← Place the piece with the fewest positions first · Cube Stacks and Their Views

Place the piece with the fewest positions first · 12 practice problems

6.G.A.4

Generated variants — 12

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

Variant 1 easy answer: B and C

The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.

A 1 1 1 1 B 1 1 1 1 C 2 1 1 D 2 1 1 seen from above 1 2 3 2
Show solution
1 · Understandwhat's really being asked

A shape of 8 unit cubes was built from two of the four four-cube pieces. We want which two.

Givens
  • Each of the four pieces is made of four unit cubes.
  • The finished shape holds 8 cubes.
  • Exactly two different pieces were used.
Unknowns
  • The letters of the two pieces.
Constraints
  • The pieces may be turned or flipped, but not overlapped.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #17 Visualize Spatial Relationships#10 Create a Physical Representation

Two pieces of four make eight, so the shape splits exactly in half. Place the piece with the fewest possible positions first: once it is down, what is left has only one shape to recognise.

3 · Execute4 carry out the plan

1Count the cubes

#10 Create a Physical Representation 6.G.A.4
Two pieces of four cubes each.
4+4=84 + 4 = 8
The shape splits exactly in two.

2Find the piece with the fewest places to go

#3 Eliminate Possibilities 6.G.A.4
Piece A fits the shape in only 0 ways, so it is the one to try first.
A:0\text{A}: 0
Fewest options, least guessing.

3Look at what is left

#17 Visualize Spatial Relationships 6.G.A.4
Removing that piece leaves four cubes in one shape, and that shape is one of the four -- possibly turned over.
8−4=48 - 4 = 4
One shape to recognise.

4Name both pieces

#3 Eliminate Possibilities 6.G.A.4
The two that fit are B and C.
B, C\text{B},\ \text{C}
B and C.
Answer: B and C
4 · Reviewdoes it hold up?

No other pairing works: of the six possible pairs, only B with C covers every cube exactly once.

Another way: Trying each pair in turn reaches the same answer, but it means testing six pairs instead of placing one piece.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Decomposing a solid into named pieces.
💡Takeaway. Start with the piece that has the fewest places it could go. Everything after that is forced.
Variant 2 easy answer: A and C

The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.

A 1 1 1 1 B 1 1 1 1 C 2 1 1 D 2 1 1 seen from above 3 2 2 1
Show solution
1 · Understandwhat's really being asked

A shape of 8 unit cubes was built from two of the four four-cube pieces. We want which two.

Givens
  • Each of the four pieces is made of four unit cubes.
  • The finished shape holds 8 cubes.
  • Exactly two different pieces were used.
Unknowns
  • The letters of the two pieces.
Constraints
  • The pieces may be turned or flipped, but not overlapped.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #17 Visualize Spatial Relationships#10 Create a Physical Representation

Two pieces of four make eight, so the shape splits exactly in half. Place the piece with the fewest possible positions first: once it is down, what is left has only one shape to recognise.

3 · Execute4 carry out the plan

1Count the cubes

#10 Create a Physical Representation 6.G.A.4
Two pieces of four cubes each.
4+4=84 + 4 = 8
The shape splits exactly in two.

2Find the piece with the fewest places to go

#3 Eliminate Possibilities 6.G.A.4
Piece B fits the shape in only 0 ways, so it is the one to try first.
B:0\text{B}: 0
Fewest options, least guessing.

3Look at what is left

#17 Visualize Spatial Relationships 6.G.A.4
Removing that piece leaves four cubes in one shape, and that shape is one of the four -- possibly turned over.
8−4=48 - 4 = 4
One shape to recognise.

4Name both pieces

#3 Eliminate Possibilities 6.G.A.4
The two that fit are A and C.
A, C\text{A},\ \text{C}
A and C.
Answer: A and C
4 · Reviewdoes it hold up?

No other pairing works: of the six possible pairs, only A with C covers every cube exactly once.

