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← 4-1 · Flipping or turning digits forms new digits · Transformations Preserve Measures

Flipping or turning digits forms new digits · 8 practice problems

4.NBT.B.44.G.A.3

Generated variants — 8

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 answer: Largest = 652; rotated = 529; difference = 652 - 529 = 123

Representative Problem

From 5 number cards, choose 3 different cards to form the largest possible three-digit number. Then rotate that number 180°180\degree clockwise (turn all three digits at once, as one block) to read a new number, and find the difference between the original number and the rotated number.

Number cards: 00, 11, 22, 55, 66

When a card is turned 180°180\degree, each digit looks like another digit: 0→00 \to 0, 1→11 \to 1, 2→52 \to 5, 5→25 \to 2, 6→96 \to 9. Remember the whole number is flipped at once, so the order of the digits also reverses.

  • The largest three-digit number you can make is [ ].
  • Rotating that number 180°180\degree clockwise gives [ ].
  • Therefore the difference of the two numbers is [ ] −- [ ] == [ ].
0 1 2 5 6
Show solution

Understand

From the number cards 0, 1, 2, 5, 6, pick 3 different cards to build the largest three-digit number. Then turn that number 180 degrees as one block (each digit changes shape and the whole order reverses) to read a new number, and subtract to find the difference.

Givens
  • Number cards available: 0, 1, 2, 5, 6.
  • When a card is turned 180 degrees each digit maps to its upside-down shape (for example 9 to 6, 6 to 9, 5 to 5).
  • The whole number is turned at once, so the digit order also reverses.
  • Exactly 3 different cards are used to form a three-digit number.
Unknowns
  • The largest three-digit number.
  • The number read after turning it 180 degrees.
  • The difference between the two numbers.
Constraints
  • Three distinct cards (no repeats).
  • The first digit cannot be 0 (it must be a three-digit number).

Plan

#2 Make a Systematic List · also uses: #1 Draw a Diagram

To get the largest number I order the usable digits from greatest to least and place them left to right. Then I diagram the 180-degree turn (each digit's new shape, and the reversed order) to read the rotated number, and finally subtract.

Execute

#2 Make a Systematic List 4.NBT.B.4
Order the digits from greatest to least: 6, 5, 2, 1, 0. The largest three-digit number puts the three biggest in the hundreds, tens, and ones places.
largest=652\text{largest} = 652
Bigger digits in higher place values make a bigger number.
#1 Draw a Diagram 4.G.A.3
Turning the digits of 652 each 180 degrees changes their shapes.
6→9,5→2,2→56 \to 9,\quad 5 \to 2,\quad 2 \to 5
A half-turn changes each digit into the shape it looks like upside down.
#1 Draw a Diagram 4.G.A.3
Because the whole number is turned at once, the order reverses too. Reading the turned digits 5, 2, 9 gives the rotated number.
652→180∘529652 \xrightarrow{180^\circ} 529
Spinning a strip of digits halfway flips left-right as well as turning each symbol.
#2 Make a Systematic List 4.NBT.B.4
Find the difference between the original number and the rotated number.
652−529=123652 - 529 = 123
Straightforward multi-digit subtraction once both numbers are known.
Answer: Largest = 652; rotated = 529; difference = 652 - 529 = 123

Review

652 is the biggest three-digit number from the cards, and 529 uses only valid turned digits. 652 - 529 = 123 is a difference consistent with the two numbers.

Guess and check: test a few large candidates, confirm the greatest, then verify the rotation by turning the written number upside down.

Standards · min grade 4

  • 4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Forming the largest number using place value and subtracting to get the difference.
  • 4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Understanding how each digit's shape changes and the order reverses under a 180-degree turn.
💡 Put the biggest digits first to make 652, then turn it upside-down (digits change AND flip order) to get 529 - Grade 4 place-value and subtraction!
Variant 2 answer: Largest = 652; rotated = 529; difference = 652 - 529 = 123

Representative Problem

From 5 number cards, choose 3 different cards to form the largest possible three-digit number. Then rotate that number 180°180\degree clockwise (turn all three digits at once, as one block) to read a new number, and find the difference between the original number and the rotated number.

