Practice · A cube net's outline is always 14 edges · Sensim Math

Variant 1 easy answer: 6 cm

A net of a cube has a perimeter of $84 \text{cm}$ . The net is folded up to make the cube. Find the length of one edge of the cube.

Show solution

1 · Understandwhat's really being asked

A flat net that folds into a cube has an outline 84 cm long. We need the length of one edge of the finished cube.

Givens

The net's perimeter is 84 cm.
The net is six squares that fold into a cube.
Every square in the net has the same side, which is the cube's edge.

Unknowns

The length of one edge of the cube.

Constraints

Only the outer boundary counts; the fold lines inside do not.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #7 Identify Subproblems

Count how many square sides the outline is built from. Once that number is known, the perimeter is just that many equal pieces and a division finishes it.

3 · Execute2 carry out the plan

1Count the edges on the outline

#1 Draw a Diagram 3.MD.D.8

Trace the outside boundary of the net. Going all the way around, the outline is built from 14 square sides -- the fold lines inside are not part of it. Six squares have 24 sides in all, and folding glues five pairs together, hiding 10 of them: 24 - 10 = 14.

\text{perimeter} = 14 \times \text{one edge}

14 equal pieces make the outline.

2Share the perimeter equally

#7 Identify Subproblems 3.OA.A.3

All 14 border pieces are the same length, so one edge length is 84 cm split into 14 equal parts.

84 \div 14 = 6

Each edge of the cube is 6 cm.

Answer: 6 cm

4 · Reviewdoes it hold up?

Multiply back: 14 x 6 = 84 cm, which is the perimeter given.

Another way: The net's shape does not matter. Any net of a cube has an outline of 14 edges, because six squares always bring 24 sides and folding always hides ten of them.

Standardsmin grade 3

3.MD.D.8 Solve real-world problems involving perimeters of polygons — Reading the net's outline as a count of equal square sides.
3.OA.A.3 Use multiplication and division within 100 to solve word problems — Dividing the perimeter into that many equal parts.

💡Takeaway. Folding hides the edges that get glued, so a cube's net always shows the same number of edges around the outside.

Variant 2 easy answer: 7 cm

A net of a cube has a perimeter of $98 \text{cm}$ . The net is folded up to make the cube. Find the length of one edge of the cube.

Show solution

1 · Understandwhat's really being asked

A flat net that folds into a cube has an outline 98 cm long. We need the length of one edge of the finished cube.

Givens

The net's perimeter is 98 cm.
The net is six squares that fold into a cube.
Every square in the net has the same side, which is the cube's edge.

Unknowns

The length of one edge of the cube.

Constraints

Only the outer boundary counts; the fold lines inside do not.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #7 Identify Subproblems

Count how many square sides the outline is built from. Once that number is known, the perimeter is just that many equal pieces and a division finishes it.

3 · Execute2 carry out the plan

1Count the edges on the outline

#1 Draw a Diagram 3.MD.D.8

Trace the outside boundary of the net. Going all the way around, the outline is built from 14 square sides -- the fold lines inside are not part of it. Six squares have 24 sides in all, and folding glues five pairs together, hiding 10 of them: 24 - 10 = 14.

\text{perimeter} = 14 \times \text{one edge}

14 equal pieces make the outline.

2Share the perimeter equally

#7 Identify Subproblems 3.OA.A.3

All 14 border pieces are the same length, so one edge length is 98 cm split into 14 equal parts.

98 \div 14 = 7

Each edge of the cube is 7 cm.

Answer: 7 cm

4 · Reviewdoes it hold up?

Multiply back: 14 x 7 = 98 cm, which is the perimeter given.

Another way: The net's shape does not matter. Any net of a cube has an outline of 14 edges, because six squares always bring 24 sides and folding always hides ten of them.

Standardsmin grade 3

3.MD.D.8 Solve real-world problems involving perimeters of polygons — Reading the net's outline as a count of equal square sides.
3.OA.A.3 Use multiplication and division within 100 to solve word problems — Dividing the perimeter into that many equal parts.

💡Takeaway. Folding hides the edges that get glued, so a cube's net always shows the same number of edges around the outside.

