Mathematics and Statistics
September 2011
Waipuna Conference Centre
Fun With Algebra
[Level 1, 2 and 3]
Bina Kachwalla
Mathematics Facilitator
Purpose:
• Explore patterns and
relationship
• Discuss key characteristics of
pre-algebra
• Solve some algebraic problems
–Using teaching model
What is Algebra?
Awareness of Mathematical Pattern and
Structure
“An Awareness of Mathematical Pattern and
Structure (AMPS) generalises across early
mathematical concepts, can be reliably
measured, and is correlated with mathematical
understanding”
(Mulligan & Mitchelmore, 2009)
What is the research saying?
• Young children learn mathematical ideas by
seeing patterns in an organised way looking for
sameness and difference.
• New research, from psychologists and
neuroscientists, shows that early development of
visual pattern and structure helps mathematical
development. Pre-school and school based
intervention focused on patterning can lead to a
significant improvement in mathematical
outcomes.
(Joanne Mulligan, 2010)
Why do some children fail in mathematics?
Some children go through their entire schooling
without learning any real mathematics because
they do not abstract ideas in a way that
promotes mathematical thinking … pattern,
structure and relationships – that’s the
essence of mathematics.
Findings – ‘less able’ children
• Lack of awareness of pattern and structure
• Focus on non-mathematical superficial features
• No clear developmental patterns
• Some children revert to primitive strategies and images
• Some children ‘crowd’ their thinking with surface features
• Poor visual memory
Activities to make connections
with numbers.
• What is a pattern?
• What is a structure?
• How do we make mathematical connections?
Or
• Develop mathematical relationships?
Problem solve…
• Family Maths activity.
Name some of the different types of
patterns.
Discuss with a partner.
Match these patterns:
Repeat these patterns:
• abc abc abc abc abc abc abc abc
• clap tap click clap tap click clap tap click
What is a growing pattern?
Number line - Hundreds
Board: activities
Family Maths - Problem Solve
Understanding equality:
• Discuss: What do we understand by?
=
The ‘equals’ sign
What does the equals sign mean in each of
these situations?
7+8+9=
x=3
4+5=+3
How many ways can you make 16?
16
How many ways can you make 16?
3+ 12
1 + 15
4x4
30 -14
16
2+2+2+2+2+2+2+2
2 + 14 = 3 + ?
2 + 14
32 - 16
Figure it out: Problem solve
[FIO number 2 level 3-4 pg 21]
Staircases:
One block is needed to make a 1-step upand-down staircase. It takes one step to get
up and one step to get down.
. This is a called a 2-step staircase as it
takes two steps to go up and two steps to
go down
How many cubes they think would be needed to
make a 5-step staircase.
What do you notice?
How would you explain in words?
What rule can you come up with?
Solution:
Look at this growing pattern?
Describe your formation of this pattern in
words.
Can you see this pattern in any other way?
How many sticks would be needed to make the
tenth/fifteenth pattern?
Can you describe this pattern with an algebraic
equation?
Fish pattern
Neil writes Tn = 6 + 4 (n-1)
Iris writes Tn = 2 n + 4 (n-1)
Can you explain their ways of thinking?
Fish pattern
6
6+4
6+4+4
6 + 2 lots of 4
6 + 4 (n-1)
Fish pattern
1st
2nd
pattern
pattern
3rd
pattern
2 lots of 3 parallel sticks
4 lots of mountains with 2 sticks
2 x n + 4 (n-1)
2x3 + 4 (n-1)
6+8
Materials
Imaging
Property of
numbers
Generalisation
from numbers
Dynamic dictionary to record.
•
•
•
•
•
Reference words
Meanings (associated language)
Diagrams
Symbols
Representations
Access Mathematics Symposium