MathBrush

Practice

Same pattern as Net of a cube — the opposite face. New numbers, new story. Try each one on paper, then check the working below — or watch it drawn out, the same way the problem above is.

Question 1

In the school workshop, Mr Rajan traces a net onto a sheet of plywood. The six squares of the net are lettered B, C, D, E, F, G. The plywood pieces are joined along the fold lines to make a wooden block. Which letter is on the face opposite G?

A net of six squares, lettered B, C, D, E, F, G, folded to make a cube.BCDEFG

Work it out on paper, then check below. ▶ See the working

Question 2

A net for a tissue box is printed on a sheet of card. The six squares are lettered B, C, D, E, F, G. The card is folded along the lines to make the tissue box. Which letter is on the face opposite D?

A net of six squares, lettered B, C, D, E, F, G, folded to make a cube.BCDEFG

Work it out on paper, then check below. ▶ See the working

Question 3

A cardboard net for a storage cube is laid out on the floor of the store room. Its six squares are lettered B, C, D, E, F, G. The net is folded up along the lines to make the storage cube. Which letter is on the face opposite C?

A net of six squares, lettered B, C, D, E, F, G, folded to make a cube.BCDEFG

Work it out on paper, then check below. ▶ See the working

Question 4

Priya has a flat net for a puzzle cube from the toy corner. Each of its six squares is lettered P, Q, R, S, T, U. She folds the net along the lines to make the puzzle cube. Which letter lands opposite T?

A net of six squares, lettered P, Q, R, S, T, U, folded to make a cube.PQRSTU

Work it out on paper, then check below. ▶ See the working

Question 5

A sheet of paper is cut into the net shown. Each of its six squares is lettered: K, L, M, N, X, Y. The net is folded up into a paper cube. When it is folded, which letter faces away from M?

A net of six squares, lettered K, L, M, N, X, Y, folded to make a cube.KLMNXY

Work it out on paper, then check below. ▶ See the working

Question 6

A sheet of paper is cut into the net shown. Each of its six squares is lettered: B, C, D, E, F, G. The net is folded up into a paper cube. When it is folded, which letter faces away from F?

A net of six squares, lettered B, C, D, E, F, G, folded to make a cube.BCDEFG

Work it out on paper, then check below. ▶ See the working

Question 7

A sheet of paper is cut into the net shown. Each of its six squares is lettered: B, C, D, E, F, G. The net is folded up into a paper cube. When it is folded, which letter faces away from E?

A net of six squares, lettered B, C, D, E, F, G, folded to make a cube.BCDEFG

Work it out on paper, then check below. ▶ See the working

Question 8

For the Mid-Autumn Festival display, Farhan cuts out the net of a cube-shaped lantern. Its six squares are lettered P, Q, R, S, T, U. The net is folded along the lines to make the lantern. Which letter is on the panel opposite U?

A net of six squares, lettered P, Q, R, S, T, U, folded to make a cube.PQRSTU

Work it out on paper, then check below. ▶ See the working

Question 9

A blank dice is opened out flat into the net shown. Its faces are lettered P, Q, R, S, T, U. The net is folded back up into the dice. Which letter is on the face opposite T?

A net of six squares, lettered P, Q, R, S, T, U, folded to make a cube.PQRSTU

Work it out on paper, then check below. ▶ See the working

Question 10

A blank dice is opened out flat into the net shown. Its faces are lettered K, L, M, N, X, Y. The net is folded back up into the dice. Which letter is on the face opposite X?

A net of six squares, lettered K, L, M, N, X, Y, folded to make a cube.KLMNXY

Work it out on paper, then check below. ▶ See the working

Question 11

At the craft stall, Siti cuts out a net to make a cube-shaped lamp shade. The six squares are lettered K, L, M, N, X, Y. The shade is folded up along the lines to complete the cube. Which letter faces away from L?

A net of six squares, lettered K, L, M, N, X, Y, folded to make a cube.KLMNXY

Work it out on paper, then check below. ▶ See the working

Question 12

The figure shows a net of six squares. The squares are lettered P, Q, R, S, T, U. The net is folded along the lines to make a cube. Which letter is on the face opposite Q?

A net of six squares, lettered P, Q, R, S, T, U, folded to make a cube.PQRSTU

Work it out on paper, then check below. ▶ See the working

Question 13

The figure shows a net of six squares. The squares are lettered K, L, M, N, X, Y. The net is folded along the lines to make a cube. Which letter is on the face opposite M?

A net of six squares, lettered K, L, M, N, X, Y, folded to make a cube.KLMNXY

Work it out on paper, then check below. ▶ See the working

Question 14

During Chinese New Year, Grandma flattens a cube-shaped biscuit tin to show Wei Jie its net. The six squares of the net are lettered B, C, D, E, F, G. The net is folded back up along the lines to make the tin. Which letter is on the face opposite E?

