This document provides information about patterns and algebra for a Department of Education. It defines what a pattern is and discusses different types of patterns including repeating, increasing, and decreasing patterns. It provides examples of numeric, object, and shape patterns. The document outlines learning objectives and competencies around identifying, continuing, and determining missing elements in patterns. It includes activities for students to practice translating patterns, predicting subsequent terms, and finding relationships between increasing/decreasing patterns.

1. PATTERNS & ALGEBRA 2
DEPARTMENT OF EDUCATION

2. Objectives:
DEPARTMENT OF EDUCATION
At the end of this session, you should be able
to:
 identify a repeating pattern
 build simple number patterns
 continue simple number patterns and
determine missing elements
 relate addition and subtraction facts

3. Learning Competency:
DEPARTMENT OF EDUCATION
• Determines the missing term/s in a
given combination of continuous and
repeating pattern

4. What is PATTERN?
A pattern is…..
a sequence or order of objects that repeat
or grow.

5. What will occur next in the pattern?
A CB

6.  Kindergarteners are asked to make
patterns and to continue a pattern by
coloring.
So by 2nd grade we better be asking a
little more… Making the steps toward
generalizing

7. Pattern Vocabulary
The pattern rule is the relationship
between number or objects in a
pattern.
The core is the main unit of the
pattern that is repeated.
A term is each one of the parts
making up the pattern.

8. The core of this pattern would be A, B.
There are two terms in each core of this
pattern.
There are six terms in the pattern.
ABABAB

9. Non-numerical patterns can be
translated into a letter code (ABBA)
and then extended to make predictions and solve problems.
A AB B

10. Group activity
DEPARTMENT OF EDUCATION

11. Learning Tasks – Translating Patterns
Mix and Match
•Create a 2- to 4-element core, using your choice of
materials; e.g., colour, orientation, size.
•Extend your pattern 2 more times.
These are both
AABB patterns.

12. DEPARTMENT OF EDUCATION
Presentation of
outputs

13. DIFINITION:
The same grouping over and over.
The pattern never changes.
The pattern can have long or short units.
The pattern can include any items such
as...
numbers, shapes, objects, symbols and
colours.

14. • People patterns:
• Patterns involving actions:
• Patterns with sounds:
boy – girl – boy – girl – boy - girl
jump – jump – hop – jump – jump – hop - jump
snap – clap – clap – snap – clap – clap – snap

15. • Patterns with objects:
• Patterns with geometric shapes:
• Patterns with pictures or symbols:

16. Patterns can be repeating and made up of a core
set of elements—a core unit that is iterated.
Patterns can be increasing or decreasing and
created by orderly change.
9 7 5 3
32 16 8 4 2

17. Also sometimes referred to as “Growing Patterns”
These patterns grow/ increase by the same number of object each time.
Frame 1 Frame 2 Frame 3 Frame 4

18. Learning Tasks – Increasing/Decreasing Patterns
Frame 1 Frame 2 Frame 3 Frame 4
legs 2 4 6 8 ?
body parts 1 2 3 4 5
Add 2 legs each time, skip count
by 2 (recursive), legs go up by
twos, bodies go up by ones.
Look at relationships across
categories (function), double
the body parts.

19. Learning Tasks – Increasing/Decreasing Patterns
Legs and heads 3 5 ? ? ? ? ?
Body parts 1 2 3 4 5 10 100
What’s the relation?
Doubles plus 1
22

20. Learning Tasks – Increasing/Decreasing Patterns
Note: Caterpillars, Worms and Pattern Block Trees are adapted from Lessons for Algebraic Thinking: Grades K–2,
pp. 2–11, 89–98, 157–170, by Leyani von Rotz and Marilyn Burns. Copyright © 2002 by Math Solutions Publications.

21. Pattern rules reveal mathematical relationships.
Pattern rules describe how a pattern grows and can
be used to make logical predictions.
What changes?
What stays the same?

22. A pattern rule must account for all elements of a pattern, including
the first one.
Body Parts 4 7 10 13 ? ? ?
Age 1 2 3 4 5 10 100
Body parts:
Start at 4 and add 3 each time
Age:
Start at 1 and add 1 each time
Relationship:
Body parts—3 times the age plus 1

23. Learning Tasks
Predicting Patterns
Making the link between repeating and increasing patterns
2 31
5 10 15
a) What would the 20th shape be?
b) What would the 30th shape be?
c) What would the 32nd shape be?

24. Learning Tasks
5
2 31
10 15
30 31 322515105 20
2 322717127 22
30 32 33 34 352515105 20
What would the
32nd shape be?

25. • Think for 20 seconds
• Write and draw silently for 60 seconds
• Switch papers with another table
• Start again

26. – create, represent and continue a variety
of number patterns and supply missing
elements

27. –build number relationships
(addition and subtraction facts to at least 20)

28. make generalizations about number
relationships
‘When I add zero it
does not change the
number’‘when I count by
fives the last
number goes
five, zero, five,
zero, …’
An odd number
plus an odd
number always
equals an even
number’

29. Group activity
DEPARTMENT OF EDUCATION

30. Learning Tasks
5
2 31
10 15
a) Create a pattern in which the 15th shape is a .
b) Create a pattern in which the 12th shape is a .
c) Create a pattern in which the 6th and 9th shapes are both
.
Your Turn
Activity 1

31. Paper Folding
Fold a piece of paper in half, and then in
half again, and again, until you make six folds.
When you open it up, how many sections will
there be? Make a chart. Continue to fold as
you look for a pattern.
Activity 2

32. Paper Tearing
Tear a piece of paper in half and give half to
someone else. Each person then tears the piece of paper in
half and passes half on to another person. How many
people will have a piece of paper after 10 rounds of tearing
paper like this? Continue tearing paper and record on a
chart. Look for patterns as you complete each round.
Activity 3

33. Activity 4
DEPARTMENT OF EDUCATION
TABLE PROBLEM:
In a school library, the librarian are using square tables that can be put together
to make rectangles.
• One table can seat 4 pupils
• Two tables can seat 6 people
• Three tables can seat 8 people
1. Make a representation of the situation.
2. Do you see any pattern?
3. Make a table for your findings.
4. Describe the pattern.
5. If you will add 2 more tables how many learners could be seated?

34. Activity 1
DEPARTMENT OF EDUCATION
Presentation
of outputs

35. DEPARTMENT OF EDUCATION
Presentati
on of
outputs

36. DEPARTMENT OF EDUCATION
Presentati
on of
outputs

37. DEPARTMENT OF EDUCATION
Presentati
on of
outputs

38. Parting
thoughts
DEPARTMENT OF EDUCATION

39. “Doingmathematicsshouldalwaysmean
findingpatternsandcraftingbeautifuland
meaningfulexplanations.”
(Paul Lockhart)
DEPARTMENT OF EDUCATION