Students find a box's inside size from its outside and walls, design a case for an Uno from the part outwards (part, gap, wall), meet Sam's one-wall slip, change the wall thickness, build the case in Tinkercad 3D by typed dimensions, and find the smallest case that fits.
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Students will be able to
I can work out a box's inside from its outside and walls.
I can design a case from the part outwards.
I can set exact sizes in Tinkercad.
Timing
Predict and Try 6 min · Worked example 8 min · Vary 6 min · Tinkercad 12 min · Practise and Make 8 min
Before class
The board is a 2D top view; heights work the same way (a floor and a lid instead of side walls). Measure the real part with calipers if you have them: published sizes don't include sockets that stick out (the Uno's USB and power sockets do). Tinkercad: the same class code as Circuits.
Running the lesson
Predict: draw a box on the board and point at both walls.
Worked example: write it outwards, live.
Tinkercad: ask why the hole box is placed 2 mm in and up.
The hard part (on purpose)
Students drag shapes to 'about right'. Make typing dimensions the rule.
When students get stuck
What you will see
A question to ask
The fix
A student's case is 2 mm too small.
How many walls does a box have across its width?
Two: subtract (or add) both.
Answers to the checks
inside width: A box is 40 mm wide on the outside, with 2 mm walls. How wide is the inside? 36 mm: 40 − 2 − 2. There is a wall on the left and one on the right.
Thicker walls: Make the walls 3 mm. How much did the inside width shrink?
From 56 to 54: 2 mm for a 1 mm thicker wall, because there are two walls.
Inside 60: Now change the outside width so the inside is exactly 60 mm (walls still 3 mm).
Outside = 60 + 3 + 3 = 66 mm.
From the part outwards: The Uno is 53.4 mm deep. With a 1 mm gap and a 2 mm wall each side, how deep is the case outside (mm)? 59.4 53.4 + 2 × 1 + 2 × 2 = 59.4 mm.
Find the mistake: Sam's 57 mm part won't go in. Click the line where Sam's working first goes wrong. line 3 Line 3: there is a wall on each side, so the inside is 60 − 2 − 2 = 56 mm. The 57 mm part is 1 mm too big.
The case: Set the outside size so the Uno fits with 1 to 1.5 mm to spare on the tightest side (2 mm walls).
About 75 × 59.5 mm outside.
Thicker walls: Now make the walls 3 mm for a tougher case, keeping a 1 to 1.5 mm gap.
Each dimension grows by 2 mm: about 77 × 61.5 mm.
Inside: A box is 80 mm outside with 2.5 mm walls. Inside width (mm)? 75 80 − 2.5 − 2.5 = 75 mm.
Outside: A 30 mm part, a 0.5 mm gap each side, 2 mm walls. Outside width (mm)? 35 30 + 2 × 0.5 + 2 × 2 = 35 mm.
the smallest case: Make the smallest case you can with 1.5 mm walls and at least 0.5 mm to spare: no more than 73 × 58 mm.
73 × 57.5 mm: every millimetre traced back to the part, a gap and a wall.
Solutions
One possible solution for each task. Other correct programs are fine.
Vary: change one thing › The case
Open task: any program that does what the step asks.
Vary: change one thing › Thicker walls
Open task: any program that does what the step asks.
the smallest case
Open task: any program that does what the step asks.
Stretch and support
Stretch: Add holes in the case wall for the Uno's USB and power sockets, measured from the board's edge.
Support: A drawn cross-section with part, gap and wall labelled on both sides.
Exit ticket
A part is 50 mm wide. With a 1 mm gap and 3 mm walls, how wide is the case outside?
50 + 2 × 1 + 2 × 3 = 58 mm.
What each step is for
inside width: Committing to the inside width tests the new move: a wall on each side comes off.
Try: walls and inside: Changing the wall on the board settles the prediction: the inside shrinks by twice the change.
Worked example: a case for an Uno: Working outwards from the part (part + gaps + walls) models the move; Sam's one-wall slip is planted after the method.
Vary: change one thing: Designing the case on the board, then changing only the wall, shows the outside must grow by twice the change to keep the same gap.
Build it in Tinkercad: Building the hollow box in Tinkercad by typing dimensions (not dragging) is the habit that makes parts fit.
sizes: Inside and outside both ways.
the smallest case: Finding the smallest case that still fits reverses the process: start from a limit and work back to the dimensions.