Number cards: 66, 11, 55, 00, 22

When a card is turned 180°180\degree, each digit looks like another digit: 0→00 \to 0, 1→11 \to 1, 2→52 \to 5, 5→25 \to 2, 6→96 \to 9. Remember the whole number is flipped at once, so the order of the digits also reverses.

  • The largest three-digit number you can make is [ ].
  • Rotating that number 180°180\degree clockwise gives [ ].
  • Therefore the difference of the two numbers is [ ] −- [ ] == [ ].
6 1 5 0 2
Show solution

Understand

From the number cards 6, 1, 5, 0, 2, pick 3 different cards to build the largest three-digit number. Then turn that number 180 degrees as one block (each digit changes shape and the whole order reverses) to read a new number, and subtract to find the difference.

Givens
  • Number cards available: 6, 1, 5, 0, 2.
  • When a card is turned 180 degrees each digit maps to its upside-down shape (for example 9 to 6, 6 to 9, 5 to 5).
  • The whole number is turned at once, so the digit order also reverses.
  • Exactly 3 different cards are used to form a three-digit number.
Unknowns
  • The largest three-digit number.
  • The number read after turning it 180 degrees.
  • The difference between the two numbers.
Constraints
  • Three distinct cards (no repeats).
  • The first digit cannot be 0 (it must be a three-digit number).

Plan

#2 Make a Systematic List · also uses: #1 Draw a Diagram

To get the largest number I order the usable digits from greatest to least and place them left to right. Then I diagram the 180-degree turn (each digit's new shape, and the reversed order) to read the rotated number, and finally subtract.

Execute

#2 Make a Systematic List 4.NBT.B.4
Order the digits from greatest to least: 6, 5, 2, 1, 0. The largest three-digit number puts the three biggest in the hundreds, tens, and ones places.
largest=652\text{largest} = 652
Bigger digits in higher place values make a bigger number.
#1 Draw a Diagram 4.G.A.3
Turning the digits of 652 each 180 degrees changes their shapes.
6→9,5→2,2→56 \to 9,\quad 5 \to 2,\quad 2 \to 5
A half-turn changes each digit into the shape it looks like upside down.
#1 Draw a Diagram 4.G.A.3
Because the whole number is turned at once, the order reverses too. Reading the turned digits 5, 2, 9 gives the rotated number.
652→180∘529652 \xrightarrow{180^\circ} 529
Spinning a strip of digits halfway flips left-right as well as turning each symbol.
#2 Make a Systematic List 4.NBT.B.4
Find the difference between the original number and the rotated number.
652−529=123652 - 529 = 123
Straightforward multi-digit subtraction once both numbers are known.
Answer: Largest = 652; rotated = 529; difference = 652 - 529 = 123

Review

652 is the biggest three-digit number from the cards, and 529 uses only valid turned digits. 652 - 529 = 123 is a difference consistent with the two numbers.

Guess and check: test a few large candidates, confirm the greatest, then verify the rotation by turning the written number upside down.

Standards · min grade 4

  • 4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Forming the largest number using place value and subtracting to get the difference.
  • 4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Understanding how each digit's shape changes and the order reverses under a 180-degree turn.
💡 Put the biggest digits first to make 652, then turn it upside-down (digits change AND flip order) to get 529 - Grade 4 place-value and subtraction!
Variant 3 answer: Largest = 985; rotated = 286; difference = 985 - 286 = 699

Representative Problem

From 5 number cards, choose 3 different cards to form the largest possible three-digit number. Then rotate that number 180°180\degree clockwise (turn all three digits at once, as one block) to read a new number, and find the difference between the original number and the rotated number.

Number cards: 88, 55, 99, 11, 00

When a card is turned 180°180\degree, each digit looks like another digit: 0→00 \to 0, 1→11 \to 1, 5→25 \to 2, 8→88 \to 8, 9→69 \to 6. Remember the whole number is flipped at once, so the order of the digits also reverses.

  • The largest three-digit number you can make is [ ].
  • Rotating that number 180°180\degree clockwise gives [ ].
  • Therefore the difference of the two numbers is [ ] −- [ ] == [ ].
8 5 9 1 0
Show solution

Understand

From the number cards 8, 5, 9, 1, 0, pick 3 different cards to build the largest three-digit number. Then turn that number 180 degrees as one block (each digit changes shape and the whole order reverses) to read a new number, and subtract to find the difference.

