Multiplicative Thinking – PLC Resources 16th May

The Learning Assessment Framework for Multiplicative Thinking

Scaffolding Numeracy in the Middle Years

Common Misunderstandings – Multiplicative Thinking

Newman’s Error Analysis – You will need to log in to PAT Teaching Resources (email as user name) Then go to Teacher Resources

Multiplication and Division – Maths Assessment Project

Multiplicative Thinking Tasks

Our learning progression brainstorm (using Multiplicative Thinking article):


  • counting and splitting
  • skip counting
  • large collections
  • repeated addition (2s, 5s, etc.)
  • repeated subtraction
  • hold both numbers in head – number of objects within each group and number of groups
  • hold both numbers and the total
  • visualise 3×4, 4×3 move from additive to multiplicative strategies
  • factors, product – arrays
  • multiplication and division – commutative, inverse relations
  • language develops – for each, times, as many
  • symbolic representation, diagrams

Implications for teaching/ learning


  • Developing opportunities for students to use effective strategies – arrays
  • Challenge to show different ways
  • Communicate – in different ways
  • Explicit role modelling
  • Language used by students – allow opportunities for talk, and for listening in to hear their language (gaining insight into their thinking)
  • Variety of representations – words, pictures, symbols
  • Moving from familiar to unfamiliar contexts
  • Questioning and enabling prompts
  • Allow opportunities for collaboration
  • Think boards
  • Visualisation – drawing how they see the problem



Maths – Staff Meeting

Reflect on the things you do not like people to say and do when you are working on maths in a group

  • This is easy
  • This isn’t useful
  • Someone dominating the group
  • Hurry up!
  • I can’t do it
  • This is boring
  • That’s not right
  • I do not want to do this
  • Put downs
  • Competitiveness
  • Distracting
  • Off task behaviour
  • Sitting in rows
  • Silence
  • Worksheets
  • This is too easy
  • Talking about other things – off task
  • That’s wrong
  • I don’t want to work with him/ her
  • Not engaged
  • I don’t understand
  • I don’t like this
  • This isn’t useful
  • It’s easy
  • Rather than take risks, students use their group as a resource for answers
  • Someone else doing everything
  • Too complicated task

Reflect on the things you do like people to say and do when you are working on maths in a group

  • I’ve worked this out
  • I’ll give you more time
  • If you need help I’m happy to lend a hand
  • Time to consider and then work collaboratively
  • Keep trying
  • Let’s work it out together
  • I love Maths
  • This is fun
  • Keep trying
  • Supportive comments
  • I like a challenge
  • Asking questions
  • Collaborating
  • Fun
  • Interactive
  • Lots of talk
  • Groups
  • Tricky
  • I have to think about that
  • Lots of chatter
  • Work with buddies
  • A challenge
  • Building off others’ ideas
  • That’s a good idea
  • Mistakes seen as opportunities to grow
  • On task
  • I like that idea
  • Could you try
  • Can I help you?
  • This is so much fun
  • I like going in this pit
  • You can do it
  • The strategy I used was…
  • Busy
  • Engaging conversations about how to solve the problem


What stuck with you today?

There is more than one way to do the task.

2,3,4 heads are better than just 1

Everyone can learn maths

Low Floor, High Ceiling – entry points and differentiation for all

Maths needs to be hands on – not sheets – to give children the opportunity to experiment

Planning for differentiation is much easier than we sometimes make it (when the task is well-designed)

Youcubed lesson plans and resources, easily accessible and ‘ready to use’

Great ‘Emoji sorting’ lesson – Will definitely try it out!

How many different ways there are to understand a simple concept like ‘what is half?’ Along with encouraging students to take those risks and make mistakes.

Who would have thought that a simple concept like ‘halving’ would result in rich conversations – growing our learning together.

I’m going to look up Jo Boaler’s Youcubed, Daily Inspiration and try some new tasks as feeling a little like the meerkat in Maths at the moment.

Youcubed week of Inspiration site excellent ideas using Emoji’s. So many things you can do with this one activity, also very relevant for kids current fads.

Importance of developing positive attitudes in maths

Open ended, collaborative maths tasks.

Finding ways of exposing misconceptions/ highlighting understandings, and things we do/ say as teachers which might create misunderstandings.

During today’s activities reinforced how everyone sees the same problem differently. Allowing students to explore and work collaboratively is extremely valuable.