Variant 3 easy answer: 8 cm

A net of a cube has a perimeter of $112 \text{cm}$ . The net is folded up to make the cube. Find the length of one edge of the cube.

Show solution

1 · Understandwhat's really being asked

A flat net that folds into a cube has an outline 112 cm long. We need the length of one edge of the finished cube.

Givens

The net's perimeter is 112 cm.
The net is six squares that fold into a cube.
Every square in the net has the same side, which is the cube's edge.

Unknowns

The length of one edge of the cube.

Constraints

Only the outer boundary counts; the fold lines inside do not.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #7 Identify Subproblems

Count how many square sides the outline is built from. Once that number is known, the perimeter is just that many equal pieces and a division finishes it.

3 · Execute2 carry out the plan

1Count the edges on the outline

#1 Draw a Diagram 3.MD.D.8

Trace the outside boundary of the net. Going all the way around, the outline is built from 14 square sides -- the fold lines inside are not part of it. Six squares have 24 sides in all, and folding glues five pairs together, hiding 10 of them: 24 - 10 = 14.

\text{perimeter} = 14 \times \text{one edge}

14 equal pieces make the outline.

2Share the perimeter equally

#7 Identify Subproblems 3.OA.A.3

All 14 border pieces are the same length, so one edge length is 112 cm split into 14 equal parts.

112 \div 14 = 8

Each edge of the cube is 8 cm.

Answer: 8 cm

4 · Reviewdoes it hold up?

Multiply back: 14 x 8 = 112 cm, which is the perimeter given.

Another way: The net's shape does not matter. Any net of a cube has an outline of 14 edges, because six squares always bring 24 sides and folding always hides ten of them.

Standardsmin grade 3

3.MD.D.8 Solve real-world problems involving perimeters of polygons — Reading the net's outline as a count of equal square sides.
3.OA.A.3 Use multiplication and division within 100 to solve word problems — Dividing the perimeter into that many equal parts.

💡Takeaway. Folding hides the edges that get glued, so a cube's net always shows the same number of edges around the outside.

Variant 4 easy answer: 9 cm

A net of a cube has a perimeter of $126 \text{cm}$ . The net is folded up to make the cube. Find the length of one edge of the cube.

Show solution

1 · Understandwhat's really being asked

A flat net that folds into a cube has an outline 126 cm long. We need the length of one edge of the finished cube.

Givens

The net's perimeter is 126 cm.
The net is six squares that fold into a cube.
Every square in the net has the same side, which is the cube's edge.

Unknowns

The length of one edge of the cube.

Constraints

Only the outer boundary counts; the fold lines inside do not.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #7 Identify Subproblems

Count how many square sides the outline is built from. Once that number is known, the perimeter is just that many equal pieces and a division finishes it.

3 · Execute2 carry out the plan

1Count the edges on the outline

#1 Draw a Diagram 3.MD.D.8

Trace the outside boundary of the net. Going all the way around, the outline is built from 14 square sides -- the fold lines inside are not part of it. Six squares have 24 sides in all, and folding glues five pairs together, hiding 10 of them: 24 - 10 = 14.

\text{perimeter} = 14 \times \text{one edge}

14 equal pieces make the outline.

2Share the perimeter equally

#7 Identify Subproblems 3.OA.A.3

All 14 border pieces are the same length, so one edge length is 126 cm split into 14 equal parts.

126 \div 14 = 9

Each edge of the cube is 9 cm.

Answer: 9 cm

4 · Reviewdoes it hold up?

Multiply back: 14 x 9 = 126 cm, which is the perimeter given.

Another way: The net's shape does not matter. Any net of a cube has an outline of 14 edges, because six squares always bring 24 sides and folding always hides ten of them.

Standardsmin grade 3

3.MD.D.8 Solve real-world problems involving perimeters of polygons — Reading the net's outline as a count of equal square sides.
3.OA.A.3 Use multiplication and division within 100 to solve word problems — Dividing the perimeter into that many equal parts.

💡Takeaway. Folding hides the edges that get glued, so a cube's net always shows the same number of edges around the outside.