Givens
  • Number cards available: 8, 5, 9, 1, 0.
  • When a card is turned 180 degrees each digit maps to its upside-down shape (for example 9 to 6, 6 to 9, 5 to 5).
  • The whole number is turned at once, so the digit order also reverses.
  • Exactly 3 different cards are used to form a three-digit number.
Unknowns
  • The largest three-digit number.
  • The number read after turning it 180 degrees.
  • The difference between the two numbers.
Constraints
  • Three distinct cards (no repeats).
  • The first digit cannot be 0 (it must be a three-digit number).

Plan

#2 Make a Systematic List · also uses: #1 Draw a Diagram

To get the largest number I order the usable digits from greatest to least and place them left to right. Then I diagram the 180-degree turn (each digit's new shape, and the reversed order) to read the rotated number, and finally subtract.

Execute

#2 Make a Systematic List 4.NBT.B.4
Order the digits from greatest to least: 9, 8, 5, 1, 0. The largest three-digit number puts the three biggest in the hundreds, tens, and ones places.
largest=985\text{largest} = 985
Bigger digits in higher place values make a bigger number.
#1 Draw a Diagram 4.G.A.3
Turning the digits of 985 each 180 degrees changes their shapes.
9→6,8→8,5→29 \to 6,\quad 8 \to 8,\quad 5 \to 2
A half-turn changes each digit into the shape it looks like upside down.
#1 Draw a Diagram 4.G.A.3
Because the whole number is turned at once, the order reverses too. Reading the turned digits 2, 8, 6 gives the rotated number.
985→180∘286985 \xrightarrow{180^\circ} 286
Spinning a strip of digits halfway flips left-right as well as turning each symbol.
#2 Make a Systematic List 4.NBT.B.4
Find the difference between the original number and the rotated number.
985−286=699985 - 286 = 699
Straightforward multi-digit subtraction once both numbers are known.
Answer: Largest = 985; rotated = 286; difference = 985 - 286 = 699

Review

985 is the biggest three-digit number from the cards, and 286 uses only valid turned digits. 985 - 286 = 699 is a difference consistent with the two numbers.

Guess and check: test a few large candidates, confirm the greatest, then verify the rotation by turning the written number upside down.

Standards · min grade 4

  • 4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Forming the largest number using place value and subtracting to get the difference.
  • 4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Understanding how each digit's shape changes and the order reverses under a 180-degree turn.
💡 Put the biggest digits first to make 985, then turn it upside-down (digits change AND flip order) to get 286 - Grade 4 place-value and subtraction!
Variant 4 answer: Largest = 952; rotated = 526; difference = 952 - 526 = 426

Representative Problem

From 5 number cards, choose 3 different cards to form the largest possible three-digit number. Then rotate that number 180°180\degree clockwise (turn all three digits at once, as one block) to read a new number, and find the difference between the original number and the rotated number.

Number cards: 99, 11, 22, 00, 55

When a card is turned 180°180\degree, each digit looks like another digit: 0→00 \to 0, 1→11 \to 1, 2→52 \to 5, 5→25 \to 2, 9→69 \to 6. Remember the whole number is flipped at once, so the order of the digits also reverses.

  • The largest three-digit number you can make is [ ].
  • Rotating that number 180°180\degree clockwise gives [ ].
  • Therefore the difference of the two numbers is [ ] −- [ ] == [ ].
9 1 2 0 5
Show solution

Understand

From the number cards 9, 1, 2, 0, 5, pick 3 different cards to build the largest three-digit number. Then turn that number 180 degrees as one block (each digit changes shape and the whole order reverses) to read a new number, and subtract to find the difference.

Givens
  • Number cards available: 9, 1, 2, 0, 5.
  • When a card is turned 180 degrees each digit maps to its upside-down shape (for example 9 to 6, 6 to 9, 5 to 5).
  • The whole number is turned at once, so the digit order also reverses.
  • Exactly 3 different cards are used to form a three-digit number.
Unknowns
  • The largest three-digit number.
  • The number read after turning it 180 degrees.
  • The difference between the two numbers.
Constraints
  • Three distinct cards (no repeats).
  • The first digit cannot be 0 (it must be a three-digit number).

