Mathematics K–6 · Years 5–6
Two strips and a split pin: quadrilaterals from their diagonals
Measurement and space
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The idea
Two strips pinned together act as the diagonals of a quadrilateral, and measuring the sides and angles of each shape they make, and folding it along its diagonals, shows which quadrilateral it is and which diagonals are lines of symmetry.
What you need
- 4 card strips per pair: two 20 cm long and two 12 cm long, each punched at its midpoint, and each 20 cm strip also punched 5 cm from one end
- 2 split pins
- a protractor, a ruler, scissors and A3 paper
How to do it
- Join the two 20 cm strips at their midpoints with a split pin and set them at a right angle on the paper. Mark the four strip ends, join them with a ruler, and measure the sides and angles of the shape.
- Keep the pin in place and open the strips to 60 degrees. Mark, join and measure again.
- Join a 20 cm strip and a 12 cm strip at their midpoints, first at a right angle, then at 60 degrees. Mark, join and measure each shape.
- Pin the hole 5 cm from the end of a 20 cm strip to the midpoint of a 12 cm strip at a right angle. Mark, join and measure.
- Record each strip arrangement, the measured sides and angles and the name of the shape in a table. Cut out each shape and fold it along each diagonal to find which diagonals are lines of symmetry.
What you should see
Equal 20 cm diagonals crossing at their midpoints at a right angle give a square with sides of 14.1 cm. Opened to 60 degrees they give a rectangle 10.0 cm by 17.3 cm. Diagonals of 20 cm and 12 cm crossing at their midpoints at a right angle give a rhombus with four sides of 11.7 cm, and at 60 degrees a parallelogram with sides of 8.7 cm and 14.0 cm. The 20 cm strip pinned 5 cm from its end to the middle of the 12 cm strip at a right angle gives a kite with two sides of 7.8 cm and two of 16.2 cm. Measured sides come out close to these computed values. Folding shows that both diagonals of the square and of the rhombus are lines of symmetry, neither diagonal of the rectangle or the parallelogram is, and the kite folds onto itself only along its 20 cm diagonal.
What changes
This activity lists no variables to change, measure and keep the same.
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- The diagonals of every rectangle cross at right angles.
- A rhombus is a square pushed over, so its diagonals are equal.
Safety card
Hazards
- split pins are sharp
- scissors
Controls
- push pins through with the card flat on a table and bend the legs flat
- cut seated at a table and pass scissors handle first
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package is not needed; ordinary classroom supervision under the school's usual risk management.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Mathematics K-10 Syllabus (2022), NSW Education Standards AuthorityMA3-2DS-01MAO-WM-01
- Australian Curriculum v9No Australian Curriculum v9 code is listed.
Sources
The pages the author read to write this activity.