Each civilisation came up with its own number system, or number systems spread with trade. Explain and discuss Roman, Hindu and Mayan number systems.
-- Whole class activity: Children explore writing numbers using different systems. Compare the merits of each system.
Highlight the prime numbers on the ITP Number grid. Christian Goldbach (1690–1764) thought that every even number greater than 4 could be made by adding 2 prime numbers (and that every odd number more than 5 could be made from adding three prime numbers), but he couldn't prove it. Centuries later, mathematicians all over the world are trying to prove or disprove his conjecture…
-- Whole class investigation: Children collaborate to investigate Goldbach’s conjecture.
Show children a set of Napier’s rods and demonstrate how they work. A similar method known as the Gelosia method was used in India in the 12th century, and may have been used even before then. Demonstrate drawing the grid for 34 × 26, then solving the calculation. Consider reading about Charles Babbage’s ‘analytical adding machine’, and how Ada Lovelace wrote what is now considered to be the first ever computer program for it.
-- Explore the use of Napier’s rods/bones for multiplication.
Write the first six terms in the Fibonacci sequence: 1, 1, 2, 3, 5, 8. Children write the next 4 terms. Share the mathematical strategy for finding the total of 10 consecutive numbers in the sequence. You multiply the 7th number by 11. Show how Pascal’s triangle is made. Can you see any patterns in this arrangement of numbers?
-- Continue to create a version of Pascal’s triangle. Explore underlying number patterns.
-- Explore Fibonacci-style sequences; test a strategy for adding ten consecutive numbers in the sequence.
-- Shade multiples on Pascal’s triangle to reveal underlying patterns.
Who was Pythagoras? Children draw, on cm-squared paper, a (3-4-5) right-angled triangle. Explain Pythagoras’ theorem: a2 + b2 = c2. Children check that the theorem works for their triangles. 3, 4, 5 is a special set of numbers that fit Pythagoras’ theorem because they are all whole numbers. Not many right-angled triangles are made from whole numbers in this way! One of our challenges today asks you to try to find some more.
-- Whole class investigation: Children explore right-angled triangles on cm-squared paper, and attempt to discover ‘Pythagorean triples’.