Plan

#2 Make a Systematic List · also uses: #1 Draw a Diagram

To get the largest number I order the usable digits from greatest to least and place them left to right. Then I diagram the 180-degree turn (each digit's new shape, and the reversed order) to read the rotated number, and finally subtract.

Execute

#2 Make a Systematic List 4.NBT.B.4
Order the digits from greatest to least: 9, 5, 2, 1, 0. The largest three-digit number puts the three biggest in the hundreds, tens, and ones places.
largest=952\text{largest} = 952
Bigger digits in higher place values make a bigger number.
#1 Draw a Diagram 4.G.A.3
Turning the digits of 952 each 180 degrees changes their shapes.
9→6,5→2,2→59 \to 6,\quad 5 \to 2,\quad 2 \to 5
A half-turn changes each digit into the shape it looks like upside down.
#1 Draw a Diagram 4.G.A.3
Because the whole number is turned at once, the order reverses too. Reading the turned digits 5, 2, 6 gives the rotated number.
952→180∘526952 \xrightarrow{180^\circ} 526
Spinning a strip of digits halfway flips left-right as well as turning each symbol.
#2 Make a Systematic List 4.NBT.B.4
Find the difference between the original number and the rotated number.
952−526=426952 - 526 = 426
Straightforward multi-digit subtraction once both numbers are known.
Answer: Largest = 952; rotated = 526; difference = 952 - 526 = 426

Review

952 is the biggest three-digit number from the cards, and 526 uses only valid turned digits. 952 - 526 = 426 is a difference consistent with the two numbers.

Guess and check: test a few large candidates, confirm the greatest, then verify the rotation by turning the written number upside down.

Standards · min grade 4

  • 4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Forming the largest number using place value and subtracting to get the difference.
  • 4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Understanding how each digit's shape changes and the order reverses under a 180-degree turn.
💡 Put the biggest digits first to make 952, then turn it upside-down (digits change AND flip order) to get 526 - Grade 4 place-value and subtraction!
Variant 5 answer: Largest = 865; rotated = 298; difference = 865 - 298 = 567

Representative Problem

From 5 number cards, choose 3 different cards to form the largest possible three-digit number. Then rotate that number 180°180\degree clockwise (turn all three digits at once, as one block) to read a new number, and find the difference between the original number and the rotated number.

Number cards: 55, 66, 11, 88, 00

When a card is turned 180°180\degree, each digit looks like another digit: 0→00 \to 0, 1→11 \to 1, 5→25 \to 2, 6→96 \to 9, 8→88 \to 8. Remember the whole number is flipped at once, so the order of the digits also reverses.

  • The largest three-digit number you can make is [ ].
  • Rotating that number 180°180\degree clockwise gives [ ].
  • Therefore the difference of the two numbers is [ ] −- [ ] == [ ].
5 6 1 8 0
Show solution

Understand

From the number cards 5, 6, 1, 8, 0, pick 3 different cards to build the largest three-digit number. Then turn that number 180 degrees as one block (each digit changes shape and the whole order reverses) to read a new number, and subtract to find the difference.

Givens
  • Number cards available: 5, 6, 1, 8, 0.
  • When a card is turned 180 degrees each digit maps to its upside-down shape (for example 9 to 6, 6 to 9, 5 to 5).
  • The whole number is turned at once, so the digit order also reverses.
  • Exactly 3 different cards are used to form a three-digit number.
Unknowns
  • The largest three-digit number.
  • The number read after turning it 180 degrees.
  • The difference between the two numbers.
Constraints
  • Three distinct cards (no repeats).
  • The first digit cannot be 0 (it must be a three-digit number).

Plan

#2 Make a Systematic List · also uses: #1 Draw a Diagram

To get the largest number I order the usable digits from greatest to least and place them left to right. Then I diagram the 180-degree turn (each digit's new shape, and the reversed order) to read the rotated number, and finally subtract.

