Place the piece with the fewest positions first
6.G.A.4
Generated variants — 12
The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.
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
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
2Find the piece with the fewest places to go
3Look at what is left
4Name both pieces
4 · Reviewdoes it hold up?
No other pairing works: of the six possible pairs, only B with C covers every cube exactly once.
Standardsmin grade 6
6.G.A.4Surface area using nets of 3D figures — Decomposing a solid into named pieces.
The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.
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
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
2Find the piece with the fewest places to go
3Look at what is left
4Name both pieces
4 · Reviewdoes it hold up?
No other pairing works: of the six possible pairs, only A with C covers every cube exactly once.
Standardsmin grade 6
6.G.A.4Surface area using nets of 3D figures — Decomposing a solid into named pieces.
The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.
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
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
2Find the piece with the fewest places to go
3Look at what is left
4Name both pieces
4 · Reviewdoes it hold up?
No other pairing works: of the six possible pairs, only A with C covers every cube exactly once.
Standardsmin grade 6
6.G.A.4Surface area using nets of 3D figures — Decomposing a solid into named pieces.
The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.
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
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
2Find the piece with the fewest places to go
3Look at what is left
4Name both pieces
4 · Reviewdoes it hold up?
No other pairing works: of the six possible pairs, only A with C covers every cube exactly once.
Standardsmin grade 6
6.G.A.4Surface area using nets of 3D figures — Decomposing a solid into named pieces.
The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.
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
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
2Find the piece with the fewest places to go
3Look at what is left
4Name both pieces
4 · Reviewdoes it hold up?
No other pairing works: of the six possible pairs, only A with C covers every cube exactly once.
Standardsmin grade 6
6.G.A.4Surface area using nets of 3D figures — Decomposing a solid into named pieces.
The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.
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
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
2Find the piece with the fewest places to go
3Look at what is left
4Name both pieces
4 · Reviewdoes it hold up?
No other pairing works: of the six possible pairs, only A with D covers every cube exactly once.
Standardsmin grade 6
6.G.A.4Surface area using nets of 3D figures — Decomposing a solid into named pieces.
The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.
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
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
2Find the piece with the fewest places to go
3Look at what is left
4Name both pieces
4 · Reviewdoes it hold up?
No other pairing works: of the six possible pairs, only B with C covers every cube exactly once.
Standardsmin grade 6
6.G.A.4Surface area using nets of 3D figures — Decomposing a solid into named pieces.
The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.
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
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
2Find the piece with the fewest places to go
3Look at what is left
4Name both pieces
4 · Reviewdoes it hold up?
No other pairing works: of the six possible pairs, only B with C covers every cube exactly once.
Standardsmin grade 6
6.G.A.4Surface area using nets of 3D figures — Decomposing a solid into named pieces.
The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.
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
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
2Find the piece with the fewest places to go
3Look at what is left
4Name both pieces
4 · Reviewdoes it hold up?
No other pairing works: of the six possible pairs, only A with D covers every cube exactly once.
Standardsmin grade 6
6.G.A.4Surface area using nets of 3D figures — Decomposing a solid into named pieces.
The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.
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
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
2Find the piece with the fewest places to go
3Look at what is left
4Name both pieces
4 · Reviewdoes it hold up?
No other pairing works: of the six possible pairs, only A with D covers every cube exactly once.
Standardsmin grade 6
6.G.A.4Surface area using nets of 3D figures — Decomposing a solid into named pieces.
The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.
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
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
2Find the piece with the fewest places to go
3Look at what is left
4Name both pieces
4 · Reviewdoes it hold up?
No other pairing works: of the six possible pairs, only A with D covers every cube exactly once.
Standardsmin grade 6
6.G.A.4Surface area using nets of 3D figures — Decomposing a solid into named pieces.
The shape at the right was built from two different pieces. Find the two pieces that were used and write their letters.
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
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
2Find the piece with the fewest places to go
3Look at what is left
4Name both pieces
4 · Reviewdoes it hold up?
No other pairing works: of the six possible pairs, only A with D covers every cube exactly once.
Standardsmin grade 6
6.G.A.4Surface area using nets of 3D figures — Decomposing a solid into named pieces.
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