Download Patterns, Relationships, and Algebra

Classification and Patterning
EDN 322
Classification and Patterning…

Fundamental to learning about the real world;

involve the creation of relationships;

are easily integrated;

can be viewed as a form of problem solving and provide
students with the opportunity to develop logical reasoning
abilities;

provide the basis for building early number concepts;

facilitate algebraic thinking;

are fun!
Classification
Making decisions about certain attributes of
objects and sorting them based on that
classification.
Difference Trains

Each car in a train is different from the
car it follows in a specified number of
ways. Find the difference pattern in this
train… Can you continue the train?
One-difference train:
Two-difference train:
Thin
Blue
Venn Diagram
Attribute Blocks
Rectangle
T
T
T
T
T
T
T
T
T
Color – Red, Yellow, Blue
Guess my Rule
T
T
T
Shape – Triangle, Square
Thickness – Thick, Thin
Size – Small, Large
Large
Triangle
T
T
T
T
T
Guess my Rule
T
T
T
T
T
Thick
T
T
Quadrilaterals
Venn Diagram
Quadrilaterals
Regular Polygon
Quadrilaterals
Trapezoids
Parallelograms
Quadrilaterals
Trapezoids
Parallelograms
Venn Diagram
Quadrilateral
Parallelograms
Seriation



Seriation is the ability to place objects in
order according to a given or chosen
criterion
Possible criteria include:
- length
- width
- height
- weight
- diameter
- tone
Prerequisite to more abstract ordering of
numbers and a foundation for math
reasoning
Types of patterns

Repeating Patterns

Growing Patterns or Sequences

Number Patterns
2, 4, 8
NEXT
Other Repeating Patterns
Fill in the missing part:
____
____
____
Examples of Patterns
Number of Boys
Number of Hands
Number of Girls
Number of
Triangles
1
2
2
4
3
6
4
8
3
1
6
2
9 12
3 4
10
20
B
2XB
45
?
N
N3
Calculator Patterns
Choose a number between 0 and 9 and add a constant
repeatedly to that number. Remember to use the automatic
constant feature. For example, to start with 7 and add 4
repeatedly, you press 7 + 4 = = = . . .
•
What digits appear in the ones place?
•
How long is the pattern before it repeats?
•
Are all patterns the same length?
•
Are there shorter ones?
•
Can you find one that is length 6? Why not?
•
How does this change when the start number changes?
•
How does it change when the skip number changes?
Calculator Patterns
Repeat the preceding exploration, but this time
use multiplication instead of addition. What do
you notice? For multiplication, the first factor
is generally the one stored. Therefore to start
with 4, for example, and repeatedly multiply by
7, press 7 x 4 = = = . . .
In this exploration the calculator will
“overload” relatively quickly. Since you are
only interested in the values of the ones digit,
how can you continue the pattern?
Calculator Patterns
Pick any one-digit number and multiply by 9,
then 99, then 999, then 9999. What do you
observe? Try other numbers such as 2, then 22,
then 222,…