Student print pack
Geometry
Engineer
Investigate shape properties, measure carefully and build a structure that passes every mathematical test.
Property Detective
Name a shape from evidence, not from the way it is turned.
Use sides, vertices and angles to support every name. Size and the way a shape is turned do not change its properties.
| Shape | Sides and vertices | Name | One property that proves it |
|---|---|---|---|
| A | |||
| B | |||
| C | |||
| D | |||
| E |
1Property riddle
I have four straight sides. Opposite sides are equal. Every angle is a right angle. Write every name that fits.
2A turned shape
Shape B is still a square because
Regular or Irregular?
A regular polygon has all sides equal and all angles equal.
What evidence would you mark on this drawing?
Which regularity condition fails?
1Same number of sides, different regularity
Draw one regular hexagon and one irregular hexagon. Your regular drawing may be approximate: the equality marks or labels are the important evidence.
2Complete the mathematical explanation
Both of my shapes are hexagons because
The first is regular because
The second is irregular because
3D Shape Investigator
Rotate the digital solid before you record what is hidden.
Vocabulary: A flat face is a flat 2D region. An edge is a line where two surfaces meet. A vertex is a corner. A cylinder, cone and sphere also have curved surfaces.
| 3D shape | Flat faces | Curved surfaces | Edges | Vertices | A property that proves its name |
|---|---|---|---|---|---|
| Cube | |||||
| Cuboid | |||||
| Triangular prism | |||||
| Square pyramid | |||||
| Cylinder | |||||
| Cone | |||||
| Sphere |
1Compare
A triangular prism and a square pyramid both have triangular faces. How are they different?
2Predict a net
Before pressing “open net”, sketch where you think the faces of one solid will go.
I know it is a because
Cube Net
Predict which faces meet, then turn six squares into one solid.
Before cutting
Face 2 will be opposite face: _____
Face 1 will meet face 4: YesNo
After building
Faces: ______ Edges: ______ Vertices: ______
One prediction I would revise: ____________________
Triangular Prism Net
Three rectangles wrap around two triangular ends.
Before cutting
Circle the two matching faces—the same shape and the same size. Put a star on a rectangular face.
Which edges of the rectangles will meet? Mark matching pairs.
After building
Flat faces: ______ Edges: ______ Vertices: ______
It is a prism because ____________________________
Boundary or Interior?
Perimeter measures the distance around. Area measures the space covered.
Each small square is 1 unit by 1 unit. Count perimeter in units and area in square units. Show how you counted.
Perimeter = ______ units
Area = ______ square units
Perimeter = ______ units
Area = ______ square units
1What did you count?
For perimeter, I counted:
For area, I counted:
2Compare your counts
Which shape covers more square units?
Shape ______
Which has the longer boundary?
Shapes A and B have the same but different
Choose One Shape Challenge
This page is optional. Try it if page 7 felt comfortable.
Choose one challenge. Use grid squares as units. You do not need a formula.
ASame area
Draw two connected shapes with area 12 square units but different perimeters.
Perimeters: ______ and ______ units
BSame perimeter
Draw two connected shapes with perimeter 16 units but different areas.
Areas: ______ and ______ square units
What did you notice?
My two shapes are different because
Plan the Structure
Design criteria are the rules your structure must meet. Turn each rule into something you can see or measure.
Design criteria
- Stands without help for 10 seconds
- Reaches at least 30 cm high
- Fits inside a 20 cm × 20 cm base
- Uses no more than 6 A4 sheets and 60 cm of tape
- Shows at least two identifiable 2D or 3D shapes
- Holds a 50 g object for 5 seconds
Material budget
A4 sheets planned: ______ / 6
Tape planned: ______ cm / 60 cm
Object used for test: __________________
My stability strategy: __________________
1Labelled side view
Show planned height, main 2D/3D shapes and where the object will rest.
2Labelled top view
Show the base dimensions and how it stays inside 20 cm × 20 cm.
The design rule most at risk is because
Test, Improve, Explain
A strong design is not merely finished—it is tested against evidence.
| Criterion | Plan check | Mid-build check | Final result / evidence |
|---|---|---|---|
| Stands for 10 seconds | □ | □ | |
| At least 30 cm high | □ | □ | ______ cm |
| Base within 20 cm × 20 cm | □ | □ | ______ cm × ______ cm |
| Within paper/tape budget | □ | □ | ______ sheets; ______ cm tape |
| At least two named shapes | □ | □ | |
| Holds object for 5 seconds | □ | □ |
My mathematical features
One 2D shape: __________________________
Its proving property: ___________________
One 3D shape: __________________________
Its proving property: ___________________
My deliberate improvement
I noticed: ______________________________
I changed: ______________________________
The new evidence showed: _______________
Exit check
Final explanation: A mathematical choice I made was ____________________________. My evidence is ________________________________________________.