Variant 5 medium answer: 11 cm

A net of a cube has a perimeter of $154 \text{cm}$ . The net is folded up to make the cube. Find the length of one edge of the cube.

Show solution

1 · Understandwhat's really being asked

A flat net that folds into a cube has an outline 154 cm long. We need the length of one edge of the finished cube.

Givens

The net's perimeter is 154 cm.
The net is six squares that fold into a cube.
Every square in the net has the same side, which is the cube's edge.

Unknowns

The length of one edge of the cube.

Constraints

Only the outer boundary counts; the fold lines inside do not.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #7 Identify Subproblems

Count how many square sides the outline is built from. Once that number is known, the perimeter is just that many equal pieces and a division finishes it.

3 · Execute2 carry out the plan

1Count the edges on the outline

#1 Draw a Diagram 3.MD.D.8

Trace the outside boundary of the net. Going all the way around, the outline is built from 14 square sides -- the fold lines inside are not part of it. Six squares have 24 sides in all, and folding glues five pairs together, hiding 10 of them: 24 - 10 = 14.

\text{perimeter} = 14 \times \text{one edge}

14 equal pieces make the outline.

2Share the perimeter equally

#7 Identify Subproblems 3.OA.A.3

All 14 border pieces are the same length, so one edge length is 154 cm split into 14 equal parts.

154 \div 14 = 11

Each edge of the cube is 11 cm.

Answer: 11 cm

4 · Reviewdoes it hold up?

Multiply back: 14 x 11 = 154 cm, which is the perimeter given.

Another way: The net's shape does not matter. Any net of a cube has an outline of 14 edges, because six squares always bring 24 sides and folding always hides ten of them.

Standardsmin grade 3

3.MD.D.8 Solve real-world problems involving perimeters of polygons — Reading the net's outline as a count of equal square sides.
3.OA.A.3 Use multiplication and division within 100 to solve word problems — Dividing the perimeter into that many equal parts.

💡Takeaway. Folding hides the edges that get glued, so a cube's net always shows the same number of edges around the outside.

Variant 6 medium answer: 12 cm

A net of a cube has a perimeter of $168 \text{cm}$ . The net is folded up to make the cube. Find the length of one edge of the cube.

Show solution

1 · Understandwhat's really being asked

A flat net that folds into a cube has an outline 168 cm long. We need the length of one edge of the finished cube.

Givens

The net's perimeter is 168 cm.
The net is six squares that fold into a cube.
Every square in the net has the same side, which is the cube's edge.

Unknowns

The length of one edge of the cube.

Constraints

Only the outer boundary counts; the fold lines inside do not.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #7 Identify Subproblems

Count how many square sides the outline is built from. Once that number is known, the perimeter is just that many equal pieces and a division finishes it.

3 · Execute2 carry out the plan

1Count the edges on the outline

#1 Draw a Diagram 3.MD.D.8

Trace the outside boundary of the net. Going all the way around, the outline is built from 14 square sides -- the fold lines inside are not part of it. Six squares have 24 sides in all, and folding glues five pairs together, hiding 10 of them: 24 - 10 = 14.

\text{perimeter} = 14 \times \text{one edge}

14 equal pieces make the outline.

2Share the perimeter equally

#7 Identify Subproblems 3.OA.A.3

All 14 border pieces are the same length, so one edge length is 168 cm split into 14 equal parts.

168 \div 14 = 12

Each edge of the cube is 12 cm.

Answer: 12 cm

4 · Reviewdoes it hold up?

Multiply back: 14 x 12 = 168 cm, which is the perimeter given.

Another way: The net's shape does not matter. Any net of a cube has an outline of 14 edges, because six squares always bring 24 sides and folding always hides ten of them.

Standardsmin grade 3

3.MD.D.8 Solve real-world problems involving perimeters of polygons — Reading the net's outline as a count of equal square sides.
3.OA.A.3 Use multiplication and division within 100 to solve word problems — Dividing the perimeter into that many equal parts.

💡Takeaway. Folding hides the edges that get glued, so a cube's net always shows the same number of edges around the outside.

