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Thursday 29th January, 2015
90 minutes
Helen, Jenni, Jill,
Charlotte, Sandra and Aimee
Warm Up – Odd One Out
6, 12, 5
 Work in pairs for 1 minute
 Work out the odd one out
 Feed back to whole group
Session Schedule
Warm up - Odd One Out – Helen / Jill - 5 mins
ROPS Mathematics Curriculum Document – Jenni 10 mins
Modelling Books / Learning Wall – Sandra 10 mins
Utilising Materials –
 ‘Idealness’ of Tools (BES paper) – Helen / Jill 5 mins
 The Number Framework – Number Fans Aimee / Jill 15 mins
Teacher Boxes (15 mins) Charlotte
Group Boxes and Strand Maintenance – Charlotte – 10 mins
Plenaries – Helen – 5 mins
The Curriculum Document
 Curriculum statements are recorded under subheadings (as they are in
each area) - 'an essence statement', planning expectations,
implementation, differentiation, assessment, student voice and eLearning.
 Overviews – Circles show the percentage of expected coverage . The
linear overview at each level - Levels 1 / 2, Levels 3 /4, Levels 5/6 shows what is to be covered in an ODD /EVEN year cycle. Teachers may
select what order they cover the work particularly considering how
topics related to the class inquiries.
 Web tool links -
 Assessment overview has school wide testing and data input
requirements / OTJ’s in mathematics are made based on evidence
arising from learning conversation, observations and formal
Classroom Implementation
What is the purpose of a
modelling book?
Modelling Books ….
 Evidence of teaching and learning
 A record of progress and coverage
 A working document for teacher ‘noticing’
 Helps capture and share students’ thinking
 A way to track formative assessment
 Evidence for OTJ’s
 Used for goal setting and next learning steps
 Supports group discussions / anchor / focusses discussion
 Record – teacher/students can refer to at a later time
 Scaffolds transition between materials, imaging and number
Modelling Books – key elements:
 Used regularly
 Can be pre-prepared / added to later / recap previous lesson
 Readily available (rich learning resource)
 Hard copy or e-book version (e.g Educreations)
 Records:
LI (good to co-construct at the end of a lesson)
Group Name
Pictures/diagrams, words and symbols
Students’ thinking (referenced)
Modelling books may also include:
 Key ideas or knowledge
 Links to numeracy stages
 Page reference to NDP ‘pink book’
 Strands other than ‘Number and Algebra’
 Notes about misconceptions
 Written recording from students
Mike Askew,
King's College, University of London
According to Askew (2004), "While a hundred square board
could be a material presence for a two-year old, it would not
have the 'ideal' dimension that it might for a ten-year old.
We are interested in how pupils come to 'read into' artefacts
the 'ideality' inscribed in the material."
In pairs, discuss why you think a hundreds square might
be more ideal for a ten-year old, than a two-year old.
A hundreds board ...
is organised in rows and columns
deepens understanding of the base ten number system/place value
rows increase in ones
columns increase in tens
adding/subtracting ones = move left or right
adding/subtracting tens = move up or down
introduces patterning and part-whole concepts
diagonals, verticals, skip counting
predict next number in a pattern
identify strategies to solve multiplication and division problems
discussion around how numbers are organised can be used to develop
number vocabulary odd/even/less than/greater than/prime numbers
 ideal tool to unpack students' misconceptions through discussion
Idealness of Materials to make meaning
(Researcher: Mike Askew, King’s College, University of London, 2004)
 Tasks/Activities: set up and initiated by the teacher
(driven from NZC and the Numeracy Maths Project)
 Artefacts/Tools: materials that allow students to make mathematical
 Actions:
how the artefacts/tools are acted upon
to promote talk to solve the task
 Talk:
how meaning is co-constructed using artefacts to solve
So What …?
 If the artefact chosen doesn't create the 'talk', then choose another artefact/s
 Use the most meaningful tools at the most IDEAL age and stage the child is
 Pink Books - guide you.
What artefacts could you use before these?
 Hundreds board (more abstract)
Arrow Cards (more abstract)
The Number Framework
Pink Book Number ???
Discuss with your neighbour ...
How many knowledge domains
are there in the number
Do you know what they are?
