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Patterns and Algebra

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when I count by fives the last number goes five, zero, five, zero, ... Five outcomes at this Stage: use letters to represent numbers ... – PowerPoint PPT presentation

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Title: 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
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