Another way: Trying each pair in turn reaches the same answer, but it means testing six pairs instead of placing one piece.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Decomposing a solid into named pieces.
💡Takeaway. Start with the piece that has the fewest places it could go. Everything after that is forced.
Variant 3 easy answer: A and C

The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.

A 1 1 1 1 B 1 1 1 1 C 2 1 1 D 2 1 1 seen from above 2 1 3 2
Show solution
1 · Understandwhat's really being asked

A shape of 8 unit cubes was built from two of the four four-cube pieces. We want which two.

Givens
  • Each of the four pieces is made of four unit cubes.
  • The finished shape holds 8 cubes.
  • Exactly two different pieces were used.
Unknowns
  • The letters of the two pieces.
Constraints
  • The pieces may be turned or flipped, but not overlapped.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #17 Visualize Spatial Relationships#10 Create a Physical Representation

Two pieces of four make eight, so the shape splits exactly in half. Place the piece with the fewest possible positions first: once it is down, what is left has only one shape to recognise.

3 · Execute4 carry out the plan

1Count the cubes

#10 Create a Physical Representation 6.G.A.4
Two pieces of four cubes each.
4+4=84 + 4 = 8
The shape splits exactly in two.

2Find the piece with the fewest places to go

#3 Eliminate Possibilities 6.G.A.4
Piece B fits the shape in only 0 ways, so it is the one to try first.
B:0\text{B}: 0
Fewest options, least guessing.

3Look at what is left

#17 Visualize Spatial Relationships 6.G.A.4
Removing that piece leaves four cubes in one shape, and that shape is one of the four -- possibly turned over.
8−4=48 - 4 = 4
One shape to recognise.

4Name both pieces

#3 Eliminate Possibilities 6.G.A.4
The two that fit are A and C.
A, C\text{A},\ \text{C}
A and C.
Answer: A and C
4 · Reviewdoes it hold up?

No other pairing works: of the six possible pairs, only A with C covers every cube exactly once.

Another way: Trying each pair in turn reaches the same answer, but it means testing six pairs instead of placing one piece.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Decomposing a solid into named pieces.
💡Takeaway. Start with the piece that has the fewest places it could go. Everything after that is forced.
Variant 4 easy answer: A and C

The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.

A 1 1 1 1 B 1 1 1 1 C 2 1 1 D 2 1 1 seen from above 2 1 3 2
Show solution
1 · Understandwhat's really being asked

A shape of 8 unit cubes was built from two of the four four-cube pieces. We want which two.

Givens
  • Each of the four pieces is made of four unit cubes.
  • The finished shape holds 8 cubes.
  • Exactly two different pieces were used.
Unknowns
  • The letters of the two pieces.
Constraints
  • The pieces may be turned or flipped, but not overlapped.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #17 Visualize Spatial Relationships#10 Create a Physical Representation

Two pieces of four make eight, so the shape splits exactly in half. Place the piece with the fewest possible positions first: once it is down, what is left has only one shape to recognise.

3 · Execute4 carry out the plan

1Count the cubes

#10 Create a Physical Representation 6.G.A.4
Two pieces of four cubes each.
4+4=84 + 4 = 8
The shape splits exactly in two.

2Find the piece with the fewest places to go

#3 Eliminate Possibilities 6.G.A.4
Piece B fits the shape in only 0 ways, so it is the one to try first.
B:0\text{B}: 0
Fewest options, least guessing.

3Look at what is left

#17 Visualize Spatial Relationships 6.G.A.4
Removing that piece leaves four cubes in one shape, and that shape is one of the four -- possibly turned over.
8−4=48 - 4 = 4
One shape to recognise.

4Name both pieces

#3 Eliminate Possibilities 6.G.A.4
The two that fit are A and C.
A, C\text{A},\ \text{C}
A and C.
Answer: A and C
4 · Reviewdoes it hold up?

No other pairing works: of the six possible pairs, only A with C covers every cube exactly once.

Another way: Trying each pair in turn reaches the same answer, but it means testing six pairs instead of placing one piece.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Decomposing a solid into named pieces.
💡Takeaway. Start with the piece that has the fewest places it could go. Everything after that is forced.
Variant 5 medium answer: A and C

The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.

