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 Proficiencies – High Band Strategy

Thanks Libby for creating the following rubric:
Maths Assessment Criteria Rubric-115uqwg

Formative Assessment strategies to add to your tool kit:

In this example, students fill out an exit pass and place it into the relevant box to show their level of understanding. The next day the teacher pairs up the level 3 and 4 students with students at the level 2 stage, asking level 2 students to ask lots of clarifying questions to their peers to really bring them into ‘the learning pit’. This allows opportunity for teacher to work more intensively with the students at level 1.

To enable students to activate each other as agents of their own learning, students can be encouraged to daily take up opportunities to:

  • offer help
  • accept help
  • politely decline help so that you can try by yourself
  • ask for help

Learning Design Assessment Moderation – LDAM

Staff collective understanding:

What does formative assessment mean to you?

  • checking in
  • building on students’ knowledge
  • informs your teaching
  • critical for differentiation
  • establishing students prior learning as a basis to inform teaching and learning cycle
  • fundamental to identify student learning and next step development
  • next step for teaching (growth points)
  • gives you constant growth points/ learning goals
  • whole class/ small group strategies to teach/ re-teach/ adapt
  • Assessment which is ongoing through a journey as opposed to summative assessments
  • Guides teaching and learning cycle to meet student’s needs

What does it look like in your class?

  • pink, green, yellow post it noes
  • thumbs
  • traffic lights
  • emojis
  • reflections
  • main thoughts
  • coloured pens
  • various exit passes
  • verbal
  • children involved – opinions about their learning
  • peer support – e.g. oral presentations – statements, questions, appraisals
  • keep it happy – enjoyment shown through recognising ah ha moments
  • whole class investigations – recapping often, during lessons
  • individual/ group/ whole class assessments – differentiation conversations about learning with students
  • Ongoing
  • Running Records
  • Folder/ SSO Book/ Sentral goals
  • PAA/ SPA allocating SSO groups and tasks
  • Feedback
  • Peer marking
  • Photographs
  • Conferencing as read/ write
  • oral sharing/ questioning
  • Think 1 – I wonder – Think 2
  • positive growth points (pink/ green)
  • goal setting – numeracy, literacy
  • individual learning goals – student, teacher
  • verbal – instant/ written feedback
  • cold pieces of work
  • work samples on display
  • discussion
  • jointly established criteria for assessment (co-construction)
  • multi-modal opportunities to express understanding
  • conferences
  • choose one or two criteria to focus on
  • 2 stars and 1 wish
  • whiteboards
  • sticky notes
  • peer/ teacher verbal/ written feedback
  • ‘The muddiest point…’

How do you currently go about formative assessment?

  • used throughout the curriculum
  • negotiated
  • scaffold to ensure students are comfortable
  • share Australian Curriculum information with students (5/6)
  • assessment – cold piece – Think 1 →set goals/ reflect/ growth points – I wonder → Reassess – final piece – Think 2
  • Highlight when marking student work for self checking
  • Questioning – e.g. – What was the sticky point in your learning? What did you achieve – new learning?
  • Pit stops
  • Stepping stones to inform next steps
  • Prior knowledge tasks
  • What have we learnt tasks

How do you and the students feel about formative assessment?

  • positive engagement
  • see it as a way to improve
  • own it
  • students like giving feedback to others
  • they listen to feedback given by their peers
  • joy excitement
  • confidence
  • crucial as staff to know where each child is at – how do you plan otherwise?
  • provides growth points for us too
  • Early years kids generally love whatever you do
  • students love feedback and take it on
  • children enjoy sharing learning
  • children enjoy knowing their strengths and goal setting
  • some students may feel stressed about presenting in front of peers (point for consideration)
  • Teachers – having a good idea about what the students are doing
  • Students – receptive to feedback/ acting on this




PowerPoint Presentation: Staff Meeting Week 1, Term 2, 2018

LDAM Strategy Staff Meeting Week 1, Term 2 2018-1du552i

DECD Literacy and Numeracy First Information for Principals:





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.




7-8 Transition Resources

Resources that were used or referred to during the 7-8 Transition Workshop

ASMI – Are, Volume and Surface Area

– Introduction to Measurement 7-8

Mathematics Assessment Project
Evaluating Statements About Length and Area
length and area r1-ts0bvx

A-E Reference

The BitL Tool – Mathematics Years F-10

Transforming Tasks
Designing tasks where students do the thinking

Beliefs and Attitudes About Mathematics


The learning progression in the area of measurement:

Measurement progression-1cacnil