The Youcubed Week of Inspiration in Maths – lesson ideas, videos and resources to use

A great Emoji task to do.

Collaborative dialogue is the key to group feeling successful.

Fun working together if group collaborative

Thanks for sharing – inspiring indeed!

Look at and explore Youcubed, Inspirational maths lessons, continue to inspire students in maths.

I have good ideas but my group has great ideas!

Once you convince yourself …convince others.




Digital Resources

CSER home page contains many helpful resources

CSER Courses are very useful. Check out the range of courses here:

Patterns to Alegbra Reception to Year 2:

Patterning Year 5 Resource:

Programming Resources

Binary Game:

Assessment of Binary

By the end of Year 6, they are able to explain how digital systems use whole numbers as a basis for representing a variety of data.

Some example questions:
Can students explain what system computers use transfer and represent data?
Are students able to convert binary numbers?
Can students explain what a ‘binary digit’, a ‘bit’, and a ‘nibble’ are?

History of QR Codes:

How QR codes work: to shorten url and create a QR code

Useful website about QR Codes:


Use Audacity to record

Staff Meetings Terms 3 and 4

Term 3

 Week  Topic  Notes
 1  Stanford Uni Maths
 2  Stanford Uni Maths
 3  Stanford Uni Maths  Discuss Modules 1
 4  Stanford Uni Maths
 5  Stanford Uni Maths
 6  PLC
 7  Partnership Meeting
 9  PLC
10 Celebrations


Term 4

 Week  Topic
 1  Stanford Uni Maths
 2  Stanford Uni Maths
 3  Stanford Uni Maths
 4  Stanford Uni Maths
 5  PLC
 9  Celebrations


Resources from Results Plus

Martin Westwell (@martinwestwell)

We need to provide students with:
* opportunities for dialogue
* authentic problem solving
* applied problem solving
* role playing methods

Easier to do in Science as a Human Endeavour, Maths proficiencies, and play based learning.
Toolkit available at

How do we design learning to stretch all students?

The rule of three – Maria Droujkova –

Provide three different ways – students to draw core idea out
– synthesise – pattern – generalisation

Di Siemen – Big Ideas in Mathematics – Victorian Education Department

Website to explore:

Adding it up – Helping Children Learn Mathematics – research that has informed Australian Curriculum

Results Through the Plus!


The Big 6

  1. Oral Language
  2. Phonological Knowledge
  3. Letter-Sound Knowledge
  4. Vocabulary
  5. Fluency
  6. Comprehension

90/10 Principle – 90% about the enactment/ pedagogy and 10% the program

Implementation trumps impact

Holding the line – Conferencing


Passive Active
Low Challenge High Challenge
teacher select books/ texts Learners select books/ texts
Teachers manage learners progress Learners monitor their progress
Teachers control the tasks and choices Learners negotiate tasks and choices

Conferencing with individual students about their reading comprehension allows:

the learner to direct the conversation, by referring to their notes

mirroring of student thinking

modelling of think-aloud

making notes for intentional teaching (catering for student needs)

activating learning goals

formative assessment



Effective conferences motivate learners to make connections, find relationships and justify their thinking.


“…it’s how they think.” – Assumptions make an impact

Top 9 aspects that make a difference to student learning:

  1. student expectations (self reported grades)
  2. response to intervention
  3. formative teacher evaluation
  4. feedback
  5. metacognitive strategies
  6. direct instruction
  7. peer tutoring
  8. classroom management
  9. parental involvement

What will you hold the line on?

How will you hold the line?

Mathematical Mindsets – Jo Boaler (text)

Most Likely to Succeed – movie

The First 20 Hours – TED Talk

Val Westwell – Maths

Multiple representations and multiple pathways  – to develop number sense

Low achievers

  • don’t use numbers flexibly
  • use harder methods

Adding it Up

  1. Ideas and methods are valued
  2. Students have autonomy in choosing and sharing their methods of solving problems
  3. There is an appreciation of the value of mistakes as a sign of learning

Dr Amie Albrecht


Important skills looked for in Careers which use Maths

  • Active learning (on the job)
  • Critical thinking
  • Complex problem solving
  • Creative problem solving
  • Interpersonal skills – oral and written communication


Operations Research in Practice follows these steps

  1. Define the problem
  2. Construct a mathematical model
  3. Solve the problem
  4. Validate the model
  5. Implement the recommendations


Maths Photo Challenge