Execute

#2 Make a Systematic List 4.NBT.B.4
Order the digits from greatest to least: 8, 6, 5, 1, 0. The largest three-digit number puts the three biggest in the hundreds, tens, and ones places.
largest=865\text{largest} = 865
Bigger digits in higher place values make a bigger number.
#1 Draw a Diagram 4.G.A.3
Turning the digits of 865 each 180 degrees changes their shapes.
8→8,6→9,5→28 \to 8,\quad 6 \to 9,\quad 5 \to 2
A half-turn changes each digit into the shape it looks like upside down.
#1 Draw a Diagram 4.G.A.3
Because the whole number is turned at once, the order reverses too. Reading the turned digits 2, 9, 8 gives the rotated number.
865→180∘298865 \xrightarrow{180^\circ} 298
Spinning a strip of digits halfway flips left-right as well as turning each symbol.
#2 Make a Systematic List 4.NBT.B.4
Find the difference between the original number and the rotated number.
865−298=567865 - 298 = 567
Straightforward multi-digit subtraction once both numbers are known.
Answer: Largest = 865; rotated = 298; difference = 865 - 298 = 567

Review

865 is the biggest three-digit number from the cards, and 298 uses only valid turned digits. 865 - 298 = 567 is a difference consistent with the two numbers.

Guess and check: test a few large candidates, confirm the greatest, then verify the rotation by turning the written number upside down.

Standards · min grade 4

  • 4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Forming the largest number using place value and subtracting to get the difference.
  • 4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Understanding how each digit's shape changes and the order reverses under a 180-degree turn.
💡 Put the biggest digits first to make 865, then turn it upside-down (digits change AND flip order) to get 298 - Grade 4 place-value and subtraction!
Variant 6 answer: Largest = 862; rotated = 598; difference = 862 - 598 = 264

Representative Problem

From 5 number cards, choose 3 different cards to form the largest possible three-digit number. Then rotate that number 180°180\degree clockwise (turn all three digits at once, as one block) to read a new number, and find the difference between the original number and the rotated number.

Number cards: 88, 11, 00, 66, 22

When a card is turned 180°180\degree, each digit looks like another digit: 0→00 \to 0, 1→11 \to 1, 2→52 \to 5, 6→96 \to 9, 8→88 \to 8. Remember the whole number is flipped at once, so the order of the digits also reverses.

  • The largest three-digit number you can make is [ ].
  • Rotating that number 180°180\degree clockwise gives [ ].
  • Therefore the difference of the two numbers is [ ] −- [ ] == [ ].
8 1 0 6 2
Show solution

Understand

From the number cards 8, 1, 0, 6, 2, pick 3 different cards to build the largest three-digit number. Then turn that number 180 degrees as one block (each digit changes shape and the whole order reverses) to read a new number, and subtract to find the difference.

Givens
  • Number cards available: 8, 1, 0, 6, 2.
  • When a card is turned 180 degrees each digit maps to its upside-down shape (for example 9 to 6, 6 to 9, 5 to 5).
  • The whole number is turned at once, so the digit order also reverses.
  • Exactly 3 different cards are used to form a three-digit number.
Unknowns
  • The largest three-digit number.
  • The number read after turning it 180 degrees.
  • The difference between the two numbers.
Constraints
  • Three distinct cards (no repeats).
  • The first digit cannot be 0 (it must be a three-digit number).

Plan

#2 Make a Systematic List · also uses: #1 Draw a Diagram

To get the largest number I order the usable digits from greatest to least and place them left to right. Then I diagram the 180-degree turn (each digit's new shape, and the reversed order) to read the rotated number, and finally subtract.

Execute

#2 Make a Systematic List 4.NBT.B.4
Order the digits from greatest to least: 8, 6, 2, 1, 0. The largest three-digit number puts the three biggest in the hundreds, tens, and ones places.
largest=862\text{largest} = 862
Bigger digits in higher place values make a bigger number.
#1 Draw a Diagram 4.G.A.3
Turning the digits of 862 each 180 degrees changes their shapes.
8→8,6→9,2→58 \to 8,\quad 6 \to 9,\quad 2 \to 5
A half-turn changes each digit into the shape it looks like upside down.
#1 Draw a Diagram 4.G.A.3
Because the whole number is turned at once, the order reverses too. Reading the turned digits 5, 9, 8 gives the rotated number.
862→180∘598862 \xrightarrow{180^\circ} 598
Spinning a strip of digits halfway flips left-right as well as turning each symbol.
#2 Make a Systematic List 4.NBT.B.4
Find the difference between the original number and the rotated number.
862−598=264862 - 598 = 264
Straightforward multi-digit subtraction once both numbers are known.
Answer: Largest = 862; rotated = 598; difference = 862 - 598 = 264

Review

862 is the biggest three-digit number from the cards, and 598 uses only valid turned digits. 862 - 598 = 264 is a difference consistent with the two numbers.

