Patterns and Algebra

1
Patterns and Algebra

• Judy Anderson and Natasha Gillard

2
Workshop Overview

• Introduction to Patterns and Algebra
• Key Ideas for each Stage
• Sample Activities

3
Introduction to Patterns and Algebra

• one of six strands
• extends from Early Stage 1 to Stage 5 (and
  beyond)
• incorporates Repeating Patterns, Number Patterns
  and Number Relationships

4
Why is it a separate Strand ?

• Patterns and Algebra concepts are currently
  contained in the Number and Space Strands
• why have separate outcomes and detailed content?
• - to emphasise its importance
• - to show that the development of
  pre-algebra concepts begin in ES1
• - to show the development of concepts across
  the continuum

5
Why is it called Patterns and Algebra ?

• to show the connections between early number
  patterns and number relationships and the more
  formal algebra concepts
• Patterns and Algebra does not include pattern
  making (this remains part of Space and Geometry)

6
Scope and Continuum of Key Ideas- handout

• shows the development of concepts across the
  Stages
• a sound arithmetic foundation is required for the
  learning of algebra
• Patterns and Algebra should be taught in
  conjunction with Number concepts

7
Key Ideas for each Stage

• Early Stage 1
• recognise, describe, create and continue
  repeating patterns

This is a three pattern
A B C A B C A B C
1 2 3 1 2 3 1 2 3
These are all three patterns
8

• continue simple number patterns that increase or
  decrease

• use the term is the same as to describe
  equality of groups

9

• Stage 1

• create, represent and continue a variety of
  number patterns and supply missing elements

10

• build number relationships (addition and
  subtraction facts to at least 20)

11

• make generalisations 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
12

• use the equals sign to record equivalent number
  relationships

13

• Stage 2

• generate, describe and record number patterns
  using a variety of strategies

• 1, 4, 7, 10,
• 2.2, 2.0, 1.8, 1.6,
• 2 3 4 5 6 7
• 4, 4, 4, 4, 4, 4, 4,

(generate using calculator, materials or mental
strategies)
14

• build number relationships (relating
  multiplication and division facts to at least 10
  x 10)

2 x 4 4 x 2 (applying the commutative
property)
The multiplication facts for 6 are double the
multiplication facts for 3
6x4 24 so 244 6 and 246 4.
(describing the relationships)
(relating multiplication and division)
15

• complete simple number sentences by
  calculating the value of a missing number

16

• Stage 3 - algebra without symbols

• build simple geometric patterns involving
  multiples

17

• complete a table of values for geometric and
  number patterns

18

• describe a pattern in words in more than one way

(determining a rule to describe the pattern from
the table)
It looks like the 3 times tables.
You multiply the top number by three to get the
bottom number.
19
- construct, verify and complete number
sentences involving the four operations with a
variety of numbers

• completing number sentences
• 5 12 4
• 7 x 7.7
• constructing number sentences to match a word
  problem
• checking solutions and describing strategies

20
Stage 4 - algebra with symbols

• Five outcomes at this Stage
• use letters to represent numbers
• describe number patterns with symbols
• simplify, expand and factorise algebraic
  expressions
• solve equations and simple inequalities
• graph on the number plane