A 1 1 1 1 B 1 1 1 1 C 2 1 1 D 2 1 1 seen from above 2 1 3 2
Show solution
1 · Understandwhat's really being asked

A shape of 8 unit cubes was built from two of the four four-cube pieces. We want which two.

Givens
  • Each of the four pieces is made of four unit cubes.
  • The finished shape holds 8 cubes.
  • Exactly two different pieces were used.
Unknowns
  • The letters of the two pieces.
Constraints
  • The pieces may be turned or flipped, but not overlapped.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #17 Visualize Spatial Relationships#10 Create a Physical Representation

Two pieces of four make eight, so the shape splits exactly in half. Place the piece with the fewest possible positions first: once it is down, what is left has only one shape to recognise.

3 · Execute4 carry out the plan

1Count the cubes

#10 Create a Physical Representation 6.G.A.4
Two pieces of four cubes each.
4+4=84 + 4 = 8
The shape splits exactly in two.

2Find the piece with the fewest places to go

#3 Eliminate Possibilities 6.G.A.4
Piece B fits the shape in only 0 ways, so it is the one to try first.
B:0\text{B}: 0
Fewest options, least guessing.

3Look at what is left

#17 Visualize Spatial Relationships 6.G.A.4
Removing that piece leaves four cubes in one shape, and that shape is one of the four -- possibly turned over.
8−4=48 - 4 = 4
One shape to recognise.

4Name both pieces

#3 Eliminate Possibilities 6.G.A.4
The two that fit are A and C.
A, C\text{A},\ \text{C}
A and C.
Answer: A and C
4 · Reviewdoes it hold up?

No other pairing works: of the six possible pairs, only A with C covers every cube exactly once.

Another way: Trying each pair in turn reaches the same answer, but it means testing six pairs instead of placing one piece.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Decomposing a solid into named pieces.
💡Takeaway. Start with the piece that has the fewest places it could go. Everything after that is forced.
Variant 6 medium answer: A and D

The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.

A 1 1 1 1 B 1 1 1 1 C 2 1 1 D 2 1 1 seen from above 2 2 2 1 1
Show solution
1 · Understandwhat's really being asked

A shape of 8 unit cubes was built from two of the four four-cube pieces. We want which two.

Givens
  • Each of the four pieces is made of four unit cubes.
  • The finished shape holds 8 cubes.
  • Exactly two different pieces were used.
Unknowns
  • The letters of the two pieces.
Constraints
  • The pieces may be turned or flipped, but not overlapped.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #17 Visualize Spatial Relationships#10 Create a Physical Representation

Two pieces of four make eight, so the shape splits exactly in half. Place the piece with the fewest possible positions first: once it is down, what is left has only one shape to recognise.

3 · Execute4 carry out the plan

1Count the cubes

#10 Create a Physical Representation 6.G.A.4
Two pieces of four cubes each.
4+4=84 + 4 = 8
The shape splits exactly in two.

2Find the piece with the fewest places to go

#3 Eliminate Possibilities 6.G.A.4
Piece A fits the shape in only 1 way, so it is the one to try first.
A:1\text{A}: 1
Fewest options, least guessing.

3Look at what is left

#17 Visualize Spatial Relationships 6.G.A.4
Removing that piece leaves four cubes in one shape, and that shape is one of the four -- possibly turned over.
8−4=48 - 4 = 4
One shape to recognise.

4Name both pieces

#3 Eliminate Possibilities 6.G.A.4
The two that fit are A and D.
A, D\text{A},\ \text{D}
A and D.
Answer: A and D
4 · Reviewdoes it hold up?

No other pairing works: of the six possible pairs, only A with D covers every cube exactly once.

Another way: Trying each pair in turn reaches the same answer, but it means testing six pairs instead of placing one piece.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Decomposing a solid into named pieces.
💡Takeaway. Start with the piece that has the fewest places it could go. Everything after that is forced.
Variant 7 medium answer: B and C

The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.