Guess and check: test a few large candidates, confirm the greatest, then verify the rotation by turning the written number upside down.

Standards · min grade 4

  • 4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Forming the largest number using place value and subtracting to get the difference.
  • 4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Understanding how each digit's shape changes and the order reverses under a 180-degree turn.
💡 Put the biggest digits first to make 862, then turn it upside-down (digits change AND flip order) to get 598 - Grade 4 place-value and subtraction!
Variant 7 answer: Largest = 852; rotated = 528; difference = 852 - 528 = 324

Representative Problem

From 5 number cards, choose 3 different cards to form the largest possible three-digit number. Then rotate that number 180°180\degree clockwise (turn all three digits at once, as one block) to read a new number, and find the difference between the original number and the rotated number.

Number cards: 55, 11, 00, 88, 22

When a card is turned 180°180\degree, each digit looks like another digit: 0→00 \to 0, 1→11 \to 1, 2→52 \to 5, 5→25 \to 2, 8→88 \to 8. Remember the whole number is flipped at once, so the order of the digits also reverses.

  • The largest three-digit number you can make is [ ].
  • Rotating that number 180°180\degree clockwise gives [ ].
  • Therefore the difference of the two numbers is [ ] −- [ ] == [ ].
5 1 0 8 2
Show solution

Understand

From the number cards 5, 1, 0, 8, 2, pick 3 different cards to build the largest three-digit number. Then turn that number 180 degrees as one block (each digit changes shape and the whole order reverses) to read a new number, and subtract to find the difference.

Givens
  • Number cards available: 5, 1, 0, 8, 2.
  • When a card is turned 180 degrees each digit maps to its upside-down shape (for example 9 to 6, 6 to 9, 5 to 5).
  • The whole number is turned at once, so the digit order also reverses.
  • Exactly 3 different cards are used to form a three-digit number.
Unknowns
  • The largest three-digit number.
  • The number read after turning it 180 degrees.
  • The difference between the two numbers.
Constraints
  • Three distinct cards (no repeats).
  • The first digit cannot be 0 (it must be a three-digit number).

Plan

#2 Make a Systematic List · also uses: #1 Draw a Diagram

To get the largest number I order the usable digits from greatest to least and place them left to right. Then I diagram the 180-degree turn (each digit's new shape, and the reversed order) to read the rotated number, and finally subtract.

Execute

#2 Make a Systematic List 4.NBT.B.4
Order the digits from greatest to least: 8, 5, 2, 1, 0. The largest three-digit number puts the three biggest in the hundreds, tens, and ones places.
largest=852\text{largest} = 852
Bigger digits in higher place values make a bigger number.
#1 Draw a Diagram 4.G.A.3
Turning the digits of 852 each 180 degrees changes their shapes.
8→8,5→2,2→58 \to 8,\quad 5 \to 2,\quad 2 \to 5
A half-turn changes each digit into the shape it looks like upside down.
#1 Draw a Diagram 4.G.A.3
Because the whole number is turned at once, the order reverses too. Reading the turned digits 5, 2, 8 gives the rotated number.
852→180∘528852 \xrightarrow{180^\circ} 528
Spinning a strip of digits halfway flips left-right as well as turning each symbol.
#2 Make a Systematic List 4.NBT.B.4
Find the difference between the original number and the rotated number.
852−528=324852 - 528 = 324
Straightforward multi-digit subtraction once both numbers are known.
Answer: Largest = 852; rotated = 528; difference = 852 - 528 = 324

Review

852 is the biggest three-digit number from the cards, and 528 uses only valid turned digits. 852 - 528 = 324 is a difference consistent with the two numbers.

