < 76,850; ones digit is 8 (even and > 5). Eliminations: B < 40,290; C ones digit is 4 (not > 5); D > 76,850.
Case 07: D
39,842: 18,600 < 39,842 < 63,450; hundreds digit is 8 (> 6). Eliminations: A < 18,600; B hundreds digit is 3; C > 63,450.
Case 08: A
70,540: 57,820 < 70,540 < 92,300; thousands digit is 0. Eliminations: B < 57,820; C thousands digit is 3; D > 92,300.
Case 09: C
53,814: 26,450 < 53,814 < 68,190; ten thousands digit is 5 (> 4). Eliminations: A < 26,450; B ten thousands digit is 3; D > 68,190.
Case 10: A
84,615: 73,100 < 84,615 < 96,500; tens digit is 1 (< 3). Eliminations: B < 73,100; C tens digit is 7; D > 96,500.
Mystery Numbers • Full Solution Guide Page 1 of 2 • Solutions 1–10
Teacher Key Mystery Numbers (Cases 11–20)
6-Digit & Challenge Cases
Case 11: B
192,450: 145,280 < 192,450 < 289,600; ten thousands digit is 9 (> 5). Eliminations: A < 145,280; C ten thousands digit is 4; D > 289,600.
Case 12: D
417,630: 320,400 < 417,630 < 560,900; thousands digit is 7 (odd). Eliminations: A < 320,400; B thousands digit is 8 (even); C > 560,900.
Case 13: B
374,620: 258,300 < 374,620 < 495,100; hundred thousands digit is 3. Eliminations: A < 258,300; C hundred thousands digit is 4; D > 495,100.
Case 14: C
614,875: 408,650 < 614,875 < 735,200; hundreds digit is 8 (value 800). Eliminations: A < 408,650; B hundreds digit is 3 (value 300); D > 735,200.
Case 15: A
630,940: 512,000 < 630,940 < 840,500; thousands digit is 0. Eliminations: B < 512,000; C thousands digit is 5; D > 840,500.
Case 16: D
283,594: 164,750 < 283,594 < 398,200; tens digit is 9 (> 7). Eliminations: A < 164,750; B tens digit is 3; C > 398,200.
Case 17: A
89,320: 82,400 < 89,320 < 95,800; hundreds digit is 3 (< 5). Eliminations: B < 82,400; C hundreds digit is 7; D > 95,800.
Case 18: B
741,920: 670,500 < 741,920 < 895,300; ten thousands digit is 4 (even). Eliminations: A < 670,500; C ten thousands digit is 3 (odd); D > 895,300.
Case 19: D
68,415: 43,900 < 68,415 < 81,250; thousands digit is 8 (> 6). Eliminations: A < 43,900; B thousands digit is 4; C > 81,250.
Case 20: A
614,290: 525,800 < 614,290 < 780,400; thousands digit is 4 (value 4,000). Eliminations: B < 525,800; C thousands digit is 9 (value 9,000); D > 780,400.
Instructional Strategies & Common Student Traps
Clue-by-Clue Sieve: Teach students to draw a quick line through choices as soon as a single clue fails rather than evaluating every clue on every number.
Place vs. Value: In Cases 04, 14, and 20, remind students that "value of 800" means an 8 in the hundreds place, not the number ending in 800.
Inequality Reversal: Watch for students confusing "greater than" with "less than" when bounds appear close (e.g., Case 01 comparing 64,381 and 62,895).
Mystery Numbers • Full Solution Guide Page 2 of 2 • Solutions 11–20
Place Value Composition Worksheet TEKS 3.2(A)
Place Value Composition
Numbers to 100,000
Name: ________________________________ Date: ______________
Score: _______ / 20
Directions: Select the best answer for each question. Use place value knowledge and expanded notation rules to solve.
01
Which expression represents the number 47,823 in expanded notation?
A\((4 \times 10,000) + (7 \times 1,000) + (8 \times 100) + (2 \times 10) + (3 \times 1)\)
B\((4 \times 1,000) + (7 \times 100) + (8 \times 10) + (2 \times 1) + 3\)
C\((4 \times 10,000) + (7 \times 100) + (8 \times 1,000) + (2 \times 10) + (3 \times 1)\)
D\((4 \times 100,000) + (7 \times 10,000) + (8 \times 1,000) + (2 \times 100) + (3 \times 10)\)
02
A number is shown in expanded notation: \((6 \times 10,000) + (4 \times 1,000) + (8 \times 10) + (5 \times 1)\). What is this number in standard form?