A 1 1 1 1 B 1 1 1 1 C 2 1 1 D 2 1 1 seen from above 1 2 1 2 2
Show solution
1 · Understandwhat's really being asked

A shape of 8 unit cubes was built from two of the four four-cube pieces. We want which two.

Givens
  • Each of the four pieces is made of four unit cubes.
  • The finished shape holds 8 cubes.
  • Exactly two different pieces were used.
Unknowns
  • The letters of the two pieces.
Constraints
  • The pieces may be turned or flipped, but not overlapped.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #17 Visualize Spatial Relationships#10 Create a Physical Representation

Two pieces of four make eight, so the shape splits exactly in half. Place the piece with the fewest possible positions first: once it is down, what is left has only one shape to recognise.

3 · Execute4 carry out the plan

1Count the cubes

#10 Create a Physical Representation 6.G.A.4
Two pieces of four cubes each.
4+4=84 + 4 = 8
The shape splits exactly in two.

2Find the piece with the fewest places to go

#3 Eliminate Possibilities 6.G.A.4
Piece D fits the shape in only 0 ways, so it is the one to try first.
D:0\text{D}: 0
Fewest options, least guessing.

3Look at what is left

#17 Visualize Spatial Relationships 6.G.A.4
Removing that piece leaves four cubes in one shape, and that shape is one of the four -- possibly turned over.
8−4=48 - 4 = 4
One shape to recognise.

4Name both pieces

#3 Eliminate Possibilities 6.G.A.4
The two that fit are B and C.
B, C\text{B},\ \text{C}
B and C.
Answer: B and C
4 · Reviewdoes it hold up?

No other pairing works: of the six possible pairs, only B with C covers every cube exactly once.

Another way: Trying each pair in turn reaches the same answer, but it means testing six pairs instead of placing one piece.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Decomposing a solid into named pieces.
💡Takeaway. Start with the piece that has the fewest places it could go. Everything after that is forced.
Variant 8 hard answer: B and C

The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.

A 1 1 1 1 B 1 1 1 1 C 2 1 1 D 2 1 1 seen from above 1 2 2 1 2
Show solution
1 · Understandwhat's really being asked

A shape of 8 unit cubes was built from two of the four four-cube pieces. We want which two.

Givens
  • Each of the four pieces is made of four unit cubes.
  • The finished shape holds 8 cubes.
  • Exactly two different pieces were used.
Unknowns
  • The letters of the two pieces.
Constraints
  • The pieces may be turned or flipped, but not overlapped.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #17 Visualize Spatial Relationships#10 Create a Physical Representation

Two pieces of four make eight, so the shape splits exactly in half. Place the piece with the fewest possible positions first: once it is down, what is left has only one shape to recognise.

3 · Execute4 carry out the plan

1Count the cubes

#10 Create a Physical Representation 6.G.A.4
Two pieces of four cubes each.
4+4=84 + 4 = 8
The shape splits exactly in two.

2Find the piece with the fewest places to go

#3 Eliminate Possibilities 6.G.A.4
Piece D fits the shape in only 0 ways, so it is the one to try first.
D:0\text{D}: 0
Fewest options, least guessing.

3Look at what is left

#17 Visualize Spatial Relationships 6.G.A.4
Removing that piece leaves four cubes in one shape, and that shape is one of the four -- possibly turned over.
8−4=48 - 4 = 4
One shape to recognise.

4Name both pieces

#3 Eliminate Possibilities 6.G.A.4
The two that fit are B and C.
B, C\text{B},\ \text{C}
B and C.
Answer: B and C
4 · Reviewdoes it hold up?

No other pairing works: of the six possible pairs, only B with C covers every cube exactly once.

Another way: Trying each pair in turn reaches the same answer, but it means testing six pairs instead of placing one piece.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Decomposing a solid into named pieces.
💡Takeaway. Start with the piece that has the fewest places it could go. Everything after that is forced.
Variant 9 hard answer: A and D

The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.