Variant 7 medium answer: 14 cm

A net of a cube has a perimeter of $196 \text{cm}$ . The net is folded up to make the cube. Find the length of one edge of the cube.

Show solution

1 · Understandwhat's really being asked

A flat net that folds into a cube has an outline 196 cm long. We need the length of one edge of the finished cube.

Givens

The net's perimeter is 196 cm.
The net is six squares that fold into a cube.
Every square in the net has the same side, which is the cube's edge.

Unknowns

The length of one edge of the cube.

Constraints

Only the outer boundary counts; the fold lines inside do not.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #7 Identify Subproblems

Count how many square sides the outline is built from. Once that number is known, the perimeter is just that many equal pieces and a division finishes it.

3 · Execute2 carry out the plan

1Count the edges on the outline

#1 Draw a Diagram 3.MD.D.8

Trace the outside boundary of the net. Going all the way around, the outline is built from 14 square sides -- the fold lines inside are not part of it. Six squares have 24 sides in all, and folding glues five pairs together, hiding 10 of them: 24 - 10 = 14.

\text{perimeter} = 14 \times \text{one edge}

14 equal pieces make the outline.

2Share the perimeter equally

#7 Identify Subproblems 3.OA.A.3

All 14 border pieces are the same length, so one edge length is 196 cm split into 14 equal parts.

196 \div 14 = 14

Each edge of the cube is 14 cm.

Answer: 14 cm

4 · Reviewdoes it hold up?

Multiply back: 14 x 14 = 196 cm, which is the perimeter given.

Another way: The net's shape does not matter. Any net of a cube has an outline of 14 edges, because six squares always bring 24 sides and folding always hides ten of them.

Standardsmin grade 3

3.MD.D.8 Solve real-world problems involving perimeters of polygons — Reading the net's outline as a count of equal square sides.
3.OA.A.3 Use multiplication and division within 100 to solve word problems — Dividing the perimeter into that many equal parts.

💡Takeaway. Folding hides the edges that get glued, so a cube's net always shows the same number of edges around the outside.

Variant 8 medium answer: 15 cm

A net of a cube has a perimeter of $210 \text{cm}$ . The net is folded up to make the cube. Find the length of one edge of the cube.

Show solution

1 · Understandwhat's really being asked

A flat net that folds into a cube has an outline 210 cm long. We need the length of one edge of the finished cube.

Givens

The net's perimeter is 210 cm.
The net is six squares that fold into a cube.
Every square in the net has the same side, which is the cube's edge.

Unknowns

The length of one edge of the cube.

Constraints

Only the outer boundary counts; the fold lines inside do not.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #7 Identify Subproblems

Count how many square sides the outline is built from. Once that number is known, the perimeter is just that many equal pieces and a division finishes it.

3 · Execute2 carry out the plan

1Count the edges on the outline

#1 Draw a Diagram 3.MD.D.8

Trace the outside boundary of the net. Going all the way around, the outline is built from 14 square sides -- the fold lines inside are not part of it. Six squares have 24 sides in all, and folding glues five pairs together, hiding 10 of them: 24 - 10 = 14.

\text{perimeter} = 14 \times \text{one edge}

14 equal pieces make the outline.

2Share the perimeter equally

#7 Identify Subproblems 3.OA.A.3

All 14 border pieces are the same length, so one edge length is 210 cm split into 14 equal parts.

210 \div 14 = 15

Each edge of the cube is 15 cm.

Answer: 15 cm

4 · Reviewdoes it hold up?

Multiply back: 14 x 15 = 210 cm, which is the perimeter given.

Another way: The net's shape does not matter. Any net of a cube has an outline of 14 edges, because six squares always bring 24 sides and folding always hides ten of them.

Standardsmin grade 3

3.MD.D.8 Solve real-world problems involving perimeters of polygons — Reading the net's outline as a count of equal square sides.
3.OA.A.3 Use multiplication and division within 100 to solve word problems — Dividing the perimeter into that many equal parts.

💡Takeaway. Folding hides the edges that get glued, so a cube's net always shows the same number of edges around the outside.