A 64,850
B 64,805
C 64,085
D 640,085
03
A Texas state park welcomed 83,509 visitors in July. Which expression shows this number in expanded notation?
A\((8 \times 10,000) + (3 \times 1,000) + (5 \times 100) + (9 \times 10)\)
B\((8 \times 10,000) + (3 \times 1,000) + (5 \times 100) + (9 \times 1)\)
C\((8 \times 1,000) + (3 \times 100) + (5 \times 10) + (9 \times 1)\)
D\((8 \times 10,000) + (3 \times 100) + (5 \times 10) + (9 \times 1)\)
04
Look at the expression: \((5 \times 100) + (9 \times 10,000) + (2 \times 1,000) + (6 \times 1)\). Which number is equivalent to this expression?
A 59,206
B 92,506
C 92,560
D 95,206
05
A student counted place value disks to represent a number as shown in the table:
Ten Thousands4
Thousands6
Hundreds2
Tens0
Ones9
Which expression represents the number modeled in the table?
A\((4 \times 10,000) + (6 \times 1,000) + (2 \times 100) + (9 \times 1)\)
B\((4 \times 1,000) + (6 \times 100) + (2 \times 10) + (9 \times 1)\)
C\((4 \times 10,000) + (6 \times 100) + (2 \times 10) + (9 \times 1)\)
D\((4 \times 10,000) + (6 \times 1,000) + (2 \times 10) + (9 \times 1)\)
TEKS 3.2(A) Practice • Place Value & Expanded Notation Page 1 of 4 • Questions 1–5
TEKS 3.2(A) Place Value Composition
Name: ___________________________ Date: ______________
06
Which expression represents the number 70,408 in expanded notation?
A\((7 \times 10,000) + (4 \times 100) + (8 \times 1)\)
B\((7 \times 10,000) + (4 \times 1,000) + (8 \times 10)\)
C\((7 \times 1,000) + (4 \times 100) + (8 \times 1)\)
D\((7 \times 10,000) + (4 \times 10) + (8 \times 1)\)
07
A mystery number is composed of 5 ten thousands, 3 thousands, 9 tens, and 4 ones. What is the standard form of this number?
A 53,904
B 53,940
C 53,094
D 50,394
08
Elena collected base-ten blocks with 3 ten thousands, 15 hundreds, 4 tens, and 6 ones. What number did Elena model?
A 31,546
B 35,460
C 31,506
D 45,460
09
A city library has 29,417 books. Which of the following shows this number written in expanded notation?
A\((2 \times 10,000) + (9 \times 1,000) + (4 \times 10) + (1 \times 10) + (7 \times 1)\)
B\((2 \times 10,000) + (9 \times 1,000) + (4 \times 100) + (1 \times 10) + (7 \times 1)\)
C\((2 \times 1,000) + (9 \times 100) + (4 \times 10) + (1 \times 1) + 7\)
D\((2 \times 10,000) + (9 \times 100) + (4 \times 1,000) + (1 \times 10) + (7 \times 1)\)
10
Which number is equivalent to \((5 \times 10,000) + (8 \times 1,000) + (7 \times 100) + (3 \times 10)\)?
A 58,703
B 58,073
C 58,730
D 580,730
TEKS 3.2(A) Practice • Place Value & Expanded Notation Page 2 of 4 • Questions 6–10
TEKS 3.2(A) Place Value Composition
Name: ___________________________ Date: ______________
11
The standard form of a number is 95,062. How is this number written in expanded notation?
A\((9 \times 10,000) + (5 \times 1,000) + (6 \times 10) + (2 \times 1)\)
B\((9 \times 10,000) + (5 \times 100) + (6 \times 10) + (2 \times 1)\)
C\((9 \times 1,000) + (5 \times 100) + (6 \times 10) + (2 \times 1)\)
D\((9 \times 10,000) + (5 \times 1,000) + (6 \times 100) + (2 \times 1)\)
12
What is the standard form of \((8 \times 10,000) + (6 \times 100) + (4 \times 1)\)?
A 86,004
B 80,640
C 80,604
D 800,604
13
Which equation shows the number 54,230 decomposed correctly into place values?
A\(54,230 = 50,000 + 4,000 + 200 + 30\)
B\(54,230 = 5,000 + 400 + 20 + 3\)
C\(54,230 = 50,000 + 400 + 200 + 30\)
D\(54,230 = 500,000 + 4,000 + 200 + 30\)
14
A place value chart displays place value chips:
Ten Thousands2
Thousands11
Hundreds4
Tens7
Ones3
Which number in standard form represents this collection?
