Chapter 5 –
Look for a Pattern – Day 1
POD – Problem #4 Page 127 –
Rectangular Dots
Put a couple of solutions on
transparency, discuss and compare
Discuss – Sequences in book – page
109
A.
1, 2, 4, ____, ____, ____, ____
B.
1, 3, 5, 7, ____,____,____,____
C.
1, 6, 11, 16, ____,____,____,____
D.
1, 4, 9, 16, ____,____,____,____
E.
1, 3, 6, 10, ____,____,____,____
F.
3, 6, 5, 10, 9, 18, 17, 34, ____,____,____,____
G.
1, 3, 4, 7, 11, 18, 29, ____,____,____,____
H.
2, 3, 5, 9, 17, 33, ____,____,____,____
I.
77, 49, 36, 18, ____ (This sequence ends here)
Look
for a Pattern
Mathematics can be characterized as the science of
patterns.
Patterns often involve objects, number relationships, and
geometric designs.
Patterns are connected with basic topics as addition and
multiplication facts, geometry, functions, ….
Patterns are present in nature, music, and art and
throughout many cultures.
Some of the key tasks involved in the study of patterns
include:
Recognize and
extend a pattern
To create a
pattern or supply some missing part
To analyze
and describe the pattern
To generalize
a pattern
First
with a verbal description
**Later
with a variable
The Look
for a Pattern strategy may be appropriate when:
® A list of data is given.
® A sequence or series of numbers is
involved.
® Listing special cases helps you
deal with complex problems.
® You are asked to make a prediction
or generalization.
® Information can be expressed and
viewed in an organized manner, such as in a table.
The study
of patterns is fundamental to mathematics.
Some different types of patterns include:
a) Patterns that have a repeating core:
AAB
AAB AAB . . .
or ABC ABC ABC . . .
b) Patterns that have a “growing: core:
c) Patterns that grow:
2, 5, 8, 11, …
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d) Nested patterns that combine two or more
patterns into one:
Pattern A: 2, 5, 8, 11, . . .
Pattern B: 3, 5, 7, 9, . . .
Nested pattern: 2, 3, 5, 5, 8, 7, 11, 9, . . .
IN CLASS – Shooting
Free Throws
John
notices that with daily practice he can increase the number of free throws he
makes before missing. On the first day
he makes only1; on the second day 5; on the third day 14; and on the fourth day
30. If this pattern should continue, how
many can he expect to make on the fifth day?
IN CLASS – Large Powers
If you
raise 3 to the 328th power, what is the unit’s digit? Look for a pattern from 
IN CLASS – Now I know my ABC’s
What is the
100th letter in the sequence A, B, C, A, B, C, A, B, C, ...
IN CLASS - Pictorial Patterns
Handout
Assignment - POD
– How many beads are hidden under the clouds
Homework:
Read Pgs 115-125 – Note - Read Dodger
Stadium, but I’d give “shorter time”
Pitter Patter Rabbits’ Feet -
again I’d use fewer total months
Similarly
with Night of the Howling Dogs – I’d
do 2 minutes
And
do Milk Lovers with only 7 days
Pg
126, #1, #3