Zone 1Session 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 Intro and Warm Up

9.30 - 11 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

• As numbers become even larger they are expressed using exponential notation

1 724 345

1,724,345

5 trillion = 512 rather than 5,000,000,000,000

•Make the most of it

Some place value activities

Number expanders 5203

5 thous ands 2 hund reds 0 te ns 3 on es

5 2 0 te ns 3 on es

Montessori cards

5 0 thou

0san

0ds

2 0 hund

0reds

7 0tens

3 ones

5 2 7 3ones

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 293What would the number be if there was a zero inthe thousands place?How can you ‘wipe out’ the 4 without changing theother digits?What number do we subtract to make thecalculator display 500 000?What number do we add to make the calculatordisplay 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 model1. 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?

Team member

Teacher

Team Leader

Team member

Triangulated DataEVIDENCE

Evidence: What can the student make, say, do or write?

Review data Plan next step 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 ifhe’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