A net is a flat pattern that folds into a solid. Six squares make a cube only if they land on six different faces; a triangular prism has two triangles and three rectangles.
A cereal box starts as one flat piece of card. Which flat shapes fold up into a box, and which ones jam?
A net is a flat pattern that folds up into a solid. A cube's net is six squares joined along their edges. A prism is a solid with two matching ends and flat rectangular sides; the net of a triangular prism is two triangles and three rectangles.
Predict: Read the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Try: Try it on the board and compare the result with your prediction.
Investigate: Work out why it happens, one step at a time.
Modify: Change the problem on purpose and see what happens.
Practise: A few on your own, to check you have it.
Make: Make your own problem using what you have learned. Expect a few tries; that is normal.
Make your prediction first. Help opens once you've locked it in.
PredictRead the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Six in a row
Picture wrapping the row round a cube: where does the fifth square go?
TryTry it on the board and compare the result with your prediction.
Fold the net
Click a square to add it or take it away. The colours show which face each square becomes.
Try it yourselfYour edits are saved in this browser.
Click squares to change the row until the board says it folds into a cube. Was your prediction right?
Use the board. This ticks when you get there.
InvestigateWork out why it happens, one step at a time.
Six squares is not enough
Think about the faces of the cube.
Read Zara's reasoning. What else must be true?
A net folds into a cube. How many squares does it have?
Zara says her block of six squares folds into a cube. Click the line where her reasoning goes wrong.
ModifyChange the problem on purpose and see what happens.
Other nets and other solids
Need a hint?
Start with a row of 4 squares.
Another hint
Add one square above and one below the row.
Need a hint?
Move one square so that two squares would land on the same face.
Another hint
A row of five with one square on top does not fold.
Need a hint?
The net area is the area of 2 triangles plus 3 rectangles.
Another hint
Slide the length L to 5.
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Make a net of a cube with a row of four squares in the middle.
Use the board. This ticks when you get there.
Make a net with six squares that does not fold into a cube.
Use the board. This ticks when you get there.
The triangle has sides 3, 4 and 5 cm. Set the length to 5 cm. What is the net's area?
Use the board. This ticks when you get there.
PractiseA few on your own, to check you have it.
Nets
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A prism has a right triangle with sides 6, 8 and 10 cm and length 5 cm. Set the board to match.
Use the board. This ticks when you get there.
Read the net's area on the board. The prism's surface area is how many square centimetres?
Review: a triangle has base 8 cm and height 5 cm. What is its area in square centimetres?
MakeMake your own problem using what you have learned. Expect a few tries; that is normal.
A net to fit
Then: why does a net show the surface area exactly, when a 3D drawing does not?
Try it yourselfYour edits are saved in this browser.
Need a hint?
Each extra centimetre of length adds 3 + 4 + 5 = 12 cm² with a 3, 4, 5 triangle.
Another hint
The two triangles give 12 cm² whatever the length.
Make a prism net with a surface area between 90 and 100 cm². Use a 3, 4, 5 triangle.
Use the board. This ticks when you get there.
For teachers
Students build nets on a grid and watch the board fold them into a cube, then find the net area of a triangular prism (AC9M7SP01, node 1). About 35 minutes.
I can tell whether a net folds into a cube, and say how I know.
I can name the faces in the net of a prism or a pyramid.
I can find the surface area of a triangular prism from its net.
Before class
Do the Run board yourself first, then fold a real cube net from card if you have time.
The one idea: a net works only if every face is covered exactly once. Counting six squares is necessary but not enough (Zara's mistake).
The board folds by rolling a cube over the squares, so the colour on each square is the face it becomes. The cube has 11 different nets; the Make task is not about finding all of them (see Stretch).
Running the lesson
Predict: ask which square would land on the first one.
Run: ask students to find a net before they check it on the board.
Investigate: ask what Zara could do to check her block.
Modify: for the prism, ask which side of the triangle each rectangle matches.
Make: ask why the area has two parts, the ends and the sides.
The hard part (on purpose)
Picturing the fold. Let students build a cube from paper or linking squares beside the board; the board's colours say where each square lands.
When students get stuck
A student says any six joined squares fold into a cube. Ask: Which two squares would land on the same face? Fix: Roll the cube across the squares, or fold a paper copy.
A student forgets the two triangles when finding a prism's area. Ask: How many faces does a triangular prism have? Fix: Five faces: three rectangles and two triangles.
A student halves the net area. Ask: Is the net the whole surface or only part? Fix: The net is the whole surface laid flat.
Stretch and support
Stretch: A cube has 11 different nets (turning or flipping a net does not count as new). Can you find them all?
Support: Give students six linking squares or a card net to fold before the board.
Where it leads
This starts AC9M7SP01.
Where it leads: views and isometric drawings (next lesson); surface area and volume of prisms (Measurement); Year 8 volume of prisms and cylinders.
What each step is for
six in a row: Committing to whether six squares in a row fold into a cube shows whether they count squares or picture the fold.
fold the net: Changing the squares of a net and watching the board fold it shows that a net works only when all six squares land on different faces.
six squares is not enough: Six squares is necessary but not enough (Zara counts only); the test is whether the faces differ; a prism net adds up its faces.
other nets and other solids: Different cube nets (a cross, six squares that fail) and the prism's net area: faces of a prism are two ends and a rectangle for each side.
nets: Prism surface area and other nets, mixed; counting faces is the planted slip; the triangle area review keeps the prism's end faces fresh.
a net to fit: Choosing the length of a prism to meet a target area applies the net as faces added up.
Now you can
Tell whether a net folds into a cube, and say how I know.
Name the faces in the net of a prism or a pyramid.
Find the surface area of a triangular prism from its net.