The Knowledge Domains are:
Number ID
and Order
/Place Value
Basic Facts
WALT: understand how number fans can be
used across a variety of knowledge stages
(as an exemplar piece of equipment)
Number Fans
 Think/Pair/Share:
 Come up with 3 advantages of using number fans:
Number Fans - Advantages
 Quick diagnostic test
 Full participation
 Easy to use with whole class
 Quick to see if students are having trouble (slower or
look around)
 Low stakes
 Scaffolding / reminders about strategies while they
 Students check their own answers e.g 81 instead of 18
 Open up Pink Book One Knowledge section and SECRETLY choose a domain / stage
and think of a question you can ask where the answer can be shown on a number fan.
 If you are a chosen goose, call your question out (scriber to write up)
 Everyone hold up your answer on your number fan.
 Now, find where the goose got the question from in the Pink Book ,
ie what stage is it and what knowledge domain is it?
 Goose: was the answer correct?
 E.g
What is the remainder for the number of three’s in 17?
Everyone holds up number fan 2
Stage =
Stage 6
Knowledge Domain = Grouping/Place Value
Gooses’ Questions:
Small Group Task – Number Fans
Now, working in year groups of 3 people in each group
Year 1 and 2
Year 3 and 4
Year 5 and 6
 Use the template provided and the Number
Framework (Book 1 pages 18-22) , make up at least five
questions at one chosen stage that you can use with
your class.
Small Group Task Template
Nbr Seq.
and Order
Some number fan activities …
 STAGE: up to Stage 3
 Show me 4
 the number that comes after
Just before 13
Between 7 and 9
A number that is less than five
A number greater than 6
Show me 19
The number that comes before 17
The number that comes after 11
 The number of people that live in
your house
 The date of your birthday
 The number of your street
Hold up double 4 (doubles to 10)
Half of 12 (halves to 20)
Hold up a 2 digit number, a 3
digit number
20 plus 35
100 minus 60
Hold up 87, 125, 490 …
Hold up a number greater than
25, less than 8
Hold up an odd number, even
What number plus this number
(hold up) make 20?
Hold up a multiple of 2, 5, 10
What is 6 + 7, 16 + 7, 26 + 7 etc?
 STAGE: 5
 All of the previous, plus
 Make a number with 3 digits. Show your
partner and read it to them.
 Make a number between 200 and 250.
 What does two stand for?
 A number greater than 175
 A number between 420 and 450
 A 3 digit number with two even and one
odd digit
 Hold up near doubles e.g double 9 + 2
 Hold up a number 100 more than 2345,
200 more than 2345
 Hold up a number greater than …, less
than …
 Hold up a factor of six
 Hold up a prime number
 Hold up a multiple of 3, of 4, of 11, of 9
 If 5 x 4 is 20, what is 6 x 4 or 4 x 4?
 I have 24 and half again. What number
do I get?
 Hold up 3 numbers that add to …
All of the previous, plus
A 4 digit number with a 3 in the hundreds
A number that is a multiple of 5.
A multiple of 7 that is more than 30.
Hold up a quarter of 36, a third of 36
I divided 25 by a number to get 5. What is it?
I multiply 3 by a number to get 12. What is it?
Show me a number that goes exactly into 42.
Show me 7 x 9
Hold up 6 squared
Hold up the square root of 36
3 out of 50 get excellence in a test. What % is
Show me 2.3
12.94 3.06
Show me a decimal greater than 3.5, less
than 0.6
greater than 2.78 but less than 3
Show me a decimal with a 3 in the tenths
Show me a decimal between 1 and 2, 1.1 and
Which is smaller? Hold up 0.69 or 0.7
Hold up the difference between 12 and 20
Stage 7
All of the previous, plus
 What is 1 more than 12.54? One tenth more than …
 Hold up 2 cubed
 What is the cubed root of 8 (small numbers only)
 Hold up a number less than -2, between -2 and 1
 What is 0.75 as a percentage?
 What is 75% as a decimal?
 What is one eighth as a decimal?
 What is 25% of 60?
 Round 36.44 to one decimal place.
 Hold up 1.2 plus 1.2
 Hold up 3.4 minus 0.2
 Subtract 1.3 from 3.5
 What is the difference between 1.7 and 3.4?