A 1 1 1 1 B 1 1 1 1 C 2 1 1 D 2 1 1 seen from above 2 1 2 1 2
Show solution
1 · Understandwhat's really being asked

A shape of 8 unit cubes was built from two of the four four-cube pieces. We want which two.

Givens
  • Each of the four pieces is made of four unit cubes.
  • The finished shape holds 8 cubes.
  • Exactly two different pieces were used.
Unknowns
  • The letters of the two pieces.
Constraints
  • The pieces may be turned or flipped, but not overlapped.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #17 Visualize Spatial Relationships#10 Create a Physical Representation

Two pieces of four make eight, so the shape splits exactly in half. Place the piece with the fewest possible positions first: once it is down, what is left has only one shape to recognise.

3 · Execute4 carry out the plan

1Count the cubes

#10 Create a Physical Representation 6.G.A.4
Two pieces of four cubes each.
4+4=84 + 4 = 8
The shape splits exactly in two.

2Find the piece with the fewest places to go

#3 Eliminate Possibilities 6.G.A.4
Piece B fits the shape in only 0 ways, so it is the one to try first.
B:0\text{B}: 0
Fewest options, least guessing.

3Look at what is left

#17 Visualize Spatial Relationships 6.G.A.4
Removing that piece leaves four cubes in one shape, and that shape is one of the four -- possibly turned over.
8−4=48 - 4 = 4
One shape to recognise.

4Name both pieces

#3 Eliminate Possibilities 6.G.A.4
The two that fit are A and D.
A, D\text{A},\ \text{D}
A and D.
Answer: A and D
4 · Reviewdoes it hold up?

No other pairing works: of the six possible pairs, only A with D covers every cube exactly once.

Another way: Trying each pair in turn reaches the same answer, but it means testing six pairs instead of placing one piece.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Decomposing a solid into named pieces.
💡Takeaway. Start with the piece that has the fewest places it could go. Everything after that is forced.
Variant 10 hard answer: A and D

The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.

A 1 1 1 1 B 1 1 1 1 C 2 1 1 D 2 1 1 seen from above 2 1 2 1 2
Show solution
1 · Understandwhat's really being asked

A shape of 8 unit cubes was built from two of the four four-cube pieces. We want which two.

Givens
  • Each of the four pieces is made of four unit cubes.
  • The finished shape holds 8 cubes.
  • Exactly two different pieces were used.
Unknowns
  • The letters of the two pieces.
Constraints
  • The pieces may be turned or flipped, but not overlapped.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #17 Visualize Spatial Relationships#10 Create a Physical Representation

Two pieces of four make eight, so the shape splits exactly in half. Place the piece with the fewest possible positions first: once it is down, what is left has only one shape to recognise.

3 · Execute4 carry out the plan

1Count the cubes

#10 Create a Physical Representation 6.G.A.4
Two pieces of four cubes each.
4+4=84 + 4 = 8
The shape splits exactly in two.

2Find the piece with the fewest places to go

#3 Eliminate Possibilities 6.G.A.4
Piece B fits the shape in only 0 ways, so it is the one to try first.
B:0\text{B}: 0
Fewest options, least guessing.

3Look at what is left

#17 Visualize Spatial Relationships 6.G.A.4
Removing that piece leaves four cubes in one shape, and that shape is one of the four -- possibly turned over.
8−4=48 - 4 = 4
One shape to recognise.

4Name both pieces

#3 Eliminate Possibilities 6.G.A.4
The two that fit are A and D.
A, D\text{A},\ \text{D}
A and D.
Answer: A and D
4 · Reviewdoes it hold up?

No other pairing works: of the six possible pairs, only A with D covers every cube exactly once.

Another way: Trying each pair in turn reaches the same answer, but it means testing six pairs instead of placing one piece.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Decomposing a solid into named pieces.
💡Takeaway. Start with the piece that has the fewest places it could go. Everything after that is forced.
Variant 11 hard answer: A and D

The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.