Variant 9 hard answer: 16 cm

A net of a cube has a perimeter of $224 \text{cm}$ . The net is folded up to make the cube. Find the length of one edge of the cube.

Show solution

1 · Understandwhat's really being asked

A flat net that folds into a cube has an outline 224 cm long. We need the length of one edge of the finished cube.

Givens

The net's perimeter is 224 cm.
The net is six squares that fold into a cube.
Every square in the net has the same side, which is the cube's edge.

Unknowns

The length of one edge of the cube.

Constraints

Only the outer boundary counts; the fold lines inside do not.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #7 Identify Subproblems

Count how many square sides the outline is built from. Once that number is known, the perimeter is just that many equal pieces and a division finishes it.

3 · Execute2 carry out the plan

1Count the edges on the outline

#1 Draw a Diagram 3.MD.D.8

Trace the outside boundary of the net. Going all the way around, the outline is built from 14 square sides -- the fold lines inside are not part of it. Six squares have 24 sides in all, and folding glues five pairs together, hiding 10 of them: 24 - 10 = 14.

\text{perimeter} = 14 \times \text{one edge}

14 equal pieces make the outline.

2Share the perimeter equally

#7 Identify Subproblems 3.OA.A.3

All 14 border pieces are the same length, so one edge length is 224 cm split into 14 equal parts.

224 \div 14 = 16

Each edge of the cube is 16 cm.

Answer: 16 cm

4 · Reviewdoes it hold up?

Multiply back: 14 x 16 = 224 cm, which is the perimeter given.

Another way: The net's shape does not matter. Any net of a cube has an outline of 14 edges, because six squares always bring 24 sides and folding always hides ten of them.

Standardsmin grade 3

3.MD.D.8 Solve real-world problems involving perimeters of polygons — Reading the net's outline as a count of equal square sides.
3.OA.A.3 Use multiplication and division within 100 to solve word problems — Dividing the perimeter into that many equal parts.

💡Takeaway. Folding hides the edges that get glued, so a cube's net always shows the same number of edges around the outside.

Variant 10 hard answer: 19 cm

A net of a cube has a perimeter of $266 \text{cm}$ . The net is folded up to make the cube. Find the length of one edge of the cube.

Show solution

1 · Understandwhat's really being asked

A flat net that folds into a cube has an outline 266 cm long. We need the length of one edge of the finished cube.

Givens

The net's perimeter is 266 cm.
The net is six squares that fold into a cube.
Every square in the net has the same side, which is the cube's edge.

Unknowns

The length of one edge of the cube.

Constraints

Only the outer boundary counts; the fold lines inside do not.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #7 Identify Subproblems

Count how many square sides the outline is built from. Once that number is known, the perimeter is just that many equal pieces and a division finishes it.

3 · Execute2 carry out the plan

1Count the edges on the outline

#1 Draw a Diagram 3.MD.D.8

Trace the outside boundary of the net. Going all the way around, the outline is built from 14 square sides -- the fold lines inside are not part of it. Six squares have 24 sides in all, and folding glues five pairs together, hiding 10 of them: 24 - 10 = 14.

\text{perimeter} = 14 \times \text{one edge}

14 equal pieces make the outline.

2Share the perimeter equally

#7 Identify Subproblems 3.OA.A.3

All 14 border pieces are the same length, so one edge length is 266 cm split into 14 equal parts.

266 \div 14 = 19

Each edge of the cube is 19 cm.

Answer: 19 cm

4 · Reviewdoes it hold up?

Multiply back: 14 x 19 = 266 cm, which is the perimeter given.

Another way: The net's shape does not matter. Any net of a cube has an outline of 14 edges, because six squares always bring 24 sides and folding always hides ten of them.

Standardsmin grade 3

3.MD.D.8 Solve real-world problems involving perimeters of polygons — Reading the net's outline as a count of equal square sides.
3.OA.A.3 Use multiplication and division within 100 to solve word problems — Dividing the perimeter into that many equal parts.

💡Takeaway. Folding hides the edges that get glued, so a cube's net always shows the same number of edges around the outside.

