Mathematics and Statistics Leaders Symposium

September 2011Waipuna Conference Centre

Fun With Algebra[Level 1, 2 and 3]

Bina KachwallaMathematics Facilitator

Purpose:• Explore patterns and

relationship• Discuss key characteristics of

pre-algebra• Solve some algebraic problems

–Using teaching model

What is Algebra?

• Discuss in your groups.

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:

• abc abc abc abc abc abc abc abc

• clap tap click clap tap click clap tap click

Repeat these patterns:

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

7 + 8 + 9 =

4 + 5 = + 3

x = 3

What does the equals sign mean in each of these situations?

How many ways can you make 16?

16

How many ways can you make 16?

161 + 15

2 + 14

30 -142 + 2 + 2 + 2 + 2 + 2 + 2 + 2

3+ 12

4 x 4

32 - 16

2 + 14 = 3 + ?

Figure it out: Problem solve[FIO number 2 level 3-4 pg 21]

Staircases:One block is needed to make a 1-step up-and-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 + 46 + 2 lots of 4

6 + 4 (n-1)

Fish pattern

2 lots of 3 parallel sticks4 lots of mountains with 2 sticks

1st pattern

2nd pattern

3rd

pattern

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 resources and links online

http://teamsolutions.wikispaces.com