MTH211 Foundations of Elementary Math 1

the one percent

Fun with whole numbers.

MTH211
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.
    pattern block hexagon, pattern block sequence, square, hexagon, square, pattern block sequence, hexagon, square, hexagon, square, hexagon, pattern block sequence, square, hexagon, square, hexagon, square, hexagon, square
    • 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.
    pattern block hexagon, pattern block sequence hexagon, trapezoid, pattern block sequence hexagon, trapezoid, rhombus, pattern block sequence hexagon, trapezoid, rhombus
    • 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.
    pattern block triangular 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