A net of six squares, lettered B, C, D, E, F, G, folded to make a cube.BCDEFG

Work it out on paper, then check below. ▶ See the working

The working

Question 1

A net of six squares, lettered B, C, D, E, F, G, folded to make a cube.BCDEFG
  1. Folding a net in your head is where this goes wrong, so use the one rule that does not need imagining.in a straight strip of three squares, the two ends fold to opposite faces
  2. Find a straight strip of three with G at one end.D — E — G
  3. G is at one end of it, so the face at the other end is the one opposite.G is opposite D
  4. The other four squares pair off the same way, which is the check: three pairs, six faces, nothing left over.B–F, C–E, D–G

D is on the face opposite G.

The pattern. You do not have to fold it in your head. Three squares in a straight line: the two ends land opposite each other, every time.

Question 2

A net of six squares, lettered B, C, D, E, F, G, folded to make a cube.BCDEFG
  1. Folding a net in your head is where this goes wrong, so use the one rule that does not need imagining.in a straight strip of three squares, the two ends fold to opposite faces
  2. Find a straight strip of three with D at one end.D — F — G
  3. D is at one end of it, so the face at the other end is the one opposite.D is opposite G
  4. The other four squares pair off the same way, which is the check: three pairs, six faces, nothing left over.B–F, C–E, D–G

G is on the face opposite D.

The pattern. You do not have to fold it in your head. Three squares in a straight line: the two ends land opposite each other, every time.

Question 3

A net of six squares, lettered B, C, D, E, F, G, folded to make a cube.BCDEFG
  1. Folding a net in your head is where this goes wrong, so use the one rule that does not need imagining.in a straight strip of three squares, the two ends fold to opposite faces
  2. Find a straight strip of three with C at one end.C — D — E
  3. C is at one end of it, so the face at the other end is the one opposite.C is opposite E
  4. The other four squares pair off the same way, which is the check: three pairs, six faces, nothing left over.B–F, C–E, D–G

E is on the face opposite C.

The pattern. You do not have to fold it in your head. Three squares in a straight line: the two ends land opposite each other, every time.

Question 4

A net of six squares, lettered P, Q, R, S, T, U, folded to make a cube.PQRSTU
  1. Folding a net in your head is where this goes wrong, so use the one rule that does not need imagining.in a straight strip of three squares, the two ends fold to opposite faces
  2. Find a straight strip of three with T at one end.P — R — T
  3. T is at one end of it, so the face at the other end is the one opposite.T is opposite P
  4. The other four squares pair off the same way, which is the check: three pairs, six faces, nothing left over.P–T, Q–S, R–U

P is on the face opposite T.

The pattern. You do not have to fold it in your head. Three squares in a straight line: the two ends land opposite each other, every time.

Question 5

A net of six squares, lettered K, L, M, N, X, Y, folded to make a cube.KLMNXY
  1. Folding a net in your head is where this goes wrong, so use the one rule that does not need imagining.in a straight strip of three squares, the two ends fold to opposite faces
  2. Find a straight strip of three with M at one end.M — N — Y
  3. M is at one end of it, so the face at the other end is the one opposite.M is opposite Y
  4. The other four squares pair off the same way, which is the check: three pairs, six faces, nothing left over.K–X, L–N, M–Y

Y is on the face opposite M.

The pattern. You do not have to fold it in your head. Three squares in a straight line: the two ends land opposite each other, every time.

Question 6

A net of six squares, lettered B, C, D, E, F, G, folded to make a cube.BCDEFG
  1. Folding a net in your head is where this goes wrong, so use the one rule that does not need imagining.in a straight strip of three squares, the two ends fold to opposite faces
  2. Find a straight strip of three with F at one end.B — D — F
  3. F is at one end of it, so the face at the other end is the one opposite.F is opposite B
  4. The other four squares pair off the same way, which is the check: three pairs, six faces, nothing left over.B–F, C–E, D–G

B is on the face opposite F.

The pattern. You do not have to fold it in your head. Three squares in a straight line: the two ends land opposite each other, every time.

Question 7

A net of six squares, lettered B, C, D, E, F, G, folded to make a cube.BCDEFG
  1. Folding a net in your head is where this goes wrong, so use the one rule that does not need imagining.in a straight strip of three squares, the two ends fold to opposite faces
  2. Find a straight strip of three with E at one end.C — D — E
  3. E is at one end of it, so the face at the other end is the one opposite.E is opposite C
  4. The other four squares pair off the same way, which is the check: three pairs, six faces, nothing left over.B–F, C–E, D–G

C is on the face opposite E.

