Whakatauki E tu kahikatea, hei wakapae uroroaAwhi mai, awhi atu, tatou, tatou e.

Kahikatea stand together; their roots intertwine, strengthening each other.

We all help one another and together we will be strong.

Lead Teacher Meeting 2 Agenda:1.Challenges,Successes, (share in group)2.Algebra workshopMorning tea 10.50 3.Effective Pedagogy:.( DVD,BES,4.What’s New?Nzmaths website-illustrations of standards digistore learning objects

Warm UP Counting /Algebra• Tahi ( slap) • Tahi rua tahi ( slap ,clap, slap)• Tahi,rua,toru,rua tahi ( slap,clap,click,)• Tahi,rua toru,wha,toru,rua,tahi …… shoulders• Tahi,rua toru wha,rima,wha,toru,rua,tahi,

…..arms up• With thanks to • Pania Te Maro, Robin Averill, Joanna Higgins ( Maori Students, Strong Achievement and Facilitators )

Quality Teaching and Learning Opportunities

in Algebra[Level 1,2 and 3]

Bina Kachwalla and adapted by Susan McDougall

Purpose:• Explore Algebraic thinking and the

progressions. • Look at Key concepts to lay the foundation of

algabraic thinking

• Look at resources/activities available to support teachers : FIO, Book 8, 9, nzmaths website

Pa……, Equ……., Fo……,Ge..............• Brainstorm the 4 big ideas about algebraic

thinking.

• Now put these ideas in order of development.

Algebra Relay from nz maths • How could you use this across a whole class?• Adapt it for juniors?• What key algebra/ knowledge did you need?• What confusions ?

What is the research saying ?

• Young children learn mathematical ideas by seeing patterns in an organised way looking for sameness and difference.

• We call this “Pattern and Structure”• New research shows that early development of visual pattern and

structure helps mathematical development ( Joanne Mulligan2010)

Points to ponder • When do students need to learn about

algebra?

• How would I recognise early algebraic reasoning?

• Where are my students at in their algebraic thinking?

Our word choice is significant• 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?

Confusions and misunderstandings • Discuss what the confusions are and how you

might teach it • • 5+3 =8+4=12

• 3+6 = __ + 4 ( the student writes it as….

• 3+6 =9 +4

FIO : Number Bk2: Fish Hooks of Ngake • • Question 3 p 21

• Looking at equivalence.• In pairs using the modelling books share your

thinking and record it .

Equations!! What level? Where do I start?What strategies should I use ?

___ + 5 =14

3n+2 =14

How many names can we find for eight?

8= 5 +P.80 Algebra: More than just

patterns.Chris Linsell,Lyn TozerTeaching Primary School

Mathematics and Statistics NZCER2010

• For this activity you need:a set of tens frames with dot patterns to 10,at least four sets of coloured counters(up to 10 of each colour.) a recording sheet, balance scales and at least 4 sets of coloured blocks ( up to 10 of each colour)

• Using the tens frames with the representation of 8 already on it the learner lays different combinations of counters on top of the black dots and then says and records ( e.g 6and 2 is the same as 8) 6+2=8

• Using the balance scales the learner puts eight of one colour into one bucket then adds different combinations of blocks to the other bucket until a balance is achieved and then says and records statements as for tens frames . A picture or diagram can also be drawn to illustrate the equation

Sentences with inequalities • Fill in the blanks with ‘is same as’, is ‘greater

than’ or ‘is less than’ in these sentences.• Use balance scales as evidence 1. Six and 2 is _____________ eight.2. 7 and two is ____________ eight3. 6 + 1 is ___________ 84. zero + eight is ________ 5. Eight takeaway3________ 5

Patterns:

Esther’s thinking shows she has achieved Level One because she can use skip counting to predict members of an ordinal counting sequence. This shows that she is able to establish a relation between the objects and the set of counting numbers.

Points of difference:• Let’s look at the NZC A0’s and notice the

difference between level 1 and level 2.

Predict the number of matches needed to make ten triangles in this pattern.

Use matchsticks to help you. Discuss all the possible ways students in your class might. solve it. Is there a way you could record it?

Assign a stage and level and standard to the ways

What is Algebra?In summary and simply • Precise and quick way of writing mathematical

statements.• Provides us with an efficient method for

solving equations for unknown quantities.• Patterns and Relationships• Equations and expressions.

Triangular patterns • Triangular numbers can be displayed in the

shape of a triangle e.g 1,1+2=3

Linking to the NZC Level 3 • Equations and Expressions:• Record and interpret additive and simple multiplicative strategies

using words, diagrams, symbols with an understanding of equality.• Patterns and Relationships• Generalise the patterns of addition and subtraction with whole

numbers.• Connect members of sequential patterns with their ordinal position• and use tables graphs and diagrams to find relationships between

successive elements of number and spatial patterns.

Level 4: Number and Algebra• Equations and expressions• Form and solve simple linear equations • Patterns and relationships:• Generalise properties of multiplication and

division with whole numbers.• Use graphs tables and rules to describe linear

relationships found in number and spatial patterns.

How do we build a shared understanding mathematical language?.• Class dictionary or maths wall • Reference words• Meanings (associated language)• Diagrams• Symbols• Representations

Algebra Resources • FIO: Algebra • Number sense

and algebraic thinking

What’s New, about to be uncovered or out soon?.• Nzmaths:• Nationalstandards (Interactive)• Digistore learning objects• BES principles • Effective Pedagogy in

mathematics/Pangaru• JAM tool • Alert indicators( students not on

track( draft) • ALIM • PMA seminar 25 June • Lead teacher symposium • 29,30 September Waipuna

Principles that underpin the philosophy of NDP • Every student has the potential to succeed in

mathematics

• Teachers are key figures in change • Understanding before algorithms.

• Derek Holton ( 2010) Marilyn Holmes