 Show me a number between 0.2 and 0.3
 A car is travelling at a speed of 50kph for half an
hour. How far does it travel?
 Hold up the quotient of 20 and 4?
 Hold up the product of 3 and 7
 Hold up 3 numbers that multiply to make 30, 12, 60
Stage 8
All of the previous, plus
 A shop has a coat marked at $65. It is in a 20%
discount sale. How much will you pay?
 -3 x -5,
 Estimate the answer to 32.6 x 0.19
 Estimate one third of 200
 Pink paint is mixed in a ratio of 1 red to 3 white.. If
Anne makes up a batch of 12 litres of pink paint,
how many litres of white did she use?
 What is 20% of $250?
 What is 3!
 Increase 0.7 by 10%.
How many: blind mice? Hours in a day? Sides on
an octagon? Holes on a golf course?
Give out 3 to 4 digit cards:
 What is the largest number you can make?
 What is the smallest number you can make?
 How many different numbers can you make?
 Put the numbers in order of size – smallest to
largest, largest to smallest
A number that is half the number I am holding up
A number that is greater than the one I am holding
Number Knowledge Stages
Number Sequence
Place Value
Number Facts
Numbers to 20
Know add/sub
groupings to 5
Numbers to 100
Numbers to 100
Know groupings to 10,
and with 10
Numbers to 1000
Numbers to 1000
Know all addition facts
to 20, and subtraction
facts to 10
Know 2, 5, 10 x tables
Numbers to 1,000,000
All whole numbers and
Recall all add/sub facts
to 20 and all mult facts
up to 10 x 10
Fractions, percentages
and negative numbers
Decimals, percentages
and powers of 10
Recall all mult / div
facts to 10 x 10
Other materials
 Explore numeracy teacher boxes and discuss in small
groups how different materials might be used to
support place value understanding.
 Demonstrate how a combination of materials can be
used together to show a concept.
 Feedback from groups.
Numeracy Teacher Boxes
Key Understandings
 Consider the different ways that materials can be used across
a variety of concepts and stages (covered today with Number
 Materials can be used in isolation, or in different
combinations to demonstrate a concept.
 It is powerful for children to have the opportunity to show
their understanding of a concept using a variety of
 One piece of equipment to show a concept for one child may
not be as meaningful as it is for another child.
Meaningful and Engaging Group Boxes
 Relevant and meaningful activities – what does this
look like?
Use to consolidate, maintain and revise knowledge
Introducing activities as part of your tumble
Keep it simple and varied – drip feed and rotate
Strand Maintenance
 Strand maintenance activities included once a week per group as part
of maths tumble.
 Important that strands are not taught in an isolated unit and then not
revisited until the next year.
 Strand maintenance activities enable students to apply, practise and
consolidate their learning over time.
 Strand box – introduce different strand maintenance activities as they
are taught through the year. (Share examples)
 Figure it out resources
 End of session – 5 minutes
 ‘Wrap up’ learning - student reflection
 Students volunteer to share/explain findings
 Derive the LI at the end of the lesson
 Formative Assessment - where to next?
 Teacher Reflection
How could I improve this lesson next time?
Spot the error
 Show a deliberate mistake with a similar calculation.
 In pairs:
 Spot the mistake
 Give the correct answer
 Suggest why the mistake may have been made and what
could be done about it
 e.g Mary says that 46 + 37 = 73. What did she do wrong?
Peer / Self Evaluation (DICE)
 How did you ...?
 What did you use to ...?
 What other materials could you have used? Why?
 Could you have worked it out another way?
 Which way was the best way? Why?
Block It! (TPS)
 In Pairs:
 Students tell each other:
1 thing I learnt
1 thing I already knew
1 question I want to ask
(Post-it note to record)
Then feedback to class
Milk Bottle Tops
 Place red card inside. Turn over.
Traffic Lights
 After a group session, use wooden pegs with names
 OR
 Colour in the traffic light in exercise books
 I don’t get it.
 I understand most of it.
 I understand this.
In groups of three (who you
have not already worked with
today), you have 10 seconds
each to tell your group
something that you will take
away with you today.
Future PD
 What future PD would YOU like?
 e.g how to teach a particular concept
 e.g how to use a certain piece of equipment
 e.g anything else you would like help with to assist your
teaching practice
Please record on the sheet provided
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