The pattern. You do not have to fold it in your head. Three squares in a straight line: the two ends land opposite each other, every time.

Question 8

A net of six squares, lettered P, Q, R, S, T, U, folded to make a cube.PQRSTU
  1. Folding a net in your head is where this goes wrong, so use the one rule that does not need imagining.in a straight strip of three squares, the two ends fold to opposite faces
  2. Find a straight strip of three with U at one end.R — T — U
  3. U is at one end of it, so the face at the other end is the one opposite.U is opposite R
  4. The other four squares pair off the same way, which is the check: three pairs, six faces, nothing left over.P–T, Q–S, R–U

R is on the face opposite U.

The pattern. You do not have to fold it in your head. Three squares in a straight line: the two ends land opposite each other, every time.

Question 9

A net of six squares, lettered P, Q, R, S, T, U, folded to make a cube.PQRSTU
  1. Folding a net in your head is where this goes wrong, so use the one rule that does not need imagining.in a straight strip of three squares, the two ends fold to opposite faces
  2. Find a straight strip of three with T at one end.R — S — T
  3. T is at one end of it, so the face at the other end is the one opposite.T is opposite R
  4. The other four squares pair off the same way, which is the check: three pairs, six faces, nothing left over.P–U, Q–S, R–T

R is on the face opposite T.

The pattern. You do not have to fold it in your head. Three squares in a straight line: the two ends land opposite each other, every time.

Question 10

A net of six squares, lettered K, L, M, N, X, Y, folded to make a cube.KLMNXY
  1. Folding a net in your head is where this goes wrong, so use the one rule that does not need imagining.in a straight strip of three squares, the two ends fold to opposite faces
  2. Find a straight strip of three with X at one end.L — N — X
  3. X is at one end of it, so the face at the other end is the one opposite.X is opposite L
  4. The other four squares pair off the same way, which is the check: three pairs, six faces, nothing left over.K–M, L–X, N–Y

L is on the face opposite X.

The pattern. You do not have to fold it in your head. Three squares in a straight line: the two ends land opposite each other, every time.

Question 11

A net of six squares, lettered K, L, M, N, X, Y, folded to make a cube.KLMNXY
  1. Folding a net in your head is where this goes wrong, so use the one rule that does not need imagining.in a straight strip of three squares, the two ends fold to opposite faces
  2. Find a straight strip of three with L at one end.L — N — X
  3. L is at one end of it, so the face at the other end is the one opposite.L is opposite X
  4. The other four squares pair off the same way, which is the check: three pairs, six faces, nothing left over.K–M, L–X, N–Y

X is on the face opposite L.

The pattern. You do not have to fold it in your head. Three squares in a straight line: the two ends land opposite each other, every time.

Question 12

A net of six squares, lettered P, Q, R, S, T, U, folded to make a cube.PQRSTU
  1. Folding a net in your head is where this goes wrong, so use the one rule that does not need imagining.in a straight strip of three squares, the two ends fold to opposite faces
  2. Find a straight strip of three with Q at one end.Q — R — S
  3. Q is at one end of it, so the face at the other end is the one opposite.Q is opposite S
  4. The other four squares pair off the same way, which is the check: three pairs, six faces, nothing left over.P–T, Q–S, R–U

S is on the face opposite Q.

The pattern. You do not have to fold it in your head. Three squares in a straight line: the two ends land opposite each other, every time.

Question 13

A net of six squares, lettered K, L, M, N, X, Y, folded to make a cube.KLMNXY
  1. Folding a net in your head is where this goes wrong, so use the one rule that does not need imagining.in a straight strip of three squares, the two ends fold to opposite faces
  2. Find a straight strip of three with M at one end.M — N — X
  3. M is at one end of it, so the face at the other end is the one opposite.M is opposite X
  4. The other four squares pair off the same way, which is the check: three pairs, six faces, nothing left over.K–Y, L–N, M–X

X is on the face opposite M.

The pattern. You do not have to fold it in your head. Three squares in a straight line: the two ends land opposite each other, every time.

Question 14

A net of six squares, lettered B, C, D, E, F, G, folded to make a cube.BCDEFG
  1. Folding a net in your head is where this goes wrong, so use the one rule that does not need imagining.in a straight strip of three squares, the two ends fold to opposite faces
  2. Find a straight strip of three with E at one end.C — D — E
  3. E is at one end of it, so the face at the other end is the one opposite.E is opposite C
  4. The other four squares pair off the same way, which is the check: three pairs, six faces, nothing left over.B–G, C–E, D–F

C is on the face opposite E.

The pattern. You do not have to fold it in your head. Three squares in a straight line: the two ends land opposite each other, every time.