A 21,473
B 31,473
C 31,743
D 211,473
15
The population of a city in Texas is 61,840. Which expression represents 61,840 in expanded notation?
A\((6 \times 10,000) + (1 \times 1,000) + (8 \times 100) + (4 \times 10)\)
B\((6 \times 10,000) + (1 \times 100) + (8 \times 10) + (4 \times 1)\)
C\((6 \times 100,000) + (1 \times 10,000) + (8 \times 1,000) + (4 \times 100)\)
D\((6 \times 1,000) + (1 \times 100) + (8 \times 10) + (4 \times 1)\)
TEKS 3.2(A) Practice • Place Value & Expanded Notation Page 3 of 4 • Questions 11–15
TEKS 3.2(A) Place Value Composition
Name: ___________________________ Date: ______________
16
Which number has an expanded notation of \((7 \times 10) + (4 \times 10,000) + (9 \times 1,000) + (5 \times 100)\)?
A 74,950
B 49,570
C 49,750
D 47,950
17
Which of the following is another way to compose the number 42,650?
A3 ten thousands, 12 thousands, 6 hundreds, 5 tens
B4 ten thousands, 2 thousands, 6 tens, 5 ones
C4 ten thousands, 26 thousands, 5 tens
D2 ten thousands, 22 thousands, 6 hundreds, 5 ones
18
Which expression shows 30,075 in expanded notation?
A\((3 \times 10,000) + (7 \times 10) + (5 \times 1)\)
B\((3 \times 1,000) + (7 \times 10) + (5 \times 1)\)
C\((3 \times 10,000) + (7 \times 100) + (5 \times 1)\)
D\((3 \times 10,000) + (7 \times 1) + (5 \times 10)\)
19
A championship game had an attendance of 52,903 fans. Which expression shows this number in expanded notation?
A\((5 \times 10,000) + (2 \times 1,000) + (9 \times 100) + (3 \times 10)\)
B\((5 \times 10,000) + (2 \times 1,000) + (9 \times 100) + (3 \times 1)\)
C\((5 \times 1,000) + (2 \times 100) + (9 \times 10) + (3 \times 1)\)
D\((5 \times 10,000) + (2 \times 100) + (9 \times 10) + (3 \times 1)\)
20
A number is modeled as \((9 \times 10,000) + (1 \times 1,000) + (14 \times 100) + (6 \times 1)\). What is this number in standard form?
A 91,406
B 92,406
C 92,460
D 914,006
TEKS 3.2(A) Practice • Place Value & Expanded Notation Page 4 of 4 • Questions 16–20
Place Value Composition Answer Key Teacher Key
TEKS 3.2(A) Answer Key
Grade 3 • Numbers to 100,000
Quick Grading Reference (Questions 1–20) Score: ____ / 20
01A
02C
03B
04B
05A
06A
07C
08A
09B
10C
11A
12C
13A
14B
15A
16B
17A
18A
19B
20B
Q 01: A
47,823: 4 ten-thousands is \((4 \times 10,000)\), 7 thousands is \((7 \times 1,000)\), 8 hundreds is \((8 \times 100)\), 2 tens is \((2 \times 10)\), and 3 ones is \((3 \times 1)\). Error Note: Choice B omits ten-thousands; C swaps thousands and hundreds places.
Q 02: C
64,085: \(60,000 + 4,000 + 80 + 5 = 64,085\). Because there is no hundreds term, a zero holds the hundreds place. Error Note: Common student error is omitting the zero placeholder to get 6,485 or misaligning to 64,850.
Q 03: B
83,509: \((8 \times 10,000) + (3 \times 1,000) + (5 \times 100) + (9 \times 1)\). There are 0 tens, so no tens term is needed. Error Note: Choice A incorrectly writes \((9 \times 10)\) instead of ones.
Q 04: B
92,506: Reordering by place value from greatest to least: \((9 \times 10,000) + (2 \times 1,000) + (5 \times 100) + (6 \times 1) = 92,506\). Error Note: Tests recognizing non-standard order rather than reading left-to-right.
Q 05: A
46,209: 4 ten-thousands + 6 thousands + 2 hundreds + 0 tens + 9 ones = \((4 \times 10,000) + (6 \times 1,000) + (2 \times 100) + (9 \times 1)\). Error Note: Choice D uses \((2 \times 10)\) for the hundreds place.
