A factor tree is a way of accurately representing a number as the product of its prime factors. Here is an example. 12 So, 12 - 2x 2x 32x 3 (product of primes) The answer will be the same no matter which factors you initially start with. i Make factor trees for the numbers 54, 31, 99, 72, and 100. . Use the trees to express each number as a product of prime numbers. Square BDFH is embedded in square ACEG. Points B, D, F, and H are the midpoints of the sides AC, CE, EG and AG respectively. Diagonals AE, GC, HD and BF meet at point X. (factor tree) 1. Draw a diagram that fits the description. ii. Identify the total number of squares of all sizes which can be traced using only the line segments in your diagram. Extension: How many triangles and rectangles? The number 6 has exactly four factors: 1, 2, 3, and 6. For each natural number less than 25 determine how many factors the number has. [Hint: use a systematic list or table] How many have exactly two factors? Read the first 2 pages of A Mathematician's Lament by Paul Lockhart (2002) - on LEO or click on the link https://www.maa.org/external_archive/devlin/Lockhartstament.pdf Consider the following questions as you read the introduction from Lockhart's book and be prepared to discuss them in your tutorial: a. Lockhart is describing the way mathematics is typically taught in American schools. What has your experience of mathematics learning been like-has it been "stupid and boring", or meaningful and relevant? b. What does/would relevant mathematics learning look like? GLOSSARY: (use your maths dictionary to ensure you understand these words) WORD factor product prime (number) midpoint diagonal natural number conjecture MEANING