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



Living Things R-2 Resources

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:





Descriptive reporting – Wording from the Department for Education

Teachers use descriptive reporting to provide information about students’ engagement and achievement, about what they have learnt, what they need to learn next, and how the teacher, student and parent/ carer can support these next steps to happen. This is done through descriptive information supporting A-E grades or word equivalents in the written reports and also through the range of oral reporting which occurs between schools and parents/ carers/ guardians, including three-way conferences, phone and other digital contact and other meetings with families and students.