Nets and Solids: a week of ready-to-teach maths

Five days of lessons for Year 5 Space. Print this pack and the week is prepared: each day has a one-page plan and a student worksheet, plus four nets to cut, fold and glue (a cube, a square pyramid, a triangular prism and a box), a mini-check and every answer.

Start here: five minutes to Monday

1. Skim the week at a glance on the next page.
2. Print the five days. Each day is two A4 sheets: a plan and a worksheet.
3. Print the two net sheets once per child, on thin card if you can, and collect a few empty boxes for Day 1.
4. Open the free interactive unit on your board. Every plan tells you which picture to show and which buttons to press.
5. Teach straight from the plan. Timings, talk prompts, misconceptions and answers are all on the one page.

No maths background needed

This pack is written for the busy generalist teacher. Each plan explains the idea in plain words, lists the misconceptions children bring, and gives the answers. The big idea of the week: a net is a solid’s faces laid out flat, joined along some of its edges. Each region of a net becomes one face, so the shapes and the number of regions tell you the solid. Not every arrangement folds: six squares make a cube only when no two land on the same face, which can be tested by rolling a dice across them.

One day, one lesson

The five lessons fill a week of maths, one lesson of about 50 minutes a day. Run them in order: each day stands on the one before. Every plan marks a split point if your timetable runs two shorter sessions.

The week at a glance

One lesson a day for a week. Each day stands on the day before, so run them in order.

How the week builds

Days 1 and 2 work with the cube, unfolding and folding; Day 3 builds other solids from their nets; Day 4 counts what a net becomes; and Day 5 designs a net from scratch. It builds on Year 4’s composite shapes and objects made from familiar ones (AC9M4SP01), and it leads to Year 6, where the parallel cross-sections of objects connect to right prisms (AC9M6SP01).

Materials for the week (one trip)

• From the classroom: scissors, glue sticks, rulers, empty cereal or tissue boxes (a few to open on Day 1, one closed per group for Day 4), a dice per pair, 1 cm grid paper, this pack printed.
• Print once per child: the two sheets of nets (Days 1, 3 and 5), on thin card if you have it.

Words for the word wall

net, face, edge, corner (vertex), fold, cube, square pyramid, triangular pyramid, triangular prism, rectangular prism, opposite

Dear families

This week in maths, Year 5 unfolds boxes into nets and folds nets into solids. A net is a solid’s faces laid out flat: six squares can fold into a cube, and a square with four triangles folds into a square pyramid.

Try this at home

• Carefully open out an empty cereal or tissue box along its glued edges. What shapes make its net?
• Find a dice. Do the opposite faces always add to 7?
• Count the faces, edges and corners of a box together.
• Spot solids around the house: a tent, a roof, a block of cheese. Which ones are prisms?

Solids I found this week

Fill one row a day. Write a solid you found and the shapes of its faces.

Printed from the free seegongsik Nets and Solids teaching pack · seegongsik.com/au/y5/space/AC9M5SP01/pack

A solid unfolded

A net is a solid’s faces laid out flat, still joined along some edges. Children open a box along its glued edges and see six faces lying flat, then fold a cube from a net of six squares. Before folding, they predict which squares end up opposite: in a row of squares, a square’s opposite is two along, never next door.

We are learning to

• unfold a box into a net and fold a net into a cube,
• see each region of a net become one face,
• predict which squares of a cube net end up opposite.

Success criteria

• I can fold a cube from its net.
• I can find the square opposite a shaded square before I fold.

You need

A few empty cereal or tissue boxes. The cube net (cut-out sheet 1), scissors and glue, one each. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B by cutting and folding the cube.

Watch for these ideas

• Thinking any six squares will fold into a cube. Tomorrow tests this.
• Choosing the square next door as the opposite one. Neighbours in a net become neighbours on the cube.
• Gluing before every line is folded, so the faces will not close.

Answers

• Part A: net 1, F; net 2, D; net 3, E.
• Part B: 12 − 5 = 7 edges are cut. Part C: drawings vary; a box’s net has six rectangles.

A solid unfolded

A. Each net folds into a cube. Which letter is opposite the shaded square?

B. Cuts and folds

A cube has 12 edges. In a net, its 6 faces stay joined along 5 edges. How many edges are cut to unfold a cube?   __________

C. Draw the net of the box you unfolded

Six squares, one cube

Six squares can be joined edge to edge in 35 ways (a turned or flipped one counts as the same), and only 11 fold into a cube. A dice tests any of them: stand it on a square, tip it onto the next square and the next, and write the number on top in each square. Six different numbers: it folds. A number twice: two squares would land on the same face.