Variant 11 hard answer: 20 cm

A net of a cube has a perimeter of $280 \text{cm}$ . The net is folded up to make the cube. Find the length of one edge of the cube.

Show solution

1 · Understandwhat's really being asked

A flat net that folds into a cube has an outline 280 cm long. We need the length of one edge of the finished cube.

Givens

The net's perimeter is 280 cm.
The net is six squares that fold into a cube.
Every square in the net has the same side, which is the cube's edge.

Unknowns

The length of one edge of the cube.

Constraints

Only the outer boundary counts; the fold lines inside do not.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #7 Identify Subproblems

Count how many square sides the outline is built from. Once that number is known, the perimeter is just that many equal pieces and a division finishes it.

3 · Execute2 carry out the plan

1Count the edges on the outline

#1 Draw a Diagram 3.MD.D.8

Trace the outside boundary of the net. Going all the way around, the outline is built from 14 square sides -- the fold lines inside are not part of it. Six squares have 24 sides in all, and folding glues five pairs together, hiding 10 of them: 24 - 10 = 14.

\text{perimeter} = 14 \times \text{one edge}

14 equal pieces make the outline.

2Share the perimeter equally

#7 Identify Subproblems 3.OA.A.3

All 14 border pieces are the same length, so one edge length is 280 cm split into 14 equal parts.

280 \div 14 = 20

Each edge of the cube is 20 cm.

Answer: 20 cm

4 · Reviewdoes it hold up?

Multiply back: 14 x 20 = 280 cm, which is the perimeter given.

Another way: The net's shape does not matter. Any net of a cube has an outline of 14 edges, because six squares always bring 24 sides and folding always hides ten of them.

Standardsmin grade 3

3.MD.D.8 Solve real-world problems involving perimeters of polygons — Reading the net's outline as a count of equal square sides.
3.OA.A.3 Use multiplication and division within 100 to solve word problems — Dividing the perimeter into that many equal parts.

💡Takeaway. Folding hides the edges that get glued, so a cube's net always shows the same number of edges around the outside.

Variant 12 hard answer: 25 cm

A net of a cube has a perimeter of $350 \text{cm}$ . The net is folded up to make the cube. Find the length of one edge of the cube.

Show solution

1 · Understandwhat's really being asked

A flat net that folds into a cube has an outline 350 cm long. We need the length of one edge of the finished cube.

Givens

The net's perimeter is 350 cm.
The net is six squares that fold into a cube.
Every square in the net has the same side, which is the cube's edge.

Unknowns

The length of one edge of the cube.

Constraints

Only the outer boundary counts; the fold lines inside do not.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #7 Identify Subproblems

Count how many square sides the outline is built from. Once that number is known, the perimeter is just that many equal pieces and a division finishes it.

3 · Execute2 carry out the plan

1Count the edges on the outline

#1 Draw a Diagram 3.MD.D.8

Trace the outside boundary of the net. Going all the way around, the outline is built from 14 square sides -- the fold lines inside are not part of it. Six squares have 24 sides in all, and folding glues five pairs together, hiding 10 of them: 24 - 10 = 14.

\text{perimeter} = 14 \times \text{one edge}

14 equal pieces make the outline.

2Share the perimeter equally

#7 Identify Subproblems 3.OA.A.3

All 14 border pieces are the same length, so one edge length is 350 cm split into 14 equal parts.

350 \div 14 = 25

Each edge of the cube is 25 cm.

Answer: 25 cm

4 · Reviewdoes it hold up?

Multiply back: 14 x 25 = 350 cm, which is the perimeter given.

Another way: The net's shape does not matter. Any net of a cube has an outline of 14 edges, because six squares always bring 24 sides and folding always hides ten of them.

Standardsmin grade 3

3.MD.D.8 Solve real-world problems involving perimeters of polygons — Reading the net's outline as a count of equal square sides.
3.OA.A.3 Use multiplication and division within 100 to solve word problems — Dividing the perimeter into that many equal parts.

💡Takeaway. Folding hides the edges that get glued, so a cube's net always shows the same number of edges around the outside.

A cube net's outline is always 14 edges · 12 practice problems

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