Download Lead teacher 2 2011

Whakatauki
E tu kahikatea, hei wakapae uroroa
Awhi 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 workshop
Morning tea 10.50
3.Effective Pedagogy:.( DVD,BES,
4.What’s New?
Nzmaths website-illustrations of standards
digistore learning objects
Warm UP Counting /Algebra
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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
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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
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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 ?
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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
What does the equals sign mean in each of these
situations?
7+8+9=
x=3
4+5=+3
Confusions and misunderstandings
• Discuss what the confusions are and how you
might teach it
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• 5+3 =8+4=12
• 3+6 = __ + 4 ( the student writes it as….
• 3+6 =9 +4
FIO : Number Bk2:
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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?
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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
8= 5 +
P.80 Algebra: More than just
patterns.Chris Linsell,Lyn Tozer
Teaching Primary School
Mathematics and Statistics
NZCER2010
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 ____________ eight
3. 6 + 1 is ___________ 8
4. 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
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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
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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?.
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Class dictionary or maths wall
Reference words
Meanings (associated language)
Diagrams
Symbols
Representations
Algebra Resources
• FIO: Algebra
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Number sense
and algebraic
thinking
What’s New, about to be
uncovered or out soon?.
• Nzmaths:
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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