## MTH211 Foundations of Elementary Math 1

### Fun with whole numbers.

Notes on Whole Numbers
Fall 2020

#### § 1.2 Patterns and Problem Solving

Types of patterns

• Figurate
• Arithmetic
• Geometric
• Recursive
• Others
##### Math Activity 2.1: Pattern Block Sequences

Math Learning Center Pattern Blocks

Explore the patterns in sequences of pattern blocks.

1. Here are the first 4 terms in the sequence.
, , ,
• Draw the 5th figure in the sequence.
• How many squares and hexagons will be in the 10th figure?
• Which pattern blocks will be at the ends of the 77th figure?
• Explain how many pattern blocks will be in the 77th figure.
2. Here are the first 4 terms in the sequence.
, , ,
• Draw the 7th figure in the sequence.
• How many hexagons will be in the 10th figure?
• Which pattern blocks will be at the ends of the 185th figure?
• Explain how many of each pattern block will be in the 186th figure.
3. Here are the first 3 terms in the sequence.
• Draw the 4th figure in the sequence.
• How many green triangles will be in the 10th figure?
• Explain how many green triangles will be in the 10th figure.
• Explain how many green triangles will be in the 100th figure.

Alternate Activity: Fibonacci Rabbits

"Fibonacci considers the growth of a hypothetical, idealized (biologically unrealistic) rabbit population, assuming that: a newly born pair of rabbits, one male, one female, are put in a field; rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits; rabbits never die and a mating pair always produces one new pair (one male, one female) every month from the second month on. Fibonacci posed the puzzle: how many pairs will there be in one year?" Wikipedia

• At the end of the first month, they mate, but there is still only 1 pair.
• At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field.
• At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field.
• At the end of the fourth month, the original female has produced yet another new pair, and the female born two months ago also produces her first pair, making 5 pairs.

Build a spreadsheet to keep track of months, new pairs, 1 month old pairs, adult pairs, and total pairs. Starter Spreadsheet