Transcript Zone 1 Session 3 2010

Zone 1
Session 3
2010
PLT conversations – place value
Homework from last session
Please bring an example of the evidence
presented by one teacher and the
documentation that arose from one Numeracy
PLT meeting. Be ready to describe the PLT
discussion
PROGRAM
Session 1: The Role of a Numeracy PLT
Session 2: PLT Conversations - Fractions
Session 3: PLT Conversations – Place value
The purpose of this session is for
participants to:
• explore the stages for understanding place
value
• experience some activities for teaching
place value
• participate in some Numeracy PLT
conversations based on evidence from AiZ
classrooms
AGENDA
9 -9.30
9.30 - 11
Intro and Warm Up
Explore the pathway for
understanding place value
11.00 – 11.30 MT
11.30 -12.30
PLT discussions based on evidence
What did we learn?
12.30 – 1.00
Plenary
Warm Up
NUMBER HANGMAN
PLACE VALUE
ONLY refers to the written form of number
Material that show groupings of 10 and highlight
the nature of 10 as a new unit are crucial to
building the knowledge of place value
For numbers > 10 there are no new symbols.
Instead, there is a set of rules that generate the new
numbers from those already learned
What are the big ideas for
understanding place value?
• A number is a representation that can be
substituted for
- materials that show a quantity
- a word that describes the quantity
- symbols that record the number succinctly
• Ten is significant in our number system
(10 ones makes 1 ten)
Stages of understanding place value
Counting (0-9) as the basis for all other numbers in
the base10 system
Thinking in 10s. 10 ones = 1 ten, 10 tens = 1 hundred
Two digit place value 20-99 first, then 11-19
Extend pattern to 3 digit numbers
continue with larger numbers
(10 hundreds = 1000, etc)
Exponents for when very large numbers are involved (106)
Early maths foundations
• Conservation: the number of items remains constant
regardless of their arrangement
• Classify: Items can be classified according to specific
criteria (eg colour, shape size)
• Comparison: establishing a relationship between
items (shorter than, fatter than, etc)
• Ordering (builds on comparison) arrange items in
line based on a rule
• Patterning: able to see, describe, extend and repeat
patterns
The layers of understanding
• Materials are used to develop
an understanding of counting
• Ten forms a new unit – bundles
are introduced
• As numbers become larger,
bundling gives way to the more
abstract material - MAB
The layers of understanding
• After 3 digit numbers the use of
material is no longer practical.
Instead the digits are group to
show thousands, millions, etc
1 724 345
1,724,345
• As numbers become even
12
5
trillion
=
5
larger they are expressed using
rather than
exponential notation
5,000,000,000,000
Some place value activities
•Make the most of it
Number expanders
5203
5
thous
ands
2
5 2 0
hund reds
0
te ns
3
te ns
on
es
3
on es
Montessori cards
5
0
thou
0
0
san
ds
2
0
0
hund
reds
7
0
tens
5
2
7 3
ones
3
ones
SNAP
Place Value Bingo
• Create a version of Bingo that could be
used to consolidate Place Value
understandings. (Consider using the three
representations of materials, words and
symbols)
• Can you make a version that involves 2
and 3 digit numbers also?
Relationships drawings
Calculator wipe-out
1 574 293
What would the number be if there was a zero in
the thousands place?
How can you ‘wipe out’ the 4 without changing the
other digits?
What number do we subtract to make the
calculator display 500 000?
What number do we add to make the calculator
display 2 000 000?
DOT PLATES
• find all the people with the same
number as you
• how else could you use these dot
plates?
Discussions
• FIFTEEN
• PENCILS
A Numeracy PLT
• is NOT about ‘sharing’ what I did in class today
or describing an engaging activity that I came
across
• is a collaborative, professional discussion
focused on identifying a starting point for
student learning and designing effective
learning opportunities to move students
along the learning continuum
Role of PLT Team Leader
•
•
•
•
•
•
•
Keep the PLT focus
PD the team
Mentor
Ensure challenge not ‘share’
Accountability
Link data to classroom practice
Team build
A Numeracy PLT model
1. Review the (triangulated) data
Seek evidence (What did the student make, say, do or write)
What do we know and how do we know it?
2. Plan the next step
Where does the student need to go next?
(progress/consolidate?)
3. Identify the strategies and resources needed
How will the student get there?
4. Stipulate the evidence required
How will we know when the student is there?
Evidence: What can the student make, say, do or write?
Team
Leader
Teacher
Triangulated Data
EVIDENCE
Team
member
Review data
Plan next step
Team
member
Strategies/resources
New evidence
Some challenging questions:
What makes you say that?
How do we know that?
What is he demonstrating that he can do well?
What are his misconceptions?
Is he ready for that?
How does the work from day to day relate?
Was the jump to addition too fast?
Is that what you expected from the student?
What will you do to manage the student’s leaning if
he’s the only one in class at this level?
Some challenging questions:
How did the work relate to the evidence in the
Rocket report?
What resources do we use to move him on?
Would you consider this a valuable piece of data?
Do we agree that he’s operating at Level C?
Is he applying a rule to equivalence?
Does he demonstrate an understanding of mixed
numbers?
Were activities organised to develop knowledge
and understanding or just ‘tricks’?
Using evidence from your own
school
1. Review the (triangulated) data
Seek evidence (What did the student make, say, do or write)
What do we know and how do we know it?
2. Plan the next step
Where does the student need to go next?
(progress/consolidate?)
3. Identify the strategies and resources needed
How will the student get there?
4. Stipulate the evidence required
How will we know when the student is there?
Our journey
•
•
•
•
•
•
•
•
•
Skills AND Thinking & Reasoning
Whole school planning for numeracy
Guiding principles for all maths lessons
What to teach? - VELS Focus statements
How can we use NAPLAN data?
Different models for unit planning
The Role of a Numeracy PLT
PLT Conversations about fractions
PLT Conversations about place value