Perimeter and Area Yr 7 QCA, HBS, Ri The Royal Institution of Great Britain www.rigb.org/engagingmaths

Pin-board shapes Draw shapes on the pin-board by joining dots. Write down the following information for the shape: Count the dots around the perimeter (D.P.) Count the dots inside the shape (D.I.) Calculate the area of the shape (A.) The Royal Institution of Great Britain www.rigb.org/engagingmaths

Pin-board shapes Shape A D.I. D.P. Comments No.1 1 4 No.2 5 10 No.3 2 4 No.2 5 10 No.3 2 8 ...

At home... Conduct your investigation and write down any patterns relating the three variables that you find. Find a formula for the area of a shape using the dots in the perimeter and number of dots in the middle. Give reasons for why your formula works. The Royal Institution of Great Britain www.rigb.org/engagingmaths

Pick’s Theorem

Does the number of dots in the perimeter give us the length of the perimeter of the shape?

Who was Pick? Georg Alexander Pick August 10, 1859 – July 26, 1942 Born in Austria, died in Bohemia, now Czech Republic Set homework to research about this mathematician, pupils present their work in the class, can make a poster, or a webpage in the VLA From Wikipedia, the free encyclopedia Georg Alexander Pick (August 10, 1859, Vienna – July 26, 1942, Theresienstadt, Bohemia, now Czech Republic) was an Austrian mathematician. He was born to Josefa Schleisinger and Adolf Josef Pick. He died in the Theresienstadt concentration camp. Today he is best known for Pick's formula for determining the area of lattice polygons. He published it in an article in 1899; it was popularized when Hugo Dyonizy Steinhaus included it in the 1969 edition of Mathematical Snapshots. Pick studied at the University of Vienna and defended his Ph.D. in 1880 under Leo Königsberger and Emil Weyr. After receiving his doctorate he was appointed an assistant to Ernest Mach at the Charles-Ferdinand University in Prague. He became a lecturer there in 1881. He took a leave from the university in 1884 during which he worked with Felix Klein at the University of Leipzig. Other than that year, he remained in Prague until his retirement in 1927 at which time he returned to Vienna. Pick headed the committee at the (then) German university of Prague which appointed Albert Einstein to a chair of mathematical physics in 1911. Pick introduced Einstein to the work of Italian mathematicians Gregorio Ricci-Curbastro and Tullio Levi-Civita in the field of absolute differential calculus, which later in 1915 helped Einstein to successfully formulate General relativity. Charles Loewner was one of his students in Prague. He also directed the doctoral theses of Josef Grünwald, Paul Kuhn, Charles Loewner, and Saly (Ramler) Struik. Pick was elected a member of the Czech Academy of Sciences and Arts, but was expelled after Nazis took over Prague. After retiring in 1927, Pick returned to Vienna, the city where he was born. After the Anschluss when the Nazis marched into Austria on March 12, 1938, Pick returned to Prague. In March 1939 the Nazis invaded Czechoslovakia. Pick was sent to Theresienstadt concentration camp July 13, 1942. He died there two weeks later. The Royal Institution of Great Britain www.rigb.org/engagingmaths

Teacher only Pick’s Theorem... … is not a relationship about perimeter and area! Teacher only

Pick’s Theorem What did you discover?

Perimeter and area Is there always a relationship between perimeter and area? Draw a shape with perimeter 24, what’s the area of your shape? What’s the smallest area you can make? Draw a shape with area 24, what’s the perimeter of your shape? What’s the longest perimeter you can make? The Royal Institution of Great Britain www.rigb.org/engagingmaths

Activity Ask pupils to investigate rectangles with the perimeter and area in the previous slide using their maths books (squared paper) Teacher only

Perimeter, area, shapes and designing clothes

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Which shapes match? ?

Make your own match In pairs, cut the sleeve of the old t-shirt. In the body of the t-shirt draw a shape that you can ‘sew’ the sleeve into – you cannot chose a circle. What is your guess of how it will look like? If you have time repeat with the other sleeve, with a different shape use the sleeve from their old t-shirt. They will detach the sleeve. In the body of the t-shirt they will draw a suitable shape to match with the sleeve -- any shape but a circle. Pupils work on the activity, in groups. Pupils are encouraged to conjecture what the sleeve will look like, how it will drape as a result of their choice of shape The Royal Institution of Great Britain www.rigb.org/engagingmaths

Plan your design, draw the shape. Cut out the shape to make a hole Plan your design, draw the shape. Cut out the shape to make a hole. Create your design by stapling the sleeve into your hole. use the sleeve from their old t-shirt. They will detach the sleeve. In the body of the t-shirt they will draw a suitable shape to match with the sleeve -- any shape but a circle. Pupils work on the activity, in groups. Pupils are encouraged to conjecture what the sleeve will look like, how it will drape as a result of their choice of shape The Royal Institution of Great Britain www.rigb.org/engagingmaths

Perimeter, area, shapes and designing clothes Can you explain your design process? How did you know you would be able to sew the sleeve into the hole? What shape was your hole? The Royal Institution of Great Britain www.rigb.org/engagingmaths

Teacher only