introduction to unit 1: patterns & sequences mathematics 12 foundations
TRANSCRIPT
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Introduction to Unit 1Introduction to Unit 1: : Patterns & Sequences Patterns & Sequences
Mathematics 12 FoundationsMathematics 12 Foundations
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DefinitionsDefinitions::1. Sequence:
An arrangement of numbers, symbols, or pictures in order.
Each item or term follows another according to a rule.
Example: {a, b, c, d, e} is the sequence of the first 5 letters
alphabetically {0, 1, 0, 1, 0, 1, ...} {0, 1, 0, 1, 0, 1, ...} {20, 25, 30, 35, ...} {20, 25, 30, 35, ...}
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DefinitionsDefinitions::2. Term:
Each item in a sequence.
3. Finite Sequence: A sequence which eventually ends.Example: {1, 3, 5, 7}
4. Infinite Sequence: A sequence which continues endlessly.
Example: {1, 2, 3, 4 ,...}
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DefinitionsDefinitions::5. Fibonacci Sequence:
A sequence which is determined by calculating the sum of the previous two terms.
Terms one and two have the value of 1. Example: {1, 1, 2, 3, 5, 8, …}
6. Fibonacci Number: A term in the Fibonacci sequence.
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Fibonacci Sequence:Fibonacci Sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... The next number is found by adding the
two numbers before it together The 2 is found by adding the two
numbers before it (1+1) The 21 is found by adding the two
numbers before it (8+13)
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Investigation #1Investigation #1 – Properties of – Properties of Designs (page 2)Designs (page 2)
In most types of construction, it is important to make and extend patterns. A bricklayer builds towers using an odd number of bricks in each row.
Each new tower has one more row than the previous tower had.
Tiffany, a bricklayer, wants to know the number of bricks needed to build a tower with 10 rows.
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Investigation #1Investigation #1 – Properties of – Properties of Designs (page 2)Designs (page 2)
She writes the number of bricks for each tower as a term in a sequence: {1, 4, 9 …}.
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Purpose Describe a patterning rule for extending a
sequence of numbers symbols, or pictures.
Procedure Use a geometrical pattern to draw below
the next three towers in the bricklayer’s project above.
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What is the Pattern or Sequence?What is the Pattern or Sequence? What numbers will we write below for this sequence?
{___, ___, ___, ___, ___, ___, ___, ___, ___, ___ …}
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Draw a graph showing the number of bricksversus the number of rows in the tower.
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Questions:Questions:1. Choose ONE of the following which best
describes the shape of the graph you drew above. Line Parabola Sine Cosine Absolute Value
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2. Explain using the idea of slope, why the graph you plotted can’t be a linear relationship.
3. Describe a rule for finding the number of bricks in a tower, if you know the number of rows in the tower.
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4. Use the rule from question #3 to determine the number of bricks in a tower with the following number of rows.
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5. Fill in the table below with the missing information..