Q 06: A
70,408: \((7 \times 10,000) + (4 \times 100) + (8 \times 1)\). The thousands and tens places have a value of 0. Error Note: Choice B writes 4 thousands instead of 4 hundreds.
Q 07: C
53,094: 5 ten thousands (50,000) + 3 thousands (3,000) + 9 tens (90) + 4 ones (4) = 53,094. Error Note: Students often put 9 in the hundreds place if reading hastily (yielding 53,904).
Q 08: A
31,546: 15 hundreds = 1 thousand and 5 hundreds. Thus: 3 ten thousands (30,000) + 1,500 + 40 + 6 = 31,546. Error Note: Important TEKS 3.2(A) non-standard regrouping skill.
Q 09: B
29,417: \((2 \times 10,000) + (9 \times 1,000) + (4 \times 100) + (1 \times 10) + (7 \times 1)\). Error Note: Choice A uses \((4 \times 10)\) for the hundreds digit 4.
Q 10: C
58,730: \(50,000 + 8,000 + 700 + 30 = 58,730\). Zero holds the ones place. Error Note: Distractor A places 3 in the ones place (58,703).
TEKS 3.2(A) Solutions • Grade 3 Mathematics Page 1 of 2 • Solutions 1–10
Teacher Key TEKS 3.2(A) Solutions (Questions 11–20)
Decomposing & Non-Standard Grouping
Q 11: A
95,062: \((9 \times 10,000) + (5 \times 1,000) + (6 \times 10) + (2 \times 1)\). Hundreds place is 0, so no hundred term exists. Error Note: Choice D incorrectly assigns 6 to hundreds place.
Q 12: C
80,604: \(80,000 + 600 + 4 = 80,604\). Thousands and tens places both require zeros. Error Note: Distractor B confuses 4 ones with 4 tens (80,640).
Q 13: A
54,230: \(50,000 + 4,000 + 200 + 30\). Expanded form adds the value of each non-zero digit. Error Note: Choice C writes 400 instead of 4,000.
Q 14: B
31,473: 2 ten thousands (20,000) + 11 thousands (11,000) = 31,000. Adding 4 hundreds (400) + 7 tens (70) + 3 ones (3) gives 31,473. Error Note: Choice A fails to add the 10 thousands into the ten thousands column.
Q 15: A
61,840: \((6 \times 10,000) + (1 \times 1,000) + (8 \times 100) + (4 \times 10)\). Error Note: Choice C inflates the number to hundred thousands place.
Q 16: B
49,570: \((4 \times 10,000) + (9 \times 1,000) + (5 \times 100) + (7 \times 10) = 40,000 + 9,000 + 500 + 70 = 49,570\). Error Note: Unscrambling places prevents reading the first number as 7 ten thousands.
Q 17: A
42,650: 3 ten thousands (30,000) + 12 thousands (12,000) = 42,000. Plus 6 hundreds (600) + 5 tens (50) = 42,650. Error Note: Choice C creates 66,050 (40,000 + 26,000 + 50).
Q 18: A
30,075: \((3 \times 10,000) + (7 \times 10) + (5 \times 1)\). Both thousands and hundreds are 0. Error Note: Choice B writes \((3 \times 1,000)\) making the total 3,075.
Q 19: B
52,903: \((5 \times 10,000) + (2 \times 1,000) + (9 \times 100) + (3 \times 1)\). Error Note: Choice A uses \((3 \times 10)\) which represents 30 rather than 3.
Q 20: B
92,406: \(90,000 + 1,000 + (14 \times 100 = 1,400) + 6 = 90,000 + 2,400 + 6 = 92,406\). Error Note: Tests regrouping 14 hundreds into 1 thousand and 4 hundreds.
STAAR Success Strategies for TEKS 3.2(A)
Expanded Form vs. Notation: Reinforce that expanded notation uses multiplication with parentheses \((d \times \text{place})\), while expanded form shows added values.
Zero Placeholders: When a term is missing (e.g., Q02, Q06, Q12), require students to write a place value chart with zeros before picking their answer.
Non-Standard Regrouping: For questions like Q08, Q14, and Q20, have students add vertically (\(20,000 + 11,000 + \dots\)) to prevent place value misalignments.
TEKS 3.2(A) Solutions • Grade 3 Mathematics Page 2 of 2 • Solutions 11–20