We are learning to

• predict whether six squares fold into a cube,
• test a net by rolling a dice across it,
• explain why some arrangements can never fold.

Success criteria

• I can test a net with a dice and say whether it folds into a cube.
• I can draw a net of a cube that is not a cross.

You need

A dice per pair. The cubes folded yesterday. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after net D of Part A; start Session B by testing nets E to H.

Watch for these ideas

• Tipping the dice two squares at once, or turning it as it moves. It tips over one edge at a time.
• Losing the way where a net branches. Tip the dice back the way it came, then on to the branch.
• Counting a turned or flipped net as a new one: turned round, it matches one already drawn.

Answers

• Part A: A yes, B no, C yes, D yes, E no, F no, G yes, H no.
• Part B: any of the 11 cube nets except the 4 in Part A (a cross is one); test each with the dice. Part C: a row of four wraps once round the cube, so a fifth square lands on the first one’s face. A 2 by 2 block puts four squares round one point, but only three faces meet at a corner of a cube.

Six squares, one cube

A. Predict, then test with a dice. Does it fold into a cube? Write yes or no.

Stand the dice on a square and write the number on top in that square. Tip it onto the next square and write the new top number. Visit every square, tipping it back the way it came to reach a branch. Six different numbers: it folds.

B. Draw two more nets of a cube that are not on this page

C. Why some never fold

1. Six squares with five of them in a row never fold into a cube. Why not?

2. Six squares with four of them in a 2 by 2 block never fold into a cube. Why not?

Nets of other solids

The faces of a net tell you its solid. A square and four triangles fold into a square pyramid: the square is the base and the triangles meet at the top point. Three rectangles and two triangles fold into a triangular prism: the rectangles wrap into a tube and the triangles close its ends. The same faces joined another way can still fold, so children read the faces, not the outline.

We are learning to

• build a square pyramid and a triangular prism from their nets,
• name the solid a net folds into from the shapes of its faces,
• add a missing face where it will fold into place.

Success criteria

• I can name the solid a net makes from its faces.
• I can draw the missing face on a net.

You need

The pyramid and prism nets (cut-out sheets 1 and 2), scissors and glue, one each. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after building the two solids; start Session B with Part A.

Watch for these ideas

• Naming a solid from how many faces it has. A square pyramid and a triangular prism both have five.
• Calling every solid with triangles a pyramid. A pyramid’s triangles meet at one point.
• Expecting every net of a solid to look like the cut-out one. The same faces joined another way can still fold.

Answers

• Part A: A rectangular prism, 6; B triangular pyramid, 4; C cube, 6; D triangular prism, 5; E square pyramid, 5 (solid, faces).
• Part B: 1. a triangle on the bottom end of any one of the rectangles. 2. a triangle on the empty side of the square (on the free side of the top or bottom triangle, next to the gap, it folds into place too).

Nets of other solids

A. Which solid does each net fold into? How many faces will it have?

Solids: cube · square pyramid · triangular prism · rectangular prism · triangular pyramid

B. Each net is missing one face. Draw it where it will fold into place.

Check with the solid you built.

Faces, edges and corners

Each region of a net becomes a face. Each edge is where two faces meet: a fold in the net, or two cut sides joined as it closes. Each corner (vertex) is a point where edges meet. Some edges hide round the back, so children tick each edge as they count it. A check from the net: the sides of its faces pair up as it folds, two sides to each edge, so a cube net’s 6 × 4 = 24 sides make 12 edges.

We are learning to

• count the faces, edges and corners of a solid,
• trace each face and edge back to the net,
• use opposite faces to number a dice net.

Success criteria

• I can count the faces, edges and corners of a solid without missing any.
• I can number a dice net so that opposite faces add to 7.

You need

The cube from Day 1 and the pyramid and prism from Day 3. A closed box (a tissue box) per group, and a dice per pair. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B with the dice net.

Watch for these ideas

• Counting an edge twice, or missing the ones underneath. Tick each edge as you count it.
• Adding up the corners of every face instead of counting the corners of the solid.
• Expecting the same number of edges from the same number of faces. The square pyramid and the triangular prism show it is not so.

Answers

• Part A: square pyramid 5, 8, 5; triangular prism 5, 9, 6; rectangular prism 6, 12, 8 (faces, edges, corners).
• Part B:

  Part C: 5 + 5 − 8 = 2; 5 + 6 − 9 = 2; 6 + 8 − 12 = 2. It is always 2.