Guess and check: test a few large candidates, confirm the greatest, then verify the rotation by turning the written number upside down.

Standards · min grade 4

  • 4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Forming the largest number using place value and subtracting to get the difference.
  • 4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Understanding how each digit's shape changes and the order reverses under a 180-degree turn.
💡 Put the biggest digits first to make 852, then turn it upside-down (digits change AND flip order) to get 528 - Grade 4 place-value and subtraction!
Variant 8 answer: Largest = 982; rotated = 586; difference = 982 - 586 = 396

Representative Problem

From 5 number cards, choose 3 different cards to form the largest possible three-digit number. Then rotate that number 180°180\degree clockwise (turn all three digits at once, as one block) to read a new number, and find the difference between the original number and the rotated number.

Number cards: 88, 22, 11, 00, 99

When a card is turned 180°180\degree, each digit looks like another digit: 0→00 \to 0, 1→11 \to 1, 2→52 \to 5, 8→88 \to 8, 9→69 \to 6. Remember the whole number is flipped at once, so the order of the digits also reverses.

  • The largest three-digit number you can make is [ ].
  • Rotating that number 180°180\degree clockwise gives [ ].
  • Therefore the difference of the two numbers is [ ] −- [ ] == [ ].
8 2 1 0 9
Show solution

Understand

From the number cards 8, 2, 1, 0, 9, pick 3 different cards to build the largest three-digit number. Then turn that number 180 degrees as one block (each digit changes shape and the whole order reverses) to read a new number, and subtract to find the difference.

Givens
  • Number cards available: 8, 2, 1, 0, 9.
  • When a card is turned 180 degrees each digit maps to its upside-down shape (for example 9 to 6, 6 to 9, 5 to 5).
  • The whole number is turned at once, so the digit order also reverses.
  • Exactly 3 different cards are used to form a three-digit number.
Unknowns
  • The largest three-digit number.
  • The number read after turning it 180 degrees.
  • The difference between the two numbers.
Constraints
  • Three distinct cards (no repeats).
  • The first digit cannot be 0 (it must be a three-digit number).

Plan

#2 Make a Systematic List · also uses: #1 Draw a Diagram

To get the largest number I order the usable digits from greatest to least and place them left to right. Then I diagram the 180-degree turn (each digit's new shape, and the reversed order) to read the rotated number, and finally subtract.

Execute

#2 Make a Systematic List 4.NBT.B.4
Order the digits from greatest to least: 9, 8, 2, 1, 0. The largest three-digit number puts the three biggest in the hundreds, tens, and ones places.
largest=982\text{largest} = 982
Bigger digits in higher place values make a bigger number.
#1 Draw a Diagram 4.G.A.3
Turning the digits of 982 each 180 degrees changes their shapes.
9→6,8→8,2→59 \to 6,\quad 8 \to 8,\quad 2 \to 5
A half-turn changes each digit into the shape it looks like upside down.
#1 Draw a Diagram 4.G.A.3
Because the whole number is turned at once, the order reverses too. Reading the turned digits 5, 8, 6 gives the rotated number.
982→180∘586982 \xrightarrow{180^\circ} 586
Spinning a strip of digits halfway flips left-right as well as turning each symbol.
#2 Make a Systematic List 4.NBT.B.4
Find the difference between the original number and the rotated number.
982−586=396982 - 586 = 396
Straightforward multi-digit subtraction once both numbers are known.
Answer: Largest = 982; rotated = 586; difference = 982 - 586 = 396

Review

982 is the biggest three-digit number from the cards, and 586 uses only valid turned digits. 982 - 586 = 396 is a difference consistent with the two numbers.

Guess and check: test a few large candidates, confirm the greatest, then verify the rotation by turning the written number upside down.

Standards · min grade 4

  • 4.NBT.B.4 Fluently add and subtract multi-digit whole numbers — Forming the largest number using place value and subtracting to get the difference.
  • 4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Understanding how each digit's shape changes and the order reverses under a 180-degree turn.
💡 Put the biggest digits first to make 982, then turn it upside-down (digits change AND flip order) to get 586 - Grade 4 place-value and subtraction!