A 1 1 1 1 B 1 1 1 1 C 2 1 1 D 2 1 1 seen from above 2 1 2 1 2
Show solution
1 · Understandwhat's really being asked

A shape of 8 unit cubes was built from two of the four four-cube pieces. We want which two.

Givens
  • Each of the four pieces is made of four unit cubes.
  • The finished shape holds 8 cubes.
  • Exactly two different pieces were used.
Unknowns
  • The letters of the two pieces.
Constraints
  • The pieces may be turned or flipped, but not overlapped.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #17 Visualize Spatial Relationships#10 Create a Physical Representation

Two pieces of four make eight, so the shape splits exactly in half. Place the piece with the fewest possible positions first: once it is down, what is left has only one shape to recognise.

3 · Execute4 carry out the plan

1Count the cubes

#10 Create a Physical Representation 6.G.A.4
Two pieces of four cubes each.
4+4=84 + 4 = 8
The shape splits exactly in two.

2Find the piece with the fewest places to go

#3 Eliminate Possibilities 6.G.A.4
Piece A fits the shape in only 1 way, so it is the one to try first.
A:1\text{A}: 1
Fewest options, least guessing.

3Look at what is left

#17 Visualize Spatial Relationships 6.G.A.4
Removing that piece leaves four cubes in one shape, and that shape is one of the four -- possibly turned over.
8−4=48 - 4 = 4
One shape to recognise.

4Name both pieces

#3 Eliminate Possibilities 6.G.A.4
The two that fit are A and D.
A, D\text{A},\ \text{D}
A and D.
Answer: A and D
4 · Reviewdoes it hold up?

No other pairing works: of the six possible pairs, only A with D covers every cube exactly once.

Another way: Trying each pair in turn reaches the same answer, but it means testing six pairs instead of placing one piece.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Decomposing a solid into named pieces.
💡Takeaway. Start with the piece that has the fewest places it could go. Everything after that is forced.
Variant 12 medium answer: A and D

The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.

A 1 1 1 1 B 1 1 1 1 C 2 1 1 D 2 1 1 seen from above 1 1 2 2 2
Show solution
1 · Understandwhat's really being asked

A shape of 8 unit cubes was built from two of the four four-cube pieces. We want which two.

Givens
  • Each of the four pieces is made of four unit cubes.
  • The finished shape holds 8 cubes.
  • Exactly two different pieces were used.
Unknowns
  • The letters of the two pieces.
Constraints
  • The pieces may be turned or flipped, but not overlapped.
2 · Planchoose the strategy

#3 Eliminate Possibilities · also uses: #17 Visualize Spatial Relationships#10 Create a Physical Representation

Two pieces of four make eight, so the shape splits exactly in half. Place the piece with the fewest possible positions first: once it is down, what is left has only one shape to recognise.

3 · Execute4 carry out the plan

1Count the cubes

#10 Create a Physical Representation 6.G.A.4
Two pieces of four cubes each.
4+4=84 + 4 = 8
The shape splits exactly in two.

2Find the piece with the fewest places to go

#3 Eliminate Possibilities 6.G.A.4
Piece A fits the shape in only 1 way, so it is the one to try first.
A:1\text{A}: 1
Fewest options, least guessing.

3Look at what is left

#17 Visualize Spatial Relationships 6.G.A.4
Removing that piece leaves four cubes in one shape, and that shape is one of the four -- possibly turned over.
8−4=48 - 4 = 4
One shape to recognise.

4Name both pieces

#3 Eliminate Possibilities 6.G.A.4
The two that fit are A and D.
A, D\text{A},\ \text{D}
A and D.
Answer: A and D
4 · Reviewdoes it hold up?

No other pairing works: of the six possible pairs, only A with D covers every cube exactly once.

Another way: Trying each pair in turn reaches the same answer, but it means testing six pairs instead of placing one piece.

Standardsmin grade 6
  • 6.G.A.4 Surface area using nets of 3D figures — Decomposing a solid into named pieces.
💡Takeaway. Start with the piece that has the fewest places it could go. Everything after that is forced.