Faces, edges and corners

A. Count on the solids you built. Tick each edge as you count it.

B. A dice net

On a dice, opposite faces add to 7. Write the missing numbers on this dice net.

C. Faces + corners − edges

Work it out for each solid in Part A.

Design a box

A box (a rectangular prism) has six rectangular faces in three matching pairs: the top and bottom, the front and back, and the two ends. For a box 3 cm long, 2 cm wide and 1 cm high: top and bottom, 3 cm by 2 cm; front and back, 3 cm by 1 cm; the two ends, 2 cm by 1 cm. In a net each face joins a neighbour along an edge of the same length, and the cube’s cross layout works for any box.

We are learning to

• list the faces of a box from its length, width and height,
• draw a net for a box of a given size,
• check a net by folding it.

Success criteria

• I can say the size of each face of a box.
• I can draw a net that folds into my box with no gaps or overlaps.

You need

1 cm grid paper, scissors and glue. The box net (cut-out sheet 2), one each. The worksheet, one per child.

Lesson flow (about 50 minutes)

Two half-sessions instead? Split after Part A; start Session B by drawing the net.

Watch for these ideas

• Making every face the same size, as on a cube.
• Joining a face along an edge of the wrong length, so it hangs over or leaves a gap.
• Putting the two faces of a pair side by side. They sit opposite each other, so in a strip of four sides they take turns.

Answers

• Part A: top and bottom, 4 cm by 3 cm; front and back, 4 cm by 2 cm; the two ends, 3 cm by 2 cm.
• Part B: nets vary. A net works when it has those six faces, each joined along an edge of the same length, and folds with no gaps or overlaps. Part C: 6 faces, 12 edges and 8 corners; the faces opposite each other are the same size.

Design a box

A. A box is 4 cm long, 3 cm wide and 2 cm high. What size is each face?

B. Draw a net for the box. Each square stands for 1 cm.

Then copy it onto 1 cm grid paper, cut it out and fold it. Does it close with no gaps or overlaps?

C. Fold the box net from cut-out sheet 2

It has ______ faces, ______ edges and ______ corners.

Which faces are the same size as each other?   ______________________________________

Nets to fold: a cube and a square pyramid

One copy per child (Days 1 and 3). Cut along the solid lines, fold along the dashed lines, and glue each grey tab under the face it meets. Fold every line before gluing.

Teacher note: a thin card stock folds more crisply than paper. Score the dashed lines with a ruler and a blunt pencil first.

Nets to fold: a triangular prism and a box

One copy per child (Days 3 and 5). Cut, fold and glue the same way. Keep the box net flat until Day 5, when it checks the box net you design.

Teacher note: the dashed lines between faces become edges when folded; the solid outer lines meet in pairs and become edges too.

What we know: Nets and Solids

Work on your own. Picture each net folding before you answer.

1. Which solid does this net fold into?   ____________________
2. Circle each net that folds into a cube.

   a

   b
3. A triangular prism has ______ faces, ______ edges and ______ corners.
4. Draw a net of a cube that is not a cross.
5. On a dice, opposite faces add to 7. Write the missing numbers on this dice net.
6. Sketch a net of a triangular prism.
7. A net of 4 triangles folds into which solid?   ____________________   How many corners has it? ______
8. A box is 5 cm long, 2 cm wide and 3 cm high. What size is each pair of faces?
   top and bottom: ______ cm by ______ cm

   front and back: ______ cm by ______ cm

   the two ends: ______ cm by ______ cm

Answers and marking guide

Answers

1. square pyramid (1 square and 4 triangles)
2. a folds, b does not fold
3. 5 faces, 9 edges, 6 corners
4. Any cube net except the cross (there are 10 others). Check it by folding or with a dice.
5. Each missing number is opposite one that is shown:  
6. 2 triangles and 3 rectangles, joined so that they fold: for example, three rectangles in a row, with a triangle on the top end of one and another on the bottom end of one.
7. triangular pyramid, 4 corners
8. top and bottom, 5 cm by 2 cm; front and back, 5 cm by 3 cm; the two ends, 2 cm by 3 cm

A quick three-level guide

Eight questions, four ideas. A child at standard answers most questions and can say why, by reading the faces of a net: their shapes, how many there are and where they join.

Weekly class record

Jot a tick as you move around the room; the mini-check fills any gaps. A tick a day is plenty.

The five columns are the five days: unfolding a box and folding a cube, testing cube nets, building other solids from nets, counting faces, edges and corners, and designing a box net.