Here is a real tissue box, and next to it a drawing of the very same box on dotted paper.
How does flat, dotted paper let us draw a solid box you could pick up? And look at the lines running back into the page: why do they all lean the same way?
Look at the cuboid on the dot paper.
First comes the front face. That is the side facing you, with its upright lines staying upright and its base lines following the dots. Next come the depth lines: these are the lines that run back into the page along the slanting dots. The way they lean is called the slant. Last, the back corners join up to close the box.
Once the box is closed you can see three faces: the front, the top and the side. Look closely at the depth lines, and be ready to say what stays the same about every one of them.
Now we draw one on the board together. Today we build a 4 wide by 3 tall by 2 deep cuboid, edge by edge. First we draw the front face, 4 wide and 3 tall. Then we draw the depth lines back for a depth of 2. Last we join up the back corners.
While one pupil taps at the board, the rest of us point in the air which way each depth line will lean before it is drawn. Watch that every depth line lands on the same slanting run of dots. Watch too for the top face and the side face appearing as the box closes.
On the dot paper in your maths copy, draw a 4 × 3 × 2 cuboid.
Draw the front face first — 4 wide and 3 tall. Then draw the depth lines back along the dots for a depth of 2, keeping every one at the same slant. Finally, join up the back corners.
Label the front face, the top face and the side face.
Now one pupil at the board builds each cuboid to match a target size, and the rest of us predict the size and confirm the answer. We start with the 4 × 3 × 2 box we already know. Then we build a 2 × 2 × 2 cube. Next comes a wider 5 × 2 × 3. Finally we build a 3 × 4 × 2 to check that the front face can be tall or wide.
For each one, the pupil at the board sets the size and presses Check, and the class watches for the match. Four boxes is the full set, but two